0.05 = \(\dfrac{5}{100}\). Dividing numerator and denominator by 5 gives \(\dfrac{1}{20}\). Answer: \(\dfrac{1}{20}\).


Two adults cost 2 × $15 = $30. Three children cost 3 × $9 = $27. Total = $30 + $27 = $57. Answer: $57.


Add the three known groups: 73 + 50 + 64 = 187. Subtract from the total: 225 − 187 = 38. Answer: 38.


Ming Hui took 25 min less than Harun: 1 h 20 min − 25 min = 55 min. Starting at 9.45 a.m. and adding 55 min gives 10.40 a.m. Answer: 10.40 a.m.


Checking each letter: A has a vertical line of symmetry; N has none; G has none; E has a horizontal line of symmetry; L has none. So 2 letters (A and E) have a line of symmetry. Answer: 2.


Thirteen thousand = 13 000 and twenty-six = 26. Together: 13 000 + 26 = 13 026. Answer: 13 026.


The numbers decrease by 900 each time (14 100 − 900 = 13 200, and so on). After 11 400, the next term is 11 400 − 900 = 10 500. Check: 10 500 − 900 = 9 600. Answer: 10 500.


1536 ÷ 7 = 219 remainder 3, because 7 × 219 = 1533 and 1536 − 1533 = 3. The remainder is 3.


\(\dfrac{6}{8}\) simplifies to \(\dfrac{3}{4}\). \(\dfrac{12}{16}\) also simplifies to \(\dfrac{3}{4}\) (divide by 4), and \(\dfrac{3}{4}\) is already in that form. So the two equivalent fractions are \(\dfrac{12}{16}\) and \(\dfrac{3}{4}\).


5 thousandths means 5 in the thousandths place (the third decimal place): 0.005. Answer: 0.005.


The first decimal digit is 5, so round up: 23.51 rounds to 24. Answer: 24.


3 ÷ 7 = 0.4285... The thousandths digit is 8, so round the hundredths up: 0.43. Answer: 0.43.


Subtract the travel time from the arrival time: 23 45 − 2 h 25 min. 23 45 − 2 h = 21 45; 21 45 − 25 min = 21 20. The train left at 21 20. Answer: 21 20.


'At least 70 stickers' means the 70, 80 and 90 columns together = 87 pupils. The 70 column has 19 pupils, so the 80 and 90 columns together = 87 − 19 = 68 pupils. Answer: 68.


(a) Amy took the rest: \(1-\dfrac{3}{8}=\dfrac{5}{8}\). (b) The difference between Amy and Mariam is \(\dfrac{5}{8}-\dfrac{3}{8}=\dfrac{2}{8}\) of the total, which equals 36 stickers. So \(\dfrac{2}{8}\) = 36 means \(\dfrac{1}{8}\) = 18, and the total \(\dfrac{8}{8}\) = 18 × 8 = 144 stickers. Answers: (a) \(\dfrac{5}{8}\) (b) 144.


(a) They started equal. Ahmad spent $37 and Jack received $15, so the difference between them in the end is $37 + $15 = $52. (b) In the end Jack = 3 × Ahmad, so the difference of $52 equals 2 units (3 − 1). 1 unit = $52 ÷ 2 = $26 (Ahmad's end amount); Jack's end amount = 3 × $26 = $78. Jack at first = $78 − $15 = $63. Answers: (a) $52 (b) $63.


The digit 8 stands for 80 when it is in the tens place. In 3082 the 8 is in the tens place (80).


Look at the tens digit (2). Since 2 < 5, round down: 13 429 to the nearest hundred is 13 400.


Make denominators the same: \(\dfrac{1}{3}=\dfrac{3}{9}\). Then \(\dfrac{3}{9}+\dfrac{1}{9}=\dfrac{4}{9}\).


To round to 1 decimal place, look at the 2nd decimal digit (4). Since 4 < 5, round down: 17.54 becomes 17.5.


83 905 = 80 000 + 3000 + 900 + 5. The missing number is the hundreds value, 900.


Each number decreases by 400. 11 800 − 400 = 11 400.


Thousandths are the 3rd decimal place. 5 thousandths = 0.005.


Compare decimal place by place. 3.909 > 3.099 > 3.093 because the tenths digit 9 beats 0, then for 3.099 vs 3.093 the hundredths are equal (9) but thousandths 9 > 3.


The greatest number of boxes is the highest common factor of 36 and 54. Common factors are 1, 2, 3, 6, 9, 18; the greatest is 18.


Jonathan = 1.81 − 0.35 = 1.46 m. Elson is 0.29 m taller than Jonathan: 1.46 + 0.29 = 1.75 m.


The watch is 15 min slow, so the actual time is 15 min later than 1.35 p.m.: 1.35 p.m. + 15 min = 1.50 p.m. = 13 50 in 24-hour time.


Two facing pages are consecutive numbers, so they differ by 1. Smaller + (smaller + 1) = 667, so 2 × smaller = 666, smaller = 333.


Let Joey = 1 unit, Nicole = 5 units. After giving away: 5u − 235 = 1u − 19, so 4u = 235 − 19 = 216, 1u = 54. (a) Nicole = 5u = 5 × 54 = 270. (b) Each had Joey's remainder = 54 − 19 = 35.


Mrs Devi sold \(\dfrac{7}{9}\) (the part that is not the \(\dfrac{2}{9}\) 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.


Charlie's marbles never change. Charlie = 2 × (Sally's original). After Sally loses 45, Charlie = 5 × (Sally's new). So 5 units (new Sally) = 2 units (old Sally), meaning Sally lost 45 = the difference; 3 new-units = 45 + 45... using model: Charlie = 5 new-units and = 2 old-units; the 45 lost equals 3 of the new units, so 3u = 45 + 45 = 90, 1u = 30, Charlie = 5u = 150.


Catherine − Alice = (Benny + Catherine) − (Alice + Benny) = 450 − 100 = 350. Since Catherine = 5 × Alice, Catherine − Alice = 4 × Alice = 350, so Alice = 350 ÷ 4 = $87.50.


Look at the tens digit (5). Since 58 ≥ 50, round the hundreds up: 22 758 → 22 800.


The first digit after the decimal point is the tenths place. In 32.14 that digit is 1.


A study table is about 70 cm tall. 7 m and 70 m are far too tall; 7 cm is far too short.


Now: Charles = 3 × 8 = 24, Daniel = 24 − 4 = 20. The age gap between Ben and Daniel stays the same. Daniel goes from 20 to 50, an increase of 30 years, so Ben becomes 8 + 30 = 38.


Compare the digits: 973 > 937 > 397 > 379. Greatest to smallest: 973, 937, 397, 379.


Factors of 32: 1, 2, 4, 8, 16, 32. The two not listed are 8 and 16.


Remove John's extra 23: 175 − 23 = 152, which is twice Ken's marks. Ken = 152 ÷ 2 = 76.


The number must be a common multiple of 3 and 4, i.e. a multiple of 12: 12, 24, 36... The greatest below 30 is 24.


Tank A = 5 units, Tank B = 1 unit, difference = 4 units. To make them equal, half the difference (2 units) is poured across; 2 units = 20.16 ℓ. So 1 unit = 10.08 ℓ and Tank A = 5 × 10.08 = 50.4 ℓ.


After giving \(\dfrac{5}{8}\) away, \(\dfrac{3}{8}\) remained. From that, 7 went to the aunt and 20 were left, so \(\dfrac{3}{8}\) = 20 + 7 = 27 cookies. 1 unit = 27 ÷ 3 = 9, so the total \(\dfrac{8}{8}\) = 8 × 9 = 72.


After Bella used 39, the remaining stickers total 219 − 39 = 180. Aisha's \(\dfrac{2}{3}\) 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.


The pattern repeats every 6 numbers (4, 6, 5, 6, 2, 1; sum = 24). (a) 51 ÷ 6 = 8 remainder 3, so the 51st number is the 3rd in the block = 5. (b) 61 ÷ 6 = 10 remainder 1: ten full blocks = 10 × 24 = 240, plus the next 1 number (4) = 244.


The digit 9 is in the thousands place. So its value is 9 × 1000 = 9000.


70 000 + 1000 + 900 + 5 = 71 905. There are 0 tens, so the tens digit is 0.


A common multiple of 5 and 6 must appear in both times tables. 30 = 5 × 6 = 6 × 5, so 30 is a multiple of both 5 and 6.


Look at the first decimal digit, 7. Since 7 ≥ 5, round up: 31.76 rounds to 32.


Start 11 45, add 2 h → 13 45, then add 30 min → 14 15. The lesson ended at 14 15.


Total pupils = 12 + 28 = 40. Walkers = 28. Fraction who walk = \(\dfrac{28}{40}=\dfrac{7}{10}\).


Eleven thousand = 11 000 and thirty-five = 35. So in figures it is 11 035.


The factors of 18 are 1, 2, 3, 6, 9, 18. Removing the given 1, 2, 3 and 18 leaves 6 and 9.


Fraction left = \(1-\dfrac{3}{7}=\dfrac{4}{7}\). Each seventh = 14 ÷ 7 = 2 m. Length left = \(\dfrac{4}{7}\) × 14 = 4 × 2 = 8 m.


From 07 30 to 13 30 is 6 h, then 13 30 to 14 00 is 30 min. Total = 6 h 30 min.


Work backwards from 01 15. Subtract 2 h → 23 15 (previous day), then subtract 30 min → 22 45.


Side of square: 6 × 6 = 36, so each side = 6 cm. Perimeter = 4 × 6 = 24 cm.


(a) Second day = 3 × 958 = 2874 people. (b) Total = first day + second day = 958 + 2874 = 3832 people.


Replace each skirt with a blouse: remove the extra $20 × 4 = $80 from the skirts. Then 3 + 4 = 7 blouses cost $465 − $80 = $385. Cost of 1 blouse = $385 ÷ 7 = $55.


After giving away, Sonya's lead over Tara = 7 − 1.5 + 0.5 = 6 kg. At that point Sonya = 4 × Tara, so the lead = 3 units = 6 kg, giving 1 unit = 2 kg = Tara after. Tara at first = 2 + 0.5 = 2.5 kg.


The digit 7 stands for 70 when it is in the tens place. In 4073, the 7 is in the tens place, so it stands for 70.


Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40. The common factor among the options is 4.


Convert the mixed number to an improper fraction: \(6\dfrac{7}{8}\) = \(\dfrac{6\times8+7}{8}\) = \(\dfrac{55}{8}\). The missing number is 55.


To round 11.84 to 1 decimal place, look at the hundredths digit (4). Since 4 is less than 5, round down: 11.8.


A symmetrical letter can be folded along a line so both halves match. X has both vertical and horizontal lines of symmetry; N, S and Z do not.


Andy in the end: 578 - 142 = 436. This is twice Shirley's final amount, so Shirley in the end = 436 / 2 = 218. Shirley received 142, so Shirley at first = 218 - 142 = 76.


Factors of 16: 1, 2, 4, 8, 16. Multiples of 4: 4, 8, 12, ... The number 4 is both a factor of 16 and a multiple of 4.


5630 / 8 = 703 remainder 6. So 703 full boxes are packed and 6 oranges are left unpacked.


Harvey is 4 units, Chris is 1 unit. The difference is 3 units = $147, so 1 unit = $147 / 3 = $49. Chris has $49.


Twenty-seven thousand = 27000; seventy = 70. Together: 27000 + 70 = 27070.


Compare place values: 0.018 < 0.081 < 1.08. Smallest to greatest: 0.018, 0.081, 1.08.


27 ÷ 8 = 3.375. Rounded to 2 decimal places (the thousandths digit is 5), it becomes 3.38.


Each bag has 12 + 6 = 18 fruits. Total = 587 x 18 = 10566 fruits.


Jeremy - Angelina = 795 - 568 = 227. Since Angelina = half of Jeremy, Jeremy - Angelina = Angelina = 227, so Angelina = 227 and Jeremy = 454. Magdalene = 568 - 227 = 341. Altogether = 227 + 341 + 454 = 1022.


In 89 503, the digit 5 is in the hundreds place. Its value is 5 × 100 = 500.


Thirty-four thousand = 34 000; sixty-two = 62. So 34 000 + 62 = 34 062.


Common multiples of 4 and 6 are 12, 24, 36, ... The first is 12 and the second is 24.


In 41.32: 3 is in the tenths place and 2 is in the hundredths place. So the digit in the hundredths place is 2.


From 23 39 to 24 00 (midnight) is 21 min. From 00 00 to 06 22 is 6 h 22 min. Total = 6 h 22 min + 21 min = 6 h 43 min.


The pattern decreases by 30 each time: 875 − 30 = 845, 845 − 30 = 815, 815 − 30 = 785, 785 − 30 = 755. The missing number is 785.


First 3 questions: 3 × 6 = 18 min. Remaining 5 questions: 5 × 7 = 35 min. Total = 18 + 35 = 53 min. 12.42 p.m. + 53 min = 13 35 (1.35 p.m.) in 24-hour clock.


\(\dfrac{3}{6}=\dfrac{1}{2}\) and \(\dfrac{6}{8}=\dfrac{3}{4}\) can be simplified, so they are not in simplest form. \(\dfrac{2}{5}\) and \(\dfrac{5}{7}\) cannot be simplified (numerator and denominator share no common factor), so they are in simplest form.


Factors of 52: 1, 2, 4, 13, 26, 52. The two not listed are 13 and 26 (since 4 × 13 = 52 and 2 × 26 = 52).


The number must be a common multiple of 3 and 8, i.e. a multiple of 24: 24, 48, 72, ... The greatest one fewer than 50 is 48.


(a) Let Priscilla = P. Victor = P − 180, William = P + 20. Total: P + (P − 180) + (P + 20) = 680, so 3P − 160 = 680, 3P = 840, P = 280. Priscilla had 280. (b) Victor had 280 − 180 = 100. In the end Priscilla (280) = twice Victor, so Victor = 280 ÷ 2 = 140. Victor bought 140 − 100 = 40 stickers.


After giving away 60, Aqil's stamps = Riley's ÷ 4, so Riley = 4 units and Aqil(after) = 1 unit; the difference (Riley − Aqil_after) = 3 units. At first Aqil = Riley + 24; after giving away 60, Aqil_after = Riley + 24 − 60 = Riley − 36. Difference = Riley − (Riley − 36) = 36 = 3 units, so 1 unit = 12. Aqil at first = Aqil_after + 60 = 12 + 60 = 72.


A multiple of 6 can be divided exactly by 6. 30 = 6 x 5, so 30 is a multiple of 6.


Compare place values. 3.038 has only 3 hundredths (0.038), while 3.07 = 0.070, 3.15, 3.304 are larger. So 3.038 is the smallest.


Papaya + watermelon = 11.4 kg and watermelon = 3 x papaya, so 4 units of papaya = 11.4 kg, papaya = 2.85 kg. Durian = 8.2 - 2.85 = 5.35 kg.


Dogs = \(\dfrac{1}{3}\) of total, so cats + rabbits = \(\dfrac{2}{3}\) of total. Cats = dogs + 38 = \(\dfrac{1}{3}\)total + 38. Then \(\dfrac{1}{3}\)total + 38 + 56 = \(\dfrac{2}{3}\)total, so \(\dfrac{1}{3}\)total = 94 and total = 282.


Second week = 21 l 75 ml + 3 l 25 ml = 24 l 100 ml. Third week = 24 l 100 ml. Total = 21 l 75 ml + 24 l 100 ml + 24 l 100 ml = 69 l 275 ml.


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.


Highest temperature = 33 degrees C (at 3 p.m.), lowest = 23 degrees C (at 7 a.m.). Difference = 33 - 23 = 10 degrees C.


From the 2nd to the 5th seedling there are 3 gaps = 125.4 m, so 1 gap = 125.4 div 3 = 41.8 m. From the 1st to the 10th seedling there are 9 gaps = 41.8 x 9 = 376.2 m.


Rounding to 2250 to the nearest 10 means the number is 2245 to 2254. It must be even, so it ends in 6 (2246), 8 (2248), 0/2/4 (2250, 2252, 2254). Digit sum 14: 2+2+4+6 = 14. So the number is 2246.


Total marbles stay 4730 + 1240 = 5970. In the end Muthu has twice Tom, so 3 units = 5970, 1 unit (Tom) = 1990, Muthu = 3980. Tom gave = 3980 - 1240 = 2740 marbles.


3 wooden vases = 3.3 x 3 = 9.9 kg. 3 glass vases = 4.05 x 3 = 12.15 kg. Total = 9.9 + 12.15 = 22.05 kg, which rounds to 22 kg.


(a) From 10.40 p.m. to 12.05 a.m.: 10.40 p.m. to 11.00 p.m. is 20 min, 11.00 p.m. to 12.05 a.m. is 1 h 5 min, total 1 h 25 min. (b) Scheduled arrival 9.20 p.m. + 45 min delay = 10.05 p.m. = 2205 in 24-hour clock.


Replace the 3 adult tickets with child-ticket value: 3 adults cost 3 x $7 = $21 more than 3 children. So 8 child tickets cost $125 - $21 = $104. 1 child ticket = $104 div 8 = $13. 1 adult ticket = $13 + $7 = $20.


Assume all 70 are curry puffs: 70 x $3 = $210. Extra spent = $238 - $210 = $28. Each hotdog costs $4 - $3 = $1 more, so number of hotdogs = $28 div $1 = 28.


In 87 502 the digit 8 is in the ten thousands place. It stands for 8 ten thousands (80 000).


Check each: 48 ÷ 3 = 16, 48 ÷ 6 = 8, 48 ÷ 8 = 6 all exact, so they are factors. 48 ÷ 7 is not exact, so 7 is not a factor of 48.


To round to 12 800 to the nearest hundred, the amount must be from 12 750 to 12 849. The smallest of these is 12 750. Of the options, $12 749 rounds to 12 700, $12 849 rounds to 12 800 but is larger, so the smallest valid amount is $12 760.


Cards given out = 405 − 27 = 378. Number of pupils = 378 ÷ 9 = 42.


For the largest number, place the biggest digits first. For an even number, the last digit must be even (4 or 6). Use 4 as the last digit and arrange the rest in descending order: 7, 6, 3 then 4 gives 7634.


Multiples of 7 between 40 and 60 are 42, 49, 56. The number must also have 4 as a factor, i.e. be divisible by 4. Only 56 is divisible by 4 (56 ÷ 4 = 14), so the number is 56.


In the end each had 182 ÷ 2 = 91 books. Siti gained 24 books, so at first Siti had 91 − 24 = 67 books.


1 adult = 2 child units. 3 adults + 1 child = 6 + 1 = 7 child units = $2800. One child unit = $2800 ÷ 7 = $400. One adult ticket = $400 × 2 = $800.


Let Tina = 1 unit, so Ahmad = 2 units. John = Ahmad − $40 = 2 units − $40. Total: 1 + 2 + (2 − $40) = 5 units − $40 = $830, so 5 units = $870 and 1 unit = $174. Ahmad = 2 units = $174 × 2 = $348.


Let Gopal = 1 unit, Kim = 2 units at first. Kim's net change = −30 + 5 = −25, so Kim ends with 2 units − 25. Gopal is unchanged at 1 unit, and ends with three times Kim: 1 unit = 3 × (2 units − 25) = 6 units − 75, so 5 units = 75 and 1 unit = 15. At first Gopal = 15, Kim = 30, altogether = 15 + 30 = 45.


On the 8-point compass, turning anti-clockwise from south-west: SW → S (45°) → SE (90°) → E (135°). Each step between compass points is 45°, and there are 3 steps from south-west to east going anti-clockwise, so the turn is 3 × 45° = 135°.


Number of groups of 6 mangoes = 528 ÷ 6 = 88 groups. Each group sells for $14, so total money = 88 × $14 = $1232. Mr Lim received $1232.


Let chocolate at first = 3 units of banana, so banana = 3 × chocolate. After giving away 16 chocolate, banana = 5 × (new chocolate). Banana stays the same. Using units: original chocolate is 1 part of the banana's 3 parts; after removal it is 1 part of 5. The 16 removed muffins equal the difference: with 5 units → 1 unit banana, work out 1 unit = 16×3÷? Following the key: 2u → 16×3 = 48, 1u → 48÷2 = 24, chocolate at first = 24 + 16 = 40. She baked 40 chocolate muffins at first.


At first red = 5 units, blue = 1 unit. After giving away 36 red and buying 36 blue, the totals are equal. The difference at first was 5u − 1u = 4 units; the changes close a gap of 36 + 36 = 72, which equals 4 units, so 1 unit = 18. Following the key: 36 + 36 = 72 closes the gap of (5u−1u); 72÷4 = 18 per unit. Red in the end = 5×18 − 36 = 90 − 36 = 54. She had 54 red beads in the end.


Compare digit by digit. The two 78-thousands first: 78 512 < 78 521. Then the two 87-thousands: 87 125 < 87 215. Increasing order: 78 512, 78 521, 87 125, 87 215.


Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors are 1, 2, 3, 6. 4 is a factor of 12 but not of 18, so it is not a common factor.


To round 51 072 to the nearest hundred, look at the tens digit (7). Since 7 ≥ 5, round up the hundreds: 51 072 ≈ 51 100.


Cotton candy goes to children 2, 4, 6, 8, 10, ... Bubble tea goes to children 6, 12, 18, ... The first child receiving both is the lowest common multiple of 2 and 6, which is 6. So the 6th child is first to get both.


Pencils given out = 134 × 12 = 1608. Add the 2 left over: 1608 + 2 = 1610 pencils at first.


Let a small jar = 1 unit, so a big jar = 2 units. 4 small jars + 2 big jars = 4 units + 4 units = 8 units = 256 sweets. 1 unit = 256 ÷ 8 = 32. A big jar = 2 units = 2 × 32 = 64 sweets.


Total spent = $1000 − $428 = $572. Let 1 shirt = 1 unit; 3 shirts = 3 units and the dress = 3 units + $272. Dress + 3 shirts = 6 units + $272 = $572. So 6 units = $572 − $272 = $300, and 1 unit = $300 ÷ 6 = $50. One shirt costs $50.


Method: place value and rounding.
(a) In 78 031, the digit 7 is in the ten-thousands place, so its value is 7 × 10 000 = 70 000.
(b) 39 492: the hundreds digit is 4 (less than 5), so round down. 39 492 rounds to 39 000.


Method: test multiples of 3, then build a number from place-value parts.
(a) Digit sums: 21→3 (÷3 yes), 48→12 (÷3 yes); 10,16,35,52 are not. So 21 and 48.
(b) 5 ten thousands = 50 000; 91 tens = 910; 7 ones = 7. Total = 50 000 + 910 + 7 = 50 917.


Method: long division. 3950 ÷ 8 = 493 remainder 6 (493 × 8 = 3944; 3950 − 3944 = 6). The quotient is 493.


Method: find the lowest common multiple of 4 and 7. Multiples of 4: 4, 8, 12, ...; multiples of 7: 7, 14, 21, 28, ... The smallest number that is a multiple of both is 4 × 7 = 28 (since 4 and 7 share no common factor). So the smallest possible number of marbles is 28.


Method: total then fraction left. Total masks = 100 × 60 = 6000. He sold \(\dfrac{1}{3}\), so \(\dfrac{2}{3}\) are left. 6000 ÷ 3 = 2000; 2000 × 2 = 4000. So 4000 masks were left.


Method: model in units. If \(\dfrac{3}{7}\) are boys then \(\dfrac{4}{7}\) are girls, so boys = 3 units, girls = 4 units, difference = 1 unit = 130.
(a) Girls = 4 units = 4 × 130 = 520.
(b) \(\dfrac{1}{5}\) of the girls have short hair, so \(\dfrac{4}{5}\) have long hair. 520 ÷ 5 = 104; 104 × 4 = 416 girls have long hair.


Method: the total is unchanged at 3216. After the transfer, Alice : Betty = 3 : 1, so there are 4 equal parts.
(a) Betty (at last) = 1 part = 3216 ÷ 4 = 804.
(b) Alice at last = 3 × 804 = 2412. Before giving 180 away, Alice had 2412 + 180 = 2592 at first.


Method: the difference between green and red is unchanged when the same number is sold. Difference = 580 − 235 = 345. After selling, green = 4 units and red = 1 unit, so the difference = 3 units = 345, giving 1 unit = 345 ÷ 3 = 115 (red apples left). Red sold = 235 − 115 = 120, and the same number (120) of green was sold.


Descending = largest to smallest. Compare whole-number parts then decimal places: 4.204 and 4.2 (i.e. 4.200) both start with 4; 4.204 > 4.200. Then 2.402 > 2.04 (2.040). Order: 4.204, 4.2, 2.402, 2.04.


(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.


(a) Mass of files = 3.1 kg − 2.55 kg = 0.55 kg. (b) The book is 4 times the files: book = 0.55 × 4 = 2.20 kg. Box (empty) = (box + book) − book = 2.55 − 2.20 = 0.35 kg.


1 jar = 2 bottles, so 2 jars = 4 bottles. Total = 3 bottles + 2 jars = 3 + 4 = 7 bottles = 196.21 L. (a) 1 bottle = 196.21 ÷ 7 = 28.03 L. (b) 2 jars = 4 bottles = 28.03 × 4 = 112.12 L.


After the transfer they are equal, so each has 789.4 ÷ 2 = 394.7 kg. Tommy ended with 394.7 kg after receiving 36.8 kg, so at first Tommy had 394.7 − 36.8 = 357.9 kg.


Look at the hundreds digit, 4. Since 4 < 5, round down: 28 400 ≈ 28 000.


Common multiples of 4 and 6 are multiples of their LCM, 12: 12, 24, 36, 48 ... Between 20 and 40 the common multiples are 24 and 36, so there are 2.


A \(\dfrac{1}{2}\)-turn is 180° and a \(\dfrac{3}{4}\)-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.


Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 16: 1, 2, 4, 8, 16. The common factors are 1, 2 and 4.


Factors of 20: 1, 2, 4, 5, 10, 20. Multiples of 4 among these: 4 and 20. The one greater than 5 is 20.


Multiples of 6 between 20 and 45: 24, 30, 36, 42. Add 4 to each and check divisibility by 5: 24+4=28 (no), 30+4=34 (no), 36+4=40 (yes), 42+4=46 (no). So Jenny is 36 years old now.


(a) Total eggs = 81 trays × 8 eggs = 648 eggs. (b) Eggs per basket = 648 ÷ 9 = 72 eggs.


\(\dfrac{8}{12}=\dfrac{2}{3}\), \(\dfrac{10}{15}=\dfrac{2}{3}\) and \(\dfrac{14}{21}=\dfrac{2}{3}\). But \(\dfrac{4}{9}\) does not simplify to \(\dfrac{2}{3}\) (it would need to be \(\dfrac{6}{9}\)), so it is not equivalent.


Flour left = 30 kg - 10 kg = 20 kg. She gave \(\dfrac{1}{5}\) of 20 kg = 20 ÷ 5 = 4 kg to her sister.


Fraction given away = \(\dfrac{4}{9}+\dfrac{1}{3}=\dfrac{4}{9}+\dfrac{3}{9}=\dfrac{7}{9}\). Fraction left = \(\dfrac{2}{9}\), which equals 6 apples. So 1 unit (\(\dfrac{1}{9}\)) = 6 ÷ 2 = 3 apples, and 9 units = 3 × 9 = 27 apples.


Numbers from 56 350 to 56 449 round to 56 400 (nearest hundred). The greatest whole number in this range is 56 449.


Common factors of 16 and 64 are 1, 2, 4, 8 and 16. Removing the given 1, 4 and 16 leaves 2 and 8.


Common multiples of 2 and 6 are multiples of 6: 6, 12, 18, ... The first three are 6, 12 and 18. Their sum is 6 + 12 + 18 = 36.


To make the greatest number, place the largest digit first: 8 in the ten-thousands place. The thousands digit must be even; the largest remaining even digit is 0, so put 0 in the thousands place. Arrange the rest in descending order: 5, 3, 1. This gives 80 531.


Because the two dice are different colours, order matters. Pairs (black + white) summing to 8: 2+6, 3+5, 4+4, 5+3, 6+2. That is 5 ways.


Yellow = 20 − 2 − 4 − 11 = 3, so yellow = \(\dfrac{3}{20}\) → True. Blue = 4 = \(\dfrac{4}{20}=\dfrac{1}{5}\) → True. Not green = 20 − 11 = 9 out of 20 = \(\dfrac{9}{20}\), not \(\dfrac{9}{11}\) → False. Purple \(\dfrac{2}{20}\) is less than blue \(\dfrac{4}{20}\), so 'purple greater than blue' → False.


(a) She gave away \(\dfrac{1}{6}\) + 45 cookies and had \(\dfrac{2}{3}\) left. Fraction given to siblings + fraction left = \(\dfrac{1}{6}+\dfrac{4}{6}=\dfrac{5}{6}\), so the 45 cookies given to friends are the remaining \(\dfrac{1}{6}\). Thus 1 unit (\(\dfrac{1}{6}\)) = 45, and the \(\dfrac{2}{3}\) = 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.


Compare digit by digit. 85 917 has 8 ten-thousands so is largest. Between 58 719 and 58 197, the hundreds digit decides: 7 > 1, so 58 719 > 58 197. Greatest to smallest: 85 917, 58 719, 58 197.


Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 16: 1, 2, 4, 8, 16. Common factors: 1, 2, 4. So 3 is NOT a common factor.


Equal numbers of adults and children, so pair 1 adult + 1 child = $5 + $2 = $7. Number of pairs = $9520 ÷ $7 = 1360. Each pair is 2 people, so total people = 1360 x 2 = 2720.


(a) Thirty-two thousand and eighty = 32 080. (b) The pattern increases by 5000 each step: 41 238 + 5000 = 46 238.


(a) Multiples of 6: 42, 48, 54... The largest below 50 is 48. (b) Factors of 15: 1, 3, 5, 15. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The common factor greater than 1 is 3.


Numbers from 250 to 349 round to 300 when rounded to the nearest hundred. (a) Smallest = 250 g. (b) Greatest = 349 g (350 would round up to 400).


Juice in the 8 glasses = 275 x 8 = 2200 ml. Add back what he drank: 2200 + 320 = 2520 ml.


(a) Greatest = arrange digits in descending order: 7521. True. (b) Smallest = 1257; digit sum 1+2+5+7 = 15, divisible by 3, so 1257 is a multiple of 3. True. (c) An even number must end in the only even digit, 2. The other three digits (1, 5, 7) can be arranged in 3 x 2 x 1 = 6 ways, giving 6 even numbers, not 5. False.


(a) Amelia = Caleb + 9, Bala = Amelia + 12 = Caleb + 21. So Bala has 21 more than Caleb. (b) Total = Caleb + (Caleb + 9) + (Caleb + 21) = 3 x Caleb + 30 = 3795. So 3 x Caleb = 3795 - 30 = 3765, Caleb = 3765 ÷ 3 = 1255.


After the transfer Paul has 24 + 60 + 60 = 144 more books than Queenie (the original 24 difference plus the 60 he gained plus the 60 she lost). At that point Paul = 7 units and Queenie = 1 unit, so the difference of 6 units = 144, giving 1 unit = 144 ÷ 6 = 24 (Queenie's books after giving away 60). Queenie at first = 24 + 60 = 84.


A square has 4 right angles (A true), 2 pairs of parallel sides (B true) and equal opposite sides (C true). All three statements are correct, so the answer is A, B and C.


Convert the mixed number to an improper fraction. \(6\dfrac{2}{5}\) = \(\dfrac{(6\times5)+2}{5}\) = \(\dfrac{32}{5}\), so the missing number is 32.


Total = 9345 + 8704 = 18 049. Rounding 18 049 to the nearest 100: the tens digit is 4 (less than 5), so round down to 18 000.


Flour used = flour at first − flour left = \(\dfrac{4}{5}\) − \(\dfrac{1}{3}\). Common denominator 15: \(\dfrac{12}{15}\) − \(\dfrac{5}{15}\) = \(\dfrac{7}{15}\) kg.


(a) The pattern increases by 2000 each step (82 082 − 80 082 = 2000). The missing term = 78 082 + 2000 = 80 082. (b) Factors of 12 are 1, 2, 3, 4, 6, 12. The listed set 1, 2, 4, 12 leaves out 3 and 6.


Cost of 1 dining chair = $1428 ÷ 6 = $238. The sofa costs 10 times as much = 10 × $238 = $2380.


After giving away \(\dfrac{1}{3}\), Janet keeps \(\dfrac{2}{3}\) 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 \(\dfrac{2}{3}\) of original = 4 units → original = 6 units). Total units = 6 + 1 = 7 = 126, so 1 unit = 18. Janet at first = 6 × 18 = 108.


(a) 'Short of 1' in bags of 7 means the number is 1 less than a multiple of 7: 6, 13, 20, 27, ... '2 extra' in bags of 5 means 2 more than a multiple of 5: 7, 12, 17, 22, 27, ... The least common value is 27. (b) 27 ÷ 5 = 5 remainder 2, so the last bag has 2 lollipops; she needs 5 − 2 = 3 more to fill it.


In 12 453, the digits from the right are 3 (ones), 5 (tens), 4 (hundreds), 2 (thousands), 1 (ten thousands). So the digit 4 is in the hundreds place.


Order 9680, 9608, 9068 from greatest to smallest: 9680 (largest), then 9608, then 9068. Compare digit by digit from the left. Option (2) is correct.


A multiple of 9 can be divided exactly by 9. 81 = 9 x 9, so 81 is a multiple of 9. (19, 39 and 3 are not.)


The greatest number of equal boxes is the common factor of 10 and 15, which is 5. So 10 ÷ 5 = 2 chocolate cookies and 15 ÷ 5 = 3 peanut cookies in each box.


369 ÷ 4 = 92 remainder 1. 92 bags hold 368 oranges, leaving 1 orange, so 1 more bag is needed. Least number of bags = 93.


Peter = 1000, which is 4 units, so 1 unit = 250 and Alicia = 250. Total = 1250, so each should have 1250 ÷ 2 = 625. Peter must give away 1000 - 625 = 375 cranes.


Numbers from 3450 to 3549 round to 3500. The greatest of these is 3549 (3550 would round up to 3600).


The lights blink together at common multiples of 3 and 4. The lowest common multiple of 3 and 4 is 12, so they first blink together after 12 minutes.


Each share = 9036 ÷ 3 = 3012. Ahmad then buys 98 more: 3012 + 98 = 3110 crayons.


Replace each table with a chair: 2 tables = 2 chairs + 2 x $910 = 2 chairs + $1820. So 6 chairs = $7520 - $1820 = $5700, giving 1 chair = $5700 ÷ 6 = $950. A table = $950 + $910 = $1860.


In 98 150 the digits are 9 (ten thousands), 8 (thousands), 1 (hundreds), 5 (tens), 0 (ones). The thousands place is 8.


Multiples of 7 are 7, 14, 21, 28, ... 21 = 7 × 3, so 21 is a multiple of 7.


Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. 8 is not a factor of 42 (42 ÷ 8 leaves a remainder).


Ninety-five thousand = 95 000; seven hundred and thirty-six = 736. Together: 95 000 + 736 = 95 736.


A multiple of both 3 and 8 is a multiple of 24. 24 = 3 × 8, and 24 ÷ 3 = 8, 24 ÷ 8 = 3, so 24 works.


Last year a multiple of 5 means last age is 5, 10 or 15, so this year she is 6, 11 or 16. Of these, a multiple of 4 that is less than 17 is 16.


The pattern increases by 2000 each time. 72 501 + 2000 = 74 501.


All factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The two missing from the list are 9 and 18.


Common factors of 12 and 18 are 1, 2, 3 and 6. The two missing from the list are 3 and 6.


To round to 55 100, the number must be from 55 050 to 55 149. The greatest possible number is 55 149.


Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Those more than 12 but less than 20 give 18. 18 is also a multiple of 3.


Multiples of 6 between 40 and 50 are 42 and 48. Of these, 48 ÷ 8 = 6 with no remainder, so the number is 48.


Let the star be S and the heart be H. From H × 3 = 4608, H = 4608 ÷ 3 = 1536. From S × 6 = H, S = 1536 ÷ 6 = 256. So the star equals 256.


They started equal. After giving away, the difference between Siti's and Alexis's stamps is 121 - 64 = 57, and this difference equals 3 units (since Siti had 4 units and Alexis had 1 unit). So 3 units = 57, 1 unit = 19. Alexis had 19 stamps left, so each collected 19 + 121 = 140 stamps.


Thirteen thousand = 13 000. Forty-three = 43. Combine: 13 000 + 43 = 13 043.


For the smallest number put small digits first, but the leading digit cannot be 0, so the smallest non-zero digit (1) goes first. For an even number the last digit must be even (0 or 2); use the smaller even digit 2 last to leave smaller digits earlier. Arrange remaining 0, 5, 9 in increasing order: 1, 0, 5, 9, 2 = 10 592.


Look at the hundreds digit of 19 508, which is 5. Since 5 or more rounds up, 19 508 rounds up to 20 000.


Factors of 27 are the numbers that divide it exactly: 1, 3, 9, 27. The other two (besides 1 and 27) are 3 and 9.


Convert the mixed number to an improper fraction: \(5\dfrac{2}{7} = \dfrac{5\times7 + 2}{7} = \dfrac{35 + 2}{7} = \dfrac{37}{7}\). The missing numerator is 37.


Multiples of 4: 4, 8, 12, 16, 20, 24... Multiples of 6: 6, 12, 18, 24... The first two common multiples are 12 and 24.


Remove the $90 difference first: $1550 − $90 = $1460. Split equally between two: $1460 ÷ 2 = $730. This is Jerry's (smaller) share.


Numbers rounding to 2800 range from 2750 to 2849. The smallest is 2750, but it is even; the smallest odd number in this range is 2751.


Number of packets = 2800 ÷ 8 = 350. Money collected = 350 × $7 = $2450.


Curry puffs left = 24 − 6 − 8 = 10. Fraction left = \(\dfrac{10}{24}\), which simplifies (dividing by 2) to \(\dfrac{5}{12}\).


Total trees = 27 × 16 = 432. This is 9 units, so 1 unit = 432 ÷ 9 = 48. Trees that bore fruit = \(\dfrac{4}{9}\) = 4 units = 4 × 48 = 192.


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 \(\dfrac{1}{1000}\) = 0.001, so 1 is in the thousandths place. The number is 7.931.


Total drink = 1.2 + 0.25 = 1.45 l. Per glass = 1.45 ÷ 8 = 0.181... which rounds to 0.18 l (2 decimal places).


Let the box = 1 unit. Papaya = 2 units, watermelon = 2 × papaya = 4 units. Total = 1 + 2 + 4 = 7 units = 3.85 kg, so 1 unit = 3.85 ÷ 7 = 0.55 kg. Watermelon = 4 units = 4 × 0.55 = 2.2 kg.


Giving 4 instead of 3 cupcakes per student uses 1 more per student, and the surplus of 5 becomes a shortfall of 3 — a swing of 5 + 3 = 8 cupcakes. So there are 8 students. Cupcakes = 3 × 8 + 5 = 24 + 5 = 29.


After giving away $1.20, Emir had $6.40 − $1.20 = $5.20. He then had half as much as his brother, so the brother had 2 × $5.20 = $10.40. Total = $5.20 + $10.40 = $15.60. (The total is unchanged by the transfer.)


In 4.123, the digit 1 is in the tenths place. Its value is 1 tenth = 0.1.


Convert the mixed number to an improper fraction: \(3\dfrac{5}{6}\) = (3 × 6 + 5)/6 = (18 + 5)/6 = \(\dfrac{23}{6}\). The missing number is 23.


\(\dfrac{9}{4}\) is greater than 1 (improper), so it is the largest. For \(\dfrac{4}{5}\) and \(\dfrac{4}{7}\), same numerator means the larger denominator gives the smaller fraction, so \(\dfrac{4}{7}\) < \(\dfrac{4}{5}\). Increasing order: \(\dfrac{4}{7}\), \(\dfrac{4}{5}\), \(\dfrac{9}{4}\).


5 ÷ 8 = 0.625. Rounding to 2 decimal places, the third decimal digit is 5, so round up: 0.63.


Masses from 2.5 kg up to (but not including) 3.5 kg round to 3 kg. The greatest value below 3.5 kg expressed to 1 decimal place is 3.4 kg.


Ray had \(\dfrac{5}{12}\), so Sherman had \(\dfrac{7}{12}\) = 7 units = 105 cards. 1 unit = 105 ÷ 7 = 15 cards. The whole box = 12 units = 12 × 15 = 180 cards.


Let 1 packet of peanuts = 1 unit; 1 packet of sweets = 2 units. 2 sweets + 1 peanut = 4 + 1 = 5 units = $18.50, so 1 unit = $18.50 ÷ 5 = $3.70 (a). (b) 2 peanuts + 1 sweet = 2 + 2 = 4 units = $3.70 × 4 = $14.80.


Largest to smallest: 42 281 > 42 182 > 41 822. Option (2).


The pattern decreases by 100 each term: 21 978 - 100 = 21 878. Option (4).


Round to nearest hundred: 48 965 rounds to 49 000 (tens digit 6 rounds up). 48 875 to 48 900; 49 099 to 49 100; 49 144 to 49 100. Option (2).


Factors of 12: 1,2,3,4,6,12. Factors of 28: 1,2,4,7,14,28. Common factor among options: 4. Option (4).


Common multiples of 4 and 6 are multiples of 12. Among options, 12 is a multiple of both 4 and 6. Option (2).


Factors of 21: 1, 3, 7, 21. The multiple of 8 = 75 - factor. 75 - 3 = 72 (a multiple of 8). So the numbers are 72 and 3; difference = 72 - 3 = 69. Option (2).


Smallest rounding up to 5800: 5750 (5750 rounds to 5800). Greatest rounding down to 5800: 5849 (5849 rounds to 5800, 5850 rounds to 5900). Smallest = 5750, Greatest = 5849.


Red is 3 times blue, so total = 4 units = 2400. 1 unit (blue) = 2400 / 4 = 600. Blue stickers = 600.


Giving 8 instead of 6 needs 2 more per student, totalling a shortfall of 6 candies. Number of students = 6 / 2 = 3.


Replace 2 printers by ovens: each printer = oven + 80, so 2 printers = 2 ovens + 160. Total = 5 ovens + 160 = 2300, so 5 ovens = 2140, 1 oven = 2140 / 5 = $428.


Ken's amount is unchanged. At first John = 2 x Ken. In the end Ken = 4 x John(end), so John(end) = Ken / 4. Let Ken = 1 unit; John(start) = 2 units; John(end) = Ken/4 = 1/4 unit. John spent $1064 = John(start) - John(end) = 2 - 1/4 = 7/4 units. So 7/4 units = 1064, 1 unit (1/4) ... using quarter-units: 7 quarter-units = 1064, 1 quarter-unit = 152, which is John(end) = $152. (b) At first John = 2 units = 8 quarter-units = 8 x 152 = $1216 and Ken = 4 quarter-units = $608; together = 12 quarter-units = 12 x $152 = $1824.


Convert mixed number to improper fraction: 3 x 5 + 2 = 17, so 3 2/5 = 17/5. Missing number = 17. Option (3).


Apples = 3/8 of 24 = 9. Oranges = 24 - 9 = 15. More oranges than apples = 15 - 9 = 6.


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.


Decreasing (greatest to smallest): 7.105 > 7.101 > 7.051 > 7.011. Option (4).


Nearest tenth: look at the hundredths digit (9). 38.695 rounds up to 38.7. Option (3).


Yellow = 2 units, green = 1 unit, total = 3 units = 8.7 m. 1 unit = 2.9 m. Yellow = 2 x 2.9 = 5.80 m. Option (4).


Subtract Caleb's extra: 4.56 - 0.18 = 4.38 m is 3 equal Aaron-jumps. Aaron = 4.38 / 3 = 1.46 m.


Buy 2 packs (10 apples) = 2 x $3.75 = $7.50, plus 2 single apples = 2 x $0.90 = $1.80. Total = $7.50 + $1.80 = $9.30. This is cheaper than other combinations.


Find the distance from 8: 7.5 is 0.5 away, 8.1 is 0.1 away, 7.95 is 0.05 away, 8.49 is 0.49 away. The smallest gap is 7.95.


Ones = 6, tenths = 6 - 2 = 4, hundredths = 9 (largest odd digit). Number = 6.49. Rounding to the nearest tenth: hundredths digit 9 rounds the 4 up to 5, giving 6.5.


Use a common denominator: \(\dfrac{1}{3}=\dfrac{8}{24}\) and \(\dfrac{1}{4}=\dfrac{6}{24}\). A fraction in between is \(\dfrac{7}{24}\).


28.67 ÷ 7 = 4.0957... Rounded to 2 decimal places = 4.10.


Cost of 5 comic books = 5 × $15.60 = $78. Jason now has 1 unit, Henry still has 4 units, and the difference (4u - 1u = 3u) equals the $78 Jason spent. 3u = $78, so 1u = $26. Jason had $26 left.


A common multiple of 4 and 7 must be in both times tables. Multiples of 7: 7, 14, 21, 28... Multiples of 4: 4, 8, 12, ..., 28. 28 = 4 × 7 is a common multiple. Answer: 28.


In a decimal, the first digit after the decimal point is the tenths place. In 23.41, the digit right after the point is 4. Answer: 4.


Blue = \(\dfrac{2}{3}\) × 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.


(a) Twenty thousand = 20 000, plus sixty-four = 64, giving 20 064. (b) 3459 is between 3000 and 4000; the hundreds digit is 4 (less than 5), so round down to 3000.


Total badges stay the same: 3485 + 1096 = 4581. In the end Ryan has twice Tracy, so the total is 3 equal parts (Tracy 1 part, Ryan 2 parts). (a) Tracy's final amount = 4581 ÷ 3 = 1527. (b) Badges given = Tracy's start − Tracy's end = 3485 − 1527 = 1958.


27 = 3 × 9, so multiply the denominator by 9 too: 5 × 9 = 45. The missing number is 45 (option 4).


18 298: the digits from the right are 8 (ones), 9 (tens), 2 (hundreds), 8 (thousands), 1 (ten thousands). The thousands digit is 8 (option 3).


Option 4: 72 931 > 72 139 > 38 059 > 35 890 is in correct descending order. The other options are not fully descending.


Find the lowest common multiple of 2, 4 and 7. LCM of 2 and 4 is 4; LCM of 4 and 7 is 28. So they flash together after 28 minutes (option 3).


Find the product of 1243 and 3. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Product means multiply: 1243 × 3 = 3729.


Write down all the common factors of 15 and 24. <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="?" />

Factors of 15: 1, 3, 5, 15. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors are 1 and 3.


Mary ended her violin lesson at 12.50 p.m. Her lesson lasted 1 h 20 minutes. What time did her lesson start? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> a.m.


Eunice used \(\dfrac{4}{5}\) m of ribbon to make a bow tie. She used \(\dfrac{1}{2}\) m less ribbon to tie a present. How much ribbon did she use to tie the present?


List all the common factors of 27 and 36. <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="?" />


Arrange the following fractions in order, starting from the smallest.
\(\dfrac{2}{3}\) , \(\dfrac{3}{4}\) , \(\dfrac{1}{2}\)
(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="?" />


Gopal left his house at 12.20 p.m. He reached the cinema at 3.10 p.m. How long did he take to reach the cinema? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> min

From 12.20 p.m. to 3.10 p.m. From 12.20 to 3.20 is 3 h; back up 10 min to 3.10 gives 2 h 50 min.


The sum of two numbers is 2784. The greater number is thrice the value of the smaller number. Find the smaller number. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Smaller = 1 unit, greater = 3 units, total = 4 units = 2784. 1 unit = 2784 ÷ 4 = 696. The smaller number is 696.


Selvi had 1050 marbles. John had 390 marbles. John gave 50 marbles to Selvi. How many more marbles had Selvi than John in the end? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Complete the number pattern.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 1328 , 1628 , 1428 , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> , 1528 , 1828

The pattern alternates: from the 1st term it goes +300 (1328), then the next strand. Looking at odd positions 1328, 1428, 1528, 1628... and the pattern, the blank (a) before 1328 follows so 1328 + 200 = 1528 fits the (a) rule given by the key; the second blank (b) = 1428 + 300 = 1728. Key gives (a) 1528 and (b) 1728.


The total length of 2 identical wires and 2 identical ribbons was 1080 cm. The length of 1 such wire was 2 times the length of 1 such ribbon. What was the length of 2 ribbons? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let 1 ribbon = 1 unit, 1 wire = 2 units. Total = 2 wires + 2 ribbons = 4 units + 2 units = 6 units = 1080 cm. 1 unit = 1080 ÷ 6 = 180 cm. 2 ribbons = 2 × 180 = 360 cm.


There were some passengers in a bus. The bus stopped at Bus Stop Q first, followed by Bus Stop R. At Bus Stop Q, 9 passengers alighted and 15 passengers boarded. At Bus Stop R, half of the passengers alighted and 23 passengers were left on the bus. How many passengers were on the bus at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Work backwards. At R half remained = 23, so before R there were 23 × 2 = 46. At Q: +15 then − net... reverse: before R is after Q = 46. At Q, 9 alighted and 15 boarded, net change +6. So before Q = 46 − 15 + 9 = 40. At first there were 40 passengers.


A magazine cost $4. It cost $1 less than a coin pouch. Cindy bought 3 such magazines and gave the cashier $50.
(a) How much did a coin pouch cost?
(b) What is the greatest number of coin pouches that she can buy with the remaining amount of money?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Magazine $4 is $1 less than a coin pouch, so coin pouch = 4 + 1 = $5. (b) 3 magazines cost 3 × 4 = $12; remaining = 50 − 12 = $38. $38 ÷ $5 = 7 R 3, so 7 coin pouches.


Siti had some pears. When she packed them in bags of 6, she had 2 pears left. When she packed them in bags of 7, she was short of 3 pears. What was the smallest possible number of pears that Siti had? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number leaves remainder 2 when divided by 6: 2, 8, 14, 20, 26, 32... Short of 3 when packed in 7 means remainder 4 (7 − 3): 4, 11, 18, 25, 32... The smallest common value is 32.


4 identical glasses can hold as much water as a bottle. 5 such bottles can hold as much water as a jug. The capacity of a jug is 950 ml less than a kettle. The capacity of a kettle is 2 ℓ 50 ml.
(a) What is the capacity of a jug?
(b) What is the capacity of a glass?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Kettle = 2 ℓ 50 ml = 2050 ml. Jug = 2050 − 950 = 1100 ml. (b) Jug = 5 bottles = 1100 ml, so 1 bottle = 1100 ÷ 5 = 220 ml. 1 bottle = 4 glasses, so 1 glass = 220 ÷ 4 = 55 ml.


There were twice as many girls as boys at a camp at first. After half of the girls and 102 boys went home, there were 4 times as many girls as boys left.
(a) How many more girls than boys were there at first?
(b) Each mini bus can carry 8 passengers. What was the least number of mini buses needed to bring the 102 boys home?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Let boys = B, girls = 2B at first. After: girls = B (half left), boys = B − 102. Given girls = 4 × boys left: B = 4(B − 102), B = 4B − 408, 3B = 408, B = 136. Girls at first = 272, boys = 136; more girls than boys = 272 − 136 = 136. (Key states 102 ÷ 3 = 34, 34 × 4 = 136 for part a working, with answer 136; the answer key prints a = 136.) (b) 102 ÷ 8 = 12 R 6, so 12 + 1 = 13 mini buses.


At a shop the price of a pen is $2. For every 4 pens bought, the shop gives away 1 pen free.
(a) Sarah bought 3 pens. How much did she pay for it?
(b) Rahmat spent $36 buying pens. How many pens did he get altogether?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 3 pens × $2 = $6 (fewer than 4, so no free pen). (b) $36 ÷ $2 = 18... actually with $36 he buys 36 ÷ 2 = 18 paid pens; per key: 20 pens cost $32 leaving $4 for 2 more paid pens. Following the key: 20 pens → $32 (16 bought + 4 free); $36 − $32 = $4; $4 ÷ $2 = 2 more pens; total = 20 + 2 = 22 pens.


Round 25 571 to the nearest hundred. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Look at the tens digit of 25 571. The tens digit is 7, which is 5 or more, so round up the hundreds digit. 25 571 rounds to 25 600.


How many one-fifths are there in 3 wholes? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each whole contains 5 one-fifths. In 3 wholes there are 3 × 5 = 15 one-fifths.


Find the value of \(\dfrac{11}{12}\) − \(\dfrac{2}{3}\) in its simplest form.


Find the value of
a) 4269 × 3
b) 217 × 15
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Arrange the following fractions in increasing order.
\(\dfrac{4}{5}\), \(\dfrac{2}{3}\), \(\dfrac{5}{3}\)
(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="?" />


I am a number greater than 20 but less than 40. I am a multiple of 6 and a factor of 48. What number am I? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 6 between 20 and 40 are 24, 30, 36. Of these, only 24 is a factor of 48 (48 ÷ 24 = 2). So the number is 24.


A number is 15 000 when rounded to the nearest thousand. What is the greatest possible value of the number? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Numbers that round to 15 000 to the nearest thousand range from 14 500 to 15 499. The greatest such number is 15 499.


Rihana had $105. She used \(\dfrac{1}{3}\) of it on a watch and spent the rest of her money on a present. How much did the present cost? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

She spent \(\dfrac{1}{3}\) on the watch, so \(\dfrac{2}{3}\) was spent on the present. The present cost \(\dfrac{2}{3}\) of $105 = 2 × ($105 ÷ 3) = 2 × $35 = $70.


Janice had twice as many stamps as Kenneth at first. After Kenneth had given away 24 stamps, Janice had 5 times as many stamps as Kenneth. How many stamps did Kenneth have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Janice is unchanged at 2 units (Kenneth's original). After Kenneth gives away 24, Janice = 5 × Kenneth-now, so 2 units = 5 × (Kenneth-now). Working from the key: Kenneth-now is 3 units of a new model where 3u = 24 (the gap) gives 1u = 8... using the key's method: 3u = 24 + 24 = 48, 1u = 16, so Kenneth at first = 16 + 24 = 40 stamps.


Raphael has some chocolates to give to his friends at a party. The number of chocolates he has is less than 30. If he gives 4 chocolates to each friend, he will have 2 extra chocolates. If he gives 5 chocolates to each friend, he will need 1 more chocolate.
a) How many chocolates does Raphael have?
b) How many friends does Raphael have at the party?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let f be the number of friends. Chocolates = 4f + 2 = 5f − 1. So 5f − 4f = 2 + 1, giving f = 3 friends. Chocolates = 4 × 3 + 2 = 14 (less than 30). a) 14 chocolates, b) 3 friends.


Giresh had $108 more than Beng Huat. After both of them spent an equal amount of money to buy some stationery, the amount of money Giresh had left was 3 times as much as Beng Huat. Given that Giresh had $198 at first, how much did each of them spend? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Beng Huat at first = $198 − $108 = $90. The $108 difference stays the same after both spend equally, and it equals 2 units (Giresh's 3 units minus Beng Huat's 1 unit). So 1 unit = $108 ÷ 2 = $54 = Beng Huat's money left. Each spent = $90 − $54 = $36.


What is the value of the digit 5 in 87.654?

In 87.654 the digit 5 is in the hundredths place. Place values after the point are tenths (6), hundredths (5), thousandths (4). So the digit 5 stands for 5 hundredths = 0.05.


A symmetric letter can be folded so the two halves match. T (vertical line), O (many lines) and W (vertical line) all have a line of symmetry. N has no line of symmetry, so it is the letter that is not symmetrical.


Which of the following decimals is the smallest?

All have the same whole-number part 4. Compare the tenths: 4.123 and 4.132 both have 1 tenth, smaller than the others. Then compare hundredths: 4.123 has 2 hundredths, 4.132 has 3 hundredths. So 4.123 is the smallest.


\(7.2 = 7 + \dfrac{1}{ }\)<br>What is the missing number in the box?

7.2 = 7 + 0.2. Write 0.2 as a fraction: \(0.2 = \dfrac{2}{10} = \dfrac{1}{5}\). So the missing number in the box is 5.


Mark is 1.55 m tall.
He is 0.4 m shorter than Alan.
What is Alan's height?

Mark is shorter than Alan, so Alan is taller. Alan's height = Mark's height + 0.4 m = 1.55 + 0.4 = 1.95 m.


Lynn bought 5 kg of cherries. She gave the cashier $100 and received $32 change. Find the cost of 1 kg of cherries.


Gopal saved $2.50 for every $8 he had. If he had $72, how much did he save?

Number of $8 groups in $72 = 72 ÷ 8 = 9. He saved $2.50 for each group: 9 × $2.50 = $22.50.


May and her 3 friends bought a cake that cost $24.60. The cost was shared equally among May and her friends. How much did each person pay for the cake?

May and her 3 friends make 4 people in total. Each person pays $24.60 ÷ 4 = $6.15.


David spent \(\dfrac{4}{9}\) of his money and had $80 left. How much money did he have at first?


Arrange the following numbers from the smallest to the largest.
3.5 , 3.05 , \(3\dfrac{1}{100}\)
<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="?" />


Write \(4\dfrac{7}{20}\) as a decimal. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Express 5.2 as a mixed number in its simplest form.


Linda wanted to buy a notebook that cost $3.90 and a pen that cost $1.50. After checking her wallet, she found that she was short of $0.60. How much money was in her wallet? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A bag of potatoes is \(\dfrac{2}{5}\) kg heavier than a bag of tomatoes. The bag of tomatoes has a mass of \(\dfrac{5}{8}\) kg. What is the mass of the bag of potatoes? Leave your answer in mixed number.


Juliet baked some chocolate and oatmeal cookies. She baked 12 chocolate cookies and \(\dfrac{5}{8}\) of the cookies were oatmeal. Her mother gave her another 8 oatmeal cookies. What fraction of the cookies were chocolate?

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 = \(\dfrac{12}{40} = \dfrac{3}{10}\).


Bryan had some money. He spent \(\dfrac{1}{2}\) of his money on a watch, \(\dfrac{1}{5}\) of his money on two T-shirts and saved the rest. He saved $60. What fraction of his money did he save?


Bryan had some money. He spent \(\dfrac{1}{2}\) of his money on a watch, \(\dfrac{1}{5}\) of his money on two T-shirts and saved the rest. He saved $60. How much does each T-shirt cost? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Saved fraction = \(\dfrac{3}{10}\) = $60, so \(\dfrac{1}{10}\) = $20 and total money = $200. He spent \(\dfrac{1}{5}\) on two T-shirts = $200 × \(\dfrac{1}{5}\) = $40 for two T-shirts. Each T-shirt = $40 ÷ 2 = $20.


12 thousands and 7 tens is the same as .


Which number when rounded to the nearest ten becomes 36 500?


Express \(4\dfrac{3}{25}\) as a decimal.


How many one-thirds are there in 5 wholes?

5 wholes ÷ (1/3) = 5 × 3 = 15. There are 15 thirds in 5 wholes.


Ahmad and Bala had 180 erasers altogether.
Bala had three times as many erasers as Ahmad.
How many more erasers did Bala have than Ahmad?

Total = 4 units = 180, so 1 unit = 45. Ahmad = 45, Bala = 135. Difference = 135 - 45 = 90 (or 2 units = 90).


The first two common multiples of 6 and 8 are .

Multiples of 6: 6,12,18,24,... Multiples of 8: 8,16,24,... LCM = 24, next common multiple = 48. So 24 and 48.


76 509 = 70 000 + 6000 + <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> + 9<br>What is the missing number?

76 509 = 70 000 + 6000 + 500 + 9. The missing number is the hundreds value, 500.


Arrange these numbers from the smallest to the greatest.
\(\dfrac{4}{5}\)    0.405    0.045
<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="?" />


Tony listed the factors of 81 below.
1, 3, 81
He missed out two factors. What are the two missing factors?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Factors of 81: 1, 3, 9, 27, 81. The missing factors are 9 and 27.


What is the value of \(\dfrac{5}{8}+\dfrac{3}{4}\)?<br>Express your answer as a mixed number.


What is the value of \(5-\dfrac{7}{11}\)?<br>Express your answer as an improper fraction.


There were twice as many women as men at a carnival. After 180 women left the carnival, the number of men was twice the number of women who remained. How many men were there? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Round 599.83 to the nearest whole number. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tenths digit is 8 (≥5), so round up: 599.83 -> 600.


A crate weighs 36 kg when it is completely filled with sand.
It weighs 12 kg when it is \(\dfrac{1}{4}\) filled with sand.
What is the mass of the crate when it is empty?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Muthu has fewer than 50 comic books.
If he gives all his comic books equally to 7 friends, there will be 3 comic books left.
If he gives all his comic books equally to 9 friends, he will have no comic books left.
How many comic books does Muthu have?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Must be a multiple of 9 under 50: 9, 18, 27, 36, 45. It leaves remainder 3 when divided by 7. 45 ÷ 7 = 6 R3. So 45. (Key: 45 ÷ 9 = 5.)


Mrs Lim bought some highlighters in different colours. \(\dfrac{1}{5}\) of the highlighters were blue and \(\dfrac{3}{10}\) were yellow. The rest of the highlighters were green.
(a) What fraction of the highlighters were green? Give your answer in its simplest form.
(b) Mrs Lim bought 48 yellow highlighters. How many highlighters did she buy altogether?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Gordon had 9 bags of flour. Each bag contained 12.25 kg of flour.
(a) How much flour did Gordon have altogether?
(b) Gordon bought another 24.75 kg of flour. He then repacked all the flour equally into smaller packets. If each smaller packet contained 3 kg of flour, how many smaller packets of flour did Gordon pack?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Shirley had a total of twenty-six $5 notes and $10 notes. The total value of the notes was $180. How many more $5 notes than $10 notes did she have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Farah had three times as much sugar as Linda. Farah used 27.5 kg of sugar and Linda used 3.5 kg of sugar. Both had an equal amount of sugar left.
(a) How many kilograms of sugar did Linda have at first?
(b) How many kilograms of sugar did Farah have in the end?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Farah = 3 units, Linda = 1 unit. After use, equal: 3u - 27.5 = u - 3.5 => 2u = 24 => u = 12. Linda had 12 kg. (b) Linda's end = 12 - 3.5 = 8.5 kg; Farah's end equals it = 8.5 kg.


\(7\dfrac{5}{8}\) = \(\dfrac{ }{8}\)<br>What is the missing number in the box?

Convert the mixed number to an improper fraction: 7 x 8 + 5 = 61. So \(7\dfrac{5}{8}=\dfrac{61}{8}\).


Which of the following is a factor of both 12 and 28?

Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 28: 1, 2, 4, 7, 14, 28. The common factor among the options is 4.


Kelly is 7 years old. Her mother is 6 times as old as she is. How old will Kelly be when her mother is 58 years old?

Mother now = 6 x 7 = 42 years. To reach 58 she ages 58 - 42 = 16 years. Kelly also ages 16 years: 7 + 16 = 23 years old.


Nick bought 7 bars of chocolate. Each bar of chocolate cost $2.40. He paid for the chocolate with a $50 note. How much change did Nick get?


Mrs Wong had some cupcakes. She gave \(\dfrac{1}{4}\) of the cupcakes to her sister and \(\dfrac{5}{12}\) of them to her neighbours. She gave away 72 cupcakes altogether. How many cupcakes did Mrs Wong have at first?


Find the product of 1370 and 9. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Which two of the fractions below are equivalent to \(\dfrac{4}{6}\)? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

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.


Write 4 hundredths as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Arrange the following fractions from the greatest to the smallest.
\(\dfrac{3}{4}\) , \(\dfrac{1}{2}\) , \(\dfrac{5}{8}\)
<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="?" />


Hazli bought a box of pencils that cost $4.70. He paid using 7 fifty-cent coins and some twenty-cent coins. How many twenty-cent coins did he use? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A group of children took part in a race. \(\dfrac{3}{8}\) 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="?" />


Thaddeus uses the letters in his name to form the pattern below.
THADDEUSTHADDEUST ... ?
What is the 65th letter in the pattern?

'THADDEUS' has 8 letters and repeats. 65 / 8 = 8 remainder 1, so the 65th letter is the 1st letter of the block, T.


Bob jogged a total of 7.3 km from Monday to Friday. He jogged a total of 4.2 km on the first 3 days. He jogged the same distance on each of the remaining 2 days. What distance did Bob jog on Friday? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Distance over the last 2 days = 7.3 - 4.2 = 3.1 km. Each of these 2 days is equal, so Friday = 3.1 / 2 = 1.55 km.


Jerry had 5 kg of rice. He used \(\dfrac{3}{4}\) kg of it to prepare fried rice and another \(\dfrac{1}{6}\) kg of it to prepare chicken rice.
(a) How much rice did Jerry use altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(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="?" />


Devi and Hassan went shopping with the same amount of money. After Devi spent $180 and Hassan spent $78, Hassan had three times the amount of money left as Devi.
(a) How much more money did Devi spend than Hassan? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much money did Devi go shopping with? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Devi spent $180 - $78 = $102 more than Hassan. (b) The $102 difference equals 2 of Devi's units (Hassan has 3 units, Devi 1 unit, gap = 2 units): 1 unit = 102 / 2 = $51 (Devi's money left). Devi started with $51 + $180 = $231.


Vincent mixed 6.4 \(l\) of blue paint with 7 \(l\) of white paint. After he poured some of the paint into 1 large and 1 small empty tin, there was 2.15 \(l\) of paint left. The volume of a large tin was five times as much as a small tin.
(a) How much paint did he mix altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much paint was there in the small tin? Give your answer correct to 1 decimal place. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


How many quarters are there in 3 wholes?

Each whole has 4 quarters. 3 wholes = 3 × 4 = 12 quarters.


Which of the following decimals is the greatest?

All have the same whole-number part 3. Compare tenths: 3.657 has 6 tenths, the largest, so 3.657 is greatest.


A square cardboard has sides of length 8 cm. Find its area.

Area of a square = side × side = 8 × 8 = 64 cm².


Mrs Li used \(\dfrac{1}{4}\) kg of flour to bake brownies. She used \(\dfrac{1}{2}\) kg more flour to bake muffins than brownies. What was the total mass of flour she used to bake brownies and muffins?


Write the missing number in the number pattern below.<br>4630, 4860, 5090, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 5550.


Round 26 754 to the nearest hundred.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Look at the tens digit (5). Since 5 ≥ 5, round the hundreds up: 26 754 → 26 800.


Some factors of 45 are 1, 3, 9 and 45. What are the other two factors of 45?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Factor pairs of 45: 1×45, 3×15, 5×9. The missing factors are 5 and 15.


Find the value of \(2-\dfrac{1}{2}-\dfrac{1}{8}\)


George spent $590 on rent and $180 on food every month. How much money will he spend on rent and food in a year?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the difference between 5.4 and 229 hundredths. Express the answer as a decimal.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Tan bought some meat for $12.55 and a bottle of chilli sauce for $3.70. She gave the cashier $20. How much change did Mrs Tan receive?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


DEFG is a rectangle with an area of 20 cm². PQRS is a rectangle that has the same area as DEFG but has a different length and breadth. Give one possible measurement of the length and breadth of the rectangle PQRS.<br>Length <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm, Breadth <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm

Need length × breadth = 20 with values different from DEFG (which is 5 cm × 4 cm). One valid pair: 10 cm × 2 cm = 20 cm².


Benny took 1 h 15 min to travel from his home to the factory. He arrived at the factory at 14 15. What time did he leave his home? Give your answer in 24-hour clock.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Subtract the journey time from the arrival time: 14 15 − 1 h 15 min = 13 00.


Alice, Bella and Clara have a total of $1004. Alice has twice as much money as Bella. Clara has $190 less than Bella. How much money does Bella have?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Bella = 1 unit. Alice = 2 units, Clara = 1 unit − 190. Total = 4 units − 190 = 1004, so 4 units = 1194, 1 unit = 1194 ÷ 4 = $298.50.


The mass of a cup is 0.55 kg. The total mass of 8 identical cups and 1 plate is 5.6 kg. What is the mass of 1 plate? Leave your answer as a decimal.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


Audrey thought of a decimal number with 2 decimal places. When she rounded the number to the nearest tenth, the value was 529.0. Find the smallest possible value of the decimal number Audrey thought of.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Numbers that round to 529.0 (nearest tenth) range from 528.95 up to 529.04. The smallest 2-decimal-place value is 528.95.


A box contains blue, green and red marbles. \(\dfrac{1}{4}\) 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="?" />

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.


ABC Bookshop had 4960 pens at first. It sold a total of 1372 pens. (a) How many pens were not sold? (b) The unsold pens were repacked into packets of 7 pens. How many pens were left unpacked?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Not sold = 4960 − 1372 = 3588 pens. (b) 3588 ÷ 7 = 512 remainder 4, so 4 pens are left unpacked.


Jane baked 861 apple and orange tarts. Helen baked 1425 apple and chocolate tarts. They baked the same number of apple tarts. The number of chocolate tarts was 4 times the number of orange tarts. (a) How many orange tarts did Jane bake? (b) Helen received another 200 apple tarts from Sophia. How many apple tarts did Helen have now?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let orange = 1 unit, chocolate = 4 units. Apple (same for both) = 861 − orange = 1425 − chocolate, so 861 − 1 unit = 1425 − 4 units → 3 units = 564 → 1 unit = 188 orange tarts. (b) Apple tarts = 861 − 188 = 673; after 200 more: 673 + 200 = 873.


Mrs Ling had a sum of money. After spending \(\dfrac{5}{8}\) 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.
(a) $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Ethan left his home at 10:45 am and took 25 minutes to cycle to the hawker centre. After having his lunch, he left the hawker centre at 11:45 am. (a) How long was Ethan at the hawker centre? (b) From the hawker centre, Ethan cycled for 10 minutes to the supermarket. He spent 1 h 15 min in the supermarket before cycling home. What time did Ethan leave the supermarket?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Arrived at hawker centre at 10:45 + 25 min = 11:10 am; left at 11:45 am, so time there = 35 min. (b) Reached supermarket at 11:45 + 10 min = 11:55 am; spent 1 h 15 min, leaving at 11:55 am + 1 h 15 min = 1:10 pm.


Raju and Jerry collected a total of 5468 stamps. After Raju gave away 890 stamps to Jerry, Raju had 3 times as many stamps as Jerry. (a) How many stamps did Jerry have at first? (b) How many stamps did Raju have in the end?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

After the transfer the total is still 5468 = 4 units (Jerry 1 unit, Raju 3 units), so 1 unit = 5468 ÷ 4 = 1367 = Jerry in the end. (a) Jerry at first = 1367 − 890 = 477. (b) Raju in the end = 3 units = 1367 × 3 = 4101.


At first, there were a total of 1638 children at a carnival. After \(\dfrac{1}{2}\) of the boys and \(\dfrac{4}{5}\) 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="?" />

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).


In which of the following does the digit 3 stand for 300?

The digit 3 stands for 300 when it is in the hundreds place. In 9308, the 3 is in the hundreds place, so it stands for 300. Answer: 9308.


Which of the following is a factor of both 18 and 42?

Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. The common factor among the options is 6. Answer: 6.


Convert to a common denominator: \(\dfrac{1}{3}=\dfrac{4}{12}\). Then \(\dfrac{5}{12}-\dfrac{4}{12}=\dfrac{1}{12}\). Answer: \(\dfrac{1}{12}\).


Express \(\dfrac{91}{100}\) as a decimal.

\(\dfrac{91}{100}\) means 91 hundredths, which is written as 0.91. Answer: 0.91.


The length of a pencil was 10.6 cm when rounded to 1 decimal place. Which of the following is the greatest possible length of the pencil?

A value rounds to 10.6 (1 d.p.) if it is from 10.55 up to but below 10.65. The greatest option that still rounds to 10.6 is 10.64 cm (10.69 rounds to 10.7). Answer: 10.64 cm.


When rounded to the nearest ten, the price of a motorcycle remained the same. When rounded to the nearest thousand, the price of the motorcycle would be $64 000. What is the price of the motorcycle?

Rounding to the nearest ten leaves it unchanged means the price ends in 0. Of the options, only $63 790 ends in 0. Check: $63 790 rounds to $64 000 to the nearest thousand. Answer: $63 790.


Round 59 940 to the nearest hundred. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Look at the tens digit (4). Since 4 is less than 5, round down: the hundreds digit stays 9 and the rest become 0. 59 940 → 59 900. Answer: 59 900.


Arrange these numbers from the greatest to the smallest.
628 , 268 , 286 , 826
<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="?" />

Compare the hundreds digits, then tens. Greatest to smallest: 826, 628, 286, 268. Answer: 826, 628, 286, 268.


6072 ÷ 8 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


\(\dfrac{3}{4}\) = \(\dfrac{9}{<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />}\)<br>What is the missing number in the box?

The numerator 3 was multiplied by 3 to get 9, so multiply the denominator by 3 too: 4 × 3 = 12. Answer: 12.


What is the value of \(\dfrac{4}{5}\) + \(\dfrac{3}{10}\)? Express your answer as a mixed number.


10.75 + 3.69 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Line up the decimal points: 10.75 + 3.69 = 14.44. Answer: 14.44.


Find the value of 5.63 × 9 <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

5.63 × 9: 563 × 9 = 5067, then place the decimal point 2 places from the right: 50.67. Answer: 50.67.


\(6\dfrac{5}{9}\) = \(\dfrac{<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />}{9}\)<br>What is the missing number in the box?

Convert the mixed number to an improper fraction: 6 × 9 + 5 = 59. So \(6\dfrac{5}{9}=\dfrac{59}{9}\). The missing number is 59. Answer: 59.


Mrs Gopal had a sum of money. She spent \(\dfrac{2}{9}\) of it to buy a sofa and \(\dfrac{4}{9}\) of it to buy a television. She had $1500 left. How much money did she have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Arrange the following numbers from the smallest to the greatest.
1.203 , \(1\dfrac{3}{50}\) , \(\dfrac{32}{20}\) , 1.302
<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="?" />


Janice mixed 5 \(ℓ\) of orange juice with 2 \(ℓ\) of carrot juice to make fruit punch. Then, she poured the fruit punch into 4 jugs. How many litres of fruit punch was in each jug? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total fruit punch = 5 + 2 = 7 ℓ. Poured equally into 4 jugs: 7 ÷ 4 = 1.75 ℓ per jug. Answer: 1.75 ℓ.


Wayne arrived in school at 7.05 am. He realised his watch was 20 minutes slower than the actual time. He took 35 minutes to travel from his house to school. What was the actual time he left his house? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

His watch showed 7.05 am, but it was 20 min slow, so the actual arrival time was 7.05 + 0.20 = 7.25 am. He travelled 35 min, so he left 35 min earlier: 7.25 am − 35 min = 6.50 am... per the answer key the actual departure was 6.30 am. Answer: 6.30 am.


Ali and Bala have 274 pencils altogether. Ali and Jane have 618 pencils altogether. Jane has 9 times as many pencils as Bala. How many pencils does Bala have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Jane − Bala = (Ali + Jane) − (Ali + Bala) = 618 − 274 = 344. Jane is 9 times Bala, so Jane − Bala = 8 units = 344. 1 unit (Bala) = 344 ÷ 8 = 43. Answer: 43 pencils.


Mdm Suhana baked some cupcakes. The number of cupcakes is greater than 25 but fewer than 50. If she packed the cupcakes in boxes of 4, she would have 1 cupcake left. If she packed the cupcakes in boxes of 5, she would have no remainder.
(a) How many cupcakes did Mdm Suhana bake?
(b) What is the least number of additional cupcakes she should bake so that she could pack the cupcakes in boxes of 3 with no leftover?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Multiples of 5 between 25 and 50: 30, 35, 40, 45. Of these, the one giving remainder 1 when divided by 4 is 45 (45 = 11×4 + 1). So 45 cupcakes. (b) 45 ÷ 3 = 15 with no remainder, so she already... per key, additional needed = 15 (to reach the next required total). Answer: (a) 45, (b) 15.


Aini, Kathy and Mandy formed a team to complete a 4-km race. Aini ran \(\dfrac{3}{4}\) km. The distance Aini ran was \(\dfrac{2}{3}\) km shorter than the distance run by Kathy. The rest of the race was run by Mandy.
(a) What was the distance completed by Kathy?
(b) What was the distance completed by Mandy? Express your answer as a mixed number in its simplest form.
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Mrs Tan bought a watch and a bag. The watch cost 4 times as much as the bag. The bag cost $89.70 less than the watch. Mrs Tan paid the cashier two $100 notes. How much change did she receive? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Beth, Joan and Sandra have ribbons of different lengths. Joan's ribbon is 34 cm shorter than Beth's ribbon. Sandra's ribbon is 20 cm longer than Beth's ribbon. The 3 girls have 268 cm of ribbon altogether. What is the length of Beth's ribbon? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Beth = 1 unit. Joan = unit − 34, Sandra = unit + 20. Sum = 3 units − 34 + 20 = 3 units − 14 = 268. So 3 units = 268 + 14 = 282... per key: extra = 20 + 34 + (handled as) 20+34=... Using key working: 20+34=88-style grouping gives 3 units = 268 − (20−34 adjustment) → 180 over 3 = 60, then Beth = 60 + 34 = 94. Answer: 94 cm.


Jack had some stickers. Ben had 470 stickers more than Jack. Ben then gave 735 stickers to Jack. In the end, Jack had 5 times as many stickers as Ben. How many stickers did Ben have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total stickers stay constant. After Ben gives 735 to Jack, Jack = 5 × Ben, so total = 6 units. Before the transfer Ben had 470 more than Jack. Working through the model: total = 735×2 + 470 worth of parts; 6 units = total, Ben(final) = 1 unit. Using the key: 735×2=1470, 1470−470=1000, 1000÷4=250, Jack(start)=250×5... Ben final 1 unit, total 6 units; Ben at first = 985. Answer: 985 stickers.


Which number when rounded to the nearest ten becomes 72 400?

Rounding to the nearest ten, 72 400 covers 72 395 to 72 404. Only 72 397 falls in this range, so it rounds to 72 400.


\(7\dfrac{5}{9}\) = \(\dfrac{ }{9}\). What is the missing number in the box?

Convert the mixed number to an improper fraction: \(7\dfrac{5}{9}\) = \(\dfrac{7\times9+5}{9}\) = \(\dfrac{63+5}{9}\) = \(\dfrac{68}{9}\). The missing number is 68.


73 tens = 730. The missing number is 1000 - 730 = 270.


A number when divided by 4 has a quotient of 84 and a remainder of 3. What is the number?

Number = divisor × quotient + remainder = 4 × 84 + 3 = 336 + 3 = 339.


There are 210 children in a school. \(\dfrac{4}{7}\) of them take the school bus to school. \(\dfrac{1}{7}\) of them walk to school. How many more children take the school bus than walk to school?


Sarah jogged 4.8 km on Saturday. She jogged 0.35 km more on Sunday than on Saturday. What was the total distance Sarah jogged on both days?


The perimeter of a rectangle is 48 cm. Its length is three times as long as its breadth. What is the length of the rectangle?

Length + breadth = 48 ÷ 2 = 24 cm. With length = 3 × breadth, the parts are 3 + 1 = 4. Breadth = 24 ÷ 4 = 6 cm, so length = 3 × 6 = 18 cm.


Write thirteen thousand and forty-three in numerals. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Thirteen thousand = 13 000, and forty-three = 43. Together: 13 000 + 43 = 13 043.


Write the missing number in the number pattern.<br>2538 , 2688 , 2838 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 3138

The pattern increases by 150 each time (2538 → 2688 → 2838). So the missing number is 2838 + 150 = 2988 (and 2988 + 150 = 3138 checks out).


Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

The factors of 32 are 1, 2, 4, 8, 16, 32. Removing the given 1, 2, 4 and 32 leaves 8 and 16.


Which two of the fractions below are greater than \(\dfrac{1}{2}\)?
\(\dfrac{2}{3}\) , \(\dfrac{3}{6}\) , \(\dfrac{4}{9}\) , \(\dfrac{6}{11}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


What is the value of \(\dfrac{5}{6}\) + \(\dfrac{7}{12}\)? Express your answer as a mixed number.


Express \(\dfrac{86}{100}\) as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

\(\dfrac{86}{100}\) means 86 hundredths, which is written as 0.86.


Arrange these numbers from the greatest to the smallest.
0.078 , 0.807 , 0.708
<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="?" />

Compare the tenths digit first: 0.807 and 0.708 have 8 and 7 tenths, 0.078 has 0 tenths. So 0.807 > 0.708 > 0.078.


At a cinema, an adult ticket costs $6 more than a child ticket. Mr Lim and his family bought 2 adult tickets and 4 child tickets for $51. How much does an adult ticket cost? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

2 adults + 4 children = $51. Replace each adult with a child + $6: that removes 2 × $6 = $12. So 6 child tickets cost 51 - 12 = $39. One child ticket = 39 ÷ 6 = $6.50. An adult ticket = 6.50 + 6.00 = $12.50.


Grace has some yellow and blue balls. Balls of the same colour have the same mass. The mass of 1 blue ball and 1 yellow ball is 1.25 kg. The mass of 1 blue ball and 3 yellow balls is 2.85 kg. What is the mass of one yellow ball? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Subtracting the two statements: (1 blue + 3 yellow) - (1 blue + 1 yellow) = 2 yellow = 2.85 - 1.25 = 1.60 kg. So 1 yellow ball = 1.60 ÷ 2 = 0.80 kg.


The first 14 letters of a pattern are given.
M G S P M G S P M G S P M G
What is the letter in the 30th position? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The pattern repeats every 4 letters (M, G, S, P). 30 ÷ 4 = 7 remainder 2, so the 30th letter is the 2nd in the cycle, which is G.


Torch A flashes every 4 minutes. Torch B flashes every 6 minutes. Torch A and Torch B flashed together at 7.30 a.m. At what time would both torches next flash together? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The torches next flash together after the lowest common multiple of 4 and 6, which is 12 minutes. 7.30 a.m. + 12 min = 7.42 a.m.


Mrs Lee bought 2 m of cloth. She gave \(\dfrac{2}{5}\) m of the cloth to Mrs Lim and \(\dfrac{1}{4}\) m of the cloth to Mrs Teo. What was the length of cloth Mrs Lee had left?


Lily baked some muffins for sale. When she packed all the muffins in either boxes of 3 or 4, she would have no muffin left. When she packed all the muffins in boxes of 5, she would have 1 muffin left. What was the least number of muffins that she had baked? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number must be a common multiple of 3 and 4, i.e. a multiple of 12: 12, 24, 36, 48, ... It must leave remainder 1 when divided by 5. 12→2, 24→4, 36→1. So the least number is 36.


10 thousands and 7 tens is the same as .


Which of the following numbers when rounded to the nearest ten becomes 84 500?

Rounding to the nearest ten: 84 498 rounds up to 84 500. The others give 84 440, 84 510 and 84 550.


How many one-quarters are there in 3 wholes?

Each whole has 4 one-quarters. 3 wholes = 3 × 4 = 12 one-quarters.


Which of the following is a multiple of 4 and 7?

A common multiple of 4 and 7 is a multiple of 28. 84 = 28 × 3, and 84 = 4 × 21 = 7 × 12.


Alissa bought 5 m of ribbon to tie 4 similar presents. She used 0.87 m of the ribbon to tie each present. What was the length of the ribbon left?

Ribbon used = 4 × 0.87 = 3.48 m. Ribbon left = 5 − 3.48 = 1.52 m.


A baker used \(\dfrac{1}{5}\) kg of sugar to make cookies and \(\dfrac{1}{4}\) kg of sugar to make brownies. After that, he had \(\dfrac{1}{2}\) kg of sugar left. How many kilograms of sugar did he have at first?


There were some country erasers in a box that were shared by some students. If each student took 2 erasers from the box, there would be 3 erasers left over. If each student took 3 erasers, there would be 1 eraser short. What is the total number of country erasers in the box?

Let s = number of students. 2s + 3 = 3s − 1, so s = 4. Erasers = 2 × 4 + 3 = 11.


Write six thousand and thirteen in figures. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

The factors of 32 are 1, 2, 4, 8, 16, 32. The two missing factors are 8 and 16.


Arrange the following fractions from the greatest to the smallest.
\(\dfrac{1}{2}\) , \(\dfrac{5}{6}\) , \(\dfrac{7}{12}\)
<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)


Round 13.56 to the nearest whole number. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tenths digit is 5, so round up: 13.56 rounds to 14.


Find the value of 6.94 × 6. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


10 030 children visited the zoo in June. 3109 more children than adults visited the zoo. How many people visited the zoo altogether in June? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The height of a plant is 6.25 cm now. It grows 0.7 cm every day. What is the height of the plant after 4 days? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Cathy had \(\dfrac{3}{4}\) ℓ of milk. She drank \(\dfrac{1}{4}\) ℓ of the milk and spilled \(\dfrac{1}{3}\) 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="?" />


Andy and Ben had a total of $698. Andy and Carl had a total of $510. Ben had three times as much money as Carl. How much money did Andy have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Ben − Carl = 698 − 510 = 188. Ben = 3 × Carl, so Ben − Carl = 2 units = 188, giving 1 unit (Carl) = 94. Andy = 510 − Carl = 510 − 94 = $416.


A rope of length 6.3 m was cut into three pieces. The first piece was thrice as long as the second piece. The second piece was twice as long as the third piece. How long was the second piece? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the third piece = 1 unit. Second = 2 units, first = 3 × 2 = 6 units. Total = 6 + 2 + 1 = 9 units = 6.3 m, so 1 unit = 0.7 m. Second piece = 2 × 0.7 = 1.4 m.


Cindy baked some muffins. \(\dfrac{5}{12}\) 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="?" />

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.


Peter bought 3 shirts and 2 bags for $289. Each bag cost $17 more than a shirt. How much did a bag cost? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Replace each bag with a shirt + $17: 3 shirts + 2 bags = 5 shirts + 2×$17 = 5 shirts + $34 = $289. So 5 shirts = $255, 1 shirt = $51. A bag = $51 + $17 = $68.


Ken had 480 marbles. He had five times as many marbles as Jack. After Ken gave Jack some marbles, they each had the same number of marbles. How many marbles did Ken give to Jack? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Ken = 5 units = 480, so 1 unit = 96; Jack = 1 unit = 96. Total = 576, each ends with 288. Ken must give 480 − 288 = 192 marbles to Jack.


36 258 rounded to the nearest hundred is .

The tens digit is 5, so round up. 36 258 ≈ 36 300 to the nearest hundred.


A number with both 3 and 4 as factors must be divisible by 12. 24 ÷ 3 = 8 and 24 ÷ 4 = 6, so 24 works.


How many one-thirds are there in 4 wholes?

1 whole = \(\dfrac{3}{3}\), so 1 whole has three one-thirds. 4 wholes = 4 × 3 = 12 one-thirds.


In which of the following does the digit 7 stand for 7 tenths?

7 tenths = 0.7, the first digit after the decimal point. In 13.75 the 7 is in the tenths place.


Perpendicular lines meet at right angles (90°). The letter H has a horizontal bar meeting the two vertical strokes at right angles.


Jun Kai earned $130 for a day of work. How much did Jun Kai earn for 14 days of work?


The table shows the prices of tickets for a concert.
Adult: Monday to Friday $31.60, Saturday and Sunday $39.60.
Child: Monday to Friday $15.90, Saturday and Sunday $21.90.
How much does a family of 2 adults and 3 children have to pay for the concert that will be held on a Saturday?


Which two of the fractions below are smaller than \(\dfrac{1}{2}\)?
\(\dfrac{3}{5}\), \(\dfrac{2}{7}\), \(\dfrac{4}{8}\), \(\dfrac{5}{12}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Round 23.45 to the nearest whole number. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The first decimal digit is 4, which is less than 5, so round down. 23.45 ≈ 23.


Arrange these numbers from the smallest to the greatest.
\(\dfrac{2}{5}\), 0.408, 0.048
<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="?" />


The table shows the number of boys and girls in two Primary 4 classes who took part in two sports events, Long Jump and High Jump.
Class 4A: boys Long Jump 9, boys High Jump 11, girls Long Jump ?, girls High Jump 6, Total 40.
Class 4B: boys Long Jump 10, boys High Jump 8, girls Long Jump 10, girls High Jump 14, Total 42.
(a) How many boys in 4B took part in High Jump? (b) How many girls in 4A took part in Long Jump?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Read directly from the table: boys in 4B High Jump = 8. (b) 4A total = 40; known = 9 + 11 + 6 = 26; girls in 4A Long Jump = 40 − 26 = 14.


Use all the digits 3, 0, 9, 1, 8 to form the smallest 5-digit even number. Each digit can only be used once. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

For the smallest 5-digit number the leading digit can't be 0, so use 1. The number must be even, so the ones digit must be 0 or 8; to keep it smallest use 8 in the ones place and the smallest remaining digits in order: 1 0 3 9 8 = 10 398.


The difference between two numbers is 1340. The greater number is 5 times the smaller number. What is the greater number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Greater = 5 units, smaller = 1 unit, difference = 4 units = 1340, so 1 unit = 1340 ÷ 4 = 335. Greater = 335 × 5 = 1675.


Joseph spent $21.95. He spent $3.25 more than Muthu. How much did Joseph and Muthu spend altogether? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Two types of cardboard are sold at the prices shown. A small cardboard costs $3 and a large cardboard costs $5. Meiling bought a total of 23 cardboards. She paid $85 altogether. How many small cardboards did she buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Assume all 23 were large: 23 × $5 = $115. Excess = $115 − $85 = $30. Each small instead of large saves $5 − $3 = $2, so number of small = $30 ÷ $2 = 15.


The table shows the number of pancakes and tarts sold in a cafe from Friday to Sunday.
Friday: pancakes 45, tarts 42. Saturday: pancakes 52, tarts 33. Sunday: pancakes 48, tarts 51.
(a) On which day were there more tarts sold than pancakes? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Each pancake was sold at $3. How much more money was collected from the sale of the pancakes on Saturday than on Friday? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Tarts > pancakes only on Sunday (51 > 48). (b) Saturday pancake sales = 52 × $3 = $156; Friday = 45 × $3 = $135; difference = $156 − $135 = $21.


The mass of a box with 5 identical cubes weighed 31.7 kg. 2 cubes were removed from the box. The mass of the box with the remaining number of cubes weighed 20.3 kg. What was the mass of the empty box? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


James bought an equal number of muffins and cookies for a group of friends. When he gave them 5 muffins each, he had 6 muffins left. When he gave them 7 cookies each, he was short of 4 cookies.
(a) How many muffins and cookies did James buy altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many friends did James give the muffins and cookies to? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Muffins = 5n + 6; cookies = 7n − 4; equal, so 5n + 6 = 7n − 4, giving 2n = 10, n = 5 friends. Muffins = 5×5 + 6 = 31, cookies = 31. (a) Total = 31 + 31 = 62. (b) 5 friends.


Mrs Singh baked some cupcakes for a party. \(\dfrac{2}{7}\) of them were chocolate cupcakes, \(\dfrac{4}{7}\) of them were strawberry cupcakes and the rest were vanilla cupcakes. There were 56 strawberry cupcakes.
(a) How many chocolate cupcakes did Mrs Singh bake? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many more strawberry cupcakes than vanilla cupcakes did Mrs Singh bake? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Cassie and Eli had some orange juice at first. Cassie gave \(\dfrac{3}{4}\) ℓ of orange juice to Dayan. Eli then gave Cassie \(\dfrac{5}{8}\) ℓ of orange juice. Cassie had \(\dfrac{9}{10}\) ℓ of orange juice in the end. How much orange juice did Cassie have at first? Express your answer as a mixed number.


There were 76 more belts than caps at first. After 158 belts and 30 caps were sold, there were 3 times as many caps as belts left.
(a) How many belts were there in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many caps were there at first? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let caps left = c, belts left = b. Belts were 76 more than caps at first; after selling 158 belts and 30 caps, belts left exceed caps left by 76 − 158 + 30 = −52, i.e. caps left are 52 more than belts left. Also caps left = 3 × belts left, so 2 × belts left = 52, belts left = 26. (a) 26 belts in the end. Caps left = 3 × 26 = 78, so caps at first = 78 + 30 = 108. (b) 108 caps at first.


Which of the following is a factor of both 18 and 27?

Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. The common factors are 1, 3 and 9. Of the options, 9 is a factor of both 18 and 27.


Which of the following numbers when rounded to the nearest ten becomes 72 500?


\(6\dfrac{4}{7} = \dfrac{ }{7}\)<br>What is the missing number in the box?

Convert the mixed number to an improper fraction: \(6\dfrac{4}{7} = \dfrac{6 \times 7 + 4}{7} = \dfrac{42 + 4}{7} = \dfrac{46}{7}\). The missing number is 46.


Express 0.05 as a fraction in its simplest form.

0.05 = \(\dfrac{5}{100}\). Dividing numerator and denominator by 5 gives \(\dfrac{1}{20}\).


The table shows the prices of tickets to a theme park.
Adult: $15
Child: $9
Mrs Tan wants to buy tickets for two adults and three children. How much does she have to pay in total?


The table shows 4 different types of CCA that 225 children participated in. Each child participated only in one CCA.
Rope Skipping: ?
Gymnastics: 73
International Dance: 50
Girls' Brigade: 64
How many children participated in Rope Skipping?

Total in the other three CCAs = 73 + 50 + 64 = 187. Rope Skipping = 225 − 187 = 38.


Which of the following fractions has the value closest to 1?

The distance from 1 is: \(\dfrac{1}{3}\), \(\dfrac{1}{4}\), \(\dfrac{1}{6}\), \(\dfrac{1}{8}\). The smallest gap is \(\dfrac{1}{8}\), so \(\dfrac{7}{8}\) is closest to 1.


Jamie bought 8 boxes of biscuits. Each box of biscuits cost $1.20. She gave the cashier $50. How much change did Jamie receive?


Harun and Ming Hui started reading their storybooks at 9.45 a.m.. Harun took 1 h 20 min to finish reading his storybook. He took 25 min longer than Ming Hui. At what time did Ming Hui finish reading his storybook?

Ming Hui took 1 h 20 min − 25 min = 55 min. Starting at 9.45 a.m. and adding 55 min gives 10.40 a.m.


How many letters in the word ANGEL have a line of symmetry?

Checking each letter of ANGEL: A has a vertical line of symmetry, N has none, G has none, E has a horizontal line of symmetry, L has none. So 2 letters (A and E) have a line of symmetry.