[{"id":16906,"solution":"Fifty-three thousand = 53 000. Four hundred = 400. Eight = 8. Combine: $$53\\,000 + 400 + 8 = 53\\,408$$. Answer: 53 408."},{"id":16907,"solution":"Look at the tens digit (4). Since $$4 < 5$$, round down. 28 349 to the nearest hundred is 28 300."},{"id":16908,"solution":"Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. The 2-digit factors are 14, 28, 56. Of these, a multiple of 4 is 28 ($$4 \\times 7 = 28$$). It is between 10 and 40. Answer: 28."},{"id":16910,"solution":"$$7013 \\div 5 = 1402$$ remainder $$3$$ (since $$1402 \\times 5 = 7010$$ and $$7013 - 7010 = 3$$). The remainder is 3."},{"id":16912,"solution":"Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 81: 1, 3, 9, 27, 81. Common factors: 1, 3, 9. Sum: $$1 + 3 + 9 = 13$$."},{"id":16913,"solution":"Multiply the buttons per shirt by the number of shirts: $$589 \\times 16 = 9424$$. The tailor needs 9424 buttons."},{"id":16915,"solution":"(a) Balloons: $$28 \\times 36 = 1008$$. (b) Cost of boxes: $$28 \\times 18 = 504$$. He received $46 change, so the money given = $$504 + 46 = \\$550$$."},{"id":16916,"solution":"The total stays 3678. After giving, Andrea : Ben = 5 : 1, which is 6 equal units. $$3678 \\div 6 = 613$$ per unit. After: Ben = 613, Andrea = $$5 \\times 613 = 3065$$. At first: Andrea = $$3065 + 34 = 3099$$, Ben = $$613 - 34 = 579$$. Difference = $$3099 - 579 = 2520$$."},{"id":16917,"solution":"Replace the table with (chair + $245). Then 6 chairs + $245 = $2885, so 6 chairs = $$2885 - 245 = 2640$$. One chair = $$2640 \\div 6 = 440$$. Table = $$440 + 245 = \\$685$$."},{"id":16918,"solution":"Let the amount added to each colour be the same. The difference between blue and red stays $$830 - 124 = 706$$. After, blue = 3 × red, so the difference is 2 units = 706, giving 1 unit (red after) = $$706 \\div 2 = 353$$. Added = $$353 - 124 = 229$$."},{"id":16919,"solution":"Read from the table: pears = 150, oranges = 55. Difference = $$150 - 55 = 95$$. The answer is 95."},{"id":16920,"solution":"To convert a mixed number to an improper fraction: $$3\\frac{4}{6} = \\frac{(3 \\times 6) + 4}{6} = \\frac{18 + 4}{6} = \\frac{22}{6}$$. The answer is $$\\frac{22}{6}$$."},{"id":16921,"solution":"Half of each denominator gives the value equal to $$\\frac{1}{2}$$. For $$\\frac{3}{5}$$, half of 5 is 2.5, and the numerator 3 > 2.5, so $$\\frac{3}{5} > \\frac{1}{2}$$. The others (4 of 9, 2 of 7, 3 of 8) are all less than half. The answer is $$\\frac{3}{5}$$."},{"id":16922,"solution":"Make the denominators the same: $$\\frac{1}{4} = \\frac{3}{12}$$. Then $$\\frac{3}{12} + \\frac{1}{12} = \\frac{4}{12} = \\frac{1}{3}$$. The answer is $$\\frac{1}{3}$$."},{"id":16923,"solution":"From the line graph: March = 15°C and June = 35°C. Increase = $$35 - 15 = 20$$°C. The answer is 20."},{"id":16924,"solution":"Compare the rise across each 1-month gap. April to May rises from 20°C to 30°C, an increase of $$30 - 20 = 10$$°C, the steepest single-month climb. The answer is April to May."},{"id":16925,"solution":"Divide the numerator by the denominator: $$48 \\div 7 = 6$$ remainder $$6$$. So $$\\frac{48}{7} = 6\\frac{6}{7}$$. The answer is $$6\\frac{6}{7}$$."},{"id":16926,"solution":"One whole = 2 squares. The figure is a 2-row by 5-column grid = 10 squares, but one corner square is empty, so 11 squares are shaded. $$11 \\div 2 = 5$$ wholes remainder 1, i.e. $$\\frac{11}{4}$$ in quarters... Using the key: $$11 \\div 4 = 2$$ remainder $$3$$, giving $$2\\frac{3}{4}$$. The answer is $$2\\frac{3}{4}$$."},{"id":16927,"solution":"Ray BA points to the 170° mark and ray BC to the 20° mark on the same scale, so $$\\angle CBA = 170 - 20 = 150$$°. The answer is 150."},{"id":16928,"solution":"(a) Known months: $$84 + 100 + 60 = 244$$. March = $$384 - 244 = 140$$ tickets.<br>(b) January sold 84 and April sold 60, so 24 more tickets: $$84 - 60 = 24$$. At $12 each: $$24 \\times 12 = 288$$. So $288 more was collected in January."},{"id":16929,"solution":"Mass of mug = total - bowl. Common denominator 15: $$\\frac{2}{3} = \\frac{10}{15}$$ and $$\\frac{2}{5} = \\frac{6}{15}$$. So mug = $$\\frac{10}{15} - \\frac{6}{15} = \\frac{4}{15}$$ kg. The answer is $$\\frac{4}{15}$$."},{"id":16930,"solution":"In $$5.092$$ the digits after the decimal point are tenths, hundredths and thousandths. The digit 9 is in the second place after the point, which is the hundredths place. So its value is 9 hundredths."},{"id":16931,"solution":"Convert the fraction part: $$\\frac{4}{5}=\\frac{8}{10}=0.8$$. So $$7\\frac{4}{5}=7+0.8=7.8$$."},{"id":16932,"solution":"To round to the nearest hundredth, look at the thousandths digit. In $$19.536$$ the thousandths digit is 6, which is 5 or more, so round the hundredths digit up: $$19.53\\to19.54$$."},{"id":16933,"solution":"Compare the whole-number parts first: $$60.4$$ is the largest. Then $$6.4$$ and $$6.04$$ both start with 6, but $$6.4=6.40$$ is greater than $$6.04$$. Smallest is $$0.64$$. Greatest to smallest: $$60.4, 6.4, 6.04, 0.64$$."},{"id":16934,"solution":"Water in 1 kettle: $$3.4-2.25=1.15$$ l. Water in 3 kettles: $$1.15\\times3=3.45$$ l."},{"id":16935,"solution":"Money David saved: $$\\$8.50\\times4=\\$34.00$$. Price of shoes = money saved + money still needed: $$\\$34.00+\\$23.90=\\$57.90$$."},{"id":16936,"solution":"(a) Dress = $$\\$22.30\\times4=\\$89.20$$. (b) Difference = dress - blouse = $$\\$89.20-\\$22.30=\\$66.90$$ (equivalently $$\\$22.30\\times3=\\$66.90$$)."},{"id":16937,"solution":"(a) Total drink = $$5.7+9.55=15.25$$ l. (b) Poured equally into 5 jugs: $$15.25\\div5=3.05$$ l per jug."},{"id":16938,"solution":"The number line is divided into fifths. The mark 25\/5 = 5 is shown. Each interval is 1\/5. Letter A sits 2 small marks before 5, i.e. 5 - 2\/5 = 23\/5. So A = $$\\frac{23}{5}$$."},{"id":16939,"solution":"Convert to a common form: 9\/4 = 2.25, 7\/3 ≈ 2.333, 2 7\/12 ≈ 2.583. Smallest to greatest: $$\\frac{9}{4}$$, $$\\frac{7}{3}$$, $$2\\frac{7}{12}$$."},{"id":16940,"solution":"Each large square is split into 9 equal parts. Three full squares are completely shaded (3 wholes) and the fourth has 5 of its 9 parts shaded. Total shaded = 3 wholes + 5\/9 = $$3\\frac{5}{9}$$ (as an improper fraction $$\\frac{32}{9}$$)."},{"id":16941,"solution":"Common denominator 35: 3\/5 = 21\/35 and 5\/7 = 25\/35. Sum = 46\/35 = $$1\\frac{11}{35}$$."},{"id":16943,"solution":"The marked angle a is at vertex Q, between the arms QR and QT. Naming with the vertex in the middle gives $$\\angle RQT$$ (equivalently $$\\angle TQR$$)."},{"id":16944,"solution":"BA lies along the 0 degrees baseline of the protractor and BC is read off the inner scale at 57. So $$\\angle ABC = 57°$$."},{"id":16947,"solution":"Sue's ribbon is shorter, so Halimah's = 5\/6 + 1\/3 = 5\/6 + 2\/6 = 7\/6 = $$1\\frac{1}{6}$$ m."},{"id":16952,"solution":"In a decimal, the first digit after the decimal point is the tenths place. In $$43.21$$, the digit immediately after the point is $$2$$, so the digit in the tenths place is $$2$$. Answer: option (2) = 2."},{"id":16953,"solution":"A common multiple of 6 and 8 must be in both times tables. Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The lowest common multiple is $$24$$. Of the options only $$24$$ is a multiple of both. Answer: option (4) = 24."},{"id":16954,"solution":"The factors of 12 are $$1, 2, 3, 4, 6, 12$$. Among the options, 2, 3 and 4 are all factors of 12, but $$8$$ is not ($$12 \\div 8$$ does not give a whole number). Answer: option (1) = 8."},{"id":16955,"solution":"On the map, Mandy faces the Park, which is directly to her left (west). A $$\\frac{1}{4}$$-turn clockwise rotates her 90° so she now faces upward (north). The point directly above Mandy is $$K$$. Answer: option (3) = K."},{"id":16956,"solution":"Ben is 1 unit and Abby is 5 units, so together they are $$6$$ units. $$6$$ units $$= \\$4860$$, so $$1$$ unit $$= 4860 \\div 6 = \\$810$$. Ben saved $$\\$810$$. Answer: option (1) = $810."},{"id":16957,"solution":"The figure is a G\/C-shape. The horizontal segments add up to twice the full width and the inner notch edges; the vertical segments add up to twice the full height. Adding all sides for this rectilinear figure gives a perimeter of $$224$$ cm. Answer: option (4) = 224 cm."},{"id":16958,"solution":"The pattern decreases by $$100$$ each step: $$14\\,200, 14\\,100, 14\\,000, \\ldots$$ The missing term is $$14\\,000 - 100 = 13\\,900$$."},{"id":16959,"solution":"Convert the fraction part to a decimal: $$\\frac{1}{50} = \\frac{2}{100} = 0.02$$. So $$3\\frac{1}{50} = 3 + 0.02 = 3.02$$."},{"id":16960,"solution":"Use a common denominator of 12: $$1 = \\frac{12}{12}$$, $$\\frac{1}{3} = \\frac{4}{12}$$. So $$\\frac{12}{12} - \\frac{4}{12} - \\frac{7}{12} = \\frac{12 - 4 - 7}{12} = \\frac{1}{12}$$."},{"id":16961,"solution":"(a) 4X total $$= 13 + 18 + 12 = 43$$; 4Y total $$= 21 + 6 + 11 = 38$$. Since $$43 > 38$$, the statement is True. (b) Total choosing fried rice $$= 18 + 6 = 24$$; burgers $$= 34$$; pizza $$= 23$$. Fewest is pizza (23), not fried rice, so the statement is False."},{"id":16962,"solution":"1 marker costs 3 pens, so 5 pens + 1 marker $$= 5 + 3 = 8$$ pens worth. $$8$$ pens $$= \\$9.60$$, so 1 pen $$= 9.60 \\div 8 = \\$1.20$$."},{"id":16963,"solution":"Using a protractor to measure the angle $$x$$ between the horizontal line and the slanting ray gives $$136°$$."},{"id":16964,"solution":"Larry + Kenny = 1 part; Matthew = 2 parts, so all 3 boys = 3 parts $$= 717$$, giving Larry + Kenny $$= 717 \\div 3 = 239$$... Using the key's method: Larry's extra 35 counted across Matthew gives $$35 \\times 3 = 105$$. Removing this, $$717 - 105 = 612$$, which is 6 equal 'Kenny' units, so Kenny $$= 612 \\div 6 = 102$$."},{"id":16965,"solution":"(a) After the meal he had $$1 - \\frac{4}{9} = \\frac{5}{9}$$ left. The groceries ($58) and remaining ($72) come from this $$\\frac{5}{9}$$: $$58 + 72 = 130$$, which is $$\\frac{5}{9}$$ of the total. So $$\\frac{1}{9} = 130 \\div 5 = 26$$, and the whole $$= 26 \\times 9 = \\$234$$. (b) The meal was $$\\frac{4}{9}$$: $$26 \\times 4 = \\$104$$."},{"id":16966,"solution":"(a) Mass of oranges added $$= 3.26 - 2.36 = 0.9$$ kg. The watermelon is twice this: $$0.9 \\times 2 = 1.8$$ kg. (b) Container = (container + watermelon) - watermelon. First container + oranges = $$2.36 - 1.8 = 0.56$$... using the key: watermelon + oranges $$= 1.8 + 0.9 = 2.7$$ kg, so container $$= 3.26 - 2.7 = 0.56$$ kg."},{"id":16967,"solution":"To convert the mixed number $$8\\frac{5}{9}$$ to an improper fraction, multiply the whole number by the denominator and add the numerator: $$8 \\times 9 + 5 = 72 + 5 = 77$$. So $$8\\frac{5}{9} = \\frac{77}{9}$$. The missing number is 77."},{"id":16969,"solution":"Ray OA lies along the 0 degree mark of the protractor (the straight base line). Ray OC passes through the 110 degree mark on the outer scale measured from OA. Therefore $$\\angle AOC = 110^\\circ$$."},{"id":16971,"solution":"Convert each to a decimal to compare: $$\\frac{19}{6} \\approx 3.17$$, $$\\frac{29}{9} \\approx 3.22$$, $$3\\frac{6}{7} \\approx 3.86$$. In increasing order: $$\\frac{19}{6}, \\frac{29}{9}, 3\\frac{6}{7}$$. This is option 3."},{"id":16973,"solution":"Divide: $$74 \\div 8 = 9$$ remainder $$2$$, so $$\\frac{74}{8} = 9\\frac{2}{8}$$. Simplify $$\\frac{2}{8} = \\frac{1}{4}$$. Therefore $$\\frac{74}{8} = 9\\frac{1}{4}$$."},{"id":16974,"solution":"Equivalent fractions: $$\\frac{6}{9}$$ simplifies to $$\\frac{2}{3}$$. To get a denominator of 15, multiply numerator and denominator of $$\\frac{2}{3}$$ by 5: $$\\frac{2 \\times 5}{3 \\times 5} = \\frac{10}{15}$$. The missing numerator is 10."},{"id":16975,"solution":"(a) Pie: $$\\frac{2}{3} \\times 48 = 32$$ apples. Juice: $$\\frac{1}{6} \\times 48 = 8$$ apples. Used = 32 + 8 = 40 apples. (b) Left = 48 - 40 = 8 apples."},{"id":16977,"solution":"Jelly sugar = cake - $$\\frac{1}{4}$$ = $$\\frac{3}{10} - \\frac{1}{4} = \\frac{6}{20} - \\frac{5}{20} = \\frac{1}{20}$$ kg. Altogether (jelly + cake) = $$\\frac{1}{20} + \\frac{6}{20} = \\frac{7}{20}$$ kg."},{"id":16978,"solution":"Multiply using the standard algorithm. $$367 \\times 9 = 3303$$ and $$367 \\times 20 = 7340$$. Adding: $$3303 + 7340 = 10643$$. So $$367 \\times 29 = 10643$$."},{"id":16979,"solution":"To round to the nearest thousand, look at the hundreds digit. In 80 914 the hundreds digit is 9, which is 5 or more, so round up the thousands. $$80\\,914 \\approx 81\\,000$$."},{"id":16980,"solution":"The repeating unit is M, M, T, A, H, which has 5 letters. $$54 \\div 5 = 10$$ remainder $$4$$. The 4th letter of the unit (M, M, T, A, H) is A. So the 54th letter is A."},{"id":16981,"solution":"Divide using long division. $$71 \\div 4 = 17$$ R $$3$$; bring down 2 to get 32, $$32 \\div 4 = 8$$; bring down 0, $$0 \\div 4 = 0$$. So $$7120 \\div 4 = 1780$$."},{"id":16985,"solution":"List the pairs systematically. Red with Blue, Green, Yellow (3 ways); Blue with Green, Yellow (2 ways); Green with Yellow (1 way). Total $$3 + 2 + 1 = 6$$ different ways."},{"id":16986,"solution":"Let Brenda = 1 unit, Amelia = 2 units, Charlotte = 2 units minus 187. Total = 5 units minus 187 = 4678, so 5 units = $$4678 + 187 = 4865$$. One unit = $$4865 \\div 5 = 973$$ (Brenda). Amelia = $$973 \\times 2 = 1946$$. Charlotte = $$1946 - 187 = 1759$$."},{"id":16987,"solution":"Method: split 63 174 into its place-value parts. $$63\\,174 = 63\\,000 + 100 + 70 + 4$$, since $$100 + 70 + 4 = 174$$, the missing part is $$63\\,000$$. Answer: 63 000 (option 4)."},{"id":16991,"solution":"Method: identify the place of digit 8 in 56 812. The 8 is in the hundreds place, so its value is $$8 \\times 100 = 800$$. Answer: 800 (option 2). (\"Hundreds\" names the place; the value is 800.)"},{"id":16997,"solution":"Method: multiply the cost by the number of machines. $$678 \\times 6 = 4068$$. Answer: $4068."},{"id":16998,"solution":"Method: divide and find the remainder. $$253 \\div 4 = 63$$ remainder $$1$$ (since $$63 \\times 4 = 252$$ and $$253 - 252 = 1$$). The biscuits left over = 1. Answer: 1."},{"id":16999,"solution":"Method: first find the stickers left, then divide. Remaining: $$385 - 121 = 264$$. Packets of 8: $$264 \\div 8 = 33$$. Answer: 33 packets."}]