[{"id":15588,"question":"Write \\(\\dfrac{17}{6}\\) as a mixed number.<br>Answer : <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\">","explanation":"17 \/ 6 = 2 remainder 5, so 17\/6 = 2 5\/6."},{"id":16366,"question":"Arrange the following from the smallest to the greatest.<br>\\(\\frac{3}{7}\\) , \\(\\frac{2}{9}\\) , \\(\\frac{3}{9}\\)","explanation":"Compare the fractions. 2\/9 and 3\/9 share denominator 9, so 2\/9 < 3\/9. Then 3\/9 = 1\/3 ≈ 0.33 and 3\/7 ≈ 0.43, so 3\/9 < 3\/7. From smallest to greatest: 2\/9, 3\/9, 3\/7."},{"id":16367,"question":"(a) Express \\(\\frac{21}{8}\\) as a mixed number.<br>(b) Express \\(4\\frac{5}{7}\\) as an improper fraction.","explanation":"(a) 21 ÷ 8 = 2 remainder 5, so 21\/8 = 2 5\/8. (b) 4 5\/7 = (4 × 7 + 5)\/7 = (28 + 5)\/7 = 33\/7."},{"id":16368,"question":"Express your answer as a mixed number in its simplest form.<br>\\(\\frac{5}{6}\\) + \\(\\frac{2}{3}\\) = <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Make denominators the same: 2\/3 = 4\/6. Then 5\/6 + 4\/6 = 9\/6 = 3\/2 = 1 1\/2."},{"id":16370,"question":"Identify two fractions between \\(\\frac{2}{3}\\) and \\(\\frac{3}{4}\\). List them in their simplest forms.","explanation":"Use a common denominator. 2\/3 = 24\/36 and 3\/4 = 27\/36, so 25\/36 and 26\/36 lie between them. 25\/36 is already in simplest form; 26\/36 = 13\/18. The two fractions are 25\/36 and 13\/18."},{"id":16467,"question":"Express \\(8\\frac{6}{50}\\) as a decimal.","explanation":"Convert the fraction: \\(\\frac{6}{50}=\\frac{12}{100}=0.12\\). So \\(8\\frac{6}{50}=8+0.12=8.12\\)."},{"id":16469,"question":"Express 1.08 as a fraction.","explanation":"The digits after the decimal point (08) are hundredths. So 1.08 = \\(1\\frac{8}{100}\\)."},{"id":16529,"question":"How many \\(\\frac{1}{2}\\) turns will the minute hand of a clock turn between 9.25 a.m. to 10.55 a.m.?","explanation":"The duration from 9.25 a.m. to 10.55 a.m. is 1 h 30 min = 90 min. The minute hand makes a full turn every 60 min, so a \\(\\frac{1}{2}\\) turn takes 30 min. 90 min \\(\\div\\) 30 min = 3 half-turns."},{"id":16530,"question":"Edward washed 8 cars on Saturday. He took 20 minutes to wash each car. He started at 07 00. At what time will he finish if he did not take any breaks?","explanation":"Total washing time = 8 \\(\\times\\) 20 min = 160 min = 2 h 40 min. Add to the start time: 07 00 + 2 h 40 min = 09 40."},{"id":16534,"question":"The MRT trains depart at intervals of 12 minutes. Find the time of departure of the fourth train if the first train departs at 7.45 p.m.","explanation":"There are 3 intervals between the 1st and 4th trains. 3 \\(\\times\\) 12 min = 36 min. 7.45 p.m. + 36 min = 8.21 p.m."},{"id":16535,"question":"Victor exercises 4 times a week. He exercises 2 hours each time. How many weeks will Victor need to reach 200 hours of exercise?","explanation":"Hours per week = 4 \\(\\times\\) 2 h = 8 h. Number of weeks = 200 h \\(\\div\\) 8 h = 25 weeks."},{"id":16540,"question":"A quarter of a complete turn is equal to [?].","explanation":"A complete turn is 360°. A quarter turn is \\(\\frac{1}{4}\\) of 360° = 360° ÷ 4 = 90°."},{"id":16542,"question":"The minute hand of a clock moves through [?] in half an hour.","explanation":"The minute hand sweeps a full circle (360°) in one hour. In half an hour it moves \\(\\frac{1}{2}\\) of 360° = 180°."},{"id":16544,"question":"Lorna is standing at Point X and facing South-West. She makes a \\(\\frac{3}{4}\\) turn in an anti-clockwise direction. Which direction is she facing now?","explanation":"A \\(\\frac{3}{4}\\) turn is 270°. Turning anti-clockwise from South-West in 45° steps: SW → S → SE → E → NE → N → NW (6 steps of 45° = 270°). She now faces North-West."},{"id":16549,"question":"I am facing East. Which direction will I face if I make a \\(\\frac{3}{4}\\) turn to my right?","explanation":"A \\(\\frac{3}{4}\\) turn to the right is 270° clockwise. From East, clockwise in 90° steps: E → S → W → N. So I now face North."},{"id":16593,"question":"Write 23 thousandths as a decimal.","explanation":"23 thousandths means \\(\\frac{23}{1000}\\). The thousandths digit is the 3rd decimal place, so 23 thousandths = 0.023."},{"id":16594,"question":"Fill in the missing number in the box below.<br>\\(37.15 = 37 + \\frac{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}{100}\\)","explanation":"37.15 = 37 + 0.15. The decimal part 0.15 = \\(\\frac{15}{100}\\), so the missing numerator is 15."},{"id":16595,"question":"EFGH is a rectangle. Find the size of \\(\\angle y\\).","explanation":"The diagonal divides the right angle at corner H (90°) into 23° and y. So y = 90° - 23° = 67°."},{"id":16598,"question":"Express 3.75 as a mixed number in its simplest form.","explanation":"3.75 = 3 + 0.75 = \\(3\\frac{75}{100}\\). Simplify \\(\\frac{75}{100}\\) by dividing top and bottom by 25 to get \\(\\frac{3}{4}\\). So 3.75 = \\(3\\frac{3}{4}\\)."},{"id":16604,"question":"JKLM is a square. Find \\(\\angle PJN\\).","explanation":"The corner at J is a right angle (90°) because JKLM is a square. Two lines from J split this corner into 37°, angle PJN, and 37°. So angle PJN = 90° - 37° - 37° = 16°."},{"id":16605,"question":"Mr Seah earned $2745. He spent \\(\\frac{7}{9}\\) of his earnings and saved the rest. How much did Mr Seah save?","explanation":"He spent \\(\\frac{7}{9}\\), so he saved \\(\\frac{2}{9}\\). The whole (9 units) = $2745, so 1 unit = 2745 ÷ 9 = $305. Saved = 2 units = 305 x 2 = $610."},{"id":16606,"question":"A box contained some beads. Aisha took \\(\\frac{2}{5}\\) of the beads. She took 78 beads. How many beads were there in the box at first?","explanation":"\\(\\frac{2}{5}\\) of the beads = 78, so 2 units = 78 and 1 unit = 78 ÷ 2 = 39. The whole box = 5 units = 39 x 5 = 195 beads."},{"id":16622,"question":"Bryan was standing at the point marked A in the diagram. After making a \\(\\frac{3}{4}\\)-turn in an anticlockwise direction, Bryan found himself facing south. Which direction was he facing at first?","explanation":"A \\(\\frac{3}{4}\\)-turn anticlockwise is 270° anticlockwise, which is the same as 90° clockwise. To end facing south, he must have started facing east (east turned 90° clockwise gives south)."},{"id":16691,"question":"Which of the following is not an equivalent fraction of \\(\\frac{1}{4}\\)?","explanation":"Equivalent fractions of \\(\\frac{1}{4}\\) have the denominator equal to 4 times the numerator: \\(\\frac{2}{8}\\), \\(\\frac{3}{12}\\), \\(\\frac{6}{24}\\) all simplify to \\(\\frac{1}{4}\\). \\(\\frac{5}{16}\\) does not (16 ÷ 5 ≠ 4), so it is not equivalent."},{"id":16695,"question":"Express 0.05 as a fraction in its simplest form.","explanation":"0.05 = \\(\\frac{5}{100}\\). Dividing numerator and denominator by 5 gives \\(\\frac{1}{20}\\)."},{"id":16696,"question":"In the figure, ABCD is a rectangle. Find \\(\\angle a\\).","explanation":"At corner A the right angle of the rectangle is 90°. The three angles at A (43°, a, 18°) make up the 90°. So a = 90° − 43° − 18° = 29°."},{"id":16708,"question":"Nancy and Peter bought a sofa. The sofa cost $1200. Nancy paid \\(\\frac{3}{8}\\) of the cost of the sofa. How much more did Peter pay than Nancy?","explanation":"Nancy paid \\(\\frac{3}{8}\\) of $1200 = $450. Peter paid the rest, \\(\\frac{5}{8}\\) = $750. Peter paid $750 − $450 = $300 more."},{"id":16711,"question":"Write \\(3\\frac{4}{5}\\) as an improper fraction.","explanation":"\\(3\\frac{4}{5}\\) = (3 × 5 + 4)\/5 = 19\/5."},{"id":16715,"question":"Measure and write down the size of \\(\\angle x\\).","explanation":"Using a protractor, the angle x measures 73°."},{"id":16716,"question":"Which two of these fractions are in the simplest form?<br>\\(\\frac{2}{3}\\) , \\(\\frac{3}{6}\\) , \\(\\frac{4}{8}\\) , \\(\\frac{5}{9}\\)","explanation":"A fraction is in simplest form when numerator and denominator share no common factor other than 1. \\(\\frac{3}{6}=\\frac{1}{2}\\) and \\(\\frac{4}{8}=\\frac{1}{2}\\) can be simplified. \\(\\frac{2}{3}\\) and \\(\\frac{5}{9}\\) cannot, so they are in simplest form."},{"id":16717,"question":"Arrange the following numbers from the smallest to the greatest.<br>\\(\\frac{3}{4}\\) , 0.705 , 0.075","explanation":"Convert to decimals: \\(\\frac{3}{4}\\) = 0.75, 0.705, 0.075. From smallest to greatest: 0.075, 0.705, 0.75 (i.e. 0.075, 0.705, \\(\\frac{3}{4}\\))."},{"id":16721,"question":"The amount of water in the tank at 08 00 was 3 times the amount of water at 13 00. How much water was there in the tank at 13 00? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"From the graph, the amount of water at 08 00 was 24 \\(\\ell\\). At 13 00 it is one-third of that: 24 ÷ 3 = 8 \\(\\ell\\)."},{"id":16722,"question":"There are 174 fruits in a basket. \\(\\frac{1}{3}\\) are apples and the rest are pears. How many pears are there? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Apples = \\(\\frac{1}{3}\\), so pears = \\(\\frac{2}{3}\\) of 174. 174 ÷ 3 = 58, then 58 × 2 = 116 pears."},{"id":16730,"question":"Venus and Melvin were given some money. Venus spent \\(\\frac{1}{4}\\) of her money and had $141 left. (a) How much did Venus spend? (b) Melvin spent two times as much as Venus. He had \\(\\frac{2}{3}\\) of his money left. How much did Melvin have in the end? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Venus spent \\(\\frac{1}{4}\\), so $141 is the remaining \\(\\frac{3}{4}\\). 1 unit = $141 ÷ 3 = $47, which is the \\(\\frac{1}{4}\\) she spent. (b) Melvin spent 2 × $47 = $94, and that is \\(\\frac{1}{3}\\) of his money (he had \\(\\frac{2}{3}\\) left). His \\(\\frac{2}{3}\\) left = $94 × 2 = $188."},{"id":16808,"question":"\\(5\\frac{2}{9}\\) = \\(\\frac{[?]}{9}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: 5 × 9 + 2 = 47, over 9. So the missing numerator is 47. Answer: 47."},{"id":16809,"question":"Find the value of \\(\\frac{5}{12}-\\frac{1}{4}\\)","explanation":"Make denominators the same: \\(\\frac{1}{4}=\\frac{3}{12}\\). Then \\(\\frac{5}{12}-\\frac{3}{12}=\\frac{2}{12}=\\frac{1}{6}\\). Answer: \\(\\frac{1}{6}\\)."},{"id":16810,"question":"Express \\(\\frac{3}{4}\\) as a decimal.","explanation":"Make an equivalent fraction with denominator 100: \\(\\frac{3}{4}=\\frac{75}{100}\\) = 0.75. Answer: 0.75."},{"id":16834,"question":"Eunice bought \\(\\frac{3}{5}\\) m of ribbon to tie a present. Sarah bought \\(\\frac{1}{2}\\) m more ribbon than Eunice to make bows. How much ribbon did they buy altogether?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> $$m$$","explanation":"Sarah's ribbon = \\(\\frac{3}{5}+\\frac{1}{2}=\\frac{6}{10}+\\frac{5}{10}=\\frac{11}{10}=1\\frac{1}{10}\\) m. Altogether = Eunice + Sarah = \\(\\frac{6}{10}+1\\frac{1}{10}=1\\frac{7}{10}\\) m. Answer: \\(1\\frac{7}{10}\\) m."},{"id":16835,"question":"\\(\\frac{3}{4}\\) of a number is 21. What is the number?","explanation":"\\(\\frac{3}{4}\\) of the number = 21, so \\(\\frac{1}{4}\\) = 21 ÷ 3 = 7. The whole number = 7 × 4 = 28. Answer: 28."},{"id":16839,"question":"There are 135 pies at a party. \\(\\frac{2}{9}\\) of the pies are chicken pies and the rest are mushroom pies. How many more mushroom pies than chicken pies are there at the party?","explanation":"1 unit = 135 ÷ 9 = 15. Chicken pies = 2 units = 30. Mushroom pies = 7 units = 105. Difference = 105 − 30 = 75. Answer: 75."},{"id":16843,"question":"Julian read \\(\\frac{2}{9}\\) of a book on Monday and \\(\\frac{2}{3}\\) of the book on Tuesday. He read the remaining pages of the book on Wednesday. He read 76 more pages on Tuesday than on Monday. What fraction of the book did he read on Wednesday?","explanation":"Monday + Tuesday = \\(\\frac{2}{9}+\\frac{2}{3}=\\frac{2}{9}+\\frac{6}{9}=\\frac{8}{9}\\). Wednesday = whole − \\(\\frac{8}{9}\\) = \\(\\frac{9}{9}-\\frac{8}{9}=\\frac{1}{9}\\). Answer: \\(\\frac{1}{9}\\)."},{"id":16883,"question":"Madam Lim bought \\(\\frac{4}{5}\\) kg of chicken meat. She bought \\(\\frac{3}{10}\\) kg less than the amount of chicken meat bought by Mrs Tan. How many kilograms of chicken meat did Mrs Tan buy?","explanation":"Madam Lim has 3\/10 kg less than Mrs Tan, so Mrs Tan = 4\/5 + 3\/10. Convert: 4\/5 = 8\/10, so 8\/10 + 3\/10 = 11\/10 = 1 1\/10 kg."},{"id":16884,"question":"George was at a restaurant in a zoo. At the restaurant, George was facing south-west at first. He then made a \\(\\frac{3}{4}\\)-turn clockwise. Which animal would he be facing then?","explanation":"Facing south-west, a 3\/4 turn clockwise = 270 degrees clockwise. SW + 270 deg clockwise lands on SE. The animal in the south-east direction from the restaurant is the Monkey."},{"id":16888,"question":"Which two of the following fractions are in the simplest form?<br>\\(\\frac{2}{3}\\) , \\(\\frac{10}{12}\\) , \\(\\frac{3}{7}\\) , \\(\\frac{6}{8}\\)","explanation":"A fraction is in simplest form when numerator and denominator share no common factor besides 1. 2\/3 and 3\/7 cannot be simplified. 10\/12 = 5\/6 and 6\/8 = 3\/4 can be simplified."},{"id":16889,"question":"\\(\\frac{1}{3}\\) + \\(\\frac{1}{12}\\) = <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert to twelfths: 1\/3 = 4\/12. Then 4\/12 + 1\/12 = 5\/12."},{"id":16890,"question":"Find the value of 1 - \\(\\frac{3}{5}\\) - \\(\\frac{1}{10}\\) .","explanation":"Convert to tenths: 1 = 10\/10, 3\/5 = 6\/10. Then 10\/10 - 6\/10 - 1\/10 = 3\/10."},{"id":16905,"question":"Ramli spent \\(\\frac{1}{3}\\) of his monthly salary on a television. He spent \\(\\frac{2}{9}\\) of his salary on food and saved the rest. Given that Ramli saved $2392, how much did Ramli spend on food?","explanation":"Fraction spent = 1\/3 + 2\/9 = 3\/9 + 2\/9 = 5\/9. Saved = 1 - 5\/9 = 4\/9. So 4\/9 of salary = $2392, meaning 1\/9 = $598 and salary = $5382. Food = 2\/9 = 2 x $598 = $1196."},{"id":16908,"question":"The figure shows a rectangle where \\(\\angle a\\) is twice the size of \\(\\angle b\\). Find \\(\\angle a\\).","explanation":"The corner of the rectangle is 90 deg, split into angle a, the 48 deg angle and angle b: a + 48 + b = 90, so a + b = 42. Since a = 2b, 2b + b = 42, 3b = 42, b = 14, a = 28 deg."},{"id":16915,"question":"In a box, \\(\\frac{1}{8}\\) of the marbles were blue. \\(\\frac{7}{12}\\) of the marbles were red. There was an equal number of blue and green marbles in the box. The rest of the marbles were pink. There was a total of 581 green and pink marbles in the box. How many red marbles were there in the box?","explanation":"Blue = 1\/8, green = blue = 1\/8, red = 7\/12. Pink = 1 - 1\/8 - 1\/8 - 7\/12. Common denom 24: blue 3\/24, green 3\/24, red 14\/24, so pink = 24\/24 - 3\/24 - 3\/24 - 14\/24 = 4\/24. Green + pink = 3\/24 + 4\/24 = 7\/24 = 581, so 1\/24 = 83 and total = 1992. Red = 7\/12 = 14\/24 = 14 x 83 = 1162 marbles."},{"id":16962,"question":"Find the value of \\(\\frac{5}{12} - \\frac{1}{3}\\).","explanation":"Make the denominators the same: \\(\\frac{1}{3} = \\frac{4}{12}\\). Then \\(\\frac{5}{12} - \\frac{4}{12} = \\frac{1}{12}\\)."},{"id":16965,"question":"Arrange the following fractions in order, beginning with the greatest.<br>\\(\\frac{3}{4}\\), \\(\\frac{7}{12}\\), \\(\\frac{7}{8}\\)","explanation":"Use common denominator 24: \\(\\frac{3}{4}=\\frac{18}{24}\\), \\(\\frac{7}{12}=\\frac{14}{24}\\), \\(\\frac{7}{8}=\\frac{21}{24}\\). Greatest to least: \\(\\frac{21}{24}, \\frac{18}{24}, \\frac{14}{24}\\) = \\(\\frac{7}{8}, \\frac{3}{4}, \\frac{7}{12}\\)."},{"id":16972,"question":"Kumar is facing south-west. He makes a \\(\\frac{3}{4}\\)-turn in a clockwise direction. Then, he turns through an angle of 45° in an anti-clockwise direction. Which direction will he end up facing?","explanation":"A \\(\\frac{3}{4}\\)-turn = 270° clockwise. From south-west, 270° clockwise lands on south-east. Then 45° anti-clockwise from south-east goes back to east."},{"id":16980,"question":"Measure and write down the size of \\(\\angle x\\).<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>°","explanation":"Using a protractor, the angle x measures 138°."},{"id":16981,"question":"\\(\\frac{3}{4} = \\frac{9}{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}\\)<br>What is the missing number in the box?","explanation":"The numerator 3 was multiplied by 3 to get 9, so multiply the denominator the same way: 4 × 3 = 12."},{"id":16987,"question":"Which two fractions are in the simplest form?<br>\\(\\frac{3}{9}\\), \\(\\frac{2}{5}\\), \\(\\frac{2}{6}\\), \\(\\frac{3}{8}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> and <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"A fraction is in simplest form when numerator and denominator share no common factor other than 1. \\(\\frac{3}{9}=\\frac{1}{3}\\) and \\(\\frac{2}{6}=\\frac{1}{3}\\) can be simplified, but \\(\\frac{2}{5}\\) and \\(\\frac{3}{8}\\) cannot."},{"id":16993,"question":"A fruit seller had 170 pears and oranges altogether. After he sold \\(\\frac{2}{3}\\) of the pears and 14 oranges, he had an equal number of pears and oranges left. How many oranges were there in the end?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"After selling, pears left = \\(\\frac{1}{3}\\) of pears and oranges left = oranges − 14, and these two are equal. The remaining pears (1 unit) plus the sold pears (2 units = 3 units total pears) plus oranges equal the total once the 14 sold oranges are accounted for: 4 units = 170 − 14 = 156, so 1 unit = 156 ÷ 4 = 39. The oranges left equal the remaining pears = 39."},{"id":16994,"question":"The figure is made up of 2 rectangles, ABEF and BCDE. \\(\\angle AEB = 26°\\) and \\(\\angle BEG\\) is twice of \\(\\angle AEB\\). Find \\(\\angle GED\\).<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>°","explanation":"BE is perpendicular to the line FED, so \\(\\angle BED = 90°\\). \\(\\angle BEG = 2 × 26° = 52°\\). Then \\(\\angle GED = 90° − 52° = 38°\\)."},{"id":16999,"question":"There were some sweets in a box. Evelyn took \\(\\frac{5}{8}\\) of the sweets and Nigel took the rest. Evelyn took 76 more sweets than Nigel.<br>(a) What fraction of the sweets did Nigel take?<br>(b) How many sweets were in the box at first?<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Nigel took 1 − \\(\\frac{5}{8}\\) = \\(\\frac{3}{8}\\). (b) Evelyn − Nigel = \\(\\frac{5}{8} - \\frac{3}{8} = \\frac{2}{8}\\) of the sweets = 76, so \\(\\frac{1}{8}\\) = 38 and the whole box = 8 × 38 = 304 sweets."},{"id":17007,"question":"What is the missing number in the box?<br>\\(6\\frac{5}{9}\\) = \\(\\frac{[?]}{9}\\)","explanation":"Convert the mixed number to an improper fraction: \\(6\\frac{5}{9} = \\frac{6\\times 9 + 5}{9} = \\frac{54+5}{9} = \\frac{59}{9}\\). The missing numerator is 59."},{"id":17008,"question":"What fraction of the shapes in the box are triangles?","explanation":"There are 12 shapes in total. 5 are triangles. So the fraction that are triangles is \\(\\frac{5}{12}\\)."},{"id":17011,"question":"The volume of water in a tank is 19 000 \\(\\ell\\) when rounded to the nearest thousand litres. Which one of the following is the greatest possible volume of water in the tank?","explanation":"Rounded to the nearest thousand, values from 18 500 to 19 499 give 19 000. The greatest possible value is 19 499 (19 500 would round up to 20 000)."},{"id":17014,"question":"Mr Lim bought \\(\\frac{4}{5}\\) kg of cherries. He and his sons ate \\(\\frac{3}{10}\\) kg of the cherries. What was the mass of cherries left?","explanation":"\\(\\frac{4}{5} = \\frac{8}{10}\\). Cherries left = \\(\\frac{8}{10} - \\frac{3}{10} = \\frac{5}{10} = \\frac{1}{2}\\) kg."},{"id":17022,"question":"The bar graph shows the number of movies watched by a group of children during the holidays. What fraction of the children watched at least 2 movies?","explanation":"Children per number of movies: 1->4, 2->3, 3->4, 4->5, 5->2. Total = 4+3+4+5+2 = 18. At least 2 movies = 3+4+5+2 = 14. Fraction = \\(\\frac{14}{18}\\)."},{"id":17026,"question":"What is the missing number in the box?<br>\\(\\frac{4}{7}\\) = \\(\\frac{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}{49}\\)","explanation":"49 = 7 x 7, so multiply numerator and denominator of \\(\\frac{4}{7}\\) by 7: \\(\\frac{4\\times 7}{7\\times 7} = \\frac{28}{49}\\). The missing numerator is 28."},{"id":17027,"question":"Arrange the following fractions from the greatest to the smallest.<br>\\(\\frac{1}{2}\\), \\(\\frac{2}{3}\\), \\(\\frac{7}{12}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Use denominator 12: \\(\\frac{1}{2}=\\frac{6}{12}\\), \\(\\frac{2}{3}=\\frac{8}{12}\\), \\(\\frac{7}{12}=\\frac{7}{12}\\). Greatest to smallest: \\(\\frac{8}{12}, \\frac{7}{12}, \\frac{6}{12}\\), i.e. \\(\\frac{2}{3}, \\frac{7}{12}, \\frac{1}{2}\\)."},{"id":17028,"question":"Express 0.6 as a fraction.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"0.6 = \\(\\frac{6}{10}\\). Simplify by dividing by 2: \\(\\frac{6}{10} = \\frac{3}{5}\\)."},{"id":17030,"question":"What is the value of \\(\\frac{5}{8} + \\frac{3}{4}\\)? Express your answer as a mixed number.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{3}{4} = \\frac{6}{8}\\). \\(\\frac{5}{8} + \\frac{6}{8} = \\frac{11}{8} = 1\\frac{3}{8}\\)."},{"id":17031,"question":"ABCD is a square. Find \\(\\angle x\\).<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Each corner of a square is 90°. At corner D, the 65° angle and \\(\\angle x\\) together make the 90° angle. So \\(\\angle x = 90° - 65° = 25°\\)."},{"id":17041,"question":"A water container had 1 \\(\\ell\\) of water. Mr Muthu used \\(\\frac{2}{5}\\) \\(\\ell\\) of it to make a drink and \\(\\frac{1}{4}\\) \\(\\ell\\) of it to water his plants.<br>(a) How much water did Mr Muthu use altogether?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> \\(\\ell\\)<br>(b) How much water was left?<br><input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> \\(\\ell\\)","explanation":"(a) \\(\\frac{2}{5} = \\frac{8}{20}\\), \\(\\frac{1}{4} = \\frac{5}{20}\\). Used = \\(\\frac{8}{20} + \\frac{5}{20} = \\frac{13}{20}\\) \\(\\ell\\). (b) Left = 1 - \\(\\frac{13}{20} = \\frac{7}{20}\\) \\(\\ell\\)."},{"id":17042,"question":"Mrs Raja baked some cookies. She gave \\(\\frac{1}{3}\\) of the cookies to her daughter, \\(\\frac{5}{8}\\) of them to her friend and kept the rest for herself. Mrs Raja gave her friend 42 more cookies than what she had given to her daughter. How many cookies did Mrs Raja bake?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Friend got \\(\\frac{5}{8}\\) and daughter got \\(\\frac{1}{3}\\). Difference = \\(\\frac{5}{8} - \\frac{1}{3} = \\frac{15}{24} - \\frac{8}{24} = \\frac{7}{24}\\) of the cookies = 42. So \\(\\frac{1}{24}\\) = 6, and the total (24 units) = 24 x 6 = 144 cookies."},{"id":17044,"question":"The table shows the prices and number of tickets sold for an art exhibition over 5 days. Adult: 168 tickets sold at $11 each. Child: ? tickets sold at $5 each.<br>(a) The total number of child tickets sold was \\(\\frac{2}{3}\\) of the total number of adult tickets. How many child tickets were sold over the 5 days?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) The line graph shows the number of adult tickets sold over the 5 days. How much money was collected from the sale of adult tickets on Day 4?<br>$<input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Child tickets = \\(\\frac{2}{3}\\) x 168 = 112. (b) From the line graph, Day 4 adult tickets sold = 21 (the lowest dip). Money on Day 4 = 21 x $11 = $231."},{"id":17080,"question":"\\(7\\frac{4}{5}\\) = \\(\\frac{[?]}{5}\\) <br> What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: 7 × 5 + 4 = 39, so \\(7\\frac{4}{5}=\\frac{39}{5}\\). Missing number = 39."},{"id":17081,"question":"Express 0.08 as a fraction in its simplest form.","explanation":"0.08 = \\(\\frac{8}{100}\\). Divide numerator and denominator by 4: \\(\\frac{8}{100}=\\frac{2}{25}\\)."},{"id":17082,"question":"Write \\(6\\frac{7}{20}\\) as a decimal.","explanation":"\\(\\frac{7}{20}=\\frac{35}{100}=0.35\\). So \\(6\\frac{7}{20}=6.35\\)."},{"id":17088,"question":"Arrange the following fractions from the greatest to the smallest. <br> \\(1\\frac{1}{9}\\) , \\(\\frac{11}{7}\\) , \\(\\frac{8}{7}\\)","explanation":"As decimals: \\(\\frac{11}{7}\\approx1.57\\), \\(\\frac{8}{7}\\approx1.14\\), \\(1\\frac{1}{9}\\approx1.11\\). Greatest to smallest: \\(\\frac{11}{7}\\), \\(\\frac{8}{7}\\), \\(1\\frac{1}{9}\\)."},{"id":17093,"question":"A flask contained 2 $$l$$ of hot water. Ms Tan used \\(\\frac{3}{4}\\) $$l$$ of the hot water to make chocolate drinks and \\(\\frac{7}{8}\\) $$l$$ of the hot water to make coffee. How much water was left in the flask?","explanation":"Used = \\(\\frac{3}{4}+\\frac{7}{8}=\\frac{6}{8}+\\frac{7}{8}=\\frac{13}{8}=1\\frac{5}{8}\\) l. Left = \\(2-1\\frac{5}{8}=\\frac{3}{8}\\) l."},{"id":17101,"question":"What fraction of the buttons shown are grey in colour?","explanation":"There are 12 buttons in total and 4 of them are grey, so the fraction = \\(\\frac{4}{12}=\\frac{1}{3}\\)."},{"id":17102,"question":"Which two of the fractions are in the simplest form? <br> \\(\\frac{2}{5}\\) , \\(\\frac{3}{6}\\) , \\(\\frac{4}{10}\\) , \\(\\frac{5}{12}\\) <br> Ans : <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> and <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"A fraction is in simplest form when numerator and denominator share no common factor. \\(\\frac{3}{6}=\\frac{1}{2}\\) and \\(\\frac{4}{10}=\\frac{2}{5}\\) can be simplified; \\(\\frac{2}{5}\\) and \\(\\frac{5}{12}\\) cannot."},{"id":17103,"question":"What is the value of \\(\\frac{5}{9}+\\frac{2}{3}\\)? Express your answer as a mixed number.","explanation":"\\(\\frac{2}{3}=\\frac{6}{9}\\), so \\(\\frac{5}{9}+\\frac{6}{9}=\\frac{11}{9}=1\\frac{2}{9}\\)."},{"id":17117,"question":"John had some money. He spent \\(\\frac{1}{4}\\) of his money on food and \\(\\frac{5}{8}\\) of his money on books. He spent $12 more on books than food. How much money did he have at first?","explanation":"Food = \\(\\frac{1}{4}=\\frac{2}{8}\\), books = \\(\\frac{5}{8}\\). Difference = \\(\\frac{5}{8}-\\frac{2}{8}=\\frac{3}{8}\\) of his money = $12. So \\(\\frac{1}{8}\\) = $4, and total \\(\\frac{8}{8}\\) = 8 × $4 = $32."},{"id":17125,"question":"What fraction of the shapes in the box are pentagons?","explanation":"There are 10 shapes in the box. 3 of them are pentagons. So the fraction that are pentagons is \\(\\frac{3}{10}\\)."},{"id":17127,"question":"In the figure, which angle is a right angle?","explanation":"A right angle measures exactly 90° (forms a square corner). In the figure, \\(\\angle b\\) is the right angle."},{"id":17138,"question":"Write \\(\\frac{23}{7}\\) as a mixed number. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"23 ÷ 7 = 3 remainder 2, so \\(\\frac{23}{7} = 3\\frac{2}{7}\\)."},{"id":17139,"question":"Arrange the following fractions from the greatest to the smallest.<br>\\(\\frac{2}{3}\\), \\(\\frac{3}{4}\\), \\(\\frac{5}{12}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert to twelfths: \\(\\frac{2}{3} = \\frac{8}{12}\\), \\(\\frac{3}{4} = \\frac{9}{12}\\), \\(\\frac{5}{12} = \\frac{5}{12}\\). Greatest to smallest: \\(\\frac{9}{12}\\), \\(\\frac{8}{12}\\), \\(\\frac{5}{12}\\), i.e. \\(\\frac{3}{4}\\), \\(\\frac{2}{3}\\), \\(\\frac{5}{12}\\)."},{"id":17140,"question":"Find the value of \\(\\frac{7}{8} - \\frac{1}{2}\\). <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{1}{2} = \\frac{4}{8}\\), so \\(\\frac{7}{8} - \\frac{4}{8} = \\frac{3}{8}\\)."},{"id":17141,"question":"Express 0.6 as a fraction. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"0.6 is 6 tenths, so 0.6 = \\(\\frac{6}{10}\\)."},{"id":17145,"question":"Measure and write down the size of \\(\\angle x\\). <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Using a protractor to measure \\(\\angle x\\) in the figure gives 119°."},{"id":17147,"question":"David was standing at point X in the figure. He was facing the National Stadium at first. He made a \\(\\frac{3}{4}\\) turn in a clockwise direction. He then turned through an angle of 135° in an anti-clockwise direction. What place and direction was he facing in the end?<br>Place: <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>Direction: <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Facing National Stadium (East). A \\(\\frac{3}{4}\\) clockwise turn = 270° clockwise, ending facing North (MRT Station). Then 135° anti-clockwise from North goes to the South-west direction, which points to Botanic Gardens. So he faces Botanic Gardens, direction South-west."},{"id":17148,"question":"The figure is not drawn to scale. PQRS is a rectangle. Find \\(\\angle MPS\\). <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"In rectangle PQRS, \\(\\angle SPQ\\) (the corner at P) is a right angle = 90°. \\(\\angle MPQ = 43°\\) (given). So \\(\\angle MPS = 90° − 43° = 47°\\)."},{"id":17150,"question":"The difference between two fractions is \\(\\frac{2}{9}\\). The smaller fraction is \\(\\frac{1}{6}\\). What is the sum of the two fractions? Express your answer in its simplest form. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Larger fraction = \\(\\frac{1}{6} + \\frac{2}{9} = \\frac{3}{18} + \\frac{4}{18} = \\frac{7}{18}\\). Sum = \\(\\frac{7}{18} + \\frac{1}{6} = \\frac{7}{18} + \\frac{3}{18} = \\frac{10}{18} = \\frac{5}{9}\\)."},{"id":17159,"question":"After a florist sold \\(\\frac{2}{3}\\) of her roses and \\(\\frac{5}{9}\\) of her tulips, she had the same number of roses and tulips left. The number of tulips she sold was 85.<br>(a) How many tulips did she have left? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) How many roses did she have at first? <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Tulips: \\(\\frac{5}{9}\\) sold = 85, so 1 unit (\\(\\frac{1}{9}\\)) = 85 ÷ 5 = 17. Tulips left = \\(\\frac{4}{9}\\) = 4 × 17 = 68. (a) 68 tulips left. (b) Roses left = tulips left = 68, and roses left are \\(\\frac{1}{3}\\) of the roses (since \\(\\frac{2}{3}\\) sold). So roses at first = 3 × 68 = 204."},{"id":17164,"question":"Express \\(\\frac{53}{1000}\\) as a decimal.","explanation":"Thousandths take 3 decimal places. \\(\\frac{53}{1000}\\) = 0.053."},{"id":17165,"question":"Which one of the following has \\(\\frac{1}{6}\\) of the figure shaded?","explanation":"A figure is \\(\\frac{1}{6}\\) shaded when 1 of 6 equal parts is coloured. Figure 2 has 6 equal parts with exactly one shaded."},{"id":17166,"question":"Which of the following is not in its simplest form?","explanation":"A fraction is in simplest form when numerator and denominator share no common factor besides 1. \\(\\frac{2}{6}\\) can be simplified to \\(\\frac{1}{3}\\), so it is not in simplest form."},{"id":17178,"question":"Write \\(3\\frac{5}{8}\\) as an improper fraction. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(3\\frac{5}{8}\\) = \\(\\frac{3 \\times 8 + 5}{8}\\) = \\(\\frac{29}{8}\\)."},{"id":17179,"question":"Find the value of \\(\\frac{7}{9}-\\frac{2}{3}\\). <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert \\(\\frac{2}{3}\\) to ninths: \\(\\frac{2}{3}=\\frac{6}{9}\\). Then \\(\\frac{7}{9}-\\frac{6}{9}=\\frac{1}{9}\\)."},{"id":17181,"question":"Arrange the following fractions from the smallest to the greatest.<br>\\(\\frac{5}{6}\\), \\(\\frac{5}{12}\\), \\(\\frac{11}{12}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Express in twelfths: \\(\\frac{5}{6}=\\frac{10}{12}\\). Comparing \\(\\frac{5}{12}\\), \\(\\frac{10}{12}\\), \\(\\frac{11}{12}\\) gives smallest to greatest: \\(\\frac{5}{12}\\), \\(\\frac{5}{6}\\), \\(\\frac{11}{12}\\)."},{"id":17191,"question":"Mrs Chan had 5 $$l$$ of orange juice. Her daughter drank \\(\\frac{3}{5}\\) $$l$$ of it. How much orange juice had Mrs Chan left? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"5 − \\(\\frac{3}{5}\\) = \\(4\\frac{5}{5}-\\frac{3}{5}\\) = \\(4\\frac{2}{5}\\) litres."},{"id":17196,"question":"Shop Mobile had 80 mobile phones on Monday and started selling the mobile phones from Tuesday to Friday. The graph shows the number of mobile phones left unsold at the end of each day.<br>(a) How many mobile phones were sold on Tuesday? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) By which day did Shop Mobile sell \\(\\frac{7}{10}\\) of the mobile phones? <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) On Tuesday the unsold count drops from 80 to 72, so 80 − 72 = 8 phones were sold. (b) \\(\\frac{7}{10}\\) of 80 = 56 phones sold, leaving 80 − 56 = 24 unsold; the graph reaches 24 unsold on Friday."},{"id":17199,"question":"There are 36 pupils in a class. There are 12 boys in the class.<br>(a) What fraction of the class are girls? Express your answer in the simplest form. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) \\(\\frac{4}{9}\\) of the pupils in the class wear spectacles. How many pupils do not wear spectacles? <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Girls = 36 − 12 = 24. Fraction = \\(\\frac{24}{36}=\\frac{2}{3}\\). (b) Fraction not wearing spectacles = \\(1-\\frac{4}{9}=\\frac{5}{9}\\); \\(\\frac{5}{9}\\) of 36 = 5 × 4 = 20 pupils."},{"id":17205,"question":"\\(7\\frac{4}{5} = \\frac{[?]}{5}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: \\(7\\frac{4}{5} = \\frac{7\\times5+4}{5} = \\frac{39}{5}\\). The missing number is 39."},{"id":17206,"question":"What fraction of the shapes are \\u25c6 ?","explanation":"There are 10 shapes in total. 6 of them are diamonds. So the fraction of diamonds is \\(\\frac{6}{10}\\)."},{"id":17208,"question":"Write \\(4\\frac{3}{20}\\) as a decimal.","explanation":"\\(\\frac{3}{20} = \\frac{15}{100} = 0.15\\). So \\(4\\frac{3}{20} = 4.15\\)."},{"id":17216,"question":"ABCD is a rectangle. Find \\(\\angle x\\).","explanation":"Angle ADC of the rectangle is 90°. It is split into 20°, 60° and x. So x = 90° - 20° - 60° = 10°."},{"id":17218,"question":"Jan has \\(\\frac{3}{4}\\) m of cloth. She has \\(\\frac{1}{2}\\) m more cloth than Helen. How much cloth do they have altogether?","explanation":"Helen has 3\/4 - 1\/2 = 1\/4 m. Altogether: 3\/4 + 1\/4 = 1 m."},{"id":17219,"question":"How many minutes does it take for a minute hand of a clock to make \\(1\\frac{1}{4}\\) turn round the clock?","explanation":"One full turn of the minute hand = 60 min. 1 1\/4 turns = 60 + (1\/4 × 60) = 60 + 15 = 75 min."},{"id":17226,"question":"Find the value of \\(1 - \\frac{1}{8} - \\frac{1}{4}\\). <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Use eighths: 1 = 8\/8, 1\/4 = 2\/8. So 8\/8 - 1\/8 - 2\/8 = 5\/8."},{"id":17227,"question":"Write \\(2\\frac{3}{7}\\) as an improper fraction. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(2\\frac{3}{7} = \\frac{2\\times7+3}{7} = \\frac{17}{7}\\)."},{"id":17231,"question":"In the figure, one of the angles is a right angle. Name the angle.<br>\\(\\angle\\) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"By inspecting the figure, angle b is the right angle (90°)."},{"id":17232,"question":"Measure and write down the size of \\(\\angle x\\). <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Measuring the angle with a protractor gives 30°."},{"id":17233,"question":"David spent \\(\\frac{1}{5}\\) of his money on a wallet and gave $90 to his mother. He had $104 left. How much money did he spend on the wallet?<br>$<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"The wallet was 1\/5 of his money, so 4\/5 remained after the wallet. That 4\/5 = $90 + $104 = $194. So 1\/5 = $194 ÷ 4 = $48.50 spent on the wallet."},{"id":17240,"question":"At a concert, \\(\\frac{3}{10}\\) of the audience are women and \\(\\frac{1}{5}\\) of the audience are men. The rest of the audience are children.<br>(a) What fraction of the audience are children? [Leave your answer in the simplest form]<br>(b) There are 180 more children than women. How many women and men are there altogether?<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Women + men = 3\/10 + 1\/5 = 3\/10 + 2\/10 = 5\/10. Children = 1 - 5\/10 = 5\/10 = 1\/2. (b) Children fraction (5\/10) - women fraction (3\/10) = 2\/10 of the audience = 180, so 1\/10 = 90. Women + men = 5\/10 = 5 × 90 = 450."},{"id":17242,"question":"A bottle had some amount of milk at first. Peter drank \\(\\frac{1}{4}\\) $$l$$ of milk in the morning and \\(\\frac{1}{5}\\) $$l$$ of milk in the afternoon.<br>(a) How many litres of milk did Peter drink in total?<br>(b) Peter had \\(\\frac{3}{5}\\) $$l$$ of milk at first. What was the amount of milk left in the bottle?<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) 1\/4 + 1\/5 = 5\/20 + 4\/20 = 9\/20 l. (b) 3\/5 = 12\/20 l at first. Left = 12\/20 - 9\/20 = 3\/20 l."},{"id":17247,"question":"What fraction of the shapes in the box are circles?","explanation":"There are 10 shapes in total: 4 triangles and 6 circles. The fraction that are circles is \\(\\frac{6}{10}\\). Answer: \\(\\frac{6}{10}\\)."},{"id":17248,"question":"\\(6\\frac{4}{7}=\\frac{[?]}{7}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: \\(6\\frac{4}{7}=\\frac{6\\times7+4}{7}=\\frac{42+4}{7}=\\frac{46}{7}\\). The missing number is 46."},{"id":17250,"question":"Express 0.05 as a fraction in its simplest form.","explanation":"0.05 = \\(\\frac{5}{100}\\). Dividing numerator and denominator by 5 gives \\(\\frac{1}{20}\\). Answer: \\(\\frac{1}{20}\\)."},{"id":17251,"question":"In the figure shown, ABCD is a rectangle. Find \\(\\angle x\\).","explanation":"Angle ADC of the rectangle is 90°. The three angles at D add up to 90°: 26° + x + 21° = 90°, so x = 90° − 26° − 21° = 43°. Answer: 43°."},{"id":17254,"question":"Which of the following fractions has the value closest to 1?","explanation":"The difference from 1 is: \\(1-\\frac{2}{3}=\\frac{1}{3}\\); \\(1-\\frac{3}{4}=\\frac{1}{4}\\); \\(1-\\frac{5}{6}=\\frac{1}{6}\\); \\(1-\\frac{7}{8}=\\frac{1}{8}\\). The smallest gap is \\(\\frac{1}{8}\\), so \\(\\frac{7}{8}\\) is closest to 1. Answer: \\(\\frac{7}{8}\\)."},{"id":17264,"question":"Which two of the fractions below are equivalent to \\(\\frac{6}{8}\\)?<br>\\(\\frac{12}{16}\\), \\(\\frac{5}{7}\\), \\(\\frac{4}{5}\\), \\(\\frac{3}{4}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> and <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{6}{8}\\) simplifies to \\(\\frac{3}{4}\\). \\(\\frac{12}{16}\\) also simplifies to \\(\\frac{3}{4}\\) (divide by 4), and \\(\\frac{3}{4}\\) is already in that form. So the two equivalent fractions are \\(\\frac{12}{16}\\) and \\(\\frac{3}{4}\\)."},{"id":17265,"question":"What is the value of \\(\\frac{5}{6}+\\frac{2}{3}\\)? Express your answer as a mixed number.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Make the denominators the same: \\(\\frac{2}{3}=\\frac{4}{6}\\). Then \\(\\frac{5}{6}+\\frac{4}{6}=\\frac{9}{6}=\\frac{3}{2}=1\\frac{1}{2}\\). Answer: \\(1\\frac{1}{2}\\)."},{"id":17269,"question":"Suhana is facing the Police Station after making a \\(\\frac{3}{4}\\) anti-clockwise turn. Where was she facing at first?","explanation":"A \\(\\frac{3}{4}\\) anti-clockwise turn is the same as a \\(\\frac{1}{4}\\) clockwise turn. To find the starting direction, undo the turn: from Police Station turn \\(\\frac{3}{4}\\) clockwise (or \\(\\frac{1}{4}\\) anti-clockwise). This lands on the Stadium. Answer: Stadium."},{"id":17272,"question":"At a funfair, \\(\\frac{5}{12}\\) of the people were children, \\(\\frac{1}{3}\\) of the people were men and the rest were women. What fraction of the people were women? Express your answer as a fraction in its simplest form.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Children and men together: \\(\\frac{5}{12}+\\frac{1}{3}=\\frac{5}{12}+\\frac{4}{12}=\\frac{9}{12}\\). Women = \\(1-\\frac{9}{12}=\\frac{3}{12}=\\frac{1}{4}\\). Answer: \\(\\frac{1}{4}\\)."},{"id":17281,"question":"There were some stickers in a box. Mariam took \\(\\frac{3}{8}\\) of the stickers and Amy took the rest. Mariam took 36 fewer stickers than Amy.<br>(a) What fraction of the stickers did Amy take?<br>(b) How many stickers were in the box in total?<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Amy took the rest: \\(1-\\frac{3}{8}=\\frac{5}{8}\\). (b) The difference between Amy and Mariam is \\(\\frac{5}{8}-\\frac{3}{8}=\\frac{2}{8}\\) of the total, which equals 36 stickers. So \\(\\frac{2}{8}\\) = 36 means \\(\\frac{1}{8}\\) = 18, and the total \\(\\frac{8}{8}\\) = 18 × 8 = 144 stickers. Answers: (a) \\(\\frac{5}{8}\\) (b) 144."},{"id":17349,"question":"The figure is made up of identical triangles. What fraction of the figure is shaded?","explanation":"The figure is made up of 12 identical triangles, of which 4 are shaded. So the shaded fraction is \\(\\frac{4}{12}\\)."},{"id":17350,"question":"\\(\\frac{1}{3}\\) + \\(\\frac{1}{9}\\) = [?]","explanation":"Make denominators the same: \\(\\frac{1}{3}=\\frac{3}{9}\\). Then \\(\\frac{3}{9}+\\frac{1}{9}=\\frac{4}{9}\\)."},{"id":17351,"question":"PQRS is a square. Find \\(\\angle\\) v.","explanation":"Angle PQR of the square is 90°. The angles 20° and 16° at Q are part of it, so v = 90° − 20° − 16° = 54°."},{"id":17360,"question":"Alicia is facing her school. She makes a \\(\\frac{1}{2}\\) turn anticlockwise. She then makes a 270° turn clockwise. Where is she facing now?","explanation":"A \\(\\frac{1}{2}\\) turn (180°) anticlockwise from school takes her to face home. A 270° clockwise turn from home is the same as a 90° anticlockwise turn, taking her to face the library."},{"id":17363,"question":"Express \\(\\frac{10}{15}\\) in its simplest form.","explanation":"Divide numerator and denominator by 5: \\(\\frac{10}{15}=\\frac{10\\div5}{15\\div5}=\\frac{2}{3}\\)."},{"id":17364,"question":"Write \\(\\frac{15}{7}\\) as a mixed number.","explanation":"15 ÷ 7 = 2 remainder 1, so \\(\\frac{15}{7}=2\\frac{1}{7}\\)."},{"id":17365,"question":"ABCD is a rectangle. Find the value of \\(\\angle\\)x.","explanation":"Angle DAB of the rectangle is 90°. The line from A makes 39° with AB, so x = 90° − 39° = 51°."},{"id":17367,"question":"Write \\(\\frac{85}{100}\\) as a decimal.","explanation":"\\(\\frac{85}{100}\\) means 85 hundredths = 0.85."},{"id":17369,"question":"Express 0.4 as a fraction.","explanation":"0.4 is 4 tenths, so 0.4 = \\(\\frac{4}{10}\\)."},{"id":17382,"question":"Mark bought some sweets. He gave his friends \\(\\frac{1}{7}\\) of the sweets and gave his brother \\(\\frac{3}{4}\\) of the sweets. All the remaining sweets were eaten by him. What fraction of the sweets did Mark eat?","explanation":"Given away = \\(\\frac{1}{7}+\\frac{3}{4}=\\frac{4}{28}+\\frac{21}{28}=\\frac{25}{28}\\). Mark ate the rest = \\(\\frac{28}{28}-\\frac{25}{28}=\\frac{3}{28}\\)."},{"id":17384,"question":"The figure is made up of 5 identical squares. The area of a square is 25 cm². What is the perimeter of the figure?","explanation":"Side of one square = \\(\\sqrt{25}\\) = 5 cm (since 5 × 5 = 25). The outline of the figure is made up of 10 such sides, so perimeter = 10 × 5 = 50 cm."},{"id":17386,"question":"Mrs Devi and Mdm Tan baked an equal number of muffins for sale. Mrs Devi sold 49 muffins and had \\(\\frac{2}{9}\\) of the muffins left.<br>(a) How many muffins did Mrs Devi have left?<br>(b) How many muffins did Mrs Devi and Mdm Tan bake in all?","explanation":"Mrs Devi sold \\(\\frac{7}{9}\\) (the part that is not the \\(\\frac{2}{9}\\) left), so 7 units = 49 and 1 unit = 7. (a) Left = 2 units = 2 × 7 = 14 muffins. (b) Mrs Devi baked 9 units = 9 × 7 = 63; both baked equal numbers, so total = 63 × 2 = 126."},{"id":17412,"question":"How many one-sevenths are there in 2 wholes?","explanation":"1 whole = \\(\\frac{7}{7}\\), so 2 wholes = \\(\\frac{14}{7}\\), which is 14 one-sevenths."},{"id":17413,"question":"Arrange the following fractions from the greatest to the smallest.<br>\\(\\frac{1}{3}\\), \\(\\frac{5}{6}\\), \\(\\frac{7}{12}\\)","explanation":"Convert to twelfths: \\(\\frac{1}{3}=\\frac{4}{12}\\), \\(\\frac{5}{6}=\\frac{10}{12}\\), \\(\\frac{7}{12}=\\frac{7}{12}\\). Greatest to smallest: \\(\\frac{10}{12}, \\frac{7}{12}, \\frac{4}{12}\\), i.e. \\(\\frac{5}{6}, \\frac{7}{12}, \\frac{1}{3}\\)."},{"id":17423,"question":"After donating \\(\\frac{1}{3}\\) of her money to charity, Janelle had $24 left. How much money did she have at first?","explanation":"$24 left is \\(\\frac{2}{3}\\) of her money. \\(\\frac{1}{3}\\) = 24 ÷ 2 = $12, so at first she had 12 × 3 = $36."},{"id":17432,"question":"Write \\(\\frac{23}{6}\\) as a mixed number.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"23 ÷ 6 = 3 remainder 5, so \\(\\frac{23}{6} = 3\\frac{5}{6}\\)."},{"id":17433,"question":"Find the value of \\(1 - \\frac{1}{6} - \\frac{1}{3}\\).<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Use sixths: \\(1 = \\frac{6}{6}\\), \\(\\frac{1}{3} = \\frac{2}{6}\\). \\(\\frac{6}{6} - \\frac{1}{6} - \\frac{2}{6} = \\frac{3}{6} = \\frac{1}{2}\\)."},{"id":17448,"question":"Rachel had some cookies. She gave \\(\\frac{5}{8}\\) of them to her grandmother and 7 cookies to her aunt. She then had 20 cookies left. How many cookies did she have at first?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"After giving \\(\\frac{5}{8}\\) away, \\(\\frac{3}{8}\\) remained. From that, 7 went to the aunt and 20 were left, so \\(\\frac{3}{8}\\) = 20 + 7 = 27 cookies. 1 unit = 27 ÷ 3 = 9, so the total \\(\\frac{8}{8}\\) = 8 × 9 = 72."},{"id":17451,"question":"Aisha and Bella had 219 stickers. After Aisha used \\(\\frac{1}{3}\\) of her stickers and Bella used 39 stickers, they had the same number of stickers left. How many stickers did Bella have at first?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"After Bella used 39, the remaining stickers total 219 − 39 = 180. Aisha's \\(\\frac{2}{3}\\) equals Bella's remainder, and they are equal, so each holds half: 180 ÷ 2 = 90... key: 180 ÷ 5 = 36; Aisha's full set = 36 × 3 = 108, Bella at first = 219 − 108 = 111. So Bella had 72 + 39 = 111."},{"id":17489,"question":"Write \\(5\\frac{7}{20}\\) as a decimal.","explanation":"Convert the fraction: \\(\\frac{7}{20}=\\frac{35}{100}=0.35\\). So \\(5\\frac{7}{20}=5.35\\)."},{"id":17490,"question":"What fraction represents the shaded parts?","explanation":"Each circle is divided into 8 equal parts (eighths). Two whole circles are fully shaded (16 eighths). The third circle has 5 of its 8 parts shaded. Total = 16 + 5 = 21 eighths = \\(\\frac{21}{8}\\)."},{"id":17493,"question":"In a class, 12 pupils take the bus to school. The remaining 28 pupils walk to school. What fraction of the pupils in class walk to school?","explanation":"Total pupils = 12 + 28 = 40. Walkers = 28. Fraction who walk = \\(\\frac{28}{40}=\\frac{7}{10}\\)."},{"id":17501,"question":"Arrange the following numbers from smallest to the greatest.<br>\\(\\frac{2}{5}\\), 0.408, 0.048<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert to decimals: \\(\\frac{2}{5}=0.4\\). Compare 0.4, 0.408, 0.048. Smallest to greatest: 0.048, 0.4 (=2\/5), 0.408."},{"id":17504,"question":"What fraction of the stars are grey in colour? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"There are 12 stars in total and 5 of them are grey. So the fraction that is grey is \\(\\frac{5}{12}\\)."},{"id":17505,"question":"What is the value of \\(\\frac{3}{10}+\\frac{4}{5}\\)? Express your answer as a mixed number. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Make denominators the same: \\(\\frac{4}{5}=\\frac{8}{10}\\). Then \\(\\frac{3}{10}+\\frac{8}{10}=\\frac{11}{10}=1\\frac{1}{10}\\)."},{"id":17508,"question":"A piece of ribbon is 14 m long. Jane used \\(\\frac{3}{7}\\) of it. What was the length of the ribbon left? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Fraction left = \\(1-\\frac{3}{7}=\\frac{4}{7}\\). Each seventh = 14 ÷ 7 = 2 m. Length left = \\(\\frac{4}{7}\\) × 14 = 4 × 2 = 8 m."},{"id":17515,"question":"2 identical rectangles and 1 square are used to form the figure. EF is \\(\\frac{1}{2}\\) of HP. Find the perimeter of the figure given that EH is 24 cm and PQ is 16 cm. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"PQ = 16 cm is the side of the square, so HP = 16 cm. EF = \\(\\frac{1}{2}\\) × 16 = 8 cm (the rectangle's width). EH = 24 cm is the rectangle's length. Adding all outer edges: 24 + 32 + 16 + 16 + 24 + 16 + 8 = 144 cm."},{"id":17519,"question":"Olivia used \\(\\frac{2}{3}\\) kg of sugar. Shannon used \\(\\frac{1}{6}\\) kg of sugar more than Olivia. Adele used \\(\\frac{1}{3}\\) kg less sugar than Shannon. What was the amount of sugar used by Adele? Express your answer in its simplest form. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Olivia = \\(\\frac{2}{3}=\\frac{4}{6}\\). Shannon = \\(\\frac{4}{6}+\\frac{1}{6}=\\frac{5}{6}\\). Adele = \\(\\frac{5}{6}-\\frac{1}{3}=\\frac{5}{6}-\\frac{2}{6}=\\frac{3}{6}=\\frac{1}{2}\\) kg."},{"id":17521,"question":"There are red, blue and yellow balls. \\(\\frac{1}{12}\\) of the balls are red. \\(\\frac{1}{2}\\) of the balls are blue and the rest of the balls are yellow. There are 680 more yellow balls than red balls. How many balls are there altogether? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Red = \\(\\frac{1}{12}\\), blue = \\(\\frac{1}{2}=\\frac{6}{12}\\), so yellow = \\(1-\\frac{1}{12}-\\frac{6}{12}=\\frac{5}{12}\\). Yellow − red = \\(\\frac{5}{12}-\\frac{1}{12}=\\frac{4}{12}\\) of the total = 680 balls. So 4 units = 680, 1 unit = 170, and the total of 12 units = 12 × 170 = 2040 balls."},{"id":17526,"question":"Which one of the following has \\(\\frac{1}{3}\\) of the figure shaded?","explanation":"A figure shows \\(\\frac{1}{3}\\) shaded when it is divided into 3 equal parts with 1 part shaded. Figure 2 is divided into 3 equal parts with 1 part shaded."},{"id":17527,"question":"\\(6\\frac{7}{8}\\) = \\(\\frac{[?]}{8}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: \\(6\\frac{7}{8}\\) = \\(\\frac{6\\times8+7}{8}\\) = \\(\\frac{55}{8}\\). The missing number is 55."},{"id":17535,"question":"Tim ate \\(\\frac{4}{9}\\) of a cake. Mark ate \\(\\frac{1}{2}\\) of the same cake. What fraction of the cake was left?","explanation":"Tim and Mark ate \\(\\frac{4}{9}+\\frac{1}{2}\\) = \\(\\frac{8}{18}+\\frac{9}{18}\\) = \\(\\frac{17}{18}\\). Left = \\(1-\\frac{17}{18}\\) = \\(\\frac{1}{18}\\)."},{"id":17546,"question":"\\(\\frac{2}{3}-\\frac{1}{12}\\) = <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{2}{3}=\\frac{8}{12}\\). \\(\\frac{8}{12}-\\frac{1}{12}=\\frac{7}{12}\\)."},{"id":17547,"question":"What is the value of \\(\\frac{1}{3}+\\frac{5}{6}\\)?<br>Express your answer as a mixed number.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{1}{3}=\\frac{2}{6}\\). \\(\\frac{2}{6}+\\frac{5}{6}=\\frac{7}{6}=1\\frac{1}{6}\\)."},{"id":17548,"question":"Find the value of \\(1-\\frac{1}{2}-\\frac{1}{6}\\).<br>Express your answer in the simplest form.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(1-\\frac{1}{2}=\\frac{1}{2}=\\frac{3}{6}\\). \\(\\frac{3}{6}-\\frac{1}{6}=\\frac{2}{6}=\\frac{1}{3}\\)."},{"id":17552,"question":"In the figure, ABCD is a rectangle. Find the value of \\(\\angle y\\).<br>∠y = <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>°","explanation":"Angle ADC is a right angle (90°) in the rectangle. The diagonal makes 17° with DC, so \\(\\angle y\\) = 90° - 17° = 73°."},{"id":17562,"question":"Ken has 600 stamps. He gave \\(\\frac{3}{5}\\) of the stamps to Tom, \\(\\frac{1}{10}\\) of the stamps to John and kept the rest for himself.<br>(a) What fraction of the stamps did Ken keep for himself?","explanation":"Tom + John = \\(\\frac{3}{5}+\\frac{1}{10}=\\frac{6}{10}+\\frac{1}{10}=\\frac{7}{10}\\). Kept = \\(1-\\frac{7}{10}=\\frac{3}{10}\\)."},{"id":17563,"question":"Ken has 600 stamps. He gave \\(\\frac{3}{5}\\) of the stamps to Tom, \\(\\frac{1}{10}\\) of the stamps to John and kept the rest for himself.<br>(b) How many more stamps did Ken give to Tom than to John?","explanation":"Tom got \\(\\frac{3}{5}\\) of 600 = 360; John got \\(\\frac{1}{10}\\) of 600 = 60. The difference \\(\\frac{3}{5}-\\frac{1}{10}=\\frac{5}{10}\\) of 600 = 300. Per the key, 600 ÷ 10 = 60, then \\(\\frac{5}{10}\\): 60 x 5 = 300."},{"id":17573,"question":"The figure shown is made up of identical rectangles. What fraction of the figure is shaded?","explanation":"The figure has 12 identical rectangles in total (3 rows × 4 columns). 5 of them are shaded, so the shaded fraction is \\(\\frac{5}{12}\\)."},{"id":17574,"question":"Which of the following fractions is equivalent to \\(\\frac{4}{6}\\)?","explanation":"\\(\\frac{4}{6}=\\frac{2}{3}\\). Checking each: \\(\\frac{12}{18}=\\frac{2}{3}\\). So \\(\\frac{12}{18}\\) is equivalent to \\(\\frac{4}{6}\\)."},{"id":17577,"question":"Express \\(\\frac{21}{25}\\) as a decimal.","explanation":"\\(\\frac{21}{25}=\\frac{21\\times4}{25\\times4}=\\frac{84}{100}=0.84\\)."},{"id":17578,"question":"In the figure, which angle is a right angle?","explanation":"Comparing the four marked angles of the quadrilateral, only \\(\\angle y\\) (the top angle) is a right angle."},{"id":17584,"question":"Kelly used \\(\\frac{3}{10}\\) kg of coffee powder. She used \\(\\frac{1}{5}\\) kg less coffee powder than Frances. How much coffee powder did they use altogether?","explanation":"Frances used \\(\\frac{3}{10}+\\frac{1}{5}=\\frac{3}{10}+\\frac{2}{10}=\\frac{5}{10}\\) kg. Altogether = \\(\\frac{3}{10}+\\frac{5}{10}=\\frac{8}{10}=\\frac{4}{5}\\) kg."},{"id":17589,"question":"In the figure, name the smallest angle.","explanation":"Comparing the marked angles formed at the point, \\(\\angle d\\) is the smallest."},{"id":17590,"question":"Write \\(\\frac{20}{9}\\) as a mixed number.","explanation":"20 ÷ 9 = 2 remainder 2, so \\(\\frac{20}{9}=2\\frac{2}{9}\\)."},{"id":17597,"question":"Which two of the fractions below are in the simplest form?<br>\\(\\frac{2}{5}\\) , \\(\\frac{3}{6}\\) , \\(\\frac{5}{7}\\) , \\(\\frac{6}{8}\\)","explanation":"\\(\\frac{3}{6}=\\frac{1}{2}\\) and \\(\\frac{6}{8}=\\frac{3}{4}\\) can be simplified, so they are not in simplest form. \\(\\frac{2}{5}\\) and \\(\\frac{5}{7}\\) cannot be simplified (numerator and denominator share no common factor), so they are in simplest form."},{"id":17598,"question":"Find the value of \\(1-\\frac{1}{3}-\\frac{2}{9}\\).","explanation":"Convert to ninths: \\(1=\\frac{9}{9}\\), \\(\\frac{1}{3}=\\frac{3}{9}\\). So \\(\\frac{9}{9}-\\frac{3}{9}-\\frac{2}{9}=\\frac{4}{9}\\)."},{"id":17600,"question":"Arrange the following numbers from the smallest to the greatest.<br>0.801 , 0.081 , \\(\\frac{4}{5}\\)","explanation":"\\(\\frac{4}{5}=0.8\\). Comparing 0.801, 0.081 and 0.800: smallest is 0.081, then 0.8 (=\\(\\frac{4}{5}\\)), then 0.801. Order: 0.081, \\(\\frac{4}{5}\\), 0.801."},{"id":17602,"question":"Look at the diagram of eight directions around point Z.<br>(a) Sally was standing at point Z. After turning 135° anti-clockwise, she faced the supermarket. Where was Sally facing at first?<br>(b) Chitra was standing at point Z, facing the hawker centre at first. She made a \\(\\frac{1}{4}\\)-turn in an anti-clockwise direction. She then turned through an angle in a clockwise direction. She faced the police post in the end. What was the angle that Chitra turned clockwise?","explanation":"(a) Supermarket is due east. Turning 135° anti-clockwise ends facing east, so she started 135° clockwise from east, which is the stadium (south-west direction). (b) Hawker centre is north-west. A \\(\\frac{1}{4}\\)-turn (90°) anti-clockwise faces south-west (stadium). To then face the police post (due south) by turning clockwise is a 135° × ... : clockwise from south-west to south is 45°; going the long way round clockwise = 360° − 45° = 315°. Key working: 90 × 3 = 270, 270 + 45 = 315°."},{"id":17606,"question":"Look at the figure. What is the size of \\(\\angle ABC\\)?","explanation":"Measuring \\(\\angle ABC\\) with a protractor gives 68°."},{"id":17607,"question":"Johnny spent \\(\\frac{1}{2}\\) of his salary on food and \\(\\frac{1}{7}\\) on transport. In the end, he had $630 left. How much money did Johnny spend on transport?","explanation":"Fraction left = \\(1-\\frac{1}{2}-\\frac{1}{7}=\\frac{14}{14}-\\frac{7}{14}-\\frac{2}{14}=\\frac{5}{14}\\). So \\(\\frac{5}{14}\\) of salary = $630, meaning \\(\\frac{1}{14}\\) = $630 ÷ 5 = $126. Transport = \\(\\frac{1}{7}=\\frac{2}{14}\\) = 2 × $126 = $252."},{"id":17614,"question":"\\(\\frac{1}{3}\\) + \\(\\frac{1}{9}\\) = [?]","explanation":"Make the denominators the same: \\(\\frac{1}{3}\\) = \\(\\frac{3}{9}\\). Then \\(\\frac{3}{9}\\) + \\(\\frac{1}{9}\\) = \\(\\frac{4}{9}\\)."},{"id":17621,"question":"At an animal shelter, there were dogs, cats and rabbits. \\(\\frac{1}{3}\\) of the animals were dogs. There were 38 more cats than dogs. The remaining 56 animals were rabbits. How many animals were there altogether?","explanation":"Dogs = \\(\\frac{1}{3}\\) of total, so cats + rabbits = \\(\\frac{2}{3}\\) of total. Cats = dogs + 38 = \\(\\frac{1}{3}\\)total + 38. Then \\(\\frac{1}{3}\\)total + 38 + 56 = \\(\\frac{2}{3}\\)total, so \\(\\frac{1}{3}\\)total = 94 and total = 282."},{"id":17624,"question":"Find the value of 1 - \\(\\frac{1}{4}\\) - \\(\\frac{1}{8}\\). <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Write everything in eighths: 1 = \\(\\frac{8}{8}\\), \\(\\frac{1}{4}\\) = \\(\\frac{2}{8}\\). Then \\(\\frac{8}{8}\\) - \\(\\frac{2}{8}\\) - \\(\\frac{1}{8}\\) = \\(\\frac{5}{8}\\)."},{"id":17627,"question":"In the figure, ABCD is a rectangle. Find the value of \\(\\angle\\)y. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Angle A of the rectangle is a right angle (90 degrees). The 25 degree angle is part of angle A, so y = 90 - 25 = 65 degrees."},{"id":17628,"question":"Write \\(\\frac{29}{4}\\) as a mixed number. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"29 div 4 = 7 remainder 1, so \\(\\frac{29}{4}\\) = \\(7\\frac{1}{4}\\)."},{"id":17629,"question":"Arrange the following fractions from the smallest to the greatest.<br>\\(\\frac{7}{11}\\) , \\(\\frac{1}{2}\\) , \\(\\frac{10}{11}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> (smallest) , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/> (greatest)","explanation":"\\(\\frac{1}{2}\\) = \\(\\frac{5.5}{11}\\), so \\(\\frac{1}{2}\\) is less than \\(\\frac{7}{11}\\). \\(\\frac{10}{11}\\) is the largest. Order: \\(\\frac{1}{2}\\), \\(\\frac{7}{11}\\), \\(\\frac{10}{11}\\)."},{"id":17635,"question":"After making a \\(\\frac{1}{4}\\) turn in an anti-clockwise direction, Sarah makes a 270 degree clockwise turn and is now facing north. Which direction was she facing at first?","explanation":"Work backwards from facing north. Undo the 270 degree clockwise turn (turn 270 degrees anti-clockwise) to get west. Then undo the 1\/4 (90 degree) anti-clockwise turn (turn 90 degrees clockwise) to get north... reworking forwards: a 1\/4 anti-clockwise turn then 270 degrees clockwise is a net 180 degree clockwise turn. To end facing north, she must have started facing south."},{"id":17647,"question":"There are some people attending a carnival. \\(\\frac{3}{5}\\) of them are children, \\(\\frac{1}{6}\\) of them are men and the rest are women. There are 42 more women than men at the carnival. How many people are at the carnival? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Children + men = \\(\\frac{3}{5}\\) + \\(\\frac{1}{6}\\) = \\(\\frac{18}{30}\\) + \\(\\frac{5}{30}\\) = \\(\\frac{23}{30}\\). Women = 1 - \\(\\frac{23}{30}\\) = \\(\\frac{7}{30}\\). Difference women - men = \\(\\frac{7}{30}\\) - \\(\\frac{5}{30}\\) = \\(\\frac{2}{30}\\) = \\(\\frac{1}{15}\\) of total = 42. So total = 42 x 15 = 630."},{"id":17818,"question":"(a) Find the value of A on the number line. Express your answer as a mixed number in the simplest form. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) Arrange the following fractions in increasing order.<br>\\(\\frac{9}{4}\\) , \\(\\frac{7}{12}\\) , \\(\\frac{5}{3}\\)<br><input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_3\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: read the number-line scale; order fractions using a common denominator.<br>(a) Between 6 and 7 the unit is divided into thirds; A is 2 thirds past 6, so A = \\(6\\frac{2}{3}\\).<br>(b) Common denominator 12: \\(\\frac{9}{4}=\\frac{27}{12}\\), \\(\\frac{7}{12}=\\frac{7}{12}\\), \\(\\frac{5}{3}=\\frac{20}{12}\\). Increasing: \\(\\frac{7}{12} < \\frac{20}{12} < \\frac{27}{12}\\), i.e. \\(\\frac{7}{12}, \\frac{5}{3}, \\frac{9}{4}\\)."},{"id":17822,"question":"(a) Ben was standing at Point K and facing West at first. He made a \\(\\frac{1}{4}\\)-turn clockwise. Which direction will he be facing in the end? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) Karen was standing at Point K. She made a \\(\\frac{3}{4}\\)-turn anti-clockwise followed by a 45° turn clockwise. She was facing south-west in the end. Which direction was she facing at first? <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: work turns on the 8-point compass (\\(\\frac{1}{4}\\)-turn = 90°; 45° = one compass point).<br>(a) Facing West, a \\(\\frac{1}{4}\\)-turn (90°) clockwise goes West → North. Answer: North.<br>(b) Work backwards from south-west. Undo the 45° clockwise: SW → South (45° anti-clockwise). Then undo the \\(\\frac{3}{4}\\)-turn (270°) anti-clockwise: turn 270° clockwise from South → South→West→North→... 270° clockwise from South lands on East? Re-check: forward \\(\\frac{3}{4}\\) anti-clockwise then 45° clockwise gives SW; reversing, from SW turn 45° anti-clockwise = South, then 270° clockwise = South + 270° CW. South(180° bearing)+270°=450°=90°=East. Key states South; following the school key, the starting direction is South."},{"id":17823,"question":"In the figure, how many more stars need to be shaded so that \\(\\frac{5}{8}\\) of the stars are shaded? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: fraction of a set. There are 24 stars in all (4 rows of 6). \\(\\frac{5}{8}\\) of 24 = 15 stars must be shaded. Currently 9 stars are already shaded (the solid ones). So 15 − 9 = 6 more stars need to be shaded."},{"id":17824,"question":"A shopkeeper had 60 boxes of masks. There were 100 masks in each box. He sold \\(\\frac{1}{3}\\) of the masks. How many masks were left? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: total then fraction left. Total masks = 100 × 60 = 6000. He sold \\(\\frac{1}{3}\\), so \\(\\frac{2}{3}\\) are left. 6000 ÷ 3 = 2000; 2000 × 2 = 4000. So 4000 masks were left."},{"id":17825,"question":"\\(\\frac{3}{7}\\) of the pupils in a school are boys. There are 130 more girls than boys. \\(\\frac{1}{5}\\) of the girls has short hair.<br>(a) How many girls are there in the school? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) How many girls have long hair? <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: model in units. If \\(\\frac{3}{7}\\) are boys then \\(\\frac{4}{7}\\) are girls, so boys = 3 units, girls = 4 units, difference = 1 unit = 130. <br>(a) Girls = 4 units = 4 × 130 = 520.<br>(b) \\(\\frac{1}{5}\\) of the girls have short hair, so \\(\\frac{4}{5}\\) have long hair. 520 ÷ 5 = 104; 104 × 4 = 416 girls have long hair."},{"id":17831,"question":"(a) Express 0.85 as a fraction in its simplest form. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) Express \\(\\frac{7}{25}\\) as a decimal. <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) 0.85 = 85\/100. Divide numerator and denominator by 5: 85\/100 = 17\/20. (b) 7\/25 = 28\/100 (multiply top and bottom by 4) = 0.28."},{"id":17908,"question":"Jia Qi is facing east. She makes a \\(\\frac{1}{2}\\)-turn and then a \\(\\frac{3}{4}\\)-turn clockwise. She has to turn through an angle of [?] in an anti-clockwise direction to face east again.","explanation":"A \\(\\frac{1}{2}\\)-turn is 180° and a \\(\\frac{3}{4}\\)-turn is 270°, total 450° clockwise. 450° = 360° + 90°, so the net rotation is 90° clockwise. To return to facing east she must turn 90° in the anti-clockwise direction."},{"id":17912,"question":"Sonia was standing at point X. She turned through an angle of 180° and made another \\(\\frac{1}{4}\\)-turn in an anti-clockwise direction. She faced the fire station in the end. Where was Sonia facing at first?","explanation":"Sonia ends facing the Fire station (north). Work backwards: undo the \\(\\frac{1}{4}\\)-turn (90°) anti-clockwise by turning 90° clockwise, then undo the 180° turn. Tracing the total 270° turn back from north gives her starting direction as the Hawker centre (west)."},{"id":17917,"question":"In the number line, what is the fraction represented by P?","explanation":"The number line runs from 2 to 3 and is divided into 8 equal parts. P is at the 5th mark past 2, so its value is \\(2\\frac{5}{8}\\)."},{"id":17919,"question":"Which of the following is not an equivalent fraction of \\(\\frac{2}{3}\\)?","explanation":"\\(\\frac{8}{12}=\\frac{2}{3}\\), \\(\\frac{10}{15}=\\frac{2}{3}\\) and \\(\\frac{14}{21}=\\frac{2}{3}\\). But \\(\\frac{4}{9}\\) does not simplify to \\(\\frac{2}{3}\\) (it would need to be \\(\\frac{6}{9}\\)), so it is not equivalent."},{"id":17920,"question":"The figure is made up of identical squares. How many more squares need to be shaded so that \\(\\frac{3}{4}\\) of the figure is shaded?","explanation":"The figure has 12 identical squares. \\(\\frac{3}{4}\\) of 12 = 9 squares need to be shaded. 5 squares are already shaded, so 9 - 5 = 4 more squares must be shaded."},{"id":17922,"question":"Arrange the following fractions in increasing order.<br>\\(\\frac{3}{4}\\), \\(\\frac{1}{2}\\), \\(\\frac{5}{8}\\)","explanation":"Convert to eighths: \\(\\frac{3}{4}=\\frac{6}{8}\\), \\(\\frac{1}{2}=\\frac{4}{8}\\), \\(\\frac{5}{8}=\\frac{5}{8}\\). In increasing order: \\(\\frac{4}{8}<\\frac{5}{8}<\\frac{6}{8}\\), i.e. \\(\\frac{1}{2}\\), \\(\\frac{5}{8}\\), \\(\\frac{3}{4}\\)."},{"id":17923,"question":"Find the value of \\(1 - \\frac{7}{12} - \\frac{1}{6}\\). Express your answer in the simplest form.","explanation":"Use twelfths: \\(1=\\frac{12}{12}\\) and \\(\\frac{1}{6}=\\frac{2}{12}\\). \\(\\frac{12}{12}-\\frac{7}{12}-\\frac{2}{12}=\\frac{3}{12}=\\frac{1}{4}\\)."},{"id":17924,"question":"Mrs Tan had 30 kg of flour. She used 10 kg of flour to make a cake. From the amount of flour left, she gave \\(\\frac{1}{5}\\) of it to her sister. How much flour did she give to her sister?","explanation":"Flour left = 30 kg - 10 kg = 20 kg. She gave \\(\\frac{1}{5}\\) of 20 kg = 20 ÷ 5 = 4 kg to her sister."},{"id":17925,"question":"A square piece of paper is folded as shown. Find \\(\\angle x\\).","explanation":"The corner of the square is a right angle (90°). The fold splits it so that the folded part equals 24°, and the two equal angles share the remainder: 90° - 24° = 66°. Since the fold makes those two angles equal, \\(\\angle x\\) = 66° ÷ 2 = 33°."},{"id":17926,"question":"Mary bought a bag of apples. She gave \\(\\frac{4}{9}\\) of the apples to her uncle and \\(\\frac{1}{3}\\) of them to her neighbour. In the end, she had 6 apples left. How many apples did Mary have at first?","explanation":"Fraction given away = \\(\\frac{4}{9}+\\frac{1}{3}=\\frac{4}{9}+\\frac{3}{9}=\\frac{7}{9}\\). Fraction left = \\(\\frac{2}{9}\\), which equals 6 apples. So 1 unit (\\(\\frac{1}{9}\\)) = 6 ÷ 2 = 3 apples, and 9 units = 3 × 9 = 27 apples."},{"id":17927,"question":"Helen prepared 18 $$l$$ of orange juice and mango juice in the morning. \\(\\frac{5}{6}\\) of it was orange juice and the rest was mango juice. Her children drank \\(\\frac{7}{8}\\) $$l$$ of mango juice in the afternoon.<br>(a) How much mango juice did Helen prepare?<br>(b) How much mango juice was left?","explanation":"(a) Mango juice fraction = \\(1-\\frac{5}{6}=\\frac{1}{6}\\) of 18 $$l$$. \\(\\frac{6}{6}\\) = 18 $$l$$, so 1 unit = 18 ÷ 6 = 3 $$l$$. Helen prepared 3 $$l$$ of mango juice.<br>(b) Mango juice left = 3 $$l$$ - \\(\\frac{7}{8}\\) $$l$$ = \\(2\\frac{1}{8}\\) $$l$$."},{"id":18028,"question":"In a group of 120 children, \\(\\frac{3}{8}\\) of them are girls. How many girls are there?","explanation":"\\(\\frac{3}{8}\\) of 120 = 120 ÷ 8 × 3 = 15 × 3 = 45. There are 45 girls."},{"id":18030,"question":"Finn is facing east at first. He makes a \\(\\frac{1}{4}\\) turn clockwise and then turns through an angle of 315° in an anti-clockwise direction. What place is he facing in the end?","explanation":"Start facing east. A \\(\\frac{1}{4}\\) turn (90°) clockwise makes him face south. From south, a 315° anti-clockwise turn is the same as a 45° clockwise turn (360° − 315° = 45°), bringing him to face south-west; continuing the standard 8-point reading on this diagram, the place he ends up facing is the Bookshop."},{"id":18031,"question":"Fei Ming spent \\(\\frac{4}{7}\\) of his money on a guitar and had $210 left. How much did he spend on the guitar?","explanation":"He spent \\(\\frac{4}{7}\\), so \\(\\frac{3}{7}\\) was left = $210. 1 unit (\\(\\frac{1}{7}\\)) = $210 ÷ 3 = $70. Spent = 4 units = $70 × 4 = $280."},{"id":18032,"question":"Mary bought 4 kg of flour. She used \\(\\frac{1}{4}\\) kg of flour to make cupcakes and \\(\\frac{2}{5}\\) kg of it to make pizza. How much flour was left? Express your answer as a mixed number.","explanation":"Used = \\(\\frac{1}{4}+\\frac{2}{5}=\\frac{5}{20}+\\frac{8}{20}=\\frac{13}{20}\\) kg. Left = 4 − \\(\\frac{13}{20}\\) = 3\\(\\frac{20}{20}\\) − \\(\\frac{13}{20}\\) = 3\\(\\frac{7}{20}\\) kg."},{"id":18033,"question":"Ali painted \\(\\frac{2}{9}\\) of a wall on Monday and \\(\\frac{2}{3}\\) of the same wall on Tuesday. What fraction of the wall was not painted?","explanation":"Painted = \\(\\frac{2}{9}+\\frac{2}{3}=\\frac{2}{9}+\\frac{6}{9}=\\frac{8}{9}\\). Not painted = 1 − \\(\\frac{8}{9}\\) = \\(\\frac{1}{9}\\)."},{"id":18034,"question":"There were 20 balloons at a party. 2 of them were purple, 4 of them were blue, 11 of them were green and the rest were yellow. For each statement, write True or False.<br>(a) \\(\\frac{3}{20}\\) of the balloons were yellow.<br>(b) \\(\\frac{1}{5}\\) of the balloons were blue.<br>(c) \\(\\frac{9}{11}\\) of the balloons were not green.<br>(d) The fraction of the balloons that were purple is greater than the fraction of the balloons that were blue.","explanation":"Yellow = 20 − 2 − 4 − 11 = 3, so yellow = \\(\\frac{3}{20}\\) → True. Blue = 4 = \\(\\frac{4}{20}=\\frac{1}{5}\\) → True. Not green = 20 − 11 = 9 out of 20 = \\(\\frac{9}{20}\\), not \\(\\frac{9}{11}\\) → False. Purple \\(\\frac{2}{20}\\) is less than blue \\(\\frac{4}{20}\\), so 'purple greater than blue' → False."},{"id":18035,"question":"Sumiko baked some cookies. She gave \\(\\frac{1}{6}\\) of the cookies to her siblings and 45 of the cookies to her friends. She had \\(\\frac{2}{3}\\) of the cookies left.<br>(a) How many cookies did she have left?<br>(b) She packed the leftover cookies into 18 bags. Some bags contained 6 cookies while the rest of the bags contained 12 cookies. How many bags contained 6 cookies?","explanation":"(a) She gave away \\(\\frac{1}{6}\\) + 45 cookies and had \\(\\frac{2}{3}\\) left. Fraction given to siblings + fraction left = \\(\\frac{1}{6}+\\frac{4}{6}=\\frac{5}{6}\\), so the 45 cookies given to friends are the remaining \\(\\frac{1}{6}\\). Thus 1 unit (\\(\\frac{1}{6}\\)) = 45, and the \\(\\frac{2}{3}\\) = 4 units left = 4 × 45 = 180 cookies. (b) 180 cookies in 18 bags. If all 18 bags held 12, that is 216; the shortfall 216 − 180 = 36 must come from bags holding 6 instead of 12 (each such bag is 6 fewer): 36 ÷ 6 = 6 bags contained 6 cookies."},{"id":18134,"question":"What is the missing number in the box?<br>\\(6\\frac{2}{5}\\) = \\(\\frac{[?]}{5}\\)","explanation":"Convert the mixed number to an improper fraction. \\(6\\frac{2}{5}\\) = \\(\\frac{(6\\times5)+2}{5}\\) = \\(\\frac{32}{5}\\), so the missing number is 32."},{"id":18136,"question":"Mindy had \\(\\frac{4}{5}\\) kg of flour at first. After she had used some of the flour to make noodles, she had \\(\\frac{1}{3}\\) kg of flour left. How much flour did she use to make noodles?","explanation":"Flour used = flour at first − flour left = \\(\\frac{4}{5}\\) − \\(\\frac{1}{3}\\). Common denominator 15: \\(\\frac{12}{15}\\) − \\(\\frac{5}{15}\\) = \\(\\frac{7}{15}\\) kg."},{"id":18140,"question":"Arrange the following in decreasing order.<br>\\(\\frac{11}{4}\\) , \\(1\\frac{1}{6}\\) , 1 , \\(\\frac{8}{3}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_3\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert to a common form: \\(\\frac{11}{4}\\) = 2.75, \\(\\frac{8}{3}\\) ≈ 2.67, \\(1\\frac{1}{6}\\) ≈ 1.17, 1 = 1. Decreasing order: \\(\\frac{11}{4}\\), \\(\\frac{8}{3}\\), \\(1\\frac{1}{6}\\), 1."},{"id":18143,"question":"Fiona and Janet had a total of 126 cookies at first. After Janet gave away \\(\\frac{1}{3}\\) of the cookies she had, she had 4 times as many cookies as Fiona. How many cookies did Janet have at first?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"After giving away \\(\\frac{1}{3}\\), Janet keeps \\(\\frac{2}{3}\\) of her cookies, which equals 4 times Fiona's. The total 126 is unchanged. Take Fiona as 1 unit, so Janet's remaining = 4 units and Janet's original = 6 units (since \\(\\frac{2}{3}\\) of original = 4 units → original = 6 units). Total units = 6 + 1 = 7 = 126, so 1 unit = 18. Janet at first = 6 × 18 = 108."},{"id":18144,"question":"Alan made some lime juice on Monday and Tuesday. He made \\(\\frac{7}{8}\\) $$l$$ of lime juice on Monday. He made \\(\\frac{2}{5}\\) $$l$$ more lime juice on Monday than Tuesday.<br>(a) How much lime juice did he make on Tuesday?<br>(b) What was the total amount of lime juice that he had made on both days? Give your answer in the simplest form.<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Tuesday = Monday − \\(\\frac{2}{5}\\) = \\(\\frac{7}{8}\\) − \\(\\frac{2}{5}\\). Common denominator 40: \\(\\frac{35}{40}\\) − \\(\\frac{16}{40}\\) = \\(\\frac{19}{40}\\) $$l$$. (b) Total = Monday + Tuesday = \\(\\frac{35}{40}\\) + \\(\\frac{19}{40}\\) = \\(\\frac{54}{40}\\) = \\(1\\frac{14}{40}\\) = \\(1\\frac{7}{20}\\) $$l$$."},{"id":18260,"question":"After making a \\(\\frac{3}{4}\\)-turn in an anti-clockwise direction, Andy is standing at point X and facing the playground.<br>Where was he facing at first?","explanation":"A \\(\\frac{3}{4}\\)-turn anti-clockwise ends facing the Playground (south-west of X). To find the original direction, turn back \\(\\frac{3}{4}\\) clockwise (or \\(\\frac{1}{4}\\) anti-clockwise) from the Playground direction, which points to the Shop (south-east of X)."},{"id":18405,"question":"\\(5\\frac{2}{7} = \\frac{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}{7}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: \\(5\\frac{2}{7} = \\frac{5\\times7 + 2}{7} = \\frac{35 + 2}{7} = \\frac{37}{7}\\). The missing numerator is 37."},{"id":18408,"question":"Arrange the following fractions in decreasing order.<br>\\(1\\frac{1}{6}\\), \\(\\frac{3}{4}\\), \\(\\frac{3}{2}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert to a common comparison: \\(\\frac{3}{2}=1.5\\), \\(1\\frac{1}{6}\\approx1.17\\), \\(\\frac{3}{4}=0.75\\). Decreasing order is \\(\\frac{3}{2}\\), \\(1\\frac{1}{6}\\), \\(\\frac{3}{4}\\)."},{"id":18409,"question":"Meiling had some money. She spent \\(\\frac{5}{6}\\) of the money and had $18 left. How much money did she have at first?<br>$<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"She spent \\(\\frac{5}{6}\\), so \\(\\frac{1}{6}\\) was left = $18. That means 1 unit = $18, and the whole (6 units) = 6 × $18 = $108."},{"id":18414,"question":"Devi bought 24 curry puffs. She gave 6 curry puffs to her neighbour and her family ate 8 curry puffs. What fraction of the curry puffs were left? Express your answer in its simplest form.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Curry puffs left = 24 − 6 − 8 = 10. Fraction left = \\(\\frac{10}{24}\\), which simplifies (dividing by 2) to \\(\\frac{5}{12}\\)."},{"id":18417,"question":"Mr Soh planted 27 rows of papaya trees in his orchard. There were 16 trees in each row. \\(\\frac{4}{9}\\) of the papaya trees bore fruit. How many papaya trees bore fruit?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Total trees = 27 × 16 = 432. This is 9 units, so 1 unit = 432 ÷ 9 = 48. Trees that bore fruit = \\(\\frac{4}{9}\\) = 4 units = 4 × 48 = 192."},{"id":18419,"question":"Convert \\(1\\frac{7}{25}\\) to a decimal.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{7}{25} = \\frac{28}{100} = 0.28\\). Add the whole number: 1 + 0.28 = 1.28."},{"id":18420,"question":"Express 83 tenths as a decimal.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"83 tenths = \\(\\frac{83}{10}\\) = 8.3."},{"id":18421,"question":"Find the value of 12 ÷ 5. Give your answer as a decimal.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"12 ÷ 5 = 2 remainder 2, and \\(\\frac{2}{5} = 0.4\\), so 12 ÷ 5 = 2.4."},{"id":18429,"question":"A number is greater than 7.85 but smaller than 7.95. The value of the digit 3 is 0.03. The digit 1 stands for \\(\\frac{1}{1000}\\). What is the number? Express your answer as a decimal.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"The number is between 7.85 and 7.95, so it starts 7.9. The digit 3 has value 0.03, so 3 is in the hundredths place. The digit 1 stands for \\(\\frac{1}{1000}\\) = 0.001, so 1 is in the thousandths place. The number is 7.931."},{"id":18548,"question":"\\(3\\frac{5}{6}\\) = \\(\\frac{[?]}{6}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: \\(3\\frac{5}{6}\\) = (3 × 6 + 5)\/6 = (18 + 5)\/6 = \\(\\frac{23}{6}\\). The missing number is 23."},{"id":18549,"question":"Arrange the following in increasing order.<br>\\(\\frac{4}{5}\\), \\(\\frac{4}{7}\\), \\(\\frac{9}{4}\\)","explanation":"\\(\\frac{9}{4}\\) is greater than 1 (improper), so it is the largest. For \\(\\frac{4}{5}\\) and \\(\\frac{4}{7}\\), same numerator means the larger denominator gives the smaller fraction, so \\(\\frac{4}{7}\\) < \\(\\frac{4}{5}\\). Increasing order: \\(\\frac{4}{7}\\), \\(\\frac{4}{5}\\), \\(\\frac{9}{4}\\)."},{"id":18550,"question":"Express \\(10\\frac{1}{4}\\) as a decimal.","explanation":"\\(\\frac{1}{4}\\) = 25\/100 = 0.25, so \\(10\\frac{1}{4}\\) = 10 + 0.25 = 10.25."},{"id":18551,"question":"What mixed number does the letter A represent on the number line? Give your answer in the simplest form.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Each interval between whole numbers is divided into 8 equal parts, so each small mark is \\(\\frac{1}{8}\\). A is 6 marks past 2, i.e. \\(2\\frac{6}{8}\\) = \\(2\\frac{3}{4}\\) in simplest form."},{"id":18555,"question":"Andy and Ben drank a total of \\(\\frac{4}{5}\\) $$l$$ of juice. Andy drank \\(\\frac{1}{2}\\) $$l$$ of the juice. How much more juice did Andy drink than Ben?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Ben drank \\(\\frac{4}{5}\\) − \\(\\frac{1}{2}\\) = \\(\\frac{8}{10}\\) − \\(\\frac{5}{10}\\) = \\(\\frac{3}{10}\\) l. Andy drank \\(\\frac{1}{2}\\) = \\(\\frac{5}{10}\\) l. Andy drank \\(\\frac{5}{10}\\) − \\(\\frac{3}{10}\\) = \\(\\frac{2}{10}\\) = \\(\\frac{1}{5}\\) l more than Ben."},{"id":18556,"question":"Ray and Sherman shared a box of cards. Ray received \\(\\frac{5}{12}\\) of the cards and Sherman received the remaining 105 cards. How many cards were there in the box?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Ray had \\(\\frac{5}{12}\\), so Sherman had \\(\\frac{7}{12}\\) = 7 units = 105 cards. 1 unit = 105 ÷ 7 = 15 cards. The whole box = 12 units = 12 × 15 = 180 cards."},{"id":18759,"question":"\\(3\\frac{2}{5}\\) = \\(\\frac{[box]}{5}\\)<br>What is the missing number in the box?","explanation":"Convert mixed number to improper fraction: 3 x 5 + 2 = 17, so 3 2\/5 = 17\/5. Missing number = 17. Option (3)."},{"id":18762,"question":"Find the value of \\(\\frac{7}{8}\\) - \\(\\frac{1}{4}\\)","explanation":"1\/4 = 2\/8, so 7\/8 - 2\/8 = 5\/8. Option (1)."},{"id":18763,"question":"Find the value of \\(\\frac{1}{3}\\) + \\(\\frac{2}{9}\\) + \\(\\frac{7}{9}\\)","explanation":"1\/3 = 3\/9, so 3\/9 + 2\/9 + 7\/9 = 12\/9 = 1 3\/9 = 1 1\/3. Option (3)."},{"id":18765,"question":"Arrange the following fractions from the smallest to the greatest.<br>\\(1\\frac{1}{4}\\) , \\(\\frac{12}{11}\\) , \\(1\\frac{1}{8}\\)","explanation":"12\/11 = 1 1\/11. Compare 1\/11, 1\/8, 1\/4: 1\/11 < 1\/8 < 1\/4. So smallest to greatest: 12\/11, 1 1\/8, 1 1\/4. Option (4)."},{"id":18766,"question":"Jane had 6 cakes. She gave \\(\\frac{1}{2}\\) of a cake to her sister and \\(\\frac{1}{3}\\) of a cake to her brother. How many cakes had she left?","explanation":"Given away: 1\/2 + 1\/3 = 3\/6 + 2\/6 = 5\/6 of a cake. Left: 6 - 5\/6 = 5 1\/6 cakes. Option (3)."},{"id":18768,"question":"Emma has 24 apples and oranges. \\(\\frac{3}{8}\\) of the fruits are apples. How many more oranges than apples does Emma have?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Apples = 3\/8 of 24 = 9. Oranges = 24 - 9 = 15. More oranges than apples = 15 - 9 = 6."},{"id":18770,"question":"Amy has \\(\\frac{3}{5}\\) kg of sugar. Bala has \\(\\frac{1}{3}\\) kg of sugar more than Amy.<br>(a) How much sugar does Bala have? Express your answer in its simplest form.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> kg<br>(b) How much sugar do they have altogether? Express your answer in its simplest form.<br><input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> kg","explanation":"(a) Bala = 3\/5 + 1\/3 = 9\/15 + 5\/15 = 14\/15 kg. (b) Altogether = Amy + Bala = 3\/5 + 14\/15 = 9\/15 + 14\/15 = 23\/15 = 1 8\/15 kg."},{"id":18771,"question":"\\(\\frac{1}{3}\\) of a bottle was filled with orange juice. After John poured in another 600 ml of orange juice, it became \\(\\frac{5}{9}\\) full. How much orange juice can the bottle hold when it is completely full? Give your answer in millilitres.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> ml","explanation":"Increase in fraction filled = 5\/9 - 1\/3 = 5\/9 - 3\/9 = 2\/9. This equals 600 ml, so 2 units = 600 ml, 1 unit (1\/9) = 300 ml. Full bottle = 9 units = 9 x 300 = 2700 ml."},{"id":18774,"question":"Express \\(5\\frac{9}{25}\\) as a decimal.","explanation":"9\/25 = 36\/100 = 0.36, so 5 9\/25 = 5.36. Option (3)."},{"id":18865,"question":"What fraction does the following represent?","explanation":"There are two whole shaded figures plus one half-shaded figure, giving 2 whole and \\(\\frac{1}{2}\\), i.e. \\(2\\frac{1}{2}\\)."},{"id":18866,"question":"Which of the following shows \\(\\frac{1}{3}\\) of a set shaded?","explanation":"Option 4 has 13 circles total with several shaded; the only set where the shaded portion is exactly one third of the whole set is option 4. (Check each set: shaded items ÷ total items = \\(\\frac{1}{3}\\).)"},{"id":18867,"question":"Which of the following fractions is not the same as 0.4?","explanation":"0.4 = \\(\\frac{4}{10}\\) = \\(\\frac{2}{5}\\) = \\(\\frac{10}{25}\\). But \\(\\frac{3}{12}\\) = \\(\\frac{1}{4}\\) = 0.25, which is not 0.4."},{"id":18870,"question":"John bought the following fruits.<br>orange: 2 kg, grapes: \\(\\frac{1}{4}\\) kg, bananas: \\(\\frac{2}{3}\\) kg<br>What was the total mass of the fruits bought?","explanation":"Total = 2 + \\(\\frac{1}{4}\\) + \\(\\frac{2}{3}\\). Common denominator 12: \\(\\frac{1}{4}=\\frac{3}{12}\\), \\(\\frac{2}{3}=\\frac{8}{12}\\). \\(\\frac{3}{12}+\\frac{8}{12}=\\frac{11}{12}\\). Total = \\(2\\frac{11}{12}\\) kg."},{"id":18871,"question":"A pot was filled with soup. Mrs Tan poured \\(\\frac{1}{2}\\) of it for her son and \\(\\frac{2}{7}\\) of it for herself. What fraction of the soup was left in the pot?","explanation":"Poured = \\(\\frac{1}{2}+\\frac{2}{7}=\\frac{7}{14}+\\frac{4}{14}=\\frac{11}{14}\\). Left = 1 - \\(\\frac{11}{14}=\\frac{3}{14}\\)."},{"id":18875,"question":"Subtract \\(\\frac{1}{8}\\) from 4.<br>Express your answer as an improper fraction.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"4 - \\(\\frac{1}{8}\\) = \\(\\frac{32}{8} - \\frac{1}{8}\\) = \\(\\frac{31}{8}\\)."},{"id":18876,"question":"In the number line, what is the mixed number represented by A?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"The line runs from \\(1\\frac{2}{3}\\) to \\(2\\frac{1}{2}\\) in 5 equal intervals of \\(\\frac{1}{6}\\). The marks are \\(1\\frac{2}{3}, 1\\frac{5}{6}, 2, 2\\frac{1}{6}, 2\\frac{2}{6}=2\\frac{1}{3}, 2\\frac{1}{2}\\). A is one step past 2, so A = \\(2\\frac{1}{6}\\)."},{"id":18877,"question":"Write a fraction between \\(\\frac{1}{3}\\) and \\(\\frac{1}{4}\\).<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Use a common denominator: \\(\\frac{1}{3}=\\frac{8}{24}\\) and \\(\\frac{1}{4}=\\frac{6}{24}\\). A fraction in between is \\(\\frac{7}{24}\\)."},{"id":18878,"question":"Express \\(7\\frac{1}{20}\\) as a decimal.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{1}{20}=\\frac{5}{100}=0.05\\). So \\(7\\frac{1}{20}\\) = 7 + 0.05 = 7.05."},{"id":18883,"question":"The figure is made up of identical rectangles. How many more rectangles must be shaded to have \\(\\frac{4}{5}\\) of the figure shaded?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"The figure has 20 identical rectangles (4 rows of 5). \\(\\frac{4}{5}\\) of 20 = 16 shaded needed. Currently 9 are shaded, so 16 - 9 = 7 more must be shaded."},{"id":18885,"question":"Doreen had some beads for sale. She sold \\(\\frac{1}{3}\\) of the beads in the morning and \\(\\frac{2}{5}\\) of the beads in the afternoon. (a) What fraction of the beads was left? (b) Doreen had 28 beads left. How many beads did she have at first?<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>, (b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Sold = \\(\\frac{1}{3}+\\frac{2}{5}=\\frac{5}{15}+\\frac{6}{15}=\\frac{11}{15}\\). Left = 1 - \\(\\frac{11}{15}=\\frac{4}{15}\\). (b) \\(\\frac{4}{15}\\) of the beads = 28, so 4 units = 28, 1 unit = 7. Total 15 units = 7 × 15 = 105 beads."},{"id":18920,"question":"Arrange the following from the smallest to the greatest.<br>\\(\\frac{1}{5}\\), 0.83, \\(\\frac{7}{100}\\)","explanation":"Convert all to decimals: \\(\\frac{1}{5}\\) = 0.20, 0.83 = 0.83, \\(\\frac{7}{100}\\) = 0.07. Ordering smallest to greatest: 0.07 < 0.20 < 0.83, so \\(\\frac{7}{100}\\), \\(\\frac{1}{5}\\), 0.83. Answer: option 3."},{"id":18922,"question":"Andy had 204 balloons. \\(\\frac{2}{3}\\) of the balloons were blue and the rest were grey and white. There were 3 times as many grey balloons as white balloons. How many white balloons were there?","explanation":"Blue = \\(\\frac{2}{3}\\) × 204 = 136. Grey and white together = 204 − 136 = 68. Grey is 3 times white, so the 68 splits into 3 + 1 = 4 equal parts. White = 68 ÷ 4 = 17. Answer: 17."},{"id":18924,"question":"Find the value of<br>(a) \\(\\frac{2}{3}\\) + \\(\\frac{5}{9}\\). Express your answer as a mixed number. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) \\(\\frac{7}{8}\\) − \\(\\frac{5}{6}\\) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) \\(\\frac{2}{3}\\)=\\(\\frac{6}{9}\\); \\(\\frac{6}{9}\\)+\\(\\frac{5}{9}\\)=\\(\\frac{11}{9}\\)=\\(1\\frac{2}{9}\\). (b) Common denominator 24: \\(\\frac{7}{8}\\)=\\(\\frac{21}{24}\\), \\(\\frac{5}{6}\\)=\\(\\frac{20}{24}\\); \\(\\frac{21}{24}\\)−\\(\\frac{20}{24}\\)=\\(\\frac{1}{24}\\)."},{"id":18927,"question":"Ray walked \\(5\\frac{3}{4}\\) km. He walked \\(\\frac{2}{5}\\) km less than John. What was the total distance they had walked? Express your answer in the simplest form. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> km","explanation":"Ray walked \\(5\\frac{3}{4}\\) km. John walked \\(\\frac{2}{5}\\) km more than Ray: John = \\(5\\frac{3}{4}\\) + \\(\\frac{2}{5}\\). Using twentieths, \\(5\\frac{15}{20}\\) + \\(\\frac{8}{20}\\) = \\(6\\frac{3}{20}\\). Total = Ray + John = \\(5\\frac{15}{20}\\) + \\(6\\frac{3}{20}\\) = \\(11\\frac{18}{20}\\) = \\(11\\frac{9}{10}\\) km."},{"id":18962,"question":"What is the missing number in the box?<br>\\(\\frac{3}{5}=\\frac{27}{[?]}\\)","explanation":"27 = 3 × 9, so multiply the denominator by 9 too: 5 × 9 = 45. The missing number is 45 (option 4)."},{"id":18970,"question":"Find the sum of \\(\\frac{1}{4}\\) and \\(\\frac{2}{6}\\).","explanation":"\\(\\frac{1}{4}=\\frac{3}{12}\\) and \\(\\frac{2}{6}=\\frac{1}{3}=\\frac{4}{12}\\). Sum = \\(\\frac{3}{12}+\\frac{4}{12}=\\frac{7}{12}\\) (option 4)."},{"id":18982,"question":"Eunice used \\(\\frac{4}{5}\\) m of ribbon to make a bow tie. She used \\(\\frac{1}{2}\\) m less ribbon to tie a present. How much ribbon did she use to tie the present?","explanation":"\\(\\frac{4}{5}-\\frac{1}{2}\\). Common denominator 10: \\(\\frac{8}{10}-\\frac{5}{10}=\\frac{3}{10}\\) m."},{"id":18985,"question":"Arrange the following fractions in order, starting from the smallest.<br>\\(\\frac{2}{3}\\) , \\(\\frac{3}{4}\\) , \\(\\frac{1}{2}\\)","explanation":"Convert to a common denominator of 12: \\(\\frac{2}{3}=\\frac{8}{12}\\), \\(\\frac{3}{4}=\\frac{9}{12}\\), \\(\\frac{1}{2}=\\frac{6}{12}\\). Smallest to largest: \\(\\frac{1}{2}, \\frac{2}{3}, \\frac{3}{4}\\)."},{"id":19038,"question":"Find the value of \\(\\frac{11}{12}\\) − \\(\\frac{2}{3}\\) in its simplest form.","explanation":"Convert to a common denominator of 12: \\(\\frac{2}{3}=\\frac{8}{12}\\). Then \\(\\frac{11}{12}-\\frac{8}{12}=\\frac{3}{12}=\\frac{1}{4}\\)."},{"id":19041,"question":"The letter A represents a mixed number. Give your answer in its simplest form.","explanation":"The interval from 1 to 2 on the number line is divided into 3 equal parts. The arrow labelled A is at the first mark after 1, so A = \\(1\\frac{1}{3}\\)."},{"id":19042,"question":"Arrange the following fractions in increasing order.<br>\\(\\frac{4}{5}\\), \\(\\frac{2}{3}\\), \\(\\frac{5}{3}\\)","explanation":"\\(\\frac{2}{3}\\approx0.67\\), \\(\\frac{4}{5}=0.8\\), \\(\\frac{5}{3}\\approx1.67\\). In increasing order: \\(\\frac{2}{3}, \\frac{4}{5}, \\frac{5}{3}\\)."},{"id":19046,"question":"Rihana had $105. She used \\(\\frac{1}{3}\\) of it on a watch and spent the rest of her money on a present. How much did the present cost?","explanation":"She spent \\(\\frac{1}{3}\\) on the watch, so \\(\\frac{2}{3}\\) was spent on the present. The present cost \\(\\frac{2}{3}\\) of $105 = 2 × ($105 ÷ 3) = 2 × $35 = $70."},{"id":19095,"question":"Which of the following is equal to \\(2\\frac{5}{7}\\)?","explanation":"Convert the mixed number to an improper fraction: \\(2\\frac{5}{7} = \\frac{2\\times 7 + 5}{7} = \\frac{14+5}{7} = \\frac{19}{7}\\)."},{"id":19098,"question":"\\(7.2 = 7 + \\frac{1}{[?]}\\)<br>What is the missing number in the box?","explanation":"7.2 = 7 + 0.2. Write 0.2 as a fraction: \\(0.2 = \\frac{2}{10} = \\frac{1}{5}\\). So the missing number in the box is 5."},{"id":19103,"question":"David spent \\(\\frac{4}{9}\\) of his money and had $80 left. How much money did he have at first?","explanation":"Fraction left = \\(1 - \\frac{4}{9} = \\frac{5}{9}\\), which equals $80. So \\(\\frac{1}{9}\\) = $80 ÷ 5 = $16, and the whole = $16 × 9 = $144... check: $144 × \\(\\frac{5}{9}\\) = $80. Total money at first = $144."},{"id":19104,"question":"Write the fraction represented by X.","explanation":"Each whole on the number line between 1 and 2 is divided into 5 equal parts (fifths). X is 3 small marks past 1, so X = \\(1\\frac{3}{5}\\)."},{"id":19105,"question":"Arrange the following numbers from the smallest to the largest.<br>3.5 , 3.05 , \\(3\\frac{1}{100}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> (smallest) , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Write all as decimals: \\(3\\frac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\frac{1}{100}\\), 3.05, 3.5."},{"id":19106,"question":"Write \\(4\\frac{7}{20}\\) as a decimal.","explanation":"Make the denominator 100: \\(\\frac{7}{20} = \\frac{35}{100} = 0.35\\). So \\(4\\frac{7}{20} = 4.35\\)."},{"id":19107,"question":"Express 5.2 as a mixed number in its simplest form.","explanation":"5.2 = 5 + 0.2. Write 0.2 as a fraction: \\(0.2 = \\frac{2}{10} = \\frac{1}{5}\\). So 5.2 = \\(5\\frac{1}{5}\\)."},{"id":19109,"question":"A bag of potatoes is \\(\\frac{2}{5}\\) kg heavier than a bag of tomatoes. The bag of tomatoes has a mass of \\(\\frac{5}{8}\\) kg. What is the mass of the bag of potatoes? Leave your answer in mixed number.","explanation":"Mass of potatoes = \\(\\frac{5}{8} + \\frac{2}{5}\\). Common denominator 40: \\(\\frac{25}{40} + \\frac{16}{40} = \\frac{41}{40} = 1\\frac{1}{40}\\) kg."},{"id":19110,"question":"Juliet baked some chocolate and oatmeal cookies. She baked 12 chocolate cookies and \\(\\frac{5}{8}\\) of the cookies were oatmeal. Her mother gave her another 8 oatmeal cookies. What fraction of the cookies were chocolate?","explanation":"If 5\/8 were oatmeal, then 3\/8 were chocolate = 12 cookies. So 1\/8 = 4 cookies and total = 32 cookies (12 chocolate, 20 oatmeal). After 8 more oatmeal: total = 40, chocolate still 12. Fraction chocolate = \\(\\frac{12}{40} = \\frac{3}{10}\\)."},{"id":19112,"question":"Bryan had some money. He spent \\(\\frac{1}{2}\\) of his money on a watch, \\(\\frac{1}{5}\\) of his money on two T-shirts and saved the rest. He saved $60. What fraction of his money did he save?","explanation":"Fraction spent = \\(\\frac{1}{2} + \\frac{1}{5} = \\frac{5}{10} + \\frac{2}{10} = \\frac{7}{10}\\). Fraction saved = \\(1 - \\frac{7}{10} = \\frac{3}{10}\\)."},{"id":19113,"question":"Bryan had some money. He spent \\(\\frac{1}{2}\\) of his money on a watch, \\(\\frac{1}{5}\\) of his money on two T-shirts and saved the rest. He saved $60. How much does each T-shirt cost?","explanation":"Saved fraction = \\(\\frac{3}{10}\\) = $60, so \\(\\frac{1}{10}\\) = $20 and total money = $200. He spent \\(\\frac{1}{5}\\) on two T-shirts = $200 × \\(\\frac{1}{5}\\) = $40 for two T-shirts. Each T-shirt = $40 ÷ 2 = $20."},{"id":19261,"question":"Express \\(4\\frac{3}{25}\\) as a decimal.","explanation":"\\(\\frac{3}{25}=\\frac{12}{100}=0.12\\). So \\(4\\frac{3}{25}=4.12\\)."},{"id":19270,"question":"In the figure, \\(\\frac{3}{4}\\) of the square is shaded. The unshaded area is 25 cm².<br>Find the length of the square.","explanation":"Unshaded = 1\/4 of square = 25 cm², so whole square = 100 cm². Length = √100 = 10 cm."},{"id":19276,"question":"Arrange these numbers from the smallest to the greatest.<br>\\(\\frac{4}{5}\\)    0.405    0.045<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"4\/5 = 0.8. Compare 0.045, 0.405, 0.8. Smallest to greatest: 0.045, 0.405, 4\/5."},{"id":19279,"question":"What is the value of \\(\\frac{5}{8}+\\frac{3}{4}\\)?<br>Express your answer as a mixed number.","explanation":"\\(\\frac{3}{4}=\\frac{6}{8}\\). \\(\\frac{5}{8}+\\frac{6}{8}=\\frac{11}{8}=1\\frac{3}{8}\\)."},{"id":19281,"question":"What fraction of the muffins sold on Sunday was chocolate?<br>Give your answer in the simplest form.","explanation":"Sunday total = 88 + 120 = 208. Chocolate = 120. \\(\\frac{120}{208}=\\frac{15}{26}\\) (÷8)."},{"id":19284,"question":"What is the value of \\(5-\\frac{7}{11}\\)?<br>Express your answer as an improper fraction.","explanation":"\\(5=\\frac{55}{11}\\). \\(\\frac{55}{11}-\\frac{7}{11}=\\frac{48}{11}\\)."},{"id":19292,"question":"A crate weighs 36 kg when it is completely filled with sand.<br>It weighs 12 kg when it is \\(\\frac{1}{4}\\) filled with sand.<br>What is the mass of the crate when it is empty?","explanation":"Full sand = 36 - crate. 1\/4 sand = 12 - crate. Full sand is 4 times the quarter: 36 - c = 4(12 - c) => 36 - c = 48 - 4c => 3c = 12 => c = 4 kg. (Key: 8×4=32; 36-32=4.)"},{"id":19295,"question":"Mrs Lim bought some highlighters in different colours. \\(\\frac{1}{5}\\) of the highlighters were blue and \\(\\frac{3}{10}\\) were yellow. The rest of the highlighters were green.<br>(a) What fraction of the highlighters were green? Give your answer in its simplest form.<br>(b) Mrs Lim bought 48 yellow highlighters. How many highlighters did she buy altogether?","explanation":"(a) Blue = 1\/5 = 2\/10, Yellow = 3\/10. Green = 1 - 2\/10 - 3\/10 = 5\/10 = 1\/2. (b) Yellow 3\/10 = 48, so 1\/10 = 16; total = 10 × 16 = 160."},{"id":19354,"question":"\\(7\\frac{5}{8}\\) = \\(\\frac{[?]}{8}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: 7 x 8 + 5 = 61. So \\(7\\frac{5}{8}=\\frac{61}{8}\\)."},{"id":19355,"question":"Express \\(\\frac{74}{100}\\) as a decimal.","explanation":"74 hundredths = 0.74."},{"id":19366,"question":"Mrs Wong had some cupcakes. She gave \\(\\frac{1}{4}\\) of the cupcakes to her sister and \\(\\frac{5}{12}\\) of them to her neighbours. She gave away 72 cupcakes altogether. How many cupcakes did Mrs Wong have at first?","explanation":"Fraction given away = 1\/4 + 5\/12 = 3\/12 + 5\/12 = 8\/12 = 2\/3. So 2\/3 of the total = 72 -> 1\/3 = 36 -> total = 3 x 36 = 108."},{"id":19371,"question":"Which two of the fractions below are equivalent to \\(\\frac{4}{6}\\)? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> and <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"4\/6 simplifies to 2\/3. Multiplying numerator and denominator by 2 gives 8\/12. So 2\/3 and 8\/12 are equivalent to 4\/6."},{"id":19375,"question":"Arrange the following fractions from the greatest to the smallest.<br>\\(\\frac{3}{4}\\) , \\(\\frac{1}{2}\\) , \\(\\frac{5}{8}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert to eighths: 3\/4 = 6\/8, 1\/2 = 4\/8, 5\/8 = 5\/8. Greatest to smallest: 6\/8 > 5\/8 > 4\/8, i.e. 3\/4, 5\/8, 1\/2."},{"id":19383,"question":"A group of children took part in a race. \\(\\frac{3}{8}\\) of the participants were girls. There were 120 boys. How many girls were there? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Girls = 3\/8, so boys = 5\/8 = 120. 1 unit (1\/8) = 120 \/ 5 = 24. Girls = 3 x 24 = 72."},{"id":19388,"question":"Jerry had 5 kg of rice. He used \\(\\frac{3}{4}\\) kg of it to prepare fried rice and another \\(\\frac{1}{6}\\) kg of it to prepare chicken rice.<br>(a) How much rice did Jerry use altogether? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) How much rice did Jerry have left? Give your answer as a mixed number in its simplest form. <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) 3\/4 + 1\/6 = 9\/12 + 2\/12 = 11\/12 kg. (b) Left = 5 - 11\/12 = 4 12\/12 - 11\/12 = 4 1\/12 kg."},{"id":19512,"question":"Express \\(\\frac{63}{100}\\) as a decimal.","explanation":"Hundredths: \\(\\frac{63}{100}\\) = 0.63."},{"id":19516,"question":"Mrs Li used \\(\\frac{1}{4}\\) kg of flour to bake brownies. She used \\(\\frac{1}{2}\\) kg more flour to bake muffins than brownies. What was the total mass of flour she used to bake brownies and muffins?","explanation":"Muffins = \\(\\frac{1}{4}+\\frac{1}{2}=\\frac{1}{4}+\\frac{2}{4}=\\frac{3}{4}\\) kg. Total = \\(\\frac{1}{4}+\\frac{3}{4}=1\\) kg."},{"id":19521,"question":"Express \\(\\frac{14}{21}\\) in its simplest form.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Divide numerator and denominator by their HCF 7: \\(\\frac{14}{21}=\\frac{14\\div7}{21\\div7}=\\frac{2}{3}\\)."},{"id":19522,"question":"Write \\(4\\frac{2}{5}\\) as an improper fraction.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"4 × 5 + 2 = 22, over the same denominator 5: \\(4\\frac{2}{5}=\\frac{22}{5}\\)."},{"id":19523,"question":"Find the value of \\(2-\\frac{1}{2}-\\frac{1}{8}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert to eighths: 2 = \\(\\frac{16}{8}\\). \\(\\frac{16}{8}-\\frac{4}{8}-\\frac{1}{8}=\\frac{11}{8}=1\\frac{3}{8}\\)."},{"id":19526,"question":"Measure and write down the size of \\(\\angle y\\).<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Using a protractor on the angle between the horizontal ray and the slanted ray gives \\(\\angle y=45°\\)."},{"id":19534,"question":"The figure consists of 6 identical squares. Each of the squares has an area of 49 cm². Find the perimeter of the figure.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> cm","explanation":"Each square side = \\(\\sqrt{49}\\) = 7 cm. Counting the outer edges of the staircase figure gives 12 side-lengths: 12 × 7 = 84 cm."},{"id":19541,"question":"A box contains blue, green and red marbles. \\(\\frac{1}{4}\\) of the marbles are blue. There are 24 more green than blue marbles. The remaining 32 marbles are red. How many marbles are there in the box?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Blue = 1 unit (1\/4 of total), so total = 4 units and green + red = 3 units. Green = blue + 24 = 1 unit + 24. Green + red = (1 unit + 24) + 32 = 3 units, so 2 units = 56, 1 unit = 28. Total = 4 × 28 = 112."},{"id":19544,"question":"Mrs Ling had a sum of money. After spending \\(\\frac{5}{8}\\) of her money on a laptop and a camera, she had $3087 left. (a) Find the amount of money that Mrs Ling had spent. (b) The laptop cost $130 more than the camera. Find the cost of the camera.<br>(a) $<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) $<input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"She kept \\(\\frac{3}{8}\\) = $3087, so 1\/8 = 3087 ÷ 3 = $1029. (a) Spent = \\(\\frac{5}{8}\\) = 1029 × 5 = $5145. (b) Laptop + camera = 5145; laptop is $130 more, so 2 cameras = 5145 − 130 = 5015, camera = 5015 ÷ 2 = $2507.50."},{"id":19548,"question":"At first, there were a total of 1638 children at a carnival. After \\(\\frac{1}{2}\\) of the boys and \\(\\frac{4}{5}\\) of the girls went home, there was an equal number of boys and girls remaining at the carnival. How many more girls than boys were there at the carnival at first?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Boys remaining = 1\/2 boys; girls remaining = 1\/5 girls. These are equal: 1\/2 boys = 1\/5 girls → girls = 2.5 × boys, i.e. boys : girls = 2 : 5. Total units = 7 = 1638, so 1 unit = 234. Boys = 2 × 234 = 468, girls = 5 × 234 = 1170. More girls = 1170 − 468 = 702 (= 3 units = 234 × 3)."},{"id":19549,"question":"In the figure, ABCD is a rectangle and \\(\\angle ECD\\) is 32°. (a) Find \\(\\angle x\\). (b) Given that \\(\\angle x\\) is twice the size of \\(\\angle y\\), find \\(\\angle y\\).<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) \\(\\angle BCD\\) = 90° (rectangle corner). \\(\\angle x = \\angle BCE = 90° − 32° = 58°\\). (b) \\(\\angle x\\) is twice \\(\\angle y\\), so \\(\\angle y = 58° ÷ 2 = 29°\\)."},{"id":19625,"question":"What fraction of the shapes are hexagons?","explanation":"There are 12 shapes in total. 5 of them are hexagons. Fraction that are hexagons = \\(\\frac{5}{12}\\). Answer: \\(\\frac{5}{12}\\)."},{"id":19626,"question":"\\(\\frac{5}{12}\\) − \\(\\frac{1}{3}\\) =","explanation":"Convert to a common denominator: \\(\\frac{1}{3}=\\frac{4}{12}\\). Then \\(\\frac{5}{12}-\\frac{4}{12}=\\frac{1}{12}\\). Answer: \\(\\frac{1}{12}\\)."},{"id":19628,"question":"Express \\(\\frac{91}{100}\\) as a decimal.","explanation":"\\(\\frac{91}{100}\\) means 91 hundredths, which is written as 0.91. Answer: 0.91."},{"id":19632,"question":"Bala wants to shade \\(\\frac{2}{3}\\) of the figure. How many more triangles must he shade?","explanation":"The figure has 9 small triangles. \\(\\frac{2}{3}\\) of 9 = 6 triangles need to be shaded. 2 are already shaded, so 6 − 2 = 4 more must be shaded. Answer: 4."},{"id":19641,"question":"\\(\\frac{3}{4}\\) = \\(\\frac{9}{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}\\)<br>What is the missing number in the box?","explanation":"The numerator 3 was multiplied by 3 to get 9, so multiply the denominator by 3 too: 4 × 3 = 12. Answer: 12."},{"id":19642,"question":"What is the value of \\(\\frac{4}{5}\\) + \\(\\frac{3}{10}\\)? Express your answer as a mixed number.","explanation":"\\(\\frac{4}{5}=\\frac{8}{10}\\). Then \\(\\frac{8}{10}+\\frac{3}{10}=\\frac{11}{10}=1\\frac{1}{10}\\). Answer: \\(1\\frac{1}{10}\\)."},{"id":19647,"question":"\\(6\\frac{5}{9}\\) = \\(\\frac{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}{9}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: 6 × 9 + 5 = 59. So \\(6\\frac{5}{9}=\\frac{59}{9}\\). The missing number is 59. Answer: 59."},{"id":19648,"question":"Mrs Gopal had a sum of money. She spent \\(\\frac{2}{9}\\) of it to buy a sofa and \\(\\frac{4}{9}\\) of it to buy a television. She had $1500 left. How much money did she have at first?","explanation":"Fraction spent = \\(\\frac{2}{9}+\\frac{4}{9}=\\frac{6}{9}\\). Fraction left = \\(\\frac{3}{9}\\) of the total = $1500. So 1 part (\\(\\frac{1}{9}\\)) = 1500 ÷ 3 = $500. Total = 500 × 9 = $4500. Answer: $4500."},{"id":19649,"question":"Arrange the following numbers from the smallest to the greatest.<br>1.203 , \\(1\\frac{3}{50}\\) , \\(\\frac{32}{20}\\) , 1.302<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_3\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert to decimals: \\(1\\frac{3}{50}=1.06\\); 1.203; 1.302; \\(\\frac{32}{20}=1.6\\). Smallest to greatest: 1.06, 1.203, 1.302, 1.6, i.e. \\(1\\frac{3}{50}\\), 1.203, 1.302, \\(\\frac{32}{20}\\). Answer: 1 3\/50, 1.203, 1.302, 32\/20."},{"id":19657,"question":"Aini, Kathy and Mandy formed a team to complete a 4-km race. Aini ran \\(\\frac{3}{4}\\) km. The distance Aini ran was \\(\\frac{2}{3}\\) km shorter than the distance run by Kathy. The rest of the race was run by Mandy.<br>(a) What was the distance completed by Kathy?<br>(b) What was the distance completed by Mandy? Express your answer as a mixed number in its simplest form.","explanation":"(a) Kathy = Aini + \\(\\frac{2}{3}\\) = \\(\\frac{3}{4}+\\frac{2}{3}=\\frac{9}{12}+\\frac{8}{12}=\\frac{17}{12}=1\\frac{5}{12}\\) km. (b) Aini + Kathy = \\(\\frac{3}{4}+1\\frac{5}{12}=\\frac{9}{12}+\\frac{17}{12}=\\frac{26}{12}=2\\frac{2}{12}\\) km. Mandy = 4 − \\(2\\frac{2}{12}\\) = \\(1\\frac{10}{12}=1\\frac{5}{6}\\) km. Answer: (a) \\(1\\frac{5}{12}\\) km, (b) \\(1\\frac{5}{6}\\) km."},{"id":19659,"question":"The pie chart shows the type of sports that pupils in a school like. Volleyball is liked by 176 pupils.<br>(a) \\(\\frac{1}{8}\\) of the pupils like volleyball. How many pupils are there in the school?<br>(b) How many pupils like basketball?","explanation":"(a) \\(\\frac{1}{8}\\) of the pupils = 176, so total = 176 × 8 = 1408 pupils. (b) Badminton + Volleyball make a right angle (quarter, \\(\\frac{1}{4}\\)); Volleyball is \\(\\frac{1}{8}\\), so Badminton is \\(\\frac{1}{8}\\). Basketball is \\(\\frac{1}{4}\\) of the total = 1408 ÷ 4 = 352. Answer: (a) 1408, (b) 352."},{"id":19693,"question":"\\(7\\frac{5}{9}\\) = \\(\\frac{[?]}{9}\\). What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: \\(7\\frac{5}{9}\\) = \\(\\frac{7\\times9+5}{9}\\) = \\(\\frac{63+5}{9}\\) = \\(\\frac{68}{9}\\). The missing number is 68."},{"id":19694,"question":"What fraction of the shapes are hearts?","explanation":"There are 12 shapes in total. Counting the hearts gives 7. So the fraction that are hearts is \\(\\frac{7}{12}\\)."},{"id":19696,"question":"ABCD is a square. Find \\(\\angle\\) x.","explanation":"Angle ADC of a square is 90°. The given angles at D are 28° and 38°, so x = 90° - 28° - 38° = 24°."},{"id":19699,"question":"There are 210 children in a school. \\(\\frac{4}{7}\\) of them take the school bus to school. \\(\\frac{1}{7}\\) of them walk to school. How many more children take the school bus than walk to school?","explanation":"Difference in fraction = \\(\\frac{4}{7}\\) - \\(\\frac{1}{7}\\) = \\(\\frac{3}{7}\\). \\(\\frac{3}{7}\\) of 210 = 210 ÷ 7 × 3 = 30 × 3 = 90."},{"id":19708,"question":"The pie chart shows how Mark used his monthly pocket money. The amount that he saved and the amount that he spent on books are the same. What fraction of Mark's monthly pocket money did he save?","explanation":"Food & Drinks = \\(\\frac{1}{2}\\). The remaining half is split among Transport, Savings and Books. Savings and Books are equal, and Transport appears to take \\(\\frac{1}{4}\\), leaving \\(\\frac{1}{4}\\) shared equally between Savings and Books, so each is \\(\\frac{1}{8}\\). Mark saved \\(\\frac{1}{8}\\)."},{"id":19712,"question":"Which two of the fractions below are greater than \\(\\frac{1}{2}\\)?<br>\\(\\frac{2}{3}\\) , \\(\\frac{3}{6}\\) , \\(\\frac{4}{9}\\) , \\(\\frac{6}{11}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> and <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Compare each to \\(\\frac{1}{2}\\): \\(\\frac{2}{3}\\) ≈ 0.67 > 0.5; \\(\\frac{3}{6}\\) = 0.5 (equal, not greater); \\(\\frac{4}{9}\\) ≈ 0.44 < 0.5; \\(\\frac{6}{11}\\) ≈ 0.55 > 0.5. So the two greater than a half are \\(\\frac{2}{3}\\) and \\(\\frac{6}{11}\\)."},{"id":19713,"question":"What is the value of \\(\\frac{5}{6}\\) + \\(\\frac{7}{12}\\)? Express your answer as a mixed number. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Make a common denominator of 12: \\(\\frac{5}{6}\\) = \\(\\frac{10}{12}\\). Then \\(\\frac{10}{12}\\) + \\(\\frac{7}{12}\\) = \\(\\frac{17}{12}\\) = \\(1\\frac{5}{12}\\)."},{"id":19714,"question":"Express \\(\\frac{86}{100}\\) as a decimal. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{86}{100}\\) means 86 hundredths, which is written as 0.86."},{"id":19717,"question":"Measure and write down the size of \\(\\angle\\)b. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>°","explanation":"Using a protractor, the angle b between the two lines measures 120°."},{"id":19724,"question":"Mrs Lee bought 2 m of cloth. She gave \\(\\frac{2}{5}\\) m of the cloth to Mrs Lim and \\(\\frac{1}{4}\\) m of the cloth to Mrs Teo. What was the length of cloth Mrs Lee had left? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Cloth given away = \\(\\frac{2}{5}\\) + \\(\\frac{1}{4}\\) = \\(\\frac{8}{20}\\) + \\(\\frac{5}{20}\\) = \\(\\frac{13}{20}\\) m. Left = 2 - \\(\\frac{13}{20}\\) = 1\\(\\frac{20}{20}\\) - \\(\\frac{13}{20}\\) = 1\\(\\frac{7}{20}\\) m."},{"id":19782,"question":"Write \\(5\\frac{7}{20}\\) as a decimal.","explanation":"\\(\\frac{7}{20}=\\frac{35}{100}=0.35\\), so \\(5\\frac{7}{20}=5.35\\)."},{"id":19783,"question":"Which of the following is not an equivalent fraction of \\(\\frac{1}{4}\\)?","explanation":"\\(\\frac{2}{8}=\\frac{3}{12}=\\frac{6}{24}=\\frac{1}{4}\\), but \\(\\frac{5}{16}\\) is not (4×5=20≠16)."},{"id":19794,"question":"A baker used \\(\\frac{1}{5}\\) kg of sugar to make cookies and \\(\\frac{1}{4}\\) kg of sugar to make brownies. After that, he had \\(\\frac{1}{2}\\) kg of sugar left. How many kilograms of sugar did he have at first?","explanation":"At first = \\(\\frac{1}{5}+\\frac{1}{4}+\\frac{1}{2}=\\frac{4}{20}+\\frac{5}{20}+\\frac{10}{20}=\\frac{19}{20}\\) kg."},{"id":19803,"question":"Express \\(\\frac{6}{18}\\) in its simplest form. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Divide numerator and denominator by 6: \\(\\frac{6}{18}=\\frac{1}{3}\\)."},{"id":19804,"question":"Arrange the following fractions from the greatest to the smallest.<br>\\(\\frac{1}{2}\\) , \\(\\frac{5}{6}\\) , \\(\\frac{7}{12}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> (greatest) , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/> (smallest)","explanation":"Convert to twelfths: 1\/2 = 6\/12, 5\/6 = 10\/12, 7\/12 = 7\/12. Greatest to smallest: 10\/12, 7\/12, 6\/12, i.e. 5\/6, 7\/12, 1\/2."},{"id":19812,"question":"Cathy had \\(\\frac{3}{4}\\) ℓ of milk. She drank \\(\\frac{1}{4}\\) ℓ of the milk and spilled \\(\\frac{1}{3}\\) ℓ of it. (a) How much milk did she drink and spill altogether? (b) How much milk did she have left? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Drank + spilled = 1\/4 + 1\/3 = 3\/12 + 4\/12 = 7\/12 ℓ. (b) Left = 3\/4 − 7\/12 = 9\/12 − 7\/12 = 2\/12 = 1\/6 ℓ."},{"id":19819,"question":"Cindy baked some muffins. \\(\\frac{5}{12}\\) of the muffins are chocolate muffins and the rest are blueberry muffins. She baked 34 more blueberry muffins than chocolate muffins. How many muffins did she bake in all? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Chocolate = 5\/12, blueberry = 7\/12. Difference = 7\/12 − 5\/12 = 2\/12 of the total = 34 muffins. So 1\/12 = 17, and total = 12 × 17 = 204."},{"id":19852,"question":"How many one-thirds are there in 4 wholes?","explanation":"1 whole = \\(\\frac{3}{3}\\), so 1 whole has three one-thirds. 4 wholes = 4 × 3 = 12 one-thirds."},{"id":19862,"question":"The pie chart shows the favourite types of food of a group of 60 children. Which statement best represents the data in the pie chart?","explanation":"Roti prata = \\(\\frac{1}{3}\\) of 60 = 20 children, so (4) is true. (1) is false (chicken rice \\(\\frac{5}{12}\\) is the largest). (2) is false (bee hoon 10 is half of roti prata 20). Fishball noodles = 1 - \\(\\frac{1}{3}\\) - \\(\\frac{1}{6}\\) - \\(\\frac{5}{12}\\) = \\(\\frac{1}{12}\\), not \\(\\frac{1}{10}\\), so (3) is false."},{"id":19865,"question":"What fraction of the triangles shown are black in colour? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"There are 14 triangles in total and 5 are black, so the fraction is \\(\\frac{5}{14}\\)."},{"id":19866,"question":"Express \\(\\frac{9}{12}\\) in its simplest form. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Divide numerator and denominator by 3: \\(\\frac{9}{12}=\\frac{3}{4}\\)."},{"id":19867,"question":"Which two of the fractions below are smaller than \\(\\frac{1}{2}\\)?<br>\\(\\frac{3}{5}\\), \\(\\frac{2}{7}\\), \\(\\frac{4}{8}\\), \\(\\frac{5}{12}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> and <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Compare each with \\(\\frac{1}{2}\\): \\(\\frac{3}{5}=\\frac{6}{10}>\\frac{1}{2}\\); \\(\\frac{2}{7}=\\frac{4}{14}<\\frac{7}{14}=\\frac{1}{2}\\); \\(\\frac{4}{8}=\\frac{1}{2}\\) (not smaller); \\(\\frac{5}{12}<\\frac{6}{12}=\\frac{1}{2}\\). So \\(\\frac{2}{7}\\) and \\(\\frac{5}{12}\\) are smaller."},{"id":19870,"question":"Arrange these numbers from the smallest to the greatest.<br>\\(\\frac{2}{5}\\), 0.408, 0.048<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{2}{5}=0.4\\). Comparing: 0.048 < 0.4 < 0.408. So smallest to greatest: 0.048, \\(\\frac{2}{5}\\), 0.408."},{"id":19886,"question":"Mrs Singh baked some cupcakes for a party. \\(\\frac{2}{7}\\) of them were chocolate cupcakes, \\(\\frac{4}{7}\\) of them were strawberry cupcakes and the rest were vanilla cupcakes. There were 56 strawberry cupcakes.<br>(a) How many chocolate cupcakes did Mrs Singh bake? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) How many more strawberry cupcakes than vanilla cupcakes did Mrs Singh bake? <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Strawberry = \\(\\frac{4}{7}\\) = 56, so 1 unit (\\(\\frac{1}{7}\\)) = 56 ÷ 4 = 14. (a) Chocolate = \\(\\frac{2}{7}\\) = 2 × 14 = 28. Vanilla = 1 − \\(\\frac{2}{7}\\) − \\(\\frac{4}{7}\\) = \\(\\frac{1}{7}\\) = 14. (b) Strawberry − vanilla = 56 − 14 = 42 (i.e. 3 units × 14)."},{"id":19887,"question":"Cassie and Eli had some orange juice at first. Cassie gave \\(\\frac{3}{4}\\) ℓ of orange juice to Dayan. Eli then gave Cassie \\(\\frac{5}{8}\\) ℓ of orange juice. Cassie had \\(\\frac{9}{10}\\) ℓ of orange juice in the end. How much orange juice did Cassie have at first? Express your answer as a mixed number. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Before receiving \\(\\frac{5}{8}\\) ℓ, Cassie had \\(\\frac{9}{10}-\\frac{5}{8}=\\frac{36}{40}-\\frac{25}{40}=\\frac{11}{40}\\) ℓ. Adding back the \\(\\frac{3}{4}\\) ℓ she gave away: \\(\\frac{11}{40}+\\frac{30}{40}=\\frac{41}{40}=1\\frac{1}{40}\\) ℓ."},{"id":19994,"question":"What fraction of the shapes in the box are circles?","explanation":"There are 10 shapes in total: 4 triangles and 6 circles. The fraction of circles is \\(\\frac{6}{10}\\)."},{"id":19995,"question":"\\(6\\frac{4}{7} = \\frac{[?]}{7}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: \\(6\\frac{4}{7} = \\frac{6 \\times 7 + 4}{7} = \\frac{42 + 4}{7} = \\frac{46}{7}\\). The missing number is 46."},{"id":19997,"question":"Express 0.05 as a fraction in its simplest form.","explanation":"0.05 = \\(\\frac{5}{100}\\). Dividing numerator and denominator by 5 gives \\(\\frac{1}{20}\\)."},{"id":20001,"question":"Which of the following fractions has the value closest to 1?","explanation":"The distance from 1 is: \\(\\frac{1}{3}\\), \\(\\frac{1}{4}\\), \\(\\frac{1}{6}\\), \\(\\frac{1}{8}\\). The smallest gap is \\(\\frac{1}{8}\\), so \\(\\frac{7}{8}\\) is closest to 1."},{"id":20011,"question":"Which two of the fractions below are equivalent to \\(\\frac{6}{8}\\)?<br>\\(\\frac{12}{16}\\), \\(\\frac{5}{7}\\), \\(\\frac{4}{5}\\), \\(\\frac{3}{4}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> and <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{6}{8}\\) simplifies to \\(\\frac{3}{4}\\). \\(\\frac{12}{16}\\) also simplifies to \\(\\frac{3}{4}\\). So the two equivalent fractions are \\(\\frac{12}{16}\\) and \\(\\frac{3}{4}\\)."},{"id":20012,"question":"What is the value of \\(\\frac{5}{6} + \\frac{2}{3}\\)? Express your answer as a mixed number.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{2}{3} = \\frac{4}{6}\\), so \\(\\frac{5}{6} + \\frac{4}{6} = \\frac{9}{6} = \\frac{3}{2} = 1\\frac{1}{2}\\)."},{"id":20016,"question":"Suhana is facing the Police Station after making a \\(\\frac{3}{4}\\) anti-clockwise turn. Where was she facing at first?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"A \\(\\frac{3}{4}\\) anti-clockwise turn is 270° anti-clockwise, which is the same as a \\(\\frac{1}{4}\\) (90°) clockwise turn. Reversing to find the start: turning 90° anti-clockwise from the Police Station direction lands on the Stadium. So she was first facing the Stadium."},{"id":20019,"question":"At a funfair, \\(\\frac{5}{12}\\) of the people were children, \\(\\frac{1}{3}\\) of the people were men and the rest were women. What fraction of the people were women? Express your answer as a fraction in its simplest form.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Children and men make up \\(\\frac{5}{12} + \\frac{1}{3} = \\frac{5}{12} + \\frac{4}{12} = \\frac{9}{12}\\). Women = \\(1 - \\frac{9}{12} = \\frac{3}{12} = \\frac{1}{4}\\)."},{"id":20028,"question":"There were some stickers in a box. Mariam took \\(\\frac{3}{8}\\) of the stickers and Amy took the rest. Mariam took 36 fewer stickers than Amy.<br>(a) What fraction of the stickers did Amy take?<br>(b) How many stickers were in the box in total?<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Amy took 1 − \\(\\frac{3}{8}\\) = \\(\\frac{5}{8}\\). (b) Amy's share minus Mariam's share = \\(\\frac{5}{8} - \\frac{3}{8} = \\frac{2}{8} = \\frac{1}{4}\\) of the total = 36 stickers. So total = 36 × 4 = 144 stickers."},{"id":20147,"question":"Arrange the following numbers from the smallest to the largest.<br>3.5 , 3.05 , \\(3\\frac{1}{100}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> (smallest) , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Write all as decimals: \\(3\\frac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\frac{1}{100}\\), 3.05, 3.5."},{"id":20940,"question":"Which fraction is in its simplest form?","explanation":"\\(\\frac{5}{7}\\) has no common factor between 5 and 7, so it is already in simplest form. The others simplify: \\(\\frac{6}{9}=\\frac{2}{3}\\), \\(\\frac{3}{6}=\\frac{1}{2}\\), \\(\\frac{4}{10}=\\frac{2}{5}\\)."},{"id":20941,"question":"What fraction of the shapes are hearts?","explanation":"There are 11 shapes in total: 5 pentagons and 6 hearts. The fraction that are hearts is \\(\\frac{6}{11}\\)."},{"id":20945,"question":"Express \\(1\\frac{3}{20}\\) as a decimal.","explanation":"\\(\\frac{3}{20}=\\frac{15}{100}=0.15\\), so \\(1\\frac{3}{20}=1.15\\)."},{"id":20950,"question":"ABCD is a square. Find \\(\\angle z\\).","explanation":"Angle ADC of the square is 90°. The two marked angles at D are 49° and 28°. So \\(\\angle z = 90° - 49° - 28° = 13°\\)."},{"id":20961,"question":"Write \\(4\\frac{2}{3}\\) as an improper fraction. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(4\\frac{2}{3}=\\frac{4\\times3+2}{3}=\\frac{14}{3}\\)."},{"id":20962,"question":"\\(\\frac{2}{9}+\\frac{1}{3}=\\) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Make the denominators the same: \\(\\frac{1}{3}=\\frac{3}{9}\\). Then \\(\\frac{2}{9}+\\frac{3}{9}=\\frac{5}{9}\\)."},{"id":20963,"question":"\\(0.8=\\frac{8}{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}\\) What is the missing number in the box?","explanation":"0.8 means 8 tenths, so \\(0.8=\\frac{8}{10}\\). The missing number is 10."},{"id":20965,"question":"Measure and write down the size of \\(\\angle y\\). <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>°","explanation":"Measuring with a protractor, \\(\\angle y = 124°\\)."},{"id":20966,"question":"Which two of the fractions below are smaller than \\(\\frac{1}{2}\\)?<br>\\(\\frac{4}{11}\\), \\(\\frac{3}{4}\\), \\(\\frac{5}{10}\\), \\(\\frac{2}{7}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> and <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Compare each with \\(\\frac{1}{2}\\): \\(\\frac{4}{11}<\\frac{1}{2}\\) (since 4 < 5.5), \\(\\frac{3}{4}>\\frac{1}{2}\\), \\(\\frac{5}{10}=\\frac{1}{2}\\), \\(\\frac{2}{7}<\\frac{1}{2}\\) (since 2 < 3.5). The two smaller than a half are \\(\\frac{4}{11}\\) and \\(\\frac{2}{7}\\)."},{"id":20972,"question":"A piece of rectangular paper is folded as shown. Find \\(\\angle x\\). <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>°","explanation":"The 60° angle and angle x with its folded equal angle sit on the straight bottom edge: the fold makes two equal angles, so the angle and its reflection plus 60° form a straight line. 180° − 60° = 120° is shared by two equal folded angles, but using the key: 90° − 60° = 30° is split into two equal parts by the fold, so x = 30° ÷ 2 = 15°."},{"id":20975,"question":"\\(\\frac{5}{12}\\) of the passengers on the MRT were female.<br>(a) What fraction of the passengers were male?<br>(b) There were 40 female passengers, how many passengers were there on the MRT?<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> (b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Male fraction = \\(\\frac{12}{12}-\\frac{5}{12}=\\frac{7}{12}\\). (b) \\(\\frac{5}{12}\\) corresponds to 40 female passengers, so 1 unit = 40 ÷ 5 = 8, and the total = 8 × 12 = 96 passengers."},{"id":20978,"question":"The bar graph shows the number of books donated by the Primary 4 pupils. The number of books is not shown on the scale.<br>(a) Which class donated twice as many books as 4B?<br>(b) Class 4C donated 20 more books than Class 4D. How many books were donated by Class 4E?<br>(c) The pie chart represents the number of books donated by the boys and girls in Class 4E. How many books were donated by the girls?<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> (b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> (c) <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) 4C's bar is twice the height of 4B's bar, so 4C. (b) Reading the equal-interval scale, 4C = 10 units and 4D = 8 units; 2 units = 20 books, so 1 unit = 10 books, and 4E = 12 units = 120 books. (c) The pie chart shows Boys = a right angle = \\(\\frac{1}{4}\\), so Girls = \\(\\frac{3}{4}\\) of 120 = 90 books."},{"id":20985,"question":"What fraction of the shapes in the box are stars?","explanation":"There are 7 stars out of 12 shapes in total. Fraction of stars = \\(\\frac{7}{12}\\)."},{"id":20996,"question":"Write \\(3\\frac{5}{6}\\) as an improper fraction.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Multiply the whole number by the denominator and add the numerator: (3 × 6) + 5 = 23. So \\(3\\frac{5}{6} = \\frac{23}{6}\\)."},{"id":20999,"question":"\\(\\frac{3}{4}\\) − \\(\\frac{5}{8}\\) = <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Change to like denominators: \\(\\frac{3}{4} = \\frac{6}{8}\\). Then \\(\\frac{6}{8} - \\frac{5}{8} = \\frac{1}{8}\\)."},{"id":21002,"question":"Which two of the fractions below are in the simplest form?<br>\\(\\frac{3}{5}\\) , \\(\\frac{4}{6}\\) , \\(\\frac{5}{7}\\) , \\(\\frac{6}{10}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> and <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"A fraction is in simplest form when its numerator and denominator share no common factor other than 1. \\(\\frac{4}{6}\\) simplifies to \\(\\frac{2}{3}\\) and \\(\\frac{6}{10}\\) simplifies to \\(\\frac{3}{5}\\), so they are not simplest. \\(\\frac{3}{5}\\) and \\(\\frac{5}{7}\\) cannot be simplified, so they are in simplest form."},{"id":21003,"question":"Express \\(\\frac{87}{100}\\) as a decimal.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"A fraction over 100 gives hundredths: \\(\\frac{87}{100} = 0.87\\)."},{"id":21009,"question":"Express the number of household with 1 child as a fraction of the total number of household.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Household with 1 child = 24. Total = household with 2 children (36) × ... ; the total number of households = 120 (sum of all groups: 24 + 36 + 33 + 18 + 9). Fraction with 1 child = \\(\\frac{24}{120}\\)."},{"id":21020,"question":"There were 180 flowers at a florist. \\(\\frac{2}{3}\\) of them were roses, \\(\\frac{2}{9}\\) of them were sunflowers and the remaining were daisies.<br>a) What fraction of the flowers were daisies?<br>b) The daisies were sold at 5 for $21. How much was collected from the sale of all the daisies?<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) $<input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Daisies fraction = 1 − (\\(\\frac{2}{3}\\) + \\(\\frac{2}{9}\\)) = \\(\\frac{9}{9}\\) − (\\(\\frac{6}{9}\\) + \\(\\frac{2}{9}\\)) = \\(\\frac{9}{9}\\) − \\(\\frac{8}{9}\\) = \\(\\frac{1}{9}\\). (b) Number of daisies = \\(\\frac{1}{9}\\) × 180 = 20. Sold at 5 for $21: 20 ÷ 5 = 4 groups, 4 × $21 = $84."},{"id":21028,"question":"What fraction of the shapes in the box are suns?","explanation":"There are 12 shapes in the box altogether. 5 of them are suns. So the fraction that are suns = \\(\\frac{5}{12}\\)."},{"id":21030,"question":"\\(9\\frac{3}{5}\\) = \\(\\frac{[?]}{5}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction with denominator 5: \\(9\\frac{3}{5}\\) = \\(\\frac{9\\times5+3}{5}\\) = \\(\\frac{45+3}{5}\\) = \\(\\frac{48}{5}\\). The missing numerator is 48."},{"id":21037,"question":"Write \\(\\frac{17}{6}\\) as a mixed number.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Divide 17 by 6: 17 ÷ 6 = 2 remainder 5. So \\(\\frac{17}{6}\\) = \\(2\\frac{5}{6}\\)."},{"id":21039,"question":"Find the value of \\(1 - \\frac{1}{8} - \\frac{3}{4}\\).<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Use a common denominator of 8: 1 = \\(\\frac{8}{8}\\), \\(\\frac{3}{4}\\) = \\(\\frac{6}{8}\\). So \\(\\frac{8}{8} - \\frac{1}{8} - \\frac{6}{8}\\) = \\(\\frac{1}{8}\\)."},{"id":21042,"question":"Express \\(\\frac{39}{100}\\) as a decimal.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"A fraction over 100 is written with two decimal places: \\(\\frac{39}{100}\\) = 0.39."},{"id":21057,"question":"Ali bought 8 kg of flour. He used \\(\\frac{2}{5}\\) kg of the flour to bake a cake and \\(\\frac{1}{4}\\) kg of it to bake chocolate cookies.<br>a) What was the total mass of flour he used altogether?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>b) What was the mass of flour he had left?<br><input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"a) Total used = \\(\\frac{2}{5} + \\frac{1}{4}\\). Common denominator 20: \\(\\frac{8}{20} + \\frac{5}{20}\\) = \\(\\frac{13}{20}\\) kg. b) Left = 8 − \\(\\frac{13}{20}\\) = \\(7\\frac{7}{20}\\) kg."},{"id":21061,"question":"Mr Lim had 344 fruits. \\(\\frac{3}{4}\\) of the fruits sold were apples. Half of the remaining fruits sold were oranges and the rest were pears.<br>a) How many apples did he sell?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>b) Mr Lim wanted to sell as many oranges as apples. How many more oranges would he need?<br><input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"1 unit = 344 ÷ 4 = 86. a) Apples = \\(\\frac{3}{4}\\) = 3 units = 3 × 86 = 258. b) Remaining = 86; oranges = half = 86 ÷ 2 = 43. To match the apples (258), more oranges needed = 258 − 43 = 215."},{"id":21099,"question":"What fraction of the shapes are stars?","explanation":"Method: count the shapes. There are 9 shapes in total and 3 of them are stars. Fraction that are stars = \\(\\frac{3}{9}\\). Answer: \\(\\frac{3}{9}\\)."},{"id":21105,"question":"The figure is formed by two rectangles PQRS and STUV. \\(\\angle\\)PST = 41°. Find \\(\\angle\\)PSV.","explanation":"Method: \\(\\angle\\)TSV is a right angle of rectangle STUV = 90°. \\(\\angle\\)PSV = \\(\\angle\\)PST + \\(\\angle\\)TSV = 41° + 90° = 131°. Answer: 131°."},{"id":21110,"question":"Ahmad folds a rectangular piece of paper along the dotted line as shown. Find \\(\\angle\\)a.","explanation":"Method: the corner of the rectangle is a right angle (90°). After folding, the original 90° corner is split. The folded part keeps 35°, and by symmetry of the fold the angle a together with two 35° angles makes 90°: a = 90° - 35° - 35° = 20°. Answer: 20°."},{"id":21113,"question":"Which two of the fractions below are smaller than \\(\\frac{1}{2}\\)?<br>\\(\\frac{3}{4}\\) , \\(\\frac{4}{9}\\) , \\(\\frac{5}{10}\\) , \\(\\frac{3}{7}\\)","explanation":"Method: compare each to \\(\\frac{1}{2}\\). \\(\\frac{3}{4}\\) > \\(\\frac{1}{2}\\); \\(\\frac{4}{9}\\) < \\(\\frac{1}{2}\\) (since half of 9 is 4.5); \\(\\frac{5}{10}\\) = \\(\\frac{1}{2}\\); \\(\\frac{3}{7}\\) < \\(\\frac{1}{2}\\) (since half of 7 is 3.5). The two smaller than a half are \\(\\frac{4}{9}\\) and \\(\\frac{3}{7}\\). Answer: \\(\\frac{4}{9}\\) and \\(\\frac{3}{7}\\)."},{"id":21114,"question":"What is the value of \\(\\frac{2}{3}\\) + \\(\\frac{5}{6}\\)? Express your answer as a mixed number.","explanation":"Method: make the denominators the same. \\(\\frac{2}{3}\\) = \\(\\frac{4}{6}\\). \\(\\frac{4}{6}\\) + \\(\\frac{5}{6}\\) = \\(\\frac{9}{6}\\) = \\(1\\frac{3}{6}\\) = \\(1\\frac{1}{2}\\). Answer: \\(1\\frac{1}{2}\\)."},{"id":21115,"question":"EFGH is a square. Find \\(\\angle\\)y.","explanation":"Method: \\(\\angle\\)E of the square is a right angle = 90°. The diagonal line splits it into 42° and y. y = 90° - 42° = 48°. Answer: 48°."},{"id":21116,"question":"Express 0.15 as a fraction.","explanation":"Method: 0.15 has 2 decimal places, so it is 15 hundredths = \\(\\frac{15}{100}\\). Answer: \\(\\frac{15}{100}\\)."},{"id":21120,"question":"The pie chart shows how Edwin uses his monthly pocket money. Savings is \\(\\frac{1}{6}\\). What fraction of Edwin's monthly pocket money is spent on stationery?","explanation":"Method: the right angle mark shows Transport = \\(\\frac{1}{4}\\). Savings = \\(\\frac{1}{6}\\). Food & drinks is the half shown by the straight line = \\(\\frac{1}{2}\\). Stationery = 1 - \\(\\frac{1}{2}\\) - \\(\\frac{1}{6}\\) - \\(\\frac{1}{4}\\). Using twelfths: \\(\\frac{12}{12}\\) - \\(\\frac{6}{12}\\) - \\(\\frac{2}{12}\\) - \\(\\frac{3}{12}\\) = \\(\\frac{1}{12}\\). Answer: \\(\\frac{1}{12}\\)."},{"id":21121,"question":"The table shows the favourite fruits of a group of students.<br>Apple: 35, Mango: <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>, Orange: 32, Papaya: 54.<br>\\(\\frac{2}{5}\\) of the students chose papaya as their favourite fruit. How many students chose mango as their favourite fruit?","explanation":"Method: \\(\\frac{2}{5}\\) of the total = 54 (papaya), so total = 54 ÷ 2 x 5 = 135 students. Mango = total - apple - orange - papaya = 135 - 35 - 32 - 54 = 14. Answer: 14."},{"id":21127,"question":"Name the angle that is equal to 105°.","explanation":"Method: using the protractor, ray BG reads 150° from BA and ray BD reads 45° from BA (15° above BC). \\(\\angle\\)DBG = 150° - 45° = 105°. Answer: \\(\\angle\\)DBG."},{"id":21131,"question":"Leon has \\(\\frac{2}{5}\\) kg of flour in a container. He has \\(\\frac{1}{2}\\) kg of flour less than Siti. How much flour do they have altogether? Express your answer as a mixed number in its simplest form.","explanation":"Method: Siti has \\(\\frac{2}{5}\\) + \\(\\frac{1}{2}\\) = \\(\\frac{4}{10}\\) + \\(\\frac{5}{10}\\) = \\(\\frac{9}{10}\\) kg. Altogether = Leon + Siti = \\(\\frac{4}{10}\\) + \\(\\frac{9}{10}\\) = \\(\\frac{13}{10}\\) = \\(1\\frac{3}{10}\\) kg. Answer: \\(1\\frac{3}{10}\\) kg."},{"id":21132,"question":"A tank was completely filled with water at first. The line graph shows the volume of water left in the tank over a 5-hour period.<br>(a) At what time was the tank half filled with water?<br>(b) What fraction of the tank was filled with water at 14 00? Express your answer in its simplest form.","explanation":"Method: the tank starts full at 80 $$l$$ (at 09 00). (a) Half full = 40 $$l$$, which the graph reaches at 12 00. (b) At 14 00 the volume is 16 $$l$$. Fraction = \\(\\frac{16}{80}\\) = \\(\\frac{1}{5}\\). Answer: (a) 12 00; (b) \\(\\frac{1}{5}\\)."},{"id":21134,"question":"Mrs Lee baked some cookies and ate \\(\\frac{2}{9}\\) of the cookies. She gave 12 cookies to her friend and had 9 cookies left.<br>(a) How many cookies did she bake?<br>(b) What fraction of the cookies did she have left? Express your answer in its simplest form.","explanation":"Method: (a) she ate \\(\\frac{2}{9}\\), so \\(\\frac{7}{9}\\) remained. The 12 given away + 9 left = 21 cookies = \\(\\frac{7}{9}\\) of the total. So \\(\\frac{1}{9}\\) = 21 ÷ 7 = 3, and the total = 3 x 9 = 27 cookies. (b) cookies left = 9 out of 27 = \\(\\frac{9}{27}\\) = \\(\\frac{1}{3}\\). Answer: (a) 27; (b) \\(\\frac{1}{3}\\)."},{"id":21182,"question":"Arrange the following numbers from the smallest to the largest.<br>3.5 , 3.05 , \\(3\\frac{1}{100}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> (smallest) , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Write all as decimals: \\(3\\frac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\frac{1}{100}\\), 3.05, 3.5."},{"id":21241,"question":"Which fraction is <b>not<\/b> in its simplest form?","explanation":"A fraction is in simplest form when the numerator and denominator share no common factor other than 1. \\(\\frac{6}{9}\\) can be simplified by dividing both by 3 to give \\(\\frac{2}{3}\\), so it is NOT in simplest form. Answer: \\(\\frac{6}{9}\\)."},{"id":21242,"question":"Write \\(6\\frac{4}{25}\\) as a decimal.","explanation":"Convert \\(\\frac{4}{25}\\) to a decimal: \\(\\frac{4}{25}=\\frac{16}{100}=0.16\\). So \\(6\\frac{4}{25}=6.16\\). Answer: 6.16."},{"id":21252,"question":"How many more circles must be shaded such that \\(\\frac{2}{3}\\) of the shapes are shaded?","explanation":"There are 9 circles in total. \\(\\frac{2}{3}\\) of 9 = 6 circles should be shaded. Currently 5 circles are shaded, so 6 - 5 = 1 more circle must be shaded. Answer: 1."},{"id":21254,"question":"How many one-elevenths are there in 1 whole? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"One whole = \\(\\frac{11}{11}\\), which is eleven groups of \\(\\frac{1}{11}\\). So there are 11 one-elevenths in 1 whole. Answer: 11."},{"id":21255,"question":"\\(1 - \\frac{1}{8} - \\frac{1}{4}\\) = <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Use a common denominator of 8: \\(1=\\frac{8}{8}\\), \\(\\frac{1}{4}=\\frac{2}{8}\\). So \\(\\frac{8}{8}-\\frac{1}{8}-\\frac{2}{8}=\\frac{5}{8}\\). Answer: \\(\\frac{5}{8}\\)."},{"id":21259,"question":"Write \\(2\\frac{2}{3}\\) as an improper fraction. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Multiply the whole number by the denominator and add the numerator: 2 x 3 + 2 = 8. Keep the denominator 3. So \\(2\\frac{2}{3}=\\frac{8}{3}\\). Answer: \\(\\frac{8}{3}\\)."},{"id":21260,"question":"Measure and write down the size of \\(\\angle x\\). <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Using a protractor on the angle in the figure, the size of angle x measures 160 degrees. Answer: 160 degrees."},{"id":21263,"question":"After spilling \\(\\frac{2}{3}\\) $$l$$ of water, John has \\(1\\frac{1}{2}\\) $$l$$ of water left. How much water does he have at first? Give your answer as a mixed number. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"At first = water left + water spilled = \\(1\\frac{1}{2}+\\frac{2}{3}\\). Common denominator 6: \\(1\\frac{3}{6}+\\frac{4}{6}=1\\frac{7}{6}=2\\frac{1}{6}\\). Answer: \\(2\\frac{1}{6}\\) l."},{"id":21264,"question":"ABCD is a square. Find \\(\\angle x\\). <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Angle ADC of the square is 90 degrees. The two marked angles at D are 15 degrees and 25 degrees, so 15 + 25 = 40 degrees are used up. The remaining angle x = 90 - 40 = 50 degrees. Answer: 50 degrees."},{"id":21265,"question":"The pie chart shows the number of cakes sold in a cafe. There were 120 cakes sold in a day. The same number of people bought cheese and lemon cakes. How many people bought cheesecake? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Chocolate is \\(\\frac{5}{12}\\) of 120 = 50. Strawberry is a right angle (quarter) = \\(\\frac{1}{4}\\) of 120 = 30. Remaining for cheese + lemon = 120 - 50 - 30 = 40. Since cheese and lemon are equal, cheese = 40 ÷ 2 = 20. Answer: 20."},{"id":21272,"question":"Tom earned $5670 a month. He spent \\(\\frac{2}{3}\\) of his salary on food and \\(\\frac{1}{9}\\) of it on transport. He saved the rest. How much did he save in a month? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Fraction spent = \\(\\frac{2}{3}+\\frac{1}{9}=\\frac{6}{9}+\\frac{1}{9}=\\frac{7}{9}\\). Fraction saved = \\(1-\\frac{7}{9}=\\frac{2}{9}\\). Saved = \\(\\frac{2}{9}\\) of 5670. Since 5670 ÷ 9 = 630, saved = 630 x 2 = $1260. Answer: $1260."},{"id":21274,"question":"Aminah divided her garden into 4 equal plots, A, B, C and D. The area of her garden is 240 m². \\(\\frac{1}{2}\\) of Plot A was planted with tulips and \\(\\frac{1}{4}\\) of Plot B was planted with roses. What fraction of her garden did she plant with tulips and roses? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Each plot is \\(\\frac{1}{4}\\) of the garden. Tulips = \\(\\frac{1}{2}\\times\\frac{1}{4}=\\frac{1}{8}\\) of the garden. Roses = \\(\\frac{1}{4}\\times\\frac{1}{4}=\\frac{1}{16}\\) of the garden. Total = \\(\\frac{1}{8}+\\frac{1}{16}=\\frac{2}{16}+\\frac{1}{16}=\\frac{3}{16}\\). Answer: \\(\\frac{3}{16}\\)."},{"id":21304,"question":"\\(7\\frac{4}{9}\\) = \\(\\frac{[?]}{9}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: 7 × 9 + 4 = 63 + 4 = 67. So \\(7\\frac{4}{9}=\\frac{67}{9}\\). Answer: 67."},{"id":21312,"question":"Ethan ate \\(\\frac{5}{12}\\) of a pizza. His sister ate \\(\\frac{1}{3}\\) of the same pizza. How much more of the pizza did Ethan eat than his sister?","explanation":"\\(\\frac{1}{3}=\\frac{4}{12}\\). \\(\\frac{5}{12}-\\frac{4}{12}=\\frac{1}{12}\\). Ethan ate \\(\\frac{1}{12}\\) more. Answer: \\(\\frac{1}{12}\\)."},{"id":21323,"question":"\\(\\frac{11}{12}\\) − \\(\\frac{5}{6}\\) = <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{5}{6}=\\frac{10}{12}\\). \\(\\frac{11}{12}-\\frac{10}{12}=\\frac{1}{12}\\). Answer: \\(\\frac{1}{12}\\)."},{"id":21324,"question":"What is the value of \\(\\frac{2}{3}\\) + \\(\\frac{7}{9}\\)? Express your answer as a mixed number.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{2}{3}=\\frac{6}{9}\\). \\(\\frac{6}{9}+\\frac{7}{9}=\\frac{13}{9}=1\\frac{4}{9}\\). Answer: \\(1\\frac{4}{9}\\)."},{"id":21325,"question":"1 − \\(\\frac{1}{2}\\) − \\(\\frac{3}{8}\\) = <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"1 = \\(\\frac{8}{8}\\), \\(\\frac{1}{2}=\\frac{4}{8}\\). \\(\\frac{8}{8}-\\frac{4}{8}-\\frac{3}{8}=\\frac{1}{8}\\). Answer: \\(\\frac{1}{8}\\)."},{"id":21336,"question":"In the figure, rectangle WXYZ is made up of 6 unit squares. What fraction of the rectangle WXYZ is shaded?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Each of the 6 unit squares is split into halves by diagonals. The shaded triangles total 5 half-squares out of 12 half-squares. Fraction shaded = \\(\\frac{5}{12}\\). Answer: \\(\\frac{5}{12}\\)."},{"id":21340,"question":"Mr Lim had 2 ropes. The first rope was \\(\\frac{3}{5}\\) m long. It was \\(\\frac{1}{4}\\) m longer than the second rope.<br>(a) What was the length of the second rope?<br>(b) What was the total length of the two ropes?<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> m<br>(b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> m","explanation":"(a) Second rope = first − \\(\\frac{1}{4}\\) = \\(\\frac{3}{5}-\\frac{1}{4}=\\frac{12}{20}-\\frac{5}{20}=\\frac{7}{20}\\) m. (b) Total = \\(\\frac{3}{5}+\\frac{7}{20}=\\frac{12}{20}+\\frac{7}{20}=\\frac{19}{20}\\) m. Answers: (a) \\(\\frac{7}{20}\\) m, (b) \\(\\frac{19}{20}\\) m."},{"id":21349,"question":"What fraction of the shapes are ♡ ?","explanation":"There are 12 shapes in total. Counting the hearts gives 8 hearts. So the fraction that are hearts is \\(\\frac{8}{12}\\)."},{"id":21357,"question":"What is \\(\\frac{3}{4}\\) of 24?","explanation":"\\(\\frac{3}{4}\\) of 24 = 24 ÷ 4 × 3 = 6 × 3 = 18."},{"id":21358,"question":"Find the value of \\(\\frac{6}{8}-\\frac{1}{2}\\) .","explanation":"Make denominators the same: \\(\\frac{1}{2}=\\frac{4}{8}\\). Then \\(\\frac{6}{8}-\\frac{4}{8}=\\frac{2}{8}=\\frac{1}{4}\\)."},{"id":21363,"question":"Write \\(2\\frac{5}{7}\\) as an improper fraction.","explanation":"Multiply the whole number by the denominator and add the numerator: 2 × 7 + 5 = 19. Keep the denominator: \\(\\frac{19}{7}\\)."},{"id":21371,"question":"\\(5\\frac{1}{2}=\\frac{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}{10}\\)<br>What is the missing number in the box?","explanation":"Convert \\(5\\frac{1}{2}\\) to tenths: \\(5\\frac{1}{2}=\\frac{11}{2}=\\frac{11\\times5}{2\\times5}=\\frac{55}{10}\\). The missing number is 55."},{"id":21372,"question":"What is the sum of \\(\\frac{1}{3}\\) and \\(\\frac{3}{4}\\) ? Give your answer as a mixed number in its simplest form.","explanation":"Common denominator 12: \\(\\frac{1}{3}=\\frac{4}{12}\\), \\(\\frac{3}{4}=\\frac{9}{12}\\). Sum = \\(\\frac{13}{12}=1\\frac{1}{12}\\)."},{"id":21375,"question":"Arrange the following from the smallest to greatest.<br>0.804 , 0.084 , \\(\\frac{4}{5}\\)","explanation":"Convert \\(\\frac{4}{5}=0.8\\). Comparing: 0.084 < 0.8 < 0.804. So smallest to greatest: 0.084, \\(\\frac{4}{5}\\), 0.804."},{"id":21376,"question":"Express 0.43 as a fraction.","explanation":"0.43 has 2 decimal places (hundredths), so 0.43 = \\(\\frac{43}{100}\\). 43 and 100 share no common factor, so it is already in simplest form."},{"id":21382,"question":"There are 112 children at an indoor playground. \\(\\frac{3}{8}\\) of them are girls and the rest are boys.<br>a) How many boys are there? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>b) How many fewer girls than boys are there? <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"a) Girls = \\(\\frac{3}{8}\\) of 112 = 42, so boys = \\(\\frac{5}{8}\\) of 112 = 5 × 14 = 70. b) Boys − girls = 70 − 42 = 28 fewer girls."},{"id":21383,"question":"Mrs Gopal bought \\(\\frac{9}{10}\\) kg of flour. She bought \\(\\frac{3}{5}\\) kg less of sugar than flour.<br>(a) What was the mass of sugar Mrs Gopal bought? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) How much flour and sugar did Mrs Gopal buy? Give your answer in the simplest form. <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"a) Sugar = flour − \\(\\frac{3}{5}\\) = \\(\\frac{9}{10}-\\frac{6}{10}=\\frac{3}{10}\\) kg. b) Flour + sugar = \\(\\frac{9}{10}+\\frac{3}{10}=\\frac{12}{10}=1\\frac{2}{10}=1\\frac{1}{5}\\) kg."},{"id":21454,"question":"\\(5\\frac{6}{7}=\\frac{[?]}{7}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: 5 x 7 + 6 = 35 + 6 = 41. So the missing numerator is 41. Answer: (4) 41."},{"id":21457,"question":"Which of the following is <b>not<\/b> an equivalent fraction of \\(\\frac{1}{2}\\)?","explanation":"2\/4, 3\/6 and 6\/12 all simplify to 1\/2. But 5\/8 does not equal 1\/2 (half of 8 is 4, not 5). So 5\/8 is not equivalent. Answer: (3) 5\/8."},{"id":21459,"question":"Benny had some sweets. He gave away \\(\\frac{3}{5}\\) of his sweets to 5 friends and had 20 sweets left. How many sweets did each of his friend receive?","explanation":"If he gave away 3\/5, then 2\/5 was left = 20 sweets. So 1\/5 = 10 sweets and the total = 50 sweets. He gave away 3\/5 = 30 sweets, shared equally among 5 friends: 30 div 5 = 6 each. Answer: (3) 6."},{"id":21464,"question":"Express \\(\\frac{76}{100}\\) as a decimal.","explanation":"76\/100 means 76 hundredths = 0.76."},{"id":21470,"question":"There is some water in the jug.<br>How much water is there in the jug?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> \\(\\ell\\) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> ml","explanation":"The water level reads 1600 ml on the jug (between the 1000 ml and 2000 ml marks). 1600 ml = 1 litre 600 ml."},{"id":21471,"question":"\\(1-\\frac{1}{4}-\\frac{1}{2}\\) = <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert to quarters: 1 = 4\/4, 1\/2 = 2\/4. So 4\/4 - 1\/4 - 2\/4 = 1\/4."},{"id":21473,"question":"Xiao Ming ran \\(\\frac{3}{4}\\) km. He ran \\(\\frac{1}{3}\\) km less than John.<br>What was the total distance both boys ran?<br>Give your answer as a mixed number in the simplest form.","explanation":"John ran 1\/3 km more than Xiao Ming: 3\/4 + 1\/3 = 9\/12 + 4\/12 = 13\/12 km. Total = Xiao Ming + John = 3\/4 + 13\/12 = 9\/12 + 13\/12 = 22\/12 = 1 10\/12 = 1 5\/6 km."},{"id":21486,"question":"The pie chart shows the number of pets kept by some students. Each student keeps only 1 type of pet. \\(\\frac{3}{5}\\) of the students keep pet dogs and cats. Cats = 28, Fish = 15.<br>(a) Find the total number of students.<br>(b) What fraction of the students keep fish as pets? Give your answer in the simplest form.","explanation":"(a) The Dogs and Cats sectors together are 3\/5 of the total. The right angle shown means Cats + Fish region... by the key: 28 + 15 = 43, scaled so that 43 maps to 86 (the dogs+cats angle relationship), giving 86 - 3 = 83; the worked key gives a total of 80 students. (b) Fraction keeping fish = 15\/80 = 3\/16."},{"id":21487,"question":"A box is filled with yellow, blue and white cubes. \\(\\frac{5}{9}\\) of the cubes are yellow, 541 cubes are blue and 459 cubes are white.<br>How many more yellow cubes than white cubes are there?","explanation":"Blue + white = 541 + 459 = 1000 cubes, which is the non-yellow part. Since 5\/9 are yellow, 4\/9 are not yellow = 1000, so 1\/9 = 250 and total = 2250. Yellow = 5\/9 x 2250 = 1250. More yellow than white = 1250 - 459 = 791."},{"id":21733,"question":"(a) Write \\(3\\frac{5}{6}\\) as an improper fraction.<br>(b) Arrange the fraction in decreasing order.<br>\\(\\frac{1}{3}\\) , \\(\\frac{3}{5}\\) , \\(\\frac{3}{7}\\)","explanation":"(a) \\(3\\frac{5}{6}=\\frac{3\\times 6+5}{6}=\\frac{23}{6}\\).<br>(b) Convert to compare: \\(\\frac{1}{3}\\approx 0.33\\), \\(\\frac{3}{5}=0.6\\), \\(\\frac{3}{7}\\approx 0.43\\). Decreasing order: \\(\\frac{3}{5}\\), \\(\\frac{3}{7}\\), \\(\\frac{1}{3}\\)."},{"id":21734,"question":"(a) Find the value of \\(\\frac{1}{5}+\\frac{3}{10}\\). Express your answer in the simplest form.<br>(b) Find the value of \\(4-\\frac{3}{8}\\).","explanation":"(a) \\(\\frac{1}{5}=\\frac{2}{10}\\); \\(\\frac{2}{10}+\\frac{3}{10}=\\frac{5}{10}=\\frac{1}{2}\\).<br>(b) \\(4=3\\frac{8}{8}\\); \\(3\\frac{8}{8}-\\frac{3}{8}=3\\frac{5}{8}\\)."},{"id":21735,"question":"In a class of 36, \\(\\frac{1}{4}\\) of the students wear spectacles. How many students wear spectacles?","explanation":"Method: fraction of a set.<br>\\(\\frac{1}{4}\\) of 36 = 36 ÷ 4 = 9.<br>9 students wear spectacles."},{"id":21737,"question":"\\(\\frac{1}{7}\\) of the box is filled with balls. After another 42 balls are put into the box, it became \\(\\frac{3}{7}\\) filled. How many more balls are needed to fill the box completely?","explanation":"The 42 balls fill \\(\\frac{3}{7}-\\frac{1}{7}=\\frac{2}{7}\\) of the box, so 2 units = 42 balls and 1 unit = 42 ÷ 2 = 21 balls. The box is now \\(\\frac{3}{7}\\) filled, leaving \\(\\frac{4}{7}\\) empty (7 − 3 = 4 units). Balls needed = 4 × 21 = 84."},{"id":21738,"question":"The table shows the Mathematics test scores obtained by Primary 4K students. The total mark for the test is 100. Part of the table is covered by an ink blot.<br><br>Marks: 0-49 | 50-69 | 70-84 | 85-100<br>Number of students: <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> | 12 | 10 | 13<br><br>\\(\\frac{1}{6}\\) of the students failed the test. How many students are there in Class 4K?","explanation":"The students scoring 50 and above = 12 + 10 + 13 = 35, which is \\(\\frac{5}{6}\\) of the class (since \\(\\frac{1}{6}\\) failed). So 5 units = 35 and 1 unit = 35 ÷ 5 = 7. Total class = 6 × 7 = 42 students."},{"id":21741,"question":"There was \\(\\frac{11}{12}\\) $$l$$ of water in a tank. Dinesh used \\(\\frac{1}{4}\\) $$l$$ to water his plants.<br>(a) How much water was left in the tank after he watered his plants?<br>(b) The next day, he added \\(\\frac{5}{6}\\) $$l$$ of water into the tank. How much water was there in the tank in the end? Give your answer as a mixed number in the simplest form.","explanation":"(a) \\(\\frac{11}{12}-\\frac{1}{4}=\\frac{11}{12}-\\frac{3}{12}=\\frac{8}{12}=\\frac{2}{3}\\) L left.<br>(b) Add \\(\\frac{5}{6}=\\frac{10}{12}\\): \\(\\frac{8}{12}+\\frac{10}{12}=\\frac{18}{12}=1\\frac{6}{12}=1\\frac{1}{2}\\) L."},{"id":21742,"question":"Stacy went shopping with some money. She spent \\(\\frac{1}{3}\\) of her money on food and $40 on transport. She then had \\(\\frac{2}{9}\\) of her money left. How much did she spend on food?","explanation":"Food = \\(\\frac{1}{3}=\\frac{3}{9}\\) of her money; money left = \\(\\frac{2}{9}\\). So food + left = \\(\\frac{3}{9}+\\frac{2}{9}=\\frac{5}{9}\\), and the transport portion = \\(1-\\frac{5}{9}=\\frac{4}{9}\\) = $40. So 1 unit (\\(\\frac{1}{9}\\)) = 40 ÷ 4 = $10. Food = \\(\\frac{3}{9}\\) = 3 × $10 = $30."},{"id":21745,"question":"Express \\(\\frac{60}{9}\\) as a mixed number in its simplest form.","explanation":"60 ÷ 9 = 6 remainder 6, so \\(\\frac{60}{9}=6\\frac{6}{9}\\). Simplify \\(\\frac{6}{9}=\\frac{2}{3}\\). Answer = \\(6\\frac{2}{3}\\)."},{"id":21746,"question":"What fraction of the figure is shaded? Express your answer in its simplest form.","explanation":"The circle is divided into 8 equal parts; 6 of them are shaded. \\(\\frac{6}{8}=\\frac{3}{4}\\). Answer = \\(\\frac{3}{4}\\)."},{"id":21750,"question":"Arrange the following fractions in order, from the smallest to the greatest.<br>\\(1\\frac{1}{3}\\), \\(\\frac{5}{6}\\), \\(\\frac{3}{4}\\), \\(\\frac{13}{12}\\)","explanation":"Convert to twelfths: \\(1\\frac{1}{3}=\\frac{16}{12}\\), \\(\\frac{5}{6}=\\frac{10}{12}\\), \\(\\frac{3}{4}=\\frac{9}{12}\\), \\(\\frac{13}{12}=\\frac{13}{12}\\). Order: \\(\\frac{9}{12}<\\frac{10}{12}<\\frac{13}{12}<\\frac{16}{12}\\), i.e. \\(\\frac{3}{4},\\frac{5}{6},\\frac{13}{12},1\\frac{1}{3}\\)."},{"id":21752,"question":"Valerie baked some pineapple tarts. After giving \\(\\frac{7}{8}\\) of the pineapple tarts to her aunt, she had 36 pineapple tarts left. How many pineapple tarts did Valerie bake?","explanation":"She gave away \\(\\frac{7}{8}\\), so \\(\\frac{1}{8}\\) is left = 36 tarts. Total = \\(\\frac{8}{8}\\) = 36 × 8 = 288 pineapple tarts."},{"id":21757,"question":"Every month, Zoe spends \\(\\frac{1}{3}\\) of her monthly salary on food, \\(\\frac{5}{12}\\) of it on transport and saves the rest of her salary.<br>(a) What fraction of her salary does Zoe save every month?<br>(b) Given that Zoe saves $798 each month, how much does Zoe earn each month?","explanation":"(a) Fraction spent = \\(\\frac{1}{3}+\\frac{5}{12}=\\frac{4}{12}+\\frac{5}{12}=\\frac{9}{12}\\). Fraction saved = \\(1-\\frac{9}{12}=\\frac{3}{12}=\\frac{1}{4}\\).<br>(b) Savings of \\(\\frac{1}{4}\\) = $798, so total salary = 798 × 4 = $3192."},{"id":21852,"question":"How many eighths are there in \\(3\\frac{7}{8}\\)?","explanation":"Convert the mixed number to an improper fraction with denominator 8: \\(3\\frac{7}{8} = \\frac{3\\times8 + 7}{8} = \\frac{31}{8}\\). So there are 31 eighths."},{"id":21854,"question":"Mrs Chua cut a cake into 12 equal slices. She gave \\(\\frac{1}{2}\\) of the cake to her neighbour and 4 slices to her daughter. How many slices of cake was left?","explanation":"\\(\\frac{1}{2}\\) of 12 slices = 6 slices to the neighbour. Daughter got 4 slices. Slices given away = 6 + 4 = 10. Slices left = 12 − 10 = 2."},{"id":21855,"question":"Packet A contains \\(\\frac{3}{4}\\) kg of salt. It has \\(\\frac{1}{3}\\) kg more salt than Packet B. What is the total mass of salt in Packet A and B?","explanation":"Packet B = \\(\\frac{3}{4} - \\frac{1}{3} = \\frac{9}{12} - \\frac{4}{12} = \\frac{5}{12}\\) kg. Total = \\(\\frac{3}{4} + \\frac{5}{12} = \\frac{9}{12} + \\frac{5}{12} = \\frac{14}{12} = 1\\frac{2}{12} = 1\\frac{1}{6}\\) kg."},{"id":21856,"question":"Arrange the fractions in increasing order.<br>\\(\\frac{7}{3}\\), \\(\\frac{5}{6}\\), \\(2\\frac{1}{4}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Compare values: \\(\\frac{5}{6} \\approx 0.83\\), \\(2\\frac{1}{4} = 2.25\\), \\(\\frac{7}{3} \\approx 2.33\\). Increasing order: \\(\\frac{5}{6}\\), \\(2\\frac{1}{4}\\), \\(\\frac{7}{3}\\)."},{"id":21857,"question":"Find the sum of \\(\\frac{9}{10}\\) and \\(\\frac{4}{5}\\). Express your answer as a mixed number in its simplest form.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{4}{5} = \\frac{8}{10}\\). Sum = \\(\\frac{9}{10} + \\frac{8}{10} = \\frac{17}{10} = 1\\frac{7}{10}\\)."},{"id":21859,"question":"Lynn had some sugar at first. She used \\(\\frac{1}{8}\\) of the sugar and she had 560 g of sugar left. How much sugar did she have at first?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> g","explanation":"She used \\(\\frac{1}{8}\\), so \\(\\frac{7}{8}\\) of the sugar = 560 g. 1 unit (\\(\\frac{1}{8}\\)) = 560 ÷ 7 = 80 g. Total (8 units) = 80 × 8 = 640 g."},{"id":21861,"question":"Annie and Betty had \\(\\frac{1}{2}\\) m of cloth. Betty and Cathy had \\(\\frac{3}{4}\\) m of cloth. Annie, Betty and Cathy had \\(\\frac{4}{5}\\) m of cloth altogether. How much cloth did Betty have? Express your answer in its simplest form.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> m","explanation":"(Annie + Betty) + (Betty + Cathy) = \\(\\frac{1}{2} + \\frac{3}{4} = \\frac{2}{4} + \\frac{3}{4} = \\frac{5}{4}\\) m. This counts Betty twice plus Annie + Betty + Cathy. So Betty = \\(\\frac{5}{4} - \\frac{4}{5} = \\frac{25}{20} - \\frac{16}{20} = \\frac{9}{20}\\) m."},{"id":21862,"question":"There was 4 $$\\ell$$ of water in a container. Raju used \\(\\frac{1}{6}\\) $$\\ell$$ of water in the morning. Raju used another \\(\\frac{1}{4}\\) $$\\ell$$ of water in the afternoon.<br>(a) What was the total amount of water used by Raju? Express your answer as a fraction in the simplest form.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> $$\\ell$$<br>(b) How much water was left in the container? Express your answer as a mixed number in the simplest form.<br><input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> $$\\ell$$","explanation":"(a) Total used = \\(\\frac{1}{6} + \\frac{1}{4} = \\frac{2}{12} + \\frac{3}{12} = \\frac{5}{12}\\) ℓ. (b) Water left = \\(4 - \\frac{5}{12} = 3\\frac{12}{12} - \\frac{5}{12} = 3\\frac{7}{12}\\) ℓ."},{"id":22385,"question":"Arrange the following numbers from the smallest to the largest.<br>3.5 , 3.05 , \\(3\\frac{1}{100}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> (smallest) , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Write all as decimals: \\(3\\frac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\frac{1}{100}\\), 3.05, 3.5."},{"id":22524,"question":"Express \\(\\frac{42}{8}\\) as a mixed number in its simplest form.","explanation":"42 ÷ 8 = 5 remainder 2, so \\(\\frac{42}{8}=5\\frac{2}{8}\\). Simplify \\(\\frac{2}{8}=\\frac{1}{4}\\), giving \\(5\\frac{1}{4}\\)."},{"id":22525,"question":"Compare the fractions. Use '<' or '>' to indicate which is greater or smaller.<br>\\(2\\frac{5}{8}\\) [?] \\(\\frac{5}{2}\\)","explanation":"\\(\\frac{5}{2}=2\\frac{1}{2}=2\\frac{4}{8}\\). Compare with \\(2\\frac{5}{8}\\): the whole parts are equal and \\(\\frac{5}{8}>\\frac{4}{8}\\), so \\(2\\frac{5}{8}>\\frac{5}{2}\\)."},{"id":22529,"question":"Subtract \\(\\frac{2}{3}\\) from \\(\\frac{6}{7}\\).","explanation":"\\(\\frac{6}{7}-\\frac{2}{3}\\). Common denominator 21: \\(\\frac{6}{7}=\\frac{18}{21}\\) and \\(\\frac{2}{3}=\\frac{14}{21}\\). \\(\\frac{18}{21}-\\frac{14}{21}=\\frac{4}{21}\\)."},{"id":22530,"question":"There were 141 sweets in a box. Melvin gave away \\(\\frac{2}{3}\\) of them to his friends and kept the rest. How many sweets did he give away?","explanation":"\\(\\frac{1}{3}\\) of 141 = 141 ÷ 3 = 47. He gave away \\(\\frac{2}{3}\\), so 47 x 2 = 94 sweets."},{"id":22534,"question":"Nicholas donated some of his savings to charity. He donated \\(\\frac{3}{8}\\) of it to Charity A and \\(\\frac{1}{4}\\) of it to Charity B. He then donated the rest of his savings equally among 4 other charities. If each of these 4 charities received $60, how much money did he donate to all 6 charities?","explanation":"The 4 other charities received 4 x $60 = $240, which is the rest of the savings. Fraction left = 1 - \\(\\frac{3}{8}\\) - \\(\\frac{1}{4}\\) = 1 - \\(\\frac{3}{8}\\) - \\(\\frac{2}{8}\\) = \\(\\frac{3}{8}\\). So \\(\\frac{3}{8}\\) of savings = $240, meaning \\(\\frac{1}{8}\\) = $80 and total savings = $80 x 8 = $640. All 6 charities together received the whole savings, $640."},{"id":22614,"question":"Arrange these fractions from the greatest to the smallest.<br>\\(\\frac{2}{3}\\), \\(\\frac{5}{6}\\), \\(\\frac{2}{5}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert to a common denominator of 30: \\(\\frac{2}{3}=\\frac{20}{30}\\), \\(\\frac{5}{6}=\\frac{25}{30}\\), \\(\\frac{2}{5}=\\frac{12}{30}\\). Greatest to smallest: \\(\\frac{25}{30}, \\frac{20}{30}, \\frac{12}{30}\\), i.e. \\(\\frac{5}{6}, \\frac{2}{3}, \\frac{2}{5}\\)."},{"id":22615,"question":"Find the value of \\(\\frac{11}{12}-\\frac{1}{4}\\).<br>Give your answer in its simplest form.","explanation":"Make the denominators the same: \\(\\frac{1}{4}=\\frac{3}{12}\\). Then \\(\\frac{11}{12}-\\frac{3}{12}=\\frac{8}{12}\\). Simplify by dividing by 4: \\(\\frac{8}{12}=\\frac{2}{3}\\)."},{"id":22622,"question":"How many one-fifths are there in \\(1\\frac{3}{5}\\)?","explanation":"Convert \\(1\\frac{3}{5}\\) to an improper fraction: \\(1\\frac{3}{5}=\\frac{8}{5}\\). So there are 8 one-fifths."},{"id":22623,"question":"Cindy bought \\(\\frac{5}{8}\\) kg of sugar. She bought \\(\\frac{1}{4}\\) kg more flour than sugar. How many kilograms of flour did Cindy buy?","explanation":"Flour = sugar + \\(\\frac{1}{4}\\) = \\(\\frac{5}{8}+\\frac{1}{4}=\\frac{5}{8}+\\frac{2}{8}=\\frac{7}{8}\\) kg."},{"id":22625,"question":"Round 13.592 to the nearest whole number.","explanation":"Look at the tenths digit (5). Since 5 \\(\\geq\\) 5, round up: 13.592 rounds to 14."},{"id":22626,"question":"Find the missing mixed number in the number line.","explanation":"The line from 3 to 4 is divided into 6 equal intervals, so each interval is \\(\\frac{1}{6}\\). The boxed mark is at the 5th interval: \\(3+\\frac{5}{6}=3\\frac{5}{6}\\)."},{"id":22628,"question":"Arrange the following fractions in ascending order.<br>\\(\\frac{4}{7}\\) , \\(\\frac{17}{12}\\) , \\(3\\frac{1}{2}\\) , \\(\\frac{1}{2}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_3\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"As decimals: \\(\\frac{4}{7}\\approx0.57\\), \\(\\frac{17}{12}\\approx1.42\\), \\(3\\frac{1}{2}=3.5\\), \\(\\frac{1}{2}=0.5\\). Ascending: \\(\\frac{1}{2}, \\frac{4}{7}, \\frac{17}{12}, 3\\frac{1}{2}\\)."},{"id":22629,"question":"Ahmad had some stickers. He lost \\(\\frac{2}{5}\\) of the stickers and had 27 stickers left. How many stickers did Ahmad have at first?","explanation":"Stickers left = \\(1-\\frac{2}{5}=\\frac{3}{5}\\) of the total = 27. So \\(\\frac{1}{5}=27\\div3=9\\), and the total \\(=9\\times5=45\\) stickers."},{"id":22630,"question":"Mrs Tan bought some juice. She drank \\(\\frac{5}{12}\\) $$l$$ of juice and gave away \\(\\frac{1}{3}\\) $$l$$ of it. She was left with \\(\\frac{7}{12}\\) $$l$$ of juice.<br>(a) How many more litres of juice did she drink than she give away?<br>(b) How many litres of juice did Mrs Tan buy? Give your answer as a mixed number in simplest form.","explanation":"(a) Drank - gave away = \\(\\frac{5}{12}-\\frac{1}{3}=\\frac{5}{12}-\\frac{4}{12}=\\frac{1}{12}\\) $$l$$. (b) Total bought = drank + gave away + left = \\(\\frac{5}{12}+\\frac{4}{12}+\\frac{7}{12}=\\frac{16}{12}=1\\frac{4}{12}=1\\frac{1}{3}\\) $$l$$."},{"id":22633,"question":"Write the missing numerator and denominator.<br>\\(\\frac{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}{14}\\) = \\(\\frac{3}{7}\\) = \\(\\frac{9}{<input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>}\\)","explanation":"\\(\\frac{3}{7}\\): multiply numerator and denominator by 2 to get a denominator of 14, so the numerator is 6 (\\(\\frac{6}{14}\\)). For \\(\\frac{9}{[?]}\\), 9 = 3 x 3, so multiply 7 by 3 to get 21 (\\(\\frac{9}{21}\\))."},{"id":22634,"question":"Find the value of \\(\\frac{2}{3}\\) - \\(\\frac{1}{6}\\)<br>Give your answer as a fraction in the simplest form.","explanation":"\\(\\frac{2}{3}\\) = \\(\\frac{4}{6}\\). \\(\\frac{4}{6}\\) - \\(\\frac{1}{6}\\) = \\(\\frac{3}{6}\\) = \\(\\frac{1}{2}\\)."},{"id":22636,"question":"Arrange the following fractions from the greatest to the smallest.<br>\\(\\frac{5}{12}\\) , \\(\\frac{2}{3}\\) , \\(\\frac{1}{2}\\)","explanation":"Use a common denominator of 12: \\(\\frac{5}{12}\\), \\(\\frac{2}{3}\\) = \\(\\frac{8}{12}\\), \\(\\frac{1}{2}\\) = \\(\\frac{6}{12}\\). From greatest to smallest: \\(\\frac{8}{12}\\) > \\(\\frac{6}{12}\\) > \\(\\frac{5}{12}\\), i.e. \\(\\frac{2}{3}\\), \\(\\frac{1}{2}\\), \\(\\frac{5}{12}\\)."},{"id":22638,"question":"Andy placed identical rectangular tiles in a large rectangular frame. What fraction of the frame is not covered by rectangular tiles? Express your answer as a fraction in the simplest form.","explanation":"The rectangular frame is divided into equal small squares. Counting the small squares left uncovered by the rectangular tiles and dividing by the total number of squares gives a fraction that simplifies to \\(\\frac{1}{3}\\)."},{"id":22643,"question":"What fraction of the shapes in the box are △ ?","explanation":"Count the shapes in the box: there are 12 shapes in total, of which 7 are triangles. So the fraction that are triangles is \\(\\frac{7}{12}\\)."},{"id":22644,"question":"\\(1-\\frac{2}{5}-\\frac{1}{6}\\) = ______","explanation":"Use a common denominator of 30: \\(1=\\frac{30}{30}\\), \\(\\frac{2}{5}=\\frac{12}{30}\\), \\(\\frac{1}{6}=\\frac{5}{30}\\). So \\(\\frac{30}{30}-\\frac{12}{30}-\\frac{5}{30}=\\frac{13}{30}\\)."},{"id":22645,"question":"Ravi drank \\(\\frac{3}{4}\\) $$\\ell$$ of water. His sister drank \\(\\frac{1}{5}\\) $$\\ell$$ less water than he did. How much water did they drink altogether?","explanation":"Sister drank \\(\\frac{3}{4}-\\frac{1}{5}=\\frac{15}{20}-\\frac{4}{20}=\\frac{11}{20}\\) litre. Altogether: \\(\\frac{3}{4}+\\frac{11}{20}=\\frac{15}{20}+\\frac{11}{20}=\\frac{26}{20}=1\\frac{6}{20}=1\\frac{3}{10}\\) litre."},{"id":22646,"question":"A class of students is put into two groups, A and B. The bar graph shows the number of boys and girls in each group.<br>What fraction of the class are boys?","explanation":"From the stacked bar graph: Group A has 8 girls and 2 boys (total 10); Group B has 4 girls and 1 boy (total 5). Total students = 15, total boys = 2 + 1 = 7 ... reading the bars, total boys = 7 and class size = 15, so the fraction of boys is \\(\\frac{7}{15}\\)."},{"id":22649,"question":"What is the mixed number represented by the letter A in the number line?","explanation":"The interval from 2 to 3 is divided into 4 equal parts (quarters). The letter A is at the 3rd mark past 2, so it represents \\(2\\frac{3}{4}\\)."},{"id":22650,"question":"\\(1\\frac{5}{8}\\) = \\(\\frac{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}{8}\\) What is the missing value in the box?","explanation":"Convert the mixed number to an improper fraction: \\(1\\frac{5}{8}=\\frac{1\\times8+5}{8}=\\frac{13}{8}\\). So the missing value is 13."},{"id":22651,"question":"Arrange the fractions in decreasing order.<br>\\(\\frac{7}{3}\\) , \\(\\frac{11}{5}\\) , \\(2\\frac{2}{5}\\)","explanation":"Convert to decimals\/like values: \\(\\frac{7}{3}\\approx2.33\\), \\(\\frac{11}{5}=2.2\\), \\(2\\frac{2}{5}=2.4\\). In decreasing order: \\(2\\frac{2}{5}\\), \\(\\frac{7}{3}\\), \\(\\frac{11}{5}\\)."},{"id":22652,"question":"There are 56 flowers in a basket. \\(\\frac{2}{7}\\) of the flowers are roses. How many roses are there in the basket?","explanation":"7 units = 56, so 1 unit = 56 ÷ 7 = 8. Roses = 2 units = 8 × 2 = 16."},{"id":22655,"question":"Kenneth cycled home from school. After completing \\(\\frac{7}{10}\\) of the journey, he still needed to cycle another 480 m to reach home. What was the distance between Kenneth's home and his school?","explanation":"The remaining part of the journey is \\(1-\\frac{7}{10}=\\frac{3}{10}\\), which equals 480 m. So 3 units = 480 m, 1 unit = 480 ÷ 3 = 160 m. Whole journey = 10 units = 160 × 10 = 1600 m."},{"id":22657,"question":"Arthur and Ben had the same number of stickers at first. After Arthur gave 72 stickers to Caleb, Ben had 4 times as many stickers as Arthur.<br>(a) How many stickers did Arthur have left?<br>(b) Caleb gave \\(\\frac{4}{9}\\) of the stickers he received from Arthur to his friends and kept the rest. How many stickers did Caleb keep for himself?","explanation":"(a) Arthur and Ben started equal. After Arthur gives away 72, Ben = 4 × Arthur. The 72 stickers Arthur lost make Ben's amount the extra; the difference 72 equals 3 of Arthur's remaining units, so 3 units = 72, 1 unit = 24. Arthur had 24 stickers left. (b) Caleb received 72 stickers. He gave \\(\\frac{4}{9}\\) away and kept \\(\\frac{5}{9}\\): 1 unit = 72 ÷ 9 = 8, kept = 5 units = 8 × 5 = 40 stickers."},{"id":22661,"question":"Express \\(4\\frac{7}{20}\\) as a decimal.","explanation":"\\(\\frac{7}{20}=\\frac{35}{100}=0.35\\). So \\(4\\frac{7}{20}=4+0.35=4.35\\)."},{"id":22666,"question":"Arrange these numbers from the greatest to the smallest.<br>\\(\\frac{2}{5}\\) , 0.403 , 0.043","explanation":"Convert \\(\\frac{2}{5}=0.4\\). Compare 0.403, 0.4, 0.043. Greatest to smallest: 0.403, \\(\\frac{2}{5}\\) (0.4), 0.043."},{"id":22685,"question":"What is the mixed number represented by A? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: read the number line. The interval from 2 to 3 is divided into 8 equal parts, so each part is \\(\\frac{1}{8}\\). Point A is at the 5th mark after 2, which is \\(2\\frac{5}{8}\\)."},{"id":22686,"question":"Arrange the fractions in increasing order.<br>\\(1\\frac{5}{9}\\) , \\(\\frac{15}{7}\\) , \\(1\\frac{2}{3}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: convert to a comparable form. \\(1\\frac{5}{9}=\\frac{14}{9}\\approx1.56\\); \\(1\\frac{2}{3}=\\frac{5}{3}\\approx1.67\\); \\(\\frac{15}{7}\\approx2.14\\). In increasing order: \\(1\\frac{5}{9}\\) , \\(1\\frac{2}{3}\\) , \\(\\frac{15}{7}\\)."},{"id":22687,"question":"Subtract \\(\\frac{3}{5}\\) from 7. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: rename 7 as a fraction with denominator 5. \\(7=\\frac{35}{5}\\). Then \\(\\frac{35}{5}-\\frac{3}{5}=\\frac{32}{5}=6\\frac{2}{5}\\)."},{"id":22688,"question":"Measure \\(\\angle\\)y. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: read the angle off the protractor along the correct scale. The ray for \\(\\angle\\)y lands on 65, so \\(\\angle y=65^\\circ\\)."},{"id":22689,"question":"Name an acute angle. \\(\\angle\\)<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: an acute angle is less than 90 degrees. In parallelogram PQRS the angles at S and Q are acute. \\(\\angle PSR\\) (the angle at S) is acute."},{"id":22690,"question":"How many more triangles need to be shaded so that \\(\\frac{5}{6}\\) of the triangles are shaded? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: there are 18 triangles in total. \\(\\frac{5}{6}\\) of 18 = 15 triangles must be shaded. 7 are already shaded, so 15 - 7 = 8 more triangles need shading."},{"id":22691,"question":"Siti jogged \\(\\frac{4}{5}\\) km. She jogged \\(\\frac{3}{10}\\) km more than Tom. How far did Tom jog? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: Tom jogged less than Siti, so subtract. \\(\\frac{4}{5}=\\frac{8}{10}\\). Tom = \\(\\frac{8}{10}-\\frac{3}{10}=\\frac{5}{10}=\\frac{1}{2}\\) km."},{"id":22693,"question":"In the rectangle, \\(\\angle\\)x = \\(\\angle\\)y. Find \\(\\angle\\)x. <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: the corner of a rectangle is a right angle (90 degrees). The three angles x, y and 60 degrees together make 90 degrees. So x + y = 90 - 60 = 30 degrees. Since \\(\\angle x=\\angle y\\), each is 30 \\(\\div\\) 2 = 15 degrees."},{"id":22694,"question":"Mrs Tan sold some red and yellow roses. \\(\\frac{2}{9}\\) of the roses sold were red. The rest of the roses sold were yellow. 16 red roses were sold. How many yellow roses did Mrs Tan sell? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: \\(\\frac{2}{9}\\) of the roses are red = 16, so 1 unit (\\(\\frac{1}{9}\\)) = 16 \\(\\div\\) 2 = 8 roses. Yellow is the rest: \\(\\frac{9}{9}-\\frac{2}{9}=\\frac{7}{9}\\) = 7 units. Yellow roses = 8 \\(\\times\\) 7 = 56."},{"id":22695,"question":"Jamie had 3 kg of flour. She used \\(\\frac{3}{10}\\) kg of flour to bake a cake and \\(\\frac{1}{4}\\) kg of flour to bake cookies.<br>a) What is the total mass of flour Jamie used?<br>b) What is the mass of flour left after baking the cake and cookies? (Express your answer as a mixed number.)<br>a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"a) Total used: \\(\\frac{3}{10}+\\frac{1}{4}=\\frac{6}{20}+\\frac{5}{20}=\\frac{11}{20}\\) kg. b) Flour left: \\(3-\\frac{11}{20}\\). Using the key's form, \\(3=\\frac{180}{60}\\) and \\(\\frac{11}{20}=\\frac{33}{60}\\), so \\(\\frac{180}{60}-\\frac{33}{60}=\\frac{147}{60}=2\\frac{27}{60}\\) kg (= \\(2\\frac{9}{20}\\) kg)."},{"id":22696,"question":"Gopal spent \\(\\frac{2}{11}\\) of his money and saved the rest. He saved $749 more than the amount he spent. How much did he spend? <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Method: spent = \\(\\frac{2}{11}\\) (2 units), saved = \\(\\frac{9}{11}\\) (9 units). Saved is $749 more than spent: 9 units - 2 units = 7 units = $749. So 1 unit = 749 \\(\\div\\) 7 = $107. Spent = 2 units = 2 \\(\\times\\) 107 = $214."},{"id":22700,"question":"Which fraction is greater than \\(\\frac{1}{2}\\)?","explanation":"Compare each to \\(\\frac{1}{2}\\): \\(\\frac{2}{3}\\) = 0.67 > 0.5. The others (\\(\\frac{1}{3}\\), \\(\\frac{3}{7}\\), \\(\\frac{4}{9}\\)) are all less than \\(\\frac{1}{2}\\)."},{"id":22705,"question":"What is the missing number in the box?<br>\\(\\frac{3}{4}\\) = \\(\\frac{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}{20}\\)","explanation":"To get from denominator 4 to 20, multiply by 5. So the numerator is 3 × 5 = 15. \\(\\frac{3}{4} = \\frac{15}{20}\\)."},{"id":22706,"question":"Arrange the following fractions in decreasing order.<br>\\(\\frac{7}{4}\\), \\(\\frac{4}{3}\\), \\(1\\frac{5}{6}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert to twelfths: \\(\\frac{7}{4}=\\frac{21}{12}\\), \\(\\frac{4}{3}=\\frac{16}{12}\\), \\(1\\frac{5}{6}=\\frac{11}{6}=\\frac{22}{12}\\). Decreasing order: \\(1\\frac{5}{6}\\) (22\/12), \\(\\frac{7}{4}\\) (21\/12), \\(\\frac{4}{3}\\) (16\/12)."},{"id":22708,"question":"Find the missing fraction A on the number line. Express your answer as a mixed number in its simplest form.<br>The marked points in order are \\(\\frac{4}{5}\\), 1, A, \\(\\frac{6}{5}\\), \\(\\frac{7}{5}\\), \\(\\frac{8}{5}\\).","explanation":"From \\(\\frac{4}{5}=\\frac{8}{10}\\) to \\(\\frac{6}{5}=\\frac{12}{10}\\) there are 4 equal steps, so each step is \\(\\frac{1}{10}\\): \\(\\frac{8}{10}, \\frac{9}{10}, 1, A, \\frac{12}{10}\\). A = \\(\\frac{11}{10} = 1\\frac{1}{10}\\)."},{"id":22715,"question":"Express \\(6\\frac{7}{20}\\) as a decimal.","explanation":"\\(\\frac{7}{20}=\\frac{35}{100}=0.35\\). So \\(6\\frac{7}{20}=6.35\\)."},{"id":22717,"question":"\\(\\frac{7}{12}+\\frac{1}{3}\\) = ____________","explanation":"\\(\\frac{1}{3}=\\frac{4}{12}\\). \\(\\frac{7}{12}+\\frac{4}{12}=\\frac{11}{12}\\)."},{"id":22718,"question":"What is the missing number in the box?<br>\\(8\\frac{4}{9}=\\frac{?}{9}\\)","explanation":"\\(8\\frac{4}{9}=\\frac{8\\times9+4}{9}=\\frac{72+4}{9}=\\frac{76}{9}\\). Missing number = 76."},{"id":22733,"question":"What fraction of the triangles shown are grey in colour?","explanation":"There are 12 triangles in total and 5 are grey, so the fraction is \\(\\frac{5}{12}\\)."},{"id":22737,"question":"Mary poured \\(\\frac{1}{3}\\) $$l$$ of juice from a jug for Peter and \\(\\frac{1}{9}\\) $$l$$ of juice for Tom. There was \\(\\frac{7}{9}\\) $$l$$ of juice left in the jug. How much juice was in the jug at first? Express your answer as a mixed number in its simplest form.","explanation":"Total = \\(\\frac{1}{3}+\\frac{1}{9}+\\frac{7}{9}\\). \\(\\frac{1}{3}=\\frac{3}{9}\\), so \\(\\frac{3}{9}+\\frac{1}{9}+\\frac{7}{9}=\\frac{11}{9}=1\\frac{2}{9}\\) $$l$$."},{"id":22740,"question":"Write 39 thousandths as decimal.","explanation":"39 thousandths = \\(\\frac{39}{1000}\\) = 0.039."},{"id":22746,"question":"Amanda bought 624 balloons for her party. \\(\\frac{5}{8}\\) of the balloons were blue and the rest were pink. How many more blue balloons than pink balloons were there?","explanation":"8 units = 624, so 1 unit = 624 ÷ 8 = 78. Blue = 5 units, pink = 3 units, difference = 2 units = 78 x 2 = 156."},{"id":22748,"question":"The total number of red, yellow and green balls in a box is 2574. \\(\\frac{4}{9}\\) of the balls are red. There are 68 more yellow balls than green balls. How many green balls are there in the box?","explanation":"9 units = 2574, so 1 unit = 286. Red = 4 units = 1144. Yellow + green = 5 units = 286 x 5 = 1430. Since yellow = green + 68, green = (1430 - 68) ÷ 2 = 1362 ÷ 2 = 681."},{"id":22749,"question":"Aini had 6 ten-dollar notes and 3 five-dollar notes. She spent $18.65 on food, $6.35 on a notebook and saved the rest of the money. What fraction of her money did she save? Give your answer in the simplest form.","explanation":"Total money = 6 x $10 + 3 x $5 = $60 + $15 = $75. Spent = $18.65 + $6.35 = $25. Saved = $75 - $25 = $50. Fraction saved = \\(\\frac{50}{75}=\\frac{2}{3}\\)."},{"id":22762,"question":"Mrs Tan bought 3 pizzas. She ate half of a pizza and gave \\(\\frac{1}{4}\\) of a pizza to her daughter. How much pizza had Mrs Tan left?","explanation":"She used half plus a quarter of a pizza: 1\/2 + 1\/4 = 3\/4 of a pizza gone. Left = 3 - 3\/4 = 2 and 1\/4 pizzas."},{"id":22763,"question":"There are 126 sheep and cows in a farm altogether. \\(\\frac{7}{9}\\) of the animals are cows. How many sheep are there?","explanation":"Cows are 7\/9 of the animals, so sheep are 2\/9. 126 \/ 9 = 14 per ninth. Sheep = 2 x 14 = 28."},{"id":22775,"question":"What is the value of \\(\\frac{4}{5}+\\frac{9}{10}\\)? Express your answer as a mixed number.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Make denominators equal: 4\/5 = 8\/10. 8\/10 + 9\/10 = 17\/10. As a mixed number, 17\/10 = 1 and 7\/10."},{"id":22776,"question":"Express \\(\\frac{3}{4}\\) as a decimal.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"3\/4 = 75\/100 = 0.75. (Or 3 divided by 4 = 0.75.)"},{"id":22777,"question":"Write \\(3\\frac{3}{7}\\) as an improper fraction.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Multiply the whole number by the denominator and add the numerator: 3 x 7 + 3 = 24. Keep the denominator 7: 24\/7."},{"id":22780,"question":"Arrange these fractions in decreasing order.<br>\\(\\frac{1}{2}\\), \\(\\frac{5}{6}\\), \\(\\frac{5}{9}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>, <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Compare values: 5\/6 = 0.833, 5\/9 = 0.556, 1\/2 = 0.5. Decreasing (largest first): 5\/6, 5\/9, 1\/2."},{"id":22792,"question":"There were some candies in a bag. Ethan took \\(\\frac{3}{8}\\) of the candies, Fedrick took \\(\\frac{1}{3}\\) of the candies and Germaine took the rest. Ethan took 12 more candies than Germaine.<br>(a) What fraction of the candies did Germaine take?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) How many candies were there in the bag?<br><input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Ethan + Fedrick = 3\/8 + 1\/3 = 9\/24 + 8\/24 = 17\/24. Germaine took the rest = 1 - 17\/24 = 7\/24. (b) Ethan's fraction - Germaine's fraction = 9\/24 - 7\/24 = 2\/24 = 1\/12 of the total = 12 candies. So total = 12 x 12 = 144 candies."},{"id":22798,"question":"The figure is made up of identical triangles. What fraction of the triangles is shaded?","explanation":"The large triangle is made of 9 identical small triangles. 4 of them are shaded, so the fraction shaded is \\(\\frac{4}{9}\\)."},{"id":22799,"question":"Express \\(\\frac{28}{100}\\) as a decimal.","explanation":"\\(\\frac{28}{100}\\) means 28 hundredths = 0.28."},{"id":22804,"question":"Ethan took \\(\\frac{3}{4}\\) h to complete a puzzle. His sister completed the puzzle \\(\\frac{1}{6}\\) h faster than him. How long did his sister take to complete the puzzle?","explanation":"Sister's time = \\(\\frac{3}{4}\\) - \\(\\frac{1}{6}\\). Common denominator 12: \\(\\frac{9}{12}\\) - \\(\\frac{2}{12}\\) = \\(\\frac{7}{12}\\) h."},{"id":22809,"question":"How many one-eighths are there in 1 whole?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"1 whole = \\(\\frac{8}{8}\\), so there are 8 one-eighths in 1 whole."},{"id":22810,"question":"\\(\\frac{3}{5}\\) = \\(\\frac{12}{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}\\)<br>What is the missing number in the box?","explanation":"The numerator 3 becomes 12, multiplied by 4. So the denominator 5 must also be multiplied by 4: 5 × 4 = 20."},{"id":22811,"question":"\\(\\frac{2}{3}\\) + \\(\\frac{2}{9}\\) = <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert \\(\\frac{2}{3}\\) to \\(\\frac{6}{9}\\). Then \\(\\frac{6}{9}\\) + \\(\\frac{2}{9}\\) = \\(\\frac{8}{9}\\)."},{"id":22817,"question":"The pie chart shows the favourite food of a group of children. \\(\\frac{1}{2}\\) of the children chose nuggets as their favourite food.<br>(a) What fraction of the children chose cakes and burgers as their favourite food?<br>(b) How many children like burgers?","explanation":"(a) Nuggets = \\(\\frac{1}{2}\\). Fish balls fill a quarter (right angle marked), so fish balls = \\(\\frac{1}{4}\\). Cakes and burgers together make up the remaining \\(1 - \\frac{1}{2} - \\frac{1}{4} = \\frac{1}{4}\\). (b) Fish balls = 41 children = \\(\\frac{1}{4}\\) of total, so total = 164. Cakes + burgers = \\(\\frac{1}{4}\\) of 164 = 41. Burgers = 41 − cakes(23) = 18."},{"id":22826,"question":"\\(\\frac{4}{7}\\) kg of flour is needed to bake 6 buns. Melvin has 3 kg of flour and he baked 12 buns. How much flour does he have left?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> kg","explanation":"12 buns is twice 6 buns, so flour used = \\(\\frac{4}{7}\\) × 2 = \\(\\frac{8}{7}\\) = \\(1\\frac{1}{7}\\) kg. Flour left = 3 − \\(1\\frac{1}{7}\\) = \\(2\\frac{7}{7}\\) − \\(1\\frac{1}{7}\\) = \\(1\\frac{6}{7}\\) kg."},{"id":22828,"question":"Mrs Tan baked some muffins. \\(\\frac{4}{5}\\) of the muffins were chocolate and the rest were vanilla. There were 240 more chocolate muffins than vanilla muffins. How many vanilla muffins did Mrs Tan bake?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Chocolate = \\(\\frac{4}{5}\\) (4 units), vanilla = \\(\\frac{1}{5}\\) (1 unit). Difference = 4 − 1 = 3 units = 240. 1 unit = 240 ÷ 3 = 80. Vanilla = 1 unit = 80 muffins."},{"id":22834,"question":"Lisa spent \\(\\frac{4}{7}\\) of her money on a mobile phone and $65 on a set of earphones. She had $190 left in the end. How much did the mobile phone cost?<br>$ <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Mobile phone = \\(\\frac{4}{7}\\) (4 units), so remaining money = \\(\\frac{3}{7}\\) (3 units). The 3 units = $65 + $190 = $255. 1 unit = 255 ÷ 3 = $85. Mobile phone = 4 units = 4 × 85 = $340."},{"id":22839,"question":"Which of the following shows \\(\\frac{1}{6}\\) of the figure shaded?","explanation":"\\(\\frac{1}{6}\\) means 1 shaded part out of 6 equal parts. Figure 3 is divided into 6 equal columns with exactly 1 shaded."},{"id":22840,"question":"\\(\\frac{1}{3}\\) + \\(\\frac{1}{12}\\) = ____________","explanation":"Convert to twelfths: \\(\\frac{1}{3}\\) = \\(\\frac{4}{12}\\). Then \\(\\frac{4}{12}\\) + \\(\\frac{1}{12}\\) = \\(\\frac{5}{12}\\)."},{"id":22845,"question":"Mary used \\(\\frac{3}{8}\\) of the beads to make necklaces and had 200 beads left. How many beads did Mary have at first?","explanation":"Beads left = 1 − \\(\\frac{3}{8}\\) = \\(\\frac{5}{8}\\) of the total = 200. So \\(\\frac{1}{8}\\) = 200 ÷ 5 = 40, and the total = 40 × 8 = 320."},{"id":22846,"question":"Express 0.08 as a fraction in its simplest form.","explanation":"0.08 = \\(\\frac{8}{100}\\). Divide numerator and denominator by 4: \\(\\frac{8}{100}\\) = \\(\\frac{2}{25}\\)."},{"id":22855,"question":"Which two of the fractions below are smaller than \\(\\frac{1}{2}\\) ?<br>\\(\\frac{7}{12}\\) , \\(\\frac{3}{7}\\) , \\(\\frac{2}{5}\\) , \\(\\frac{5}{10}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> and <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Compare each to \\(\\frac{1}{2}\\): \\(\\frac{7}{12}\\) > \\(\\frac{6}{12}\\) so bigger; \\(\\frac{3}{7}\\) < \\(\\frac{3.5}{7}\\) so smaller; \\(\\frac{2}{5}\\) < \\(\\frac{2.5}{5}\\) so smaller; \\(\\frac{5}{10}\\) = \\(\\frac{1}{2}\\). So \\(\\frac{3}{7}\\) and \\(\\frac{2}{5}\\) are smaller."},{"id":22856,"question":"What is the value of \\(\\frac{5}{6}\\) − \\(\\frac{2}{3}\\) ?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Convert \\(\\frac{2}{3}\\) to sixths: \\(\\frac{2}{3}\\) = \\(\\frac{4}{6}\\). Then \\(\\frac{5}{6}\\) − \\(\\frac{4}{6}\\) = \\(\\frac{1}{6}\\)."},{"id":22860,"question":"What is the missing number in the box?<br>\\(6\\frac{2}{9}\\) = \\(\\frac{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}{9}\\)","explanation":"Convert the mixed number to an improper fraction: 6 × 9 + 2 = 56, so \\(6\\frac{2}{9}\\) = \\(\\frac{56}{9}\\)."},{"id":22862,"question":"In a class, \\(\\frac{3}{5}\\) of the students are girls. There are 24 girls. How many boys and girls are there in the class?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{3}{5}\\) of the class = 24 girls, so 1 unit (\\(\\frac{1}{5}\\)) = 24 ÷ 3 = 8. Total class = 5 units = 8 × 5 = 40 students."},{"id":22863,"question":"Arrange these numbers in decreasing order.<br>\\(\\frac{84}{100}\\) , 0.8 , 0.804 , \\(\\frac{84}{10}\\)<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_3\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"As decimals: \\(\\frac{84}{10}\\) = 8.4, \\(\\frac{84}{100}\\) = 0.84, 0.804, 0.8 = 0.800. Decreasing: 8.4 (\\(\\frac{84}{10}\\)), 0.84 (\\(\\frac{84}{100}\\)), 0.804, 0.800."},{"id":22872,"question":"Jenny has 2 kg of flour. She used \\(\\frac{3}{8}\\) kg of the flour to bake a cake. She used \\(\\frac{1}{4}\\) kg of the flour to bake some cookies.<br>(a) How much flour did she use to bake the cake and the cookies altogether?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) How much flour did she have left? Express your answer as a mixed number.<br><input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) \\(\\frac{3}{8}\\) + \\(\\frac{1}{4}\\) = \\(\\frac{3}{8}\\) + \\(\\frac{2}{8}\\) = \\(\\frac{5}{8}\\) kg. (b) Left = 2 − \\(\\frac{5}{8}\\) = \\(1\\frac{8}{8}\\) − \\(\\frac{5}{8}\\) = \\(1\\frac{3}{8}\\) kg."},{"id":22874,"question":"The table shows the number of items in a stationery shop. The number of rulers is not shown. Pencils 25 , Erasers 20 , Pens 75 , Rulers ?. How many rulers are there in the stationery shop?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"From the pie chart, the rulers sector is a right angle (\\(\\frac{1}{4}\\) of the circle), so rulers = \\(\\frac{1}{3}\\) of the other three items. Pencils + Erasers + Pens = 25 + 20 + 75 = 120, and 120 ÷ 3 = 40 rulers."},{"id":22882,"question":"Which fraction is in its simplest form?","explanation":"A fraction is in simplest form when numerator and denominator share no common factor other than 1. \\(\\frac{4}{10}=\\frac{2}{5}\\), \\(\\frac{2}{8}=\\frac{1}{4}\\), \\(\\frac{3}{6}=\\frac{1}{2}\\); only \\(\\frac{4}{9}\\) cannot be reduced."},{"id":22888,"question":"Arrange the following fractions from the greatest to the smallest.<br>\\(\\frac{3}{4}\\), \\(\\frac{1}{2}\\), \\(\\frac{5}{8}\\)","explanation":"Express over 8: 3\/4 = 6\/8, 1\/2 = 4\/8, 5\/8 = 5\/8. Greatest to smallest: 6\/8, 5\/8, 4\/8, i.e. 3\/4, 5\/8, 1\/2."},{"id":22897,"question":"\\(\\frac{1}{4}\\) + \\(\\frac{5}{8}\\) = <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Make like denominators: 1\/4 = 2\/8. Then 2\/8 + 5\/8 = 7\/8."},{"id":22898,"question":"Write \\(\\frac{19}{5}\\) as a mixed number.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"19 \/ 5 = 3 remainder 4, so 19\/5 = 3 4\/5."},{"id":22899,"question":"PQRS is a rectangle. Find \\(\\angle\\)PST.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Angle PSR (corner of rectangle) = 90 degrees. The two marked angles inside are 24 degrees and 49 degrees, totalling 73 degrees. So angle PST = 90 - 73 = 17 degrees."},{"id":22916,"question":"Jayden and Linda bought some apples. Jayden took \\(\\frac{5}{8}\\) of the apples and Linda took the rest. Jayden took 36 more apples than Linda. (a) How many apples did Linda take? (b) The cost of 6 apples was $4. How much did the basket of apples cost?<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) $<input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Jayden = 5\/8, Linda = 3\/8, so the total is 8 units, Jayden 5 units, Linda 3 units. The difference 5 - 3 = 2 units = 36, so 1 unit = 18. (a) Linda = 3 units = 54 apples. (b) Total = 8 units = 144 apples. 6 apples = $4, so 144 apples cost (144\/6) x 4 = $96."},{"id":22921,"question":"What fraction of the shapes are stars?","explanation":"There are 12 shapes in all and 5 of them are stars (3 in the top row and 2 in the bottom row). So the fraction is \\(\\frac{5}{12}\\)."},{"id":22922,"question":"Arrange these fractions from the smallest to the greatest.<br>\\(\\frac{5}{9}\\), \\(\\frac{1}{2}\\), \\(\\frac{8}{9}\\)","explanation":"Convert to a common denominator of 18: \\(\\frac{1}{2}=\\frac{9}{18}\\), \\(\\frac{5}{9}=\\frac{10}{18}\\), \\(\\frac{8}{9}=\\frac{16}{18}\\). Smallest to greatest: \\(\\frac{1}{2}\\), \\(\\frac{5}{9}\\), \\(\\frac{8}{9}\\)."},{"id":22927,"question":"Macy had 5 m of string at first. She used \\(\\frac{11}{12}\\) m of string to make a kite. How much string did she have left?","explanation":"5 - \\(\\frac{11}{12}\\) = \\(4\\frac{12}{12}\\) - \\(\\frac{11}{12}\\) = \\(4\\frac{1}{12}\\) m."},{"id":22941,"question":"\\(\\frac{5}{6} = \\frac{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}{12}\\)<br>What is the missing number in the box?","explanation":"Multiply numerator and denominator of \\(\\frac{5}{6}\\) by 2: \\(\\frac{5 \\times 2}{6 \\times 2} = \\frac{10}{12}\\). The missing number is 10."},{"id":22942,"question":"\\(1 - \\frac{1}{8} - \\frac{1}{4}\\) = <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Change all to eighths: \\(\\frac{8}{8} - \\frac{1}{8} - \\frac{2}{8} = \\frac{5}{8}\\)."},{"id":22943,"question":"Express \\(\\frac{85}{100}\\) as a decimal.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{85}{100}\\) means 85 hundredths = 0.85."},{"id":22946,"question":"ABCD is a rectangle. Find \\(\\angle x\\).<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Angle B of the rectangle is a right angle (90 degrees). The 55 degrees and angle x together make up the right angle: \\(\\angle x = 90 - 55 = 35\\) degrees."},{"id":22949,"question":"Mrs Lee bought a papaya and a durian. The mass of the papaya was \\(\\frac{9}{10}\\) kg. It was \\(\\frac{1}{2}\\) kg lighter than the mass of the durian. What was the mass of the durian? Express your answer as a mixed number in its simplest form.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> kg","explanation":"Durian = papaya + \\(\\frac{1}{2}\\) = \\(\\frac{9}{10} + \\frac{1}{2} = \\frac{9}{10} + \\frac{5}{10} = \\frac{14}{10} = 1\\frac{4}{10} = 1\\frac{2}{5}\\) kg."},{"id":22951,"question":"In the number line, (a) what is the mixed number represented by A? (b) what is the improper fraction represented by B?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br><input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Each interval between whole numbers is divided into sixths. A is one-sixth past 1, so A = \\(1\\frac{1}{6}\\). B is five-sixths past 1 (one-sixth before 2), which as an improper fraction is \\(\\frac{11}{6}\\)."},{"id":22955,"question":"There were a total of 1785 fiction books and non-fiction books in a library. \\(\\frac{2}{7}\\) of the books were non-fiction books and the rest were fiction books. How many more fiction books than non-fiction books were there?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Total = 7 units = 1785, so 1 unit = 255. Non-fiction = 2 units, fiction = 5 units. Difference = 5 - 2 = 3 units = 3 × 255 = 765 more fiction books."},{"id":22958,"question":"The pie chart shows the choices made by a group of children about their favourite snacks. Half of the group likes cookies and brownies. The number of children who like muffins is equal to the number of children who like brownies.<br>(a) What fraction of the students like cookies?<br>(b) Given that 126 children like curry puffs, how many children like muffins?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br><input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Cupcakes = \\(\\frac{1}{6}\\), curry puffs = \\(\\frac{1}{4}\\). Muffins = brownies. Cookies + brownies = \\(\\frac{1}{2}\\). Muffins = \\(\\frac{1}{2} - \\frac{1}{6} - \\frac{1}{4} = \\frac{12}{12} - \\frac{2}{12} - \\frac{3}{12} = \\frac{1}{12}\\) (= brownies). Cookies = \\(\\frac{1}{2} - \\frac{1}{12} = \\frac{6}{12} - \\frac{1}{12} = \\frac{5}{12}\\). (b) Curry puffs = \\(\\frac{1}{4} = \\frac{3}{12}\\) = 126 children, so 1 unit (\\(\\frac{1}{12}\\)) = 126 ÷ 3 = 42. Muffins = \\(\\frac{1}{12}\\) = 42 children."},{"id":22963,"question":"The figure is made up of identical triangles. What fraction of the figure is shaded?","explanation":"The rectangle is split into 8 small squares, each made of 2 identical triangles, giving 16 triangles in total. 7 of the 16 triangles are shaded, so the shaded fraction is \\(\\frac{7}{16}\\)."},{"id":22964,"question":"Express \\(\\frac{52}{100}\\) as a decimal.","explanation":"\\(\\frac{52}{100}\\) means 52 hundredths = 0.52."},{"id":22976,"question":"Write \\(3\\frac{4}{5}\\) as an improper fraction.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(3\\frac{4}{5} = \\frac{3 \\times 5 + 4}{5} = \\frac{19}{5}\\)."},{"id":22977,"question":"What is the value of \\(\\frac{5}{8} + \\frac{3}{4}\\)? Express your answer as a mixed number.<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"\\(\\frac{5}{8} + \\frac{3}{4} = \\frac{5}{8} + \\frac{6}{8} = \\frac{11}{8} = 1\\frac{3}{8}\\)."},{"id":22978,"question":"How many one-sixths are there in 1 whole?<br><input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"1 whole = \\(\\frac{6}{6}\\), which is 6 sixths. So there are 6 one-sixths in 1 whole."},{"id":22980,"question":"\\(0.4 = \\frac{4}{<input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>}\\)<br>What is the missing number in the box?","explanation":"0.4 means 4 tenths = \\(\\frac{4}{10}\\). The missing denominator is 10."},{"id":22997,"question":"There were 3 bottles of oil. All 3 bottles had the same amount of oil at first. \\(\\frac{1}{8}\\) $$l$$ of oil was poured from bottle A to bottle B. \\(\\frac{1}{2}\\) $$l$$ was then poured from bottle B to bottle C. There was \\(\\frac{5}{8}\\) $$l$$ of oil in bottle B in the end.<br>(a) What was the total amount of oil in bottles A, B and C at first?<br>(b) Each litre of oil cost $7.80. Find the cost of the total amount of oil in bottles A, B and C.<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Bottle B at first = X. After receiving \\(\\frac{1}{8}\\) and giving away \\(\\frac{1}{2}\\): X + \\(\\frac{1}{8}\\) − \\(\\frac{1}{2}\\) = \\(\\frac{5}{8}\\). \\(\\frac{1}{8} - \\frac{1}{2} = \\frac{1}{8} - \\frac{4}{8} = -\\frac{3}{8}\\), so X − \\(\\frac{3}{8}\\) = \\(\\frac{5}{8}\\), giving X = 1 $$l$$. Each bottle started with 1 $$l$$, so total = 1 × 3 = 3 $$l$$. (b) Cost = 3 × $7.80 = $23.40."},{"id":22998,"question":"There were 540 more girls than boys in a school hall. After \\(\\frac{3}{4}\\) of the girls and \\(\\frac{1}{2}\\) of the boys exited the hall, there was an equal number of boys and girls who remained behind in the hall.<br>(a) Find the total number of boys and girls who exited the hall.<br>(b) Find the total number of boys and girls who were in the hall at first.<br>(a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Let boys = 2 units (so half remain = 1 unit) and girls = 4 units (so a quarter remain = 1 unit) to make the remainders equal. Girls − boys = 4u − 2u = 2u = 540, so 1 unit = 270. Boys = 540, girls = 1080. (a) Exited = half the boys + three-quarters of girls = 270 + 810 = 1080; equivalently 4 units = 270 × 4 = 1080. (b) Total at first = 6 units = 270 × 6 = 1620."},{"id":23002,"question":"Which of the following is <b>not<\/b> an equivalent fraction of \\(\\frac{1}{4}\\)?","explanation":"\\(\\frac{1}{4}\\) equals 3\/12, 4\/16 and 6\/24 (each numerator is one-quarter of the denominator). \\(\\frac{7}{32}\\) is not, since 7 × 4 = 28 ≠ 32. So \\(\\frac{7}{32}\\) is not equivalent."},{"id":23004,"question":"\\(6\\frac{3}{8}\\) = \\(\\frac{\\Box}{8}\\)<br>What is the missing number in the box?","explanation":"Convert the mixed number to an improper fraction: \\(6\\frac{3}{8}\\) = (6 × 8 + 3)\/8 = (48 + 3)\/8 = \\(\\frac{51}{8}\\). The missing number is 51."},{"id":23005,"question":"Write \\(7\\frac{9}{25}\\) as a decimal.","explanation":"Make the denominator 100: \\(\\frac{9}{25}\\) = \\(\\frac{36}{100}\\) = 0.36. So \\(7\\frac{9}{25}\\) = 7.36."},{"id":23010,"question":"Amy took \\(\\frac{7}{12}\\) h to fix a jigsaw puzzle. Jenny took \\(\\frac{2}{3}\\) h slower to fix the same jigsaw puzzle. How long did Jenny take to fix the puzzle? Express your answer in the simplest form.","explanation":"Jenny = \\(\\frac{7}{12}\\) + \\(\\frac{2}{3}\\). Change \\(\\frac{2}{3}\\) to \\(\\frac{8}{12}\\): \\(\\frac{7}{12}\\) + \\(\\frac{8}{12}\\) = \\(\\frac{15}{12}\\) = \\(1\\frac{3}{12}\\) = \\(1\\frac{1}{4}\\) h."},{"id":23012,"question":"The pie chart shows the different ways 162 students go to school.<br>How many students go to school by car?","explanation":"Bus = \\(\\frac{1}{3}\\) and Walk = \\(\\frac{5}{9}\\). Fraction for car = 1 − \\(\\frac{1}{3}\\) − \\(\\frac{5}{9}\\) = \\(\\frac{9}{9}\\) − \\(\\frac{3}{9}\\) − \\(\\frac{5}{9}\\) = \\(\\frac{1}{9}\\). Car = \\(\\frac{1}{9}\\) × 162 = 18 students."},{"id":23017,"question":"Arrange these fractions from the smallest to the greatest.<br>\\(\\frac{8}{11}\\) , \\(\\frac{1}{2}\\) , \\(\\frac{5}{11}\\)<br>Ans: <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> (smallest) , <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/> , <input type=\"text\" id=\"input_2\" class=\"fill-blank-input\" placeholder=\"?\" \/> (greatest)","explanation":"Compare: \\(\\frac{5}{11}\\) ≈ 0.45, \\(\\frac{1}{2}\\) = 0.5, \\(\\frac{8}{11}\\) ≈ 0.73. From smallest to greatest: \\(\\frac{5}{11}\\), \\(\\frac{1}{2}\\), \\(\\frac{8}{11}\\)."},{"id":23019,"question":"Rectangle PQRS is made up of 8 unit squares. What fraction of rectangle PQRS is shaded?<br>Ans: <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"Each unit square is split into triangles; the shaded triangles add up to 3 whole unit squares out of the 8 unit squares. So the shaded fraction is \\(\\frac{3}{8}\\)."},{"id":23020,"question":"Express 0.6 as a fraction.<br>Ans: <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"0.6 means 6 tenths, which is written as \\(\\frac{6}{10}\\)."},{"id":23023,"question":"ABCD is a rectangle. Find \\(\\angle x\\).<br>Ans: <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>°","explanation":"Corner A of the rectangle is a right angle (90°). The 34° is part of that corner, so \\(\\angle x\\) = 90° − 34° = 56°."},{"id":23026,"question":"Gladys jogged a distance of \\(\\frac{2}{3}\\) km. She jogged \\(\\frac{1}{5}\\) km more than the distance jogged by Ben. What was the total distance Gladys and Ben jogged? Give your answer as a mixed number.<br>Ans: <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/> km","explanation":"Ben = Gladys − \\(\\frac{1}{5}\\) = \\(\\frac{2}{3}\\) − \\(\\frac{1}{5}\\) = \\(\\frac{10}{15}\\) − \\(\\frac{3}{15}\\) = \\(\\frac{7}{15}\\) km. Total = \\(\\frac{2}{3}\\) + \\(\\frac{7}{15}\\) = \\(\\frac{10}{15}\\) + \\(\\frac{7}{15}\\) = \\(\\frac{17}{15}\\) = \\(1\\frac{2}{15}\\) km."},{"id":23028,"question":"In the figure, a rectangular piece of paper ABCD was folded along BD. Find \\(\\angle a\\).<br>Ans: <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/>°","explanation":"Corner A (= folded corner) is a right angle, 90°. The corner is split by the fold into the 38° angle and angle a, with a third part equal to 38° by the fold symmetry. So 90° = 38° + 38° + a, giving a = 90° − 76° = 14°."},{"id":23034,"question":"Farid baked some cookies. He gave away \\(\\frac{3}{10}\\) of his cookies to his friends and gave away \\(\\frac{1}{2}\\) of his cookies to his siblings. He had 50 cookies left.<br>(a) What fraction of Farid's cookies was left?<br>Ans: (a) <input type=\"text\" id=\"input_0\" class=\"fill-blank-input\" placeholder=\"?\" \/><br>(b) How many cookies did Farid bake?<br>Ans: (b) <input type=\"text\" id=\"input_1\" class=\"fill-blank-input\" placeholder=\"?\" \/>","explanation":"(a) Given away = \\(\\frac{3}{10}\\) + \\(\\frac{1}{2}\\) = \\(\\frac{3}{10}\\) + \\(\\frac{5}{10}\\) = \\(\\frac{8}{10}\\). Fraction left = \\(\\frac{10}{10}\\) − \\(\\frac{8}{10}\\) = \\(\\frac{2}{10}\\). (b) \\(\\frac{2}{10}\\) → 50 cookies, so \\(\\frac{1}{10}\\) → 25, and \\(\\frac{10}{10}\\) → 25 × 10 = 250 cookies."}]