Cindy had a piece of ribbon. She used \(\dfrac{2}{7}\) of the ribbon to make 15 small identical bows and 7 large identical bows. The length of ribbon used for 3 large bows was the same as the length of ribbon used for 5 small bows.
(a) How many large bows can she make with the same length of ribbon used for 15 small bows? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many small bows can she make with \(\dfrac{3}{10}\) of the remaining ribbon? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 3 large = 5 small, so 1 small = \(\dfrac{3}{5}\) large. 15 small = 15 ÷ 5 × 3 = 9 large bows. (b) \(\dfrac{2}{7}\) made 15 small + 7 large = (9 + 7) = 16 large-equivalents, so \(\dfrac{1}{7}\) = 16 ÷ 2 = 8 large; \(\dfrac{2}{7}\) = 16 large. Remaining ribbon = \(\dfrac{5}{7}\). \(\dfrac{3}{10}\) of remaining = \(\dfrac{3}{10}\times\dfrac{5}{7}=\dfrac{3}{14}\) of whole. Since \(\dfrac{1}{14}\) = 4 large, \(\dfrac{3}{14}\) = 12 large = 12 × (5/3) small = 20 small bows.


Expand 5 703 890 in place value: 5 000 000 + 700 000 + 3 000 + 890. The missing addend is the hundred-thousands part, 700 000. Answer: 700 000 (option 4).


Find the value of \((40 + 23) - 54 \div 9 \times 2 + 8\).

Order of operations: brackets first, 40 + 23 = 63. Then \(\div\) and \(\times\) left to right: 54 \(\div\) 9 = 6, 6 \(\times\) 2 = 12. Now 63 - 12 + 8 = 59. Answer: 59 (option 2).


What is the value of \(\dfrac{4}{9} \times \dfrac{5}{6}\)?

Multiply numerators and denominators: \(\dfrac{4 \times 5}{9 \times 6} = \dfrac{20}{54}\). Simplify by dividing top and bottom by 2: \(\dfrac{10}{27}\). Answer: \(\dfrac{10}{27}\) (option 3).


There was a total of 10 boxes of books and magazines in the classroom. There were 7 boxes of books. Each box contained 8 books. Each of the remaining boxes contained 12 magazines. Which one of the following represents the correct way to find the total number of books and magazines?

Books: 7 boxes \(\times\) 8 = (7 \(\times\) 8). Magazine boxes: 10 - 7 = 3 boxes, each with 12, so (10 - 7) \(\times\) 12. Total = (7 \(\times\) 8) + (10 - 7) \(\times\) 12. Answer: option 3.


Jieming had 20 more stickers than Royston at first. Royston gave 14 of his stickers to Jieming. Jieming now has 3 times as many stickers as Royston. How many stickers did Royston have at first?

Let Royston have R at first. Jieming = R + 20. After Royston gives 14: Royston = R - 14, Jieming = R + 34. Jieming is now 3 times Royston: R + 34 = 3(R - 14) = 3R - 42, so 76 = 2R, R = 38. Answer: 38 (option 4).


Find the product of 653 and 400. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Use all the digits 4, 0, 7, 9 to form a number closest to 8000. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To be closest to 8000, the thousands digit should be 7 (since 8 is unavailable). Then make the rest as large as possible: 7940. Check: 8000 - 7940 = 60, the smallest gap possible. Answer: 7940.


Express 8 cm as a fraction of 2 m. Give your answer in the simplest form.

Convert to the same unit: 2 m = 200 cm. Fraction = \(\dfrac{8}{200}\). Simplify by dividing top and bottom by 8: \(\dfrac{1}{25}\). Answer: \(\dfrac{1}{25}\) (option 1).


Express \(\dfrac{20}{7}\) as a mixed number.

20 \(\div\) 7 = 2 remainder 6, so \(\dfrac{20}{7} = 2\dfrac{6}{7}\). (Part b of the printed paper: as a decimal to 2 d.p., 20 \(\div\) 7 = 2.857... \(\approx\) 2.86; the printed key shows 0.286 for the fractional 6/7 part rounded differently. The mixed number is the value asked here.) Answer: \(2\dfrac{6}{7}\) (option 1).


A box is 4 times as heavy as a bag. The total mass of the box and the bag is 60 kg. What is the mass of the box? Give your answer in kilograms. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Box : bag = 4 : 1, so total is 5 units = 60 kg. 1 unit = 60 \(\div\) 5 = 12 kg. Box = 4 units = 12 \(\times\) 4 = 48 kg. Answer: 48 kg.


Ross had $60 and Monica had $42 at first. They each spent an equal amount of money. In the end, Ross had three times as much money as Monica. How much did each of them spend? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The difference between them stays $60 - $42 = $18, since they spend equally. In the end Ross = 3 \(\times\) Monica, so the difference is 2 units = $18, giving 1 unit = $9 (Monica's final amount). Each spent $42 - $9 = $33. Answer: $33.


Julian bought some mangoes and watermelons for $146. He bought 6 more mangoes than watermelons. Each mango cost $3 and each watermelon cost $5. How many mangoes and watermelons did he buy altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remove the 6 extra mangoes first: 6 \(\times\) $3 = $18, leaving $146 - $18 = $128 for equal numbers of each. One mango + one watermelon = $3 + $5 = $8. Pairs = $128 \(\div\) $8 = 16. So 16 watermelons and 16 + 6 = 22 mangoes; altogether 16 + 22 = 38. Answer: 38.


A group of children visit a museum. The entrance fee for each child is $3. For every 3 children, the 4th child is free. The group of children pay $114 altogether. What is the greatest number of children in the group? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Paying children = $114 \(\div\) $3 = 38. In each group of 4, 3 pay and 1 is free. 38 \(\div\) 3 = 12 remainder 2, so there are 12 full groups of 4 plus 2 extra paying children. Free children = 12 \(\times\) 1 = 12. Greatest total = 38 paying + 12 free = 50. Answer: 50.


Write two million, eighty thousand, five hundred and nine in numerals.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Two million = 2 000 000, eighty thousand = 80 000, five hundred and nine = 509. Adding: 2 000 000 + 80 000 + 509 = 2 080 509.


In 4 023 670, what is the value of digit 2?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In 4 023 670 the digit 2 is in the ten-thousands place. Its value is 2 × 10 000 = 20 000.


What is the value of 6 + (72 − 12 × 4) ÷ 3?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Inside the brackets first: 12 × 4 = 48, so 72 − 48 = 24. Then 24 ÷ 3 = 8. Finally 6 + 8 = 14.


Mike bought 9 similar pizzas and shared them equally with 15 children. What fraction of a pizza did each child get? Express your answer in the simplest form.

Each child gets 9 ÷ 15 = \(\dfrac{9}{15}\) of a pizza. Simplifying by dividing top and bottom by 3 gives \(\dfrac{3}{5}\).


Mr Tan bought some fruits. \(\dfrac{2}{5}\) of the fruits were oranges and the rest were apples. \(\dfrac{1}{3}\) of the apples were green. What fraction of the fruits were green apples?

Apples are the rest: \(1 - \dfrac{2}{5} = \dfrac{3}{5}\) of the fruits. Green apples are \(\dfrac{1}{3}\) of the apples: \(\dfrac{3}{5} \times \dfrac{1}{3} = \dfrac{1}{5}\).


Shanti had some coloured beads in a box at first. She took out 134 red beads and added in 53 blue beads. In the end, there were 650 beads left in the box. How many beads were there in the box at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Work backwards from 650. Before adding 53 blue beads: 650 − 53 = 597. Before taking out 134 red beads: 597 + 134 = 731.


A number when divided by 500 gives a quotient of 420. What is the quotient when the same number is divided by 2000?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Qiumei has $62 and she wants to buy some files from a bookshop. The bookshop sells the files at $2 each or a pack of 5 similar files for $9. What is the most number of files she can buy with all her money?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

A pack of 5 for $9 is cheaper per file ($1.80) than $2 each, so buy as many packs as possible. $62 ÷ $9 = 6 packs (6 × $9 = $54) with $8 left. 6 packs = 30 files. The $8 left buys 8 ÷ 2 = 4 single files. Total = 30 + 4 = 34 files.


At a bakery, there are three types of tarts. \(\dfrac{4}{9}\) of the tarts are chocolate tarts and \(\dfrac{2}{5}\) of the remaining are strawberry tarts. The rest are mango tarts. There are 56 chocolate and mango tarts altogether. How many tarts are there in total?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remaining after chocolate = \(1 - \dfrac{4}{9} = \dfrac{5}{9}\). Strawberry = \(\dfrac{2}{5} \times \dfrac{5}{9} = \dfrac{2}{9}\), so mango = \(\dfrac{5}{9} - \dfrac{2}{9} = \dfrac{3}{9} = \dfrac{1}{3}\) of all tarts. Chocolate + mango = \(\dfrac{4}{9} + \dfrac{3}{9} = \dfrac{7}{9}\) of total = 56. Total = 56 ÷ 7 × 9 = 72.


There were 4 times as many boys as girls in the school hall at first. After 57 boys left the hall and 18 girls entered the hall, there was an equal number of boys and girls in the hall. How many boys were there in the hall in the end?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let girls = 1 unit, boys = 4 units at first. In the end boys = 4u − 57 and girls = 1u + 18, and these are equal: 4u − 57 = u + 18, so 3u = 75 and 1u = 25. Boys in the end = 25 + 18 = 43 (equals the equal final count).


In 561 403, which digit is in the hundred thousands place?

In 561 403, the digit places from the left are: 5 = hundred thousands, 6 = ten thousands, 1 = thousands, 4 = hundreds, 0 = tens, 3 = ones. So the digit in the hundred thousands place is 5. Answer: 5.


To round 428 567 to the nearest thousand, look at the hundreds digit (5). Since 5 ≥ 5, round the thousands up: 428 → 429 thousand. So 428 567 ≈ 429 000. Answer: 429 000.


Express \(8\dfrac{1}{20}\) as a decimal.


Find the value of $96 - 72 \div 8 + 4 \times 15$

Apply order of operations (× and ÷ before + and −): 72 ÷ 8 = 9 and 4 × 15 = 60. Then 96 − 9 + 60 = 87 + 60 = 147. Answer: 147.


Arrange these fractions from the largest to the smallest.<br>\(\dfrac{8}{7}\) , \(1\dfrac{1}{8}\) , \(\dfrac{4}{3}\)


Mr Low had some money. He used \(\dfrac{1}{3}\) of it to buy a laptop and gave \(\dfrac{1}{5}\) of the remaining money to his wife. What fraction of his money had he left?

After the laptop, remaining = \(1-\dfrac{1}{3}=\dfrac{2}{3}\). He gave \(\dfrac{1}{5}\) of this away, keeping \(\dfrac{4}{5}\) of it: \(\dfrac{4}{5}\times\dfrac{2}{3}=\dfrac{8}{15}\). Answer: \(\dfrac{8}{15}\).


Susan gave some sweets to her cousins and classmates. The ratio of the number of sweets she gave to her cousins to the number of sweets she gave to her classmates was 1 : 3. She gave 84 more sweets to her classmates than to her cousins. How many sweets did she give to her classmates?

Cousins : classmates = 1 : 3, so the difference is 3 − 1 = 2 units = 84 sweets. 1 unit = 84 ÷ 2 = 42. Classmates = 3 units = 3 × 42 = 126. Answer: 126.


List all the common factors of 16 and 36. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(2\dfrac{7}{8} - 1\dfrac{3}{5}\)


What is the missing number in the box?<br>$32 : 16 = $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> $ : 25$

32 : 16 simplifies to 2 : 1. To make the second term 25, multiply both parts by 25: 2 × 25 : 1 × 25 = 50 : 25. So the missing number is 50. Answer: 50.


Matthew and Cayden shared some cards. The ratio of the number of cards Matthew had to the number of cards Cayden had is 2 : 5. Matthew had 124 cards. How many cards did they have altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Matthew : Cayden = 2 : 5. Matthew's 2 units = 124, so 1 unit = 124 ÷ 2 = 62. Altogether = 2 + 5 = 7 units = 7 × 62 = 434 cards. Answer: 434.


6 years ago, Mdm Siti was 5 times as old as her son. Their total age is 66 years now. How old is Mdm Siti now? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

6 years ago, total age = 66 − 6 − 6 = 54. Then Siti : son = 5 : 1, so 6 units = 54, 1 unit = 9. Son was 9, Siti was 45 (6 years ago). Now Siti = 45 + 6 = 51 years old. Answer: 51.


Shop A sold twice as many doughnuts as Shop B. Shop C sold 3 times as many doughnuts as Shop A. Shop C sold 592 more doughnuts than Shop A. How many doughnuts did Shop B sell? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Shop B = 1 unit. Shop A = 2 units, Shop C = 3 × Shop A = 6 units. C − A = 6 − 2 = 4 units = 592, so 1 unit = 592 ÷ 4 = 148. Shop B = 1 unit = 148 doughnuts. Answer: 148.


Charlotte had 48 stickers and Makayla had 32 stickers. Charlotte gave 12 of her stickers to Makayla. What was the ratio of the number of Charlotte's stickers to the number of Makayla's stickers in the end? Leave your answer in its simplest form.

After giving 12 away: Charlotte = 48 − 12 = 36; Makayla = 32 + 12 = 44. Ratio 36 : 44, divide both by 4 = 9 : 11. Answer: 9 : 11.


Janna and Nadiah had some paper cranes. Janna had 78 more paper cranes than Nadiah. After Janna gave away 9 paper cranes and Nadiah gave away 7 paper cranes, the number of paper cranes Nadiah had left was \(\dfrac{1}{6}\) of the total number of paper cranes left. How many paper cranes did Nadiah have left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After giving away, Janna still has (78 − 9 + 7) = 76 more than Nadiah. Nadiah's share is \(\dfrac{1}{6}\) of the total, so Janna has \(\dfrac{5}{6}\); the difference is \(\dfrac{4}{6}\) of the total. Using units: Nadiah = 1 unit, total = 6 units, Janna = 5 units; difference = 4 units = 76, so 1 unit = 76 ÷ 4 = 19. Nadiah had 19 left. Answer: 19.


2 \(\ell\) of fruit juice was shared equally among 14 children. How many litres of fruit juice would each child receive? Leave your answer as a fraction in the simplest form.

Each child gets \(2 \div 14 = \dfrac{2}{14} = \dfrac{1}{7}\) litre.


\(\dfrac{7}{10} - \dfrac{1}{6} = \dfrac{<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />}{15}\)


Leon's baby brother weighs \(7\dfrac{2}{5}\) kg. Leon weighs 4 times as heavy as his baby brother. What is Leon's mass?


Mrs Lum bought \(3\dfrac{1}{2}\) m of cloth. She used \(1\dfrac{1}{3}\) m of cloth to make some cushion covers. How much cloth was left?


Joan had twice as many beads as Germaine. After Joan gave away \(\dfrac{5}{12}\) of her beads and Germaine bought another 25 beads, they had the same number of beads. How many beads did Joan have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Germaine have 1 unit, so Joan has 2 units. Joan keeps \(1 - \dfrac{5}{12} = \dfrac{7}{12}\) of her beads: \(2 \times \dfrac{7}{12} = \dfrac{14}{12} = \dfrac{7}{6}\) units. Germaine then has \(1\) unit + 25. Setting equal: \(\dfrac{7}{6}\) units = 1 unit + 25, so \(\dfrac{1}{6}\) unit = 25, 1 unit = 150. Joan = 2 units = 300 beads.


Justin spent \(\dfrac{3}{8}\) of his money on books and \(\dfrac{2}{5}\) of his remaining money on toys. What fraction of his money did Justin spend on toys?

Remaining after books = \(1 - \dfrac{3}{8} = \dfrac{5}{8}\). Spent on toys = \(\dfrac{5}{8} \times \dfrac{2}{5} = \dfrac{10}{40} = \dfrac{1}{4}\) of his money.


Lucas and James had the same number of stickers. Lucas gave away \(\dfrac{3}{4}\) of his stickers. James gave away \(\dfrac{1}{8}\) of his stickers. James has 75 more stickers than Lucas left. How many stickers did Lucas and James each have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Lucas has \(1 - \dfrac{3}{4} = \dfrac{1}{4}\) left; James has \(1 - \dfrac{1}{8} = \dfrac{7}{8}\) left. Difference = \(\dfrac{7}{8} - \dfrac{1}{4} = \dfrac{7}{8} - \dfrac{2}{8} = \dfrac{5}{8}\) of the original = 75 stickers. So original = \(75 \div \dfrac{5}{8} = 75 \times \dfrac{8}{5} = 120\). Each had 120 stickers at first.


Charles, Danny and Emily used \(8\dfrac{3}{4}\) kg of flour to bake some cakes. Danny used \(\dfrac{1}{4}\) kg of flour more than Charles. Emily used twice as much flour as Danny. How much flour did Charles use? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

Let Charles = 1 unit. Danny = 1 unit + \(\dfrac{1}{4}\). Emily = 2 × Danny = 2 units + \(\dfrac{1}{2}\). Total = 4 units + \(\dfrac{3}{4}\) = \(8\dfrac{3}{4}\). So 4 units = \(8\dfrac{3}{4} - \dfrac{3}{4} = 8\), 1 unit = 2 kg. Charles used 2 kg.


Liling had some money. She spent $14 on a story book, \(\dfrac{3}{7}\) of the remainder on a school bag and saved the rest. She saved $28. How much money did Liling have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the story book, \(\dfrac{3}{7}\) of the remainder went to the bag, so \(\dfrac{4}{7}\) of the remainder was saved = $28. Remainder = \(28 \div \dfrac{4}{7} = 28 \times \dfrac{7}{4} = 49\). At first = $49 + $14 = $63.


What is the value of \(312\,000 \div 400\)?

Method: divide by tens/hundreds. \(312\,000 \div 400 = 3120 \div 4 = 780\). Answer: 780.


What is the value of \(16 + (39 - 7) \div 4 \times 2\)?


What is the value of \(\dfrac{2}{7} \times \dfrac{9}{5}\)?

Method: multiply numerators and denominators. \(\dfrac{2}{7} \times \dfrac{9}{5} = \dfrac{2 \times 9}{7 \times 5} = \dfrac{18}{35}\). Answer: \(\dfrac{18}{35}\).


Donna had 168 stamps. She gave \(\dfrac{2}{3}\) of her stamps to 7 friends. Each friend received an equal number of stamps. How many stamps did each friend receive?

Method: find the fraction of the set, then divide. \(\dfrac{2}{3} \times 168 = 112\) stamps given away. \(112 \div 7 = 16\) stamps per friend. Answer: 16.


A repeated pattern is formed using numbers 3, 2, 1 and 0. The first 18 numbers are shown.
3, 0, 2, 0, 1, 3, 0, 2, 0, 1, 3, 0, 2, 0, 1, 3, 0, 2, ...
Find the sum of the first 44 numbers.

Method: identify the repeating block. The block is 3, 0, 2, 0, 1 (5 numbers, sum = 6). \(44 \div 5 = 8\) remainder 4, so there are 8 full blocks plus the first 4 of the next block (3, 0, 2, 0). Sum \(= 8 \times 6 + (3 + 0 + 2 + 0) = 48 + 5 = 53\). Answer: 53.


Write six million, twenty-seven thousand and nineteen in numerals.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: place the digits by place value. Six million = 6 000 000; twenty-seven thousand = 27 000; nineteen = 19. Total = 6 027 019. Answer: 6 027 019.


8 children shared 5 pizzas equally for lunch. What fraction of a pizza did each child get?

Method: associate division with a fraction. 5 pizzas shared among 8 children = \(5 \div 8 = \dfrac{5}{8}\). Each child gets \(\dfrac{5}{8}\) of a pizza. Answer: \(\dfrac{5}{8}\).


Express \(3\dfrac{2}{5}\) as a decimal.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: convert the fraction part to a decimal. \(\dfrac{2}{5} = \dfrac{4}{10} = 0.4\), so \(3\dfrac{2}{5} = 3 + 0.4 = 3.4\). Answer: 3.4.


Hui En bakes 420 cookies each day. She packs them into tins of 30 cookies. How many tins of cookies will she have in 9 days?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: find tins per day, then multiply by days. \(420 \div 30 = 14\) tins per day. \(14 \times 9 = 126\) tins in 9 days. Answer: 126.


On Monday, Mr Yusof bought 4 tables. Each table cost $357. On Tuesday, he bought 6 identical chairs. The 6 chairs cost as much as the 4 tables. How much did each chair cost?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: total cost of tables, then divide among chairs. 4 tables cost \(4 \times \$357 = \$1428\). The 6 chairs cost the same total, so each chair costs \(\$1428 \div 6 = \$238\). Answer: $238.


Find the missing number in the box.<br>\(\dfrac{6}{7} \times 35 = 3 \times\) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: evaluate the left side, then solve. \(\dfrac{6}{7} \times 35 = 6 \times 5 = 30\). So \(3 \times ? = 30\), giving \(? = 30 \div 3 = 10\). Answer: 10.


Prisha had some stickers at first. She gave away \(\dfrac{1}{5}\) of her stickers and bought another 372 stickers. In the end, she was left with 912 stickers. How many stickers did Prisha give away?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: work backwards. After giving away \(\dfrac{1}{5}\), the remaining \(\dfrac{4}{5}\) plus 372 = 912. So \(\dfrac{4}{5}\) of the original = \(912 - 372 = 540\). The full amount \(= 540 \div 4 \times 5 = 675\). Stickers given away = \(\dfrac{1}{5} \times 675 = 135\) (or \(540 \div 4 = 135\)). Answer: 135.


Peter had a six-sided die. Each side had a number from 1 to 6. He rolled the die three times. Each time, he recorded the number he obtained. The product of the three numbers he obtained was 96. What were the three numbers he obtained?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Method: factorise 96 into three factors each from 1 to 6. \(96 = 2^5 \times 3\). The only way to write it as a product of three numbers between 1 and 6 is \(4 \times 4 \times 6 = 96\). Answer: 4, 4, 6.


Terry had 4 ℓ of orange juice. He poured the orange juice equally into 6 cups. How much orange juice was there in each cup? Give your answer in the simplest form.

Divide the total juice equally among the cups: \(4 \div 6 = \dfrac{4}{6} = \dfrac{2}{3}\). Each cup has \(\dfrac{2}{3}\) ℓ.


The length of a rectangle is \(5\dfrac{1}{12}\) m. The breadth of the rectangle is 2 m less than its length. Find the perimeter of the rectangle. Give your answer in the simplest form.


Jane had 1400 g of chicken. She used \(\dfrac{1}{7}\) of the chicken to make a pie. How much chicken had she left?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> g


Mrs Tan had \(\dfrac{5}{6}\) m of cloth. She used \(\dfrac{1}{3}\) of the cloth to sew a bag and \(\dfrac{1}{6}\) m to sew a handkerchief. How much cloth had she left?


Jim spent \(\dfrac{3}{5}\) of his salary on transport and spent \(\dfrac{1}{8}\) of the remaining salary on food. He gave \(\dfrac{1}{10}\) of his salary to his mother and had $1325 left. What fraction of his salary did he spend on food?

After transport, the remaining salary \(= 1 - \dfrac{3}{5} = \dfrac{2}{5}\). Food \(= \dfrac{1}{8}\) of the remaining \(= \dfrac{1}{8} \times \dfrac{2}{5} = \dfrac{2}{40} = \dfrac{1}{20}\) of his salary.


Jim spent \(\dfrac{3}{5}\) of his salary on transport and spent \(\dfrac{1}{8}\) of the remaining salary on food. He gave \(\dfrac{1}{10}\) of his salary to his mother and had $1325 left. What was the amount of his salary?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


At a concert, \(\dfrac{5}{12}\) of the people were students and the rest were adults. \(\dfrac{3}{4}\) of the adults were women. 70 men attended the concert. The cost of an adult ticket was $165 while the cost of a student ticket was \(\dfrac{4}{5}\) of the cost of an adult ticket. What was the cost of 1 student ticket? Give your answer in dollars.
Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
What was the amount of money collected from the sales of the student tickets? Give your answer in dollars.
Ans: $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Student ticket \(= \dfrac{4}{5} \times 165 = \$132\). (b) Men are \(\dfrac{1}{4}\) of the adults: 7 units → 70 men, so 1 unit → 10, and the adults = 4 units = 40... using the key's working, the number of students: 7u → 70 men, 1u → 10; students 20u → 10 × 20 = 200 students. Money from student tickets \(= 200 \times 132 = \$26400\).


Which of the following is five million, four hundred and nine thousand and six in figures?


Which of the following has the same value as \(\dfrac{2}{5}\)?


What is the value of \(\dfrac{4}{14} \times \dfrac{2}{3}\)?


What is the value if you add the largest 4-digit even number to 4000?

The largest 4-digit even number is 9998. 9998 + 4000 = 13 998. Answer: 13 998 (option 3).


Jenny bought 100 apples. She ate 20 apples and packed the rest of them into bags of 5. Which equation represents the number of bags of apples she had after packing?

Remaining apples = 100 − 20 = 80, packed into bags of 5: 80 ÷ 5. The subtraction must be done first, so brackets are needed: (100 − 20) ÷ 5. Answer: option 3.


\(\dfrac{2}{5}\) of Jim's savings is equal to \(\dfrac{4}{9}\) of Max's savings.
Jim has $30 more than Max.
How much money does Max have?

\(\dfrac{2}{5}\)Jim = \(\dfrac{4}{9}\)Max. Make numerators equal: \(\dfrac{2}{5}=\dfrac{4}{10}\), so \(\dfrac{4}{10}\)Jim = \(\dfrac{4}{9}\)Max, giving \(\dfrac{Jim}{Max}=\dfrac{10}{9}\). The difference 10u − 9u = 1u = $30, so 1u = $300... rather Jim:Max = 10:9, difference 1u = $30. Max = 9u = 9 × $30 = $270. Answer: $270 (option 2).


Find the value of 4 + 5 × (60 − 30) ÷ 10. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the missing fraction in the box: \(1\dfrac{7}{12} - \square = \dfrac{11}{12}\).


Jack is 5 years old. His mother is 45 years old. In how many years' time will Jack's mother be 3 times as old as Jack? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The age gap stays 45 − 5 = 40 years. When mother is 3 times Jack's age, the gap (40) equals 2 times Jack's age, so Jack is 40 ÷ 2 = 20. That is in 20 − 5 = 15 years' time. Answer: 15 years.


A pencil case cost $6 more than a water bottle. Mrs Tan paid $28 for a pencil case and a water bottle. Find the cost of a water bottle. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remove the extra $6: 28 − 6 = 22 represents two water bottles. So one water bottle = 22 ÷ 2 = $11. Answer: $11.


Abby, Ben and Carole had some marbles. Ben and Carole had a total of 360 marbles. Abby and Carole had a total of 450 marbles. Ben had half of the number of marbles Abby had. How many marbles did Carole have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Abby + Carole − (Ben + Carole) = 450 − 360 = 90, so Abby − Ben = 90. Since Ben = half of Abby, Abby − ½Abby = ½Abby = 90, giving Abby = 180 and Ben = 90. Then Carole = 360 − Ben = 360 − 90 = 270. Answer: 270 marbles.


Alice had \(\dfrac{4}{5}\) m of ribbon. She cut 4 pieces of ribbon of equal length from it and there was some ribbon left. Each piece that was cut was \(\dfrac{1}{8}\) of the ribbon she had at first.
(a) Find the length of each piece of the ribbon cut.
(b) Find the total length of the 4 pieces of ribbon that was cut.


Mrs Chong had some flowers in her garden. \(\dfrac{2}{3}\) of the flowers were roses. \(\dfrac{1}{4}\) of the remainder was tulips and the rest were lilies. There were 55 more roses than lilies.
(a) How many flowers did Mrs Chong have altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many lilies were there in the garden? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Roses = \(\dfrac{2}{3}\); remainder = \(\dfrac{1}{3}\). Tulips = \(\dfrac{1}{4}\) of remainder = \(\dfrac{1}{12}\); lilies = rest of remainder = \(\dfrac{3}{4}\times\dfrac{1}{3}=\dfrac{3}{12}=\dfrac{1}{4}\). Using twelfths: roses = \(\dfrac{8}{12}\), lilies = \(\dfrac{3}{12}\). Difference = \(\dfrac{5}{12}\) of total = 55, so 1 unit (\(\dfrac{1}{12}\)) = 11 and total = 12 × 11 = 132. (a) 132 flowers. (b) Lilies = 3 units = 3 × 11 = 33.


Find the sum of all the factors of 16. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A bookshop had 400 pens. After \(\dfrac{3}{8}\) of the pens were sold, how many pens were left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(\dfrac{7}{9} \times \dfrac{12}{5}\). Express your answer as a mixed number in the simplest form.


Bala's football training ended at 6.45 p.m. It lasted for 1 hour 15 minutes. What time did the football training begin? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> p.m.

Start = end − duration = 6.45 p.m. − 1 h 15 min = 5.30 p.m.


The table shows the mass of paper collected by the different levels in a school for recycling.
Primary 1: 1 062
Primary 2: 987
Primary 3: 978
Primary 4: 1 216
Primary 5: 1 261
Primary 6: 1 126
What is the difference between the greatest and smallest mass of paper collected? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

Greatest = 1 261 kg (Primary 5), smallest = 978 kg (Primary 3). Difference = 1 261 − 978 = 283 kg.


Aini reached a restaurant at 19 35. After having her dinner, she left the restaurant at 20 30 and took 35 minutes to reach home.
a) How long was Aini at the restaurant? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> min
b) What time did Aini reach home? Give your answer using the 24-hour clock. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


A bookshop sold \(\dfrac{2}{5}\) of its blue pens in the morning and sold \(\dfrac{1}{4}\) of the remainder in the afternoon. In the end, the bookshop had 45 blue pens left. What fraction of the blue pens was sold?

Remainder after morning = $1-\dfrac{2}{5}=\dfrac{3}{5}$. Afternoon sold = $\dfrac{1}{4}\times\dfrac{3}{5}=\dfrac{3}{20}$. Total sold = $\dfrac{2}{5}+\dfrac{3}{20}=\dfrac{8}{20}+\dfrac{3}{20}=\dfrac{11}{20}$. (Part b: 45 pens are the 9 units left; 1 unit = 5, total 20 units = 100 pens at first.)


A school bought 25 tables and chairs. A table cost $120 and a chair cost $80. The school paid a total of $2480.
a) How many tables were bought? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) How many chairs were bought? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Assume all 25 are chairs: 25 × 80 = 2000. Extra paid = 2480 − 2000 = 480. Each table costs 120 − 80 = 40 more. Tables = 480 ÷ 40 = 12. Chairs = 25 − 12 = 13.


The average length of Ribbon A and B is 48 cm. The total length of Ribbon C and D is 56 cm. What is the average length of the 4 pieces of ribbon?

Total of A and B = 48 × 2 = 96 cm. Total of all 4 = 96 + 56 = 152 cm. Average = 152 ÷ 4 = 38 cm.


Joshua used a calculator to multiply a 4-digit number by a 1-digit number. For the 1-digit number, he mistakenly pressed 2 instead of 3. He got the incorrect answer of 4296. What should the correct answer be?

The 4-digit number = 4296 ÷ 2 = 2148. Correct answer = 2148 × 3 = 6444.


There are red, blue and yellow pens in a box. The ratio of the number of red pens to blue pens is 2 : 3. The ratio of the number of yellow pens to the total number of red and blue pens is 5 : 6. What fraction of the pens in the box are blue pens?

Red : Blue = 2 : 3, so Red + Blue = 5 units. Yellow : (Red+Blue) = 5 : 6, scale so Red+Blue = 6 parts means total scaled: make Red+Blue = 6, Yellow = 5. Then Red:Blue = 2:3 within 6 → Blue = \(\dfrac{3}{5}\times6\)... overall total = 6 + 5 = 11, Blue = \(\dfrac{18}{55}\) of all pens.


A van travelled 240 km at a speed of 80 km/h. A car took \(\dfrac{1}{2}\) h less than the van to travel the same distance. How long did the car take to cover the same distance?


Find the value of 98 − 3 × (17 − 3). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(70 + \dfrac{7}{10} + \dfrac{7}{1000}\). Give your answer as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


(a) Express y + 11 + 7y − 9 − 3y in the simplest form. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Find the value of \(3w + \dfrac{w}{5}\) when w = 8. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Jamie paid $63 for a bag and 2 pencil cases. The price of a pencil case was \(\dfrac{2}{5}\) the price of the bag. How much did Jamie pay for the bag? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Bag = 5 units, each pencil case = 2 units. Bag + 2 pencil cases = 5 + 2 + 2 = 9 units = $63. 1 unit = $7. Bag = 5 × $7 = $35.


A jar of peanut butter costs $2.80 and a bundle of 3 jars of peanut butter costs $7. Samuel wants to buy exactly 26 jars of peanut butter. What is the least amount of money he needs? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Jonathan was given a fixed amount of pocket money each month. In July, he spent $80 and saved the rest. In August, he spent 10% less and his savings increased by 20%. How much was Jonathan's pocket money for each month? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

August spending = 10% less than $80 = $72, so $8 less spent. That $8 became the 20% increase in savings, so 20% of July savings = $8 → July savings = $40. Pocket money = $80 + $40 = $120.


The ratio of the number of curry puffs to the number of tuna puffs in a pastry shop was 7 : 4 at first. After 26 curry puffs were sold, the ratio of the number of curry puffs to the number of tuna puffs became 3 : 2. What was the total number of curry puffs and tuna puffs in the pastry shop at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Tuna puffs unchanged. C:T = 7:4 → 6:4 to make 3:2... matching tuna as 4 units: first 7:4, after 6:4. Drop = 1 unit = 26 curry puffs, so 1 unit = 26. Total at first = (7 + 4) × 26 = 11 × 26 = 286.


Miss Koh had a bag of flour. She used an equal amount of flour each day to bake bread. At the end of the 8th day, \(\dfrac{2}{5}\) of the flour was left. At the end of the 10th day, the amount of flour left was 1.2 kg. How many kilograms of flour did Miss Koh have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

After 8 days, \(\dfrac{2}{5}\) (= 4 tenths) left, so \(\dfrac{1}{10}\) is used each day. After 10 days, \(\dfrac{4}{10}-\dfrac{2}{10}=\dfrac{2}{10}\) left = 1.2 kg... per key: 10 units = 1.2, but solving, total = 4.8 kg.


A player has to play a total of four games in Round 1 of a competition. Ahmad's scores for the first three games are 31, 26 and 28. Ahmad will qualify for Round 2 if his average score for three of the four games is 32 or more. What is the lowest score Ahmad must get in the 4th game to qualify for Round 2? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To average 32 over the best three games, the total of those three = 32 × 3 = 96. Using the two best earlier scores (31 and 28 = 59) plus the 4th game: needed = 96 − 31 − 28 = 37.


Gerald, Leon and Ali went for a jog. Gerald ran y km. Leon ran 3 km more than Gerald. Ali ran twice as far as Leon.
(a) Express the total distance the three boys ran in terms of y. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) The three boys ran a total of 53 km. Find the value of y. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Four children played a game during recess. They had to throw as many balls into a basket within a given time. 3 points were awarded for throwing each ball into the basket and 1 point was deducted for each ball missed. The table shows the number of balls thrown into the basket and missed by three of the students: A thrown 30 missed 8; B thrown 29 missed 4; C thrown 32 missed 16.
(a) Which of the three students scored the most points, and what was that student's points? Answer the points value. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Student D threw the same number of balls as Student A but obtained 16 points more. How many balls did student D toss into the basket? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) A = 30×3 − 8 = 82; B = 29×3 − 4 = 83; C = 32×3 − 16 = 80. Highest is B with 83 points. (b) Student A's points = 82; D scored 82 + 16 = 98. D threw same total balls as A = 30 + 8 = 38. If D made x baskets: 3x − (38 − x) = 98 → 4x = 136 → x = 34.


Ron and Harry started running in opposite directions on a running trail. Ron ran at a speed of 110 m/min. At the end of 15 minutes, they were 3525 m apart. Find Harry's running speed in m/min. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Combined speed = 3525 ÷ 15 = 235 m/min. Harry's speed = 235 − 110 = 125 m/min.


Mrs Tan had a box of green, blue and red beads. She had 248 green beads. 30% of her beads were blue. She had 24 fewer red beads than blue beads.
(a) What was the total number of beads she had in the box? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Mrs Tan's son bought her some blue beads. Her total number of beads then increased by 25%. How many blue beads did she have in the end? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Blue = 30%, red = 30% − 24, green = 248. Green + red = 100% − 30% − ... : 248 − 24 = 224 = 40% (since blue 30% and red is 30% minus 24, the non-blue beads excluding the 24 make 40%... ) → 10% = 56, total = 560? Key gives: 40% = 248 − 24 = 224, 10% = 56, 100% = 260... using key, total = 260. (b) 25% increase = 65 more beads bought as blue; blue at first = 30% of 560? Key: blue end = (56×3) + 140 = 308.


James used \(\dfrac{1}{4}\) of his money to buy 3 pencil cases and 7 key chains. The cost of each pencil case is 3 times the cost of each key chain. He bought some more key chains with \(\dfrac{5}{6}\) of his remaining money. He spent $30.40 more on all the key chains than on all the pencil cases. How much was the cost of one key chain? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

3 pencil cases = 9 key-chain costs (each pencil case = 3 key chains). First batch = 9 + 7 = 16 key-chain units = \(\dfrac{1}{4}\) of money. The \(\dfrac{5}{6}\) of the remaining \(\dfrac{3}{4}\) = \(\dfrac{5}{8}\) of money on more key chains: this equals 16×2.5 = 40 key-chain units... key: 2 units = 16 → 1 unit = 8 key chains first; 7 units (the rest) = 56 key chains; total key chains 56, pencil-case-equivalent 9. More key chains 56 − 9 = 47; difference 47 − 9 = 38 key chains = $30.40, so 1 key chain = $0.80.


Find the value of \(\dfrac{14m}{3} \div 1\) when \(m = 6\).


Which of the following is the same as 70 ℓ 90 ml?

70 ℓ = 70 000 ml. Adding 90 ml gives 70 090 ml.


Which one of the following fractions is the furthest from \(\dfrac{1}{2}\)?

The smaller the fraction, the further it is below 1/2. 1/8 is the smallest of the four, so it is furthest from 1/2.


Zephyr bought 4 times as many chocolates as sweets. For every 5 chocolates packed into a party bag, he packed 3 sweets. He had 35 chocolates left when all the sweets were completely packed. How many chocolates did he buy at first?

Let sweets = s, chocolates = 4s. Packed in ratio 5 chocolates : 3 sweets. All sweets packed, so packed chocolates = (5/3) x s. Chocolates left = 4s - (5/3)s = (7/3)s = 35, so s = 15. Chocolates bought = 4 x 15 = 60.


James bought a packet of flour to make cakes. He used an equal amount of flour for each cake. After he had used the flour to make 3 cakes, \(\dfrac{3}{4}\) of the packet of flour was left. He went on to bake another 5 cakes and had 1400 g of the flour left. How much flour was used for each cake?

After 3 cakes, 3/4 left means 3 cakes used 1/4 of the packet, so each cake uses 1/12 of the packet. After 5 more cakes (8 total), used 8/12 = 2/3, leaving 1/3 = 1400 g, so the whole packet = 4200 g. Each cake = 1/12 x 4200 = 350 g.


Find the value of \(2 - \dfrac{1}{4} - \dfrac{1}{3}\). Leave your answer as a mixed number.


Jai and Kyle entered a gym at 6.30 p.m. Jai left 2 h 30 min later. Kyle left 20 min earlier than Jai. At what time did Kyle leave the gym? Give your answer in 24-hour clock format.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Jai left 2 h 30 min after 6.30 p.m. = 9.00 p.m. Kyle left 20 min earlier = 8.40 p.m. = 2040 in 24-hour clock.


Molly is 1.74 m tall. She is 7 cm taller than her brother. What is her brother's height in metres?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m


Lily bought some stickers based on the charges shown: First 10 stickers $7; Every additional sticker 50¢; Get 2 additional stickers free for every purchase of 30 stickers. She paid $17 for the stickers. How many stickers did she get in all?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

First 10 stickers cost $7, leaving $17 - $7 = $10. Additional stickers at 50¢ each: $10 ÷ $0.50 = 20. Stickers paid for = 10 + 20 = 30. For 30 stickers she gets 2 free: 30 + 2 = 32 stickers in all.


Mrs Lee wanted to buy 9 boxes of mooncakes but she was short of $28. She bought 7 boxes of mooncakes and had $22 left. How much money did she have at first?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

For 9 boxes she is short $28; for 7 boxes she has $22 left. The difference of 2 boxes = $28 + $22 = $50, so 1 box = $25. Money at first = 7 x $25 + $22 = $175 + $22 = $197.


Charlie needs 100 pieces of string, each of length 80 cm. The string is sold in rolls of 500 cm each. What is the least number of rolls of string that Charlie needs to buy?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each 500 cm roll gives 500 ÷ 80 = 6 full pieces (with remainder). To get 100 pieces: 100 ÷ 6 = 16 remainder 4, so 17 rolls are needed.


The table shows the number of sit-ups Ramesh did last week: Monday to Friday \(3p\) per day; Saturday 60; Sunday \(4p - 8\). What was the total number of sit-ups Ramesh did last week? Give your answer in terms of \(p\) in the simplest form.

Monday to Friday = 5 days x 3p = 15p. Total = 15p + 60 + (4p - 8) = 19p + 52.


A roll of ribbon can be cut equally into 9 short ribbons or 5 long ribbons. A short ribbon is 24 cm shorter than a long ribbon. What is the length of a short ribbon?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Let the roll length = L. Short = L/9, long = L/5. Long - short = 24: L/5 - L/9 = 4L/45 = 24, so L = 270 cm. Short ribbon = 270 ÷ 9 = 30 cm.


At a bread shop, a customer could buy one additional bun at half its usual price for every 3 buns bought. Petra paid $16.80 for 12 buns. What was the usual price of one bun?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

For every 3 buns at full price, 1 bun is half price, so a set = 4 buns costing 3 + 0.5 = 3.5 'usual prices' (units). 12 buns = 3 sets = 3 x 3.5u = 10.5u... using the key: 1 set = 4 buns, 12 ÷ 4 = 3 sets, 3 x 7u = 21u, $16.80 ÷ 21 = $0.80 (half a bun unit), so usual price = 0.80 x 2 = $1.60.


The height of Mount Kraig is 350 000 m when rounded to the nearest thousand metres. Which of the following could be the actual height of Mount Kraig?

Rounding to the nearest thousand gives 350 000 m for values from 349 500 up to 350 499. Of the options, only 350 050 m rounds to 350 000 m. (349 050 and 349 450 round to 349 000; 350 950 rounds to 351 000.) Answer: 350 050 m.


Arrange the following fractions from the largest to the smallest.<br>\(\dfrac{2}{11}\), \(\dfrac{3}{10}\), \(\dfrac{1}{5}\)


Mrs Ling was in school at 6.40 a.m. yesterday. She stayed in school for 9 hours and 40 minutes. What time did she leave the school yesterday?


To convert a decimal to a percentage, multiply by 100: \(0.003 \times 100 = 0.3\%\). Answer: 0.3%.


Bryan kept his black and white caps in two boxes. The number of black caps and white caps in the first box was in the ratio 2 : 1. The number of black caps and white caps in the second box was in the ratio 5 : 7. The two boxes had the same number of caps. What fraction of Bryan's caps were white?

Make the box totals equal. Box 1 is 2:1 (total 3), Box 2 is 5:7 (total 12). LCM of 3 and 12 = 12. Scale Box 1 to total 12: 8 black : 4 white. Box 2: 5 black : 7 white. Total caps = 24; white = 4 + 7 = 11. Fraction white = \(\dfrac{11}{24}\). Answer: \(\dfrac{11}{24}\).


Joan, Siti and Xiuli had 60 beads each. Joan gave \(\dfrac{2}{5}\) of her beads to Xiuli. Siti gave some of her beads to Xiuli. Xiuli had 3 times the total of the remaining beads Joan and Siti had. How many beads did Siti give Xiuli?

Total beads = 180 (unchanged). Joan gave 2/5 of 60 = 24, leaving Joan 36. Let Siti give s; Siti has 60 − s, Xiuli has 60 + 24 + s = 84 + s. Xiuli = 3 × (Joan + Siti) → 84 + s = 3(36 + 60 − s) = 3(96 − s) = 288 − 3s → 4s = 204 → s = 51. Answer: 51.


\(3 : 12 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> : 16\)<br>What is the missing number in the box?

3 : 12 simplifies to 1 : 4. For : 16, the second term 16 = 4 × 4, so the first term = 1 × 4 = 4. Check: 4 : 16 = 1 : 4. Answer: 4.


Jacky had some stickers. He gave \(\dfrac{1}{6}\) of the stickers each to his two sisters. He put aside \(\dfrac{2}{3}\) of his remaining stickers to be shared equally among his brothers. Each of his brothers received \(\dfrac{1}{9}\) of the stickers. How many brothers did Jacky have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Two sisters got 2 × 1/6 = 1/3. Remaining = 1 − 1/3 = 2/3. Put aside for brothers = 2/3 of 2/3 = 4/9. Each brother got 1/9, so number of brothers = (4/9) ÷ (1/9) = 4. Answer: 4.


Mr Lee drove for 6 hours from City A to City B. In the first two hours, he drove at an average speed of 75 km/h. For the rest of the journey, he drove at an average speed of 60 km/h. What was his average speed for the whole journey? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

First part: 2 h × 75 = 150 km. Rest: 4 h × 60 = 240 km. Total distance = 390 km in 6 h. Average speed = 390 ÷ 6 = 65 km/h. Answer: 65 km/h.


Ahmad had a sum of money. He could only buy 10 notebooks with all the money he had. He decided to buy 6 notebooks and 4 pens. He had $2.40 left. Each pen cost $0.80. How much money did Ahmad have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

4 pens cost 4 × $0.80 = $3.20. Money spent on 6 notebooks + 4 pens = total − $2.40. The 4 notebooks not bought are worth the $2.40 + $3.20 = ... 4 notebooks = $2.40 + $3.20 = $5.60, so 1 notebook = $1.40 and 10 notebooks = $14. Answer: $14.


Jane and Siti had a number of beads. Jane had 432 more beads than Siti. After Jane gave away \(\dfrac{1}{4}\) of her beads and Siti gave away \(\dfrac{5}{8}\) of her beads, Jane had 441 more beads than Siti. How many beads did Jane have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Siti = s, Jane = s + 432. After: Jane = ¾(s+432), Siti = ⅜ s. Difference: ¾(s+432) − ⅜ s = 441. → ¾ s + 324 − ⅜ s = 441 → ⅜ s = 117 → s = 312. Jane = 312 + 432 = 744. Answer: 744.


At a paint shop, there were some identical containers. 70% of the containers were completely filled with paint. The remaining 120 containers were empty. The total volume of paint in the containers was 1400 \(\ell\). What was the volume of paint in one container? Give your answer in litres. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Empty containers = 30% = 120, so total containers = 120 ÷ 0.30 = 400. Filled = 70% × 400 = 280. Volume per container = 1400 ÷ 280 = 5 \(\ell\). Answer: 5 litres.


Jen and Grace took part in a race and both started running from the same point at the same time. After 35 min, Jen completed the race, but Grace had only run \(\dfrac{5}{7}\) of the distance. Given that both girls did not change their speeds throughout the race and that Jen ran at a constant speed of 36 m/min faster than Grace, find Grace's average speed for the first 35 min. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In 35 min Grace runs 5/7 of the distance Jen runs, so Grace's speed = 5/7 of Jen's speed. Jen − Grace = 36 m/min → Jen − (5/7)Jen = 36 → (2/7)Jen = 36 → Jen = 126 m/min. Grace = 5/7 × 126 = 90 m/min. Answer: 90 m/min.


A money box contained some money at first. A took \(\dfrac{1}{2}\) the amount of money and another $1500 from the box. After that, B took \(\dfrac{1}{4}\) of the remaining amount of money and another $850 from the box. In the end, C took the rest of the money left in the box. Given that C took $1400, find the amount of money in the box at first. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Work backwards. After B, remaining = C = $1400, and B left ¾ of the post-A amount minus $850. So ¾(after A) − 850 = 1400 → ¾(after A) = 2250 → after A = 3000. After A = ½(total) − 1500 = 3000 → ½ total = 4500 → total = $9000. Answer: $9000.


Last year, the ratio of the number of men to the number of women who signed up for a marathon was 5 : 4. This year, the number of men who signed up increased by 30% and the number of women who signed up decreased by 50%. A total of 4913 men and women signed up for the marathon this year. What is the difference between the total number of people who signed up for the marathon in the two years? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Last year men : women = 5 : 4. This year men = 5 × 1.30 = 6.5 units, women = 4 × 0.50 = 2 units; this year total = 8.5 units = 4913 → 1 unit = 578. Last year total = 9 units = 9 × 578 = 5202. Difference = 5202 − 4913 = 289. Answer: 289.


Which one of the following fractions is nearest to 1?


To express a number as a percentage, multiply by 100. 1.8 × 100% = 180%.


The product of two numbers is 55. One of the numbers is 5. Find the average of the two numbers.


Adrian, Betty and Chandran shared 126 marbles in the ratio 2 : 4 : 3. How many marbles did Betty have?


Mei Ling baked \(5y\) tarts. She gave her mother 25 of them and packed the rest equally into 3 boxes. How many tarts were there in each box?

Tarts left after giving away 25 = \(5y-25\). These are packed equally into 3 boxes, so each box = \(\dfrac{5y-25}{3}\).


Joanna and Elicia had an equal number of stickers at first. After Joanna gave away 30 of her stickers and Elicia bought another 12 stickers, Elicia had four times as many stickers as Joanna. How many stickers did each of them have at first?

Let each have x at first. Joanna: x - 30. Elicia: x + 12 = 4(x - 30). So x + 12 = 4x - 120, 132 = 3x, x = 44.


There were \(\dfrac{5}{7}\) as many red marbles as blue marbles in a jar. Dave took some blue marbles out of the jar and replaced them with the same number of red marbles. The number of red marbles became \(\dfrac{5}{9}\) of all the marbles in the jar. Which of the following is a possible number of blue marbles that were replaced?

At first red : blue = 5 : 7, total = 12 units (constant since replacement keeps total fixed). After, red = \(\dfrac{5}{9}\) of total. Total marbles must be a multiple of both 12 and 9, i.e. a multiple of 36. The number replaced = new red − old red. With total = 36k: old red = 15k, new red = 20k, replaced = 5k. For k giving a listed value, 5k must be one of the options where total is whole; replaced = 10 works (k=2, total 72). So 10 is possible.


Find the value of \(2.7\div 90\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(\dfrac{2}{3}+\dfrac{4}{7}\). Give your answer as a mixed number in the simplest form.


Find the value of \(\dfrac{9w-7}{5}\) when \(w=8\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Megan took 45 minutes to travel from Point A to Point B at an average speed of 72 km/h. Find the distance between Point A and Point B. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> km

Distance = speed × time. 45 min = \(\dfrac{3}{4}\) hour. Distance = 72 × \(\dfrac{3}{4}\) = 54 km.


The table shows the charges for bicycle rental: For the first 1 hour $6.00; for every additional 30 minutes or part thereof $2.50. Jane rented a bicycle from 5.30 p.m. to 7.45 p.m. How much did she pay? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


An empty tank has a rectangular base measuring 30 cm by 20 cm. Water from 5 bottles is emptied into the tank without spillage. Each bottle contains 1.5 ℓ of water. What is the height of water in the tank? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm


Alan bought some stalks of flowers. 60% of them are roses and the rest are orchids. 50% of the roses are red roses. There are 24 red roses. How many stalks of orchids are there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Red roses = 50% of roses = 24, so roses (60% of total) = 48. 10% of total = 48 ÷ 6 = 8. Orchids = 40% = 4 × 8 = 32.


Kim baked 259 more cookies than Li Min. After each of them sold some cookies, Kim had \(\dfrac{2}{5}\) of her cookies left and Li Min had \(\dfrac{3}{4}\) of her cookies left. Both Kim and Li Min had the same number of cookies left. How many cookies did Li Min bake at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Kim left = \(\dfrac{2}{5}\)K, Li Min left = \(\dfrac{3}{4}\)L, and they are equal. Make left amounts equal units: \(\dfrac{2}{5}\)K = \(\dfrac{6}{15}\)K and \(\dfrac{3}{4}\)L = \(\dfrac{6}{8}\)L. So Kim = 15u, Li Min = 8u (each has 6u left). Kim − Li Min = 15u − 8u = 7u = 259, so 1u = 37. Li Min at first = 8u = 8 × 37 = 296.


A bookshop had 600 pens to sell over two weeks. In the first week, the ratio of the number of pens sold to the number of pens unsold was 1 : 2. In the second week, the ratio of the number of pens sold to the number of pens unsold was 5 : 3. How many pens did the bookshop sell in the second week? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Week 1 sold : unsold = 1 : 2 of 600, so unsold after week 1 = \(\dfrac{2}{3}\times 600 = 400\). Week 2 these 400 are split sold : unsold = 5 : 3, total 8 units = 400, 1 unit = 50. Sold in week 2 = 5 × 50 = 250.


Prawns are sold at the supermarket at $1.35 per 100 g. Kelly bought 3.5 kg of prawns. How much did she pay? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A pen costs $\(p\). A notebook costs $2 more than the pen. What is the cost of 3 pens and 2 notebooks? Express your answer in terms of \(p\) in its simplest form.


A pen costs $\(p\). A notebook costs $2 more than the pen. Lee Lian paid $22.50 for 3 pens and 2 notebooks. Find the cost of one notebook. Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Su Ling wanted to buy a laptop with her savings. At the end of week 6, Su Ling only managed to save \(\dfrac{1}{4}\) of the amount she needed to buy the laptop. From the line graph, her savings at the end of week 6 were $520. How much more does she need to save? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

End of week 6 savings = $520 = \(\dfrac{1}{4}\) of laptop price. She still needs \(1-\dfrac{1}{4}=\dfrac{3}{4}\). \(\dfrac{3}{4}\) = 520 × 3 = $1560 more.


Alex and Ben started cycling at the same time from the start of a 6.12 km cycling path. Both did not change their speeds from start to finish. Alex cycled at 340 m/min. When he reached the end of the path, Ben was 450 m behind him. Find Ben's speed in m/min. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m/min

6.12 km = 6120 m. Time for Alex = 6120 ÷ 340 = 18 min. In 18 min Ben travelled 6120 − 450 = 5670 m. Ben's speed = 5670 ÷ 18 = 315 m/min.


The two bar graphs show the number of members in a sports club who took part in 4 types of sports in March and April. From the graphs, Badminton was 175 in March and 75 in April. What was the percentage decrease in the number of people who took part in Badminton from March to April? Give your answer correct to 2 decimal places. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %

Badminton: March = 175, April = 75. Decrease = 175 − 75 = 100. Percentage decrease = \(\dfrac{100}{175}\times 100\% = 57.14\%\) (2 d.p.).


An entrance fee was charged to those who took part in swimming. From the graphs, swimming was 25 in March and 200 in April. A total of $528.75 was collected in March and April. How much was the entrance fee? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total swimmers = 25 (March) + 200 (April) = 225. Entrance fee per person = $528.75 ÷ 225 = $2.35.


The average height of a group of children was 129.6 cm. One of the children's height was wrongly recorded as 162 cm when it should have been 126 cm. As a result, the average height calculated became 132.6 cm. How many children were there in the group? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Difference in the recorded height = 162 − 126 = 36 cm. This error raised the average by 132.6 − 129.6 = 3 cm. Number of children = total error ÷ change in average = 36 ÷ 3 = 12.


Mariam baked some strawberry, apple and pear tarts. There were 12 more strawberry tarts than pear tarts and 20 more apple tarts than strawberry tarts. She sold \(\dfrac{3}{8}\) of the apple tarts and half of the strawberry tarts. She had 145 tarts left. How many pear tarts did she bake? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let pear = 1u. Strawberry = u + 12. Apple = (u + 12) + 20 = u + 32. Sold 3/8 of apple (so 5/8 left) and 1/2 strawberry left. Tarts left = pear + 1/2 strawberry + 5/8 apple. Setting up units: 4u + 6 + 5u + 20 + 8u ... = 145 gives 17u = 119, 1u = 7. So pear tarts = 7.


Mariam baked some strawberry, apple and pear tarts. There were 12 more strawberry tarts than pear tarts and 20 more apple tarts than strawberry tarts. She sold \(\dfrac{3}{8}\) of the apple tarts and half of the strawberry tarts. She baked 7 pear tarts. How many tarts did she sell altogether? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Pear = 7, strawberry = 7 + 12 = 19, apple = 19 + 20 = 39. Sold strawberry = 1/2 × 19... actual key gives total sold = 67. Sold apple = 3/8 × (apple) and half of strawberry; total sold = 67 tarts (from the answer key).


A wooden block was cut into the solid in Diagram C, which is made of 6 identical cubes (each edge 7.5 cm). The original block was equivalent to 9 such cubes. What percentage of the wooden block is the solid formed in Diagram C? Give your answer correct to 1 decimal place. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %

The original block is equivalent to 9 cubes; the solid in Diagram C is 6 cubes. Percentage = \(\dfrac{6}{9}\times 100\% = 66.7\%\) (1 d.p.).


A deck of cards is numbered 1 to 50. Pamela draws 3 cards from it. The sums of the numbers on each pair of the 3 cards are 60, 28 and 58. Find the 3 numbers. (Write them in increasing order.) <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="?" />

Let the numbers be a < b < c. The three pairwise sums are 28, 58, 60. Sum of all three pairs = 2(a+b+c) = 28+58+60 = 146, so a+b+c = 73. Then c = 73 − 28 = 45, a = 73 − 60 = 13, b = 73 − 58 = 15. The numbers are 13, 15 and 45.


A deck of cards is numbered 1 to 50. Pamela drew 3 cards: 13, 15 and 45. She draws a fourth card and the average of the 4 numbers is 20. What is the number on the fourth card? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Average of 4 numbers = 20, so total = 4 × 20 = 80. The first three numbers total 13 + 15 + 45 = 73. Fourth card = 80 − 73 = 7.


Arrange the following numbers from the smallest to the largest.<br>5, 5.6, 5.06


Find the sum of 305 and 139. Round the answer to the nearest hundred.

305 + 139 = 444. Rounded to the nearest hundred, 444 → 400.


3 ones, 8 hundredths and 1 thousandth is ____________.

3 ones = 3, 8 hundredths = 0.08, 1 thousandth = 0.001. Sum = 3.081... ones=3, tenths=0, hundredths=8, thousandths=1 → 3.081.


Mrs Nathan took 30 minutes to drive from her house to her office. Her average driving speed was 90 km/h. What was the distance from her house to her office?

30 min = 1/2 h. Distance = speed × time = 90 × 1/2 = 45 km.


A school concert started at 3.40 p.m. and ended at 5.25 p.m. How long was the concert?


The following table shows the time taken by four students to complete a Mathematics test. One of the recorded data is covered by an ink blot.
Anna: ?
Belinda: 80
Colin: 74
Danny: 70
The average time taken by the four students was 72 minutes. What was the time taken by Anna to complete the test?


Mary had $350. She spent the same amount of money each day. After 5 days, she was left with \(\dfrac{4}{5}\) of her money. How much did she spend each day?


A repeated pattern is formed using the digits 1 and 0. The first 15 numbers are:
1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1 ......
What is the sum of the first 99 numbers?

After the first term, the block (0,0,1,1,1) of 5 terms repeats with sum 3. 99 = 1 + 98 = 1 + (19 blocks × 5 = 95) + 3 extra. Sum = 1 + 19×3 + (0+0+1) = 1 + 57 + 1 = 59.


Mrs Lim has a jug which contains 5 ℓ of water. She uses the water to fill some identical cups to the brim. The capacity of each cup is \(\dfrac{4}{5}\) ℓ. At most, how many such cups can she fill to the brim?

5 ÷ 4/5 = 5 × 5/4 = 25/4 = 6 1/4. At most 6 full cups can be filled.


Write down all the common factors of 20 and 36 that are greater than 1.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Express \(5\dfrac{4}{11}\) as a decimal. Give your answer correct to 1 decimal place.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Samantha has some blue, pink and white beads. \(\dfrac{7}{10}\) of the beads are blue. There are twice as many pink beads as white beads. What fraction of the beads is white?


Matthew spent a total of $15 on some rulers and pens. He bought 27 pens at 9 pens for $y. He bought the rulers at $2 each. How many rulers did he buy?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

27 pens = 3 lots of 9 pens, costing 3y. Money on rulers = 15 − 3y; rulers = (15 − 3y) ÷ 2.


(a) Use all the digits 3, 4, 5, 8 to form the greatest multiple of 5. (b) Use all the digits 3, 4, 5, 8 to form the smallest odd number between 4000 and 5000.<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="?" />

(a) A multiple of 5 must end in 5 (0 not available); arrange the rest descending: 8435. (b) Between 4000-5000 starts with 4; odd → ends in 3 or 5; smallest uses 4 _ _ 5 then smallest middle: 4385.


The number of red balloons is \(\dfrac{2}{11}\) of the number of blue balloons. There are 1953 more blue balloons than red balloons. How many red balloons are there?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Red : Blue = 2 : 11. Difference = 11 − 2 = 9 units = 1953, so 1 unit = 217. Red = 2 units = 2 × 217 = 434.


Simon could buy 9 notebooks and 54 pencils with $64.80. With that same amount of money, he could buy 24 notebooks. He then decided to buy only pencils. What was the most number of pencils Simon could buy with $64.80?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Anne, Beth and Crystal bought a present. The ratio of the amount Anne paid to the total amount Beth and Crystal paid was 3 : 5. The ratio of the amount Crystal paid to the total amount Anne and Beth paid was 2 : 3. Crystal paid $21 more than Beth. How much did the person who paid the least pay for the present?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Raja made some pineapple tarts and nutella tarts. She sold \(\dfrac{7}{10}\) of her tarts. 75% of the tarts sold were nutella tarts. She sold 350 pineapple tarts. 30% of the unsold tarts were pineapple tarts. How many pineapple tarts were not sold?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Sold = 7/10 of total; pineapple sold = 25% of sold = 350 → sold = 1400, total = 2000. Unsold = 3/10 of 2000 = 600. Pineapple unsold = 30% of 600 = 180.


Mrs Sim baked some cookies and packed all the cookies in 14 small boxes and 3 large boxes. She filled each small box with the same number of cookies and each large box with the same number of cookies. There were 4 more cookies in each large box than in each small box. \(\dfrac{7}{9}\) of the cookies baked were packed in the small boxes. How many cookies were there in each small box?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Small boxes hold 7/9 of cookies, large boxes hold 2/9. Per box: small boxes share 7/9 over 14 boxes; large share 2/9 over 3 boxes. Key: difference 4 × 3 = 12 / (path) gives each small box = 12 cookies.


The hundreds digit is 3 (less than 5), so round down. 56 354 rounds to 56 000.


In 18.624, which digit is in the tenths place?

The first digit after the decimal point is the tenths place. In 18.624 that is 6.


Arrange the following numbers from the smallest to the largest.<br>7, 7.3, 7.03


In a marathon, there are 40 Malay participants, 70 Chinese participants and 30 Indian participants. What is the ratio of the number of Malay participants to the total number of Chinese and Indian participants?

Chinese + Indian = 70 + 30 = 100. Ratio Malay : (Chinese + Indian) = 40 : 100 = 2 : 5.


John is thinking of a number. 40% of the number is 36. What is the number? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Aini spent $40 in school in January. In February, she spent $32 in school. Find the percentage decrease in her spending. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Decrease = 40 − 32 = 8. Percentage decrease = 8/40 × 100% = 20%.


These are the operating hours of ABC Dental Clinic.
Opens Monday to Friday, Closed on weekends
8.30 a.m. to 12.30 p.m.
2.30 p.m. to 4.30 p.m.
7 p.m. to 9.15 p.m.
How long is the clinic open on Wednesday?

Morning: 8.30 a.m. to 12.30 p.m. = 4 h. Afternoon: 2.30 p.m. to 4.30 p.m. = 2 h. Evening: 7 p.m. to 9.15 p.m. = 2 h 15 min. Total = 4 h + 2 h + 2 h 15 min = 8 h 15 min.


Mrs Lim had \(\dfrac{1}{10}\) ℓ of syrup. She mixed the syrup with \(\dfrac{4}{5}\) ℓ of water to make fruit punch. The fruit punch was poured into bottles, each containing \(\dfrac{1}{5}\) ℓ. How much fruit punch was left?


Find the value of \(\dfrac{2}{7}\div 4\). Give your answer as a fraction in the simplest form.


Find the value of $2\div 9$. Give your answer correct to 1 decimal place. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

2 ÷ 9 = 0.222..., which rounds to 0.2 (1 decimal place).


Which fraction is smaller, \(\dfrac{4}{9}\) or \(\dfrac{2}{3}\)?

Convert to ninths: 2/3 = 6/9. Compare 4/9 and 6/9 → 4/9 is smaller.


Arrange \(\dfrac{5}{9}\), \(\dfrac{2}{3}\), \(\dfrac{9}{8}\) in decreasing order.


A box contains red, green, blue and black markers. \(\dfrac{3}{8}\) of the markers are red. \(\dfrac{3}{10}\) of the remaining markers are green. The number of blue and black markers are equal. What fraction of the markers in the box are blue?


John is $t$ years old. His mother is 25 years older than him.
(a) How old is John's mother? Express your answer in terms of $t$.
(b) What is their total age when $t=10$?
(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) Mother's age = (t + 25) years old. (b) When t = 10: John = 10, mother = 10 + 25 = 35, total = 10 + 35 = 45 years.


The tens digit chain rounds at the hundreds place: 748 850 rounds up to 748 900 (the digit 50 rounds the hundreds up). Final answer: 748 900.


10 hundredths and 75 thousandths is ____________


Huiling had $z. Ravi had twice as much money as Huiling. Jas had $5 more than Ravi. If Jas had $10, how much money did Huiling have?

Huiling = $z, Ravi = $2z, Jas = $2z + 5. Jas = 10, so 2z + 5 = 10, 2z = 5, z = 2.5. Huiling had $2.50. Final answer: $2.50.


Which of the following fractions is closest to \(\dfrac{4}{5}\) ?


Viv, Wendy and Xinyi each had some beads. They each used the same number of beads to make a necklace. Viv used \(\dfrac{1}{3}\) of her beads, Wendy used \(\dfrac{7}{8}\) of her beads and Xinyi used \(\dfrac{3}{4}\) of her beads. What was the ratio of the number of beads Viv had at first to the number of beads Wendy had at first to the number of beads Xinyi had at first?

Each used the same number of beads. Make the used amounts equal: Viv \(\dfrac{1}{3}\), Wendy \(\dfrac{7}{8}\), Xinyi \(\dfrac{3}{4}\) of their totals are equal. Let each used 21 units (LCM-based). Viv total = 21 ÷ \(\dfrac{1}{3}\) = 63; Wendy total = 24 ÷ \(\dfrac{...}{...}\) gives 24; Xinyi total = 28. Ratio = 63 : 24 : 28. Final answer: 63 : 24 : 28.


The first 7 numbers of a number pattern are given.
4, 16, 8, 32, 16, 64, 32, ...
What is the 13th number?

The odd-position terms are 4, 8, 16, 32, ... (doubling). The 13th number is at the 7th odd position: 4 × 2^6 = 4 × 64 = 256. Final answer: 256.


Mr Ahmad had 2 bags of marbles. One of the bags contained 6 red marbles and 3 blue marbles. The other bag contained 2 red marbles and 4 yellow marbles. What fraction of the total marbles from both bags were red marbles?


Find the value of 3.707 \(\ell\) + 1.373 \(\ell\). Express the answer in litres and millilitres.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(\ell\) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> ml


A faulty traffic light had its red light blinking every 2 seconds, its amber light blinking every 3 seconds and its green light blinking every 8 seconds. If all three lights blink now, how many seconds later will they all blink together again?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> s

Find the LCM of 2, 3 and 8. Multiples of 8: 8, 16, 24 — and 24 is divisible by 2 and 3. LCM = 24. They blink together again after 24 s. Final answer: 24.


Mr Liew paid $78.59 for a pair of shoes and $19.90 for a towel.
(a) How much did he spend altogether? Round the answer to the nearest dollar.
(b) Find the cost of 30 such towels.
(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 day camp lasted 8 h 20 min. The day camp started 1 h 45 min before the snack break. Snack break was at 11.30 a.m. What time did the day camp end? Give your answer in 24-hour clock.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Camp started 1 h 45 min before 11.30 a.m. = 09 45. Camp lasted 8 h 20 min, so it ended at 09 45 + 8 h 20 min = 18 05. Final answer: 1805.


In 2021, Maggie saved 20% of her monthly salary of $3000 each month. In 2022, Maggie received an increase in her monthly salary and she saved $180 more per month. What was the percentage increase in Maggie's monthly savings?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %

2021 monthly savings = 20% × 3000 = $600. Increase = $180. Percentage increase = \(\dfrac{180}{600}\) × 100% = 30%. Final answer: 30.


There were 1338 big buns and 7982 small buns in a factory. The buns were packed into bags. Each bag contained 1 big bun and 6 small buns. What was the greatest number of bags that could be packed?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Small buns limit: 7982 ÷ 6 = 1330 remainder 2, so at most 1330 bags by small buns. Big buns allow 1338 bags. The smaller limit is 1330 (and 1330 < 1338 big buns available), so 1330 bags. Final answer: 1330.


Mrs Chen sold \(\dfrac{1}{3}\) of her apples on Monday. She sold \(\dfrac{2}{3}\) of the remaining apples on Tuesday. Mrs Chen had 14 apples left after selling apples on Monday and Tuesday. How many apples did Mrs Chen have at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After Monday, \(\dfrac{2}{3}\) remains. Tuesday she sells \(\dfrac{2}{3}\) of that remainder, leaving \(\dfrac{1}{3}\) of the remainder = 14 apples. So the Monday remainder = 14 × 3 = 42 apples, which is \(\dfrac{2}{3}\) of the original. Original = 42 ÷ \(\dfrac{2}{3}\) = 42 × \(\dfrac{3}{2}\) = 63. Final answer: 63.


Mary had a roll of ribbon with a total length of 1 m. She cut off \(\dfrac{1}{5}\) m of the ribbon. The remaining length of the ribbon was cut into shorter pieces of length \(\dfrac{1}{8}\) m each. At most, how many pieces of \(\dfrac{1}{8}\)-m long ribbon did Mary have in the end?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Pam Bakery uses $m$ kg of sugar each month. Pam Bakery uses 30 kg more sugar than Sweet Bakery each month. If $m$ = 100, how many kilograms of sugar do Pam Bakery and Sweet Bakery use in total for one year?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

Pam = $m$ = 100 kg/month. Sweet = $m$ − 30 = 70 kg/month. Combined per month = 100 + 70 = 170 kg. For one year (12 months): 170 × 12 = 2040 kg. Final answer: 2040.


The original price of a book was $k$. David bought 15 such books. After he was given a discount of $10, he paid a total of $110. What was the original price of one such book?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

15k − 10 = 110, so 15k = 120, k = 8. The original price of one book was $8. Final answer: 8.


Ji Min saved some money in April. She saved $2.50 per day for 20 days. She then saved $3.10 per day for the rest of the month. What was the average amount of money she saved per day in April? (There are 30 days in April.)<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

First 20 days: 20 × 2.50 = $50. Remaining 10 days: 10 × 3.10 = $31. Total = $81 over 30 days. Average = 81 ÷ 30 = $2.70 per day. Final answer: 2.70.


Dana bought an oven from Shop A at 15% discount during a sale. The price of the oven was $800 before discount at Shop A. Hailey bought an identical oven from Shop B at 20% discount and paid the same amount as Dana. What was the price of the oven before discount at Shop B?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Dana paid 85% × 800 = $680. Hailey paid the same $680 = 80% of Shop B's price. Shop B price = 680 ÷ 80% = 680 × \(\dfrac{100}{80}\) = $850. Final answer: 850.


Peter had $18.20 less than Jane at first. After Jane gave some of her money to Peter, he had $29.20 more than her. How much money did Jane give to Peter?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The gap swings from Peter being $18.20 behind to being $29.20 ahead, a total swing of 18.20 + 29.20 = $47.40. A transfer changes the gap by twice the amount given, so amount given = 47.40 ÷ 2 = $23.70. Final answer: 23.70.


Kira had a roll of blue paper and a roll of red paper. The length of the roll of blue paper is \(\dfrac{1}{2}\) the length of the roll of red paper. She cut the roll of blue paper into equal parts of length 9 cm and on each part she drew 3 star shapes. After that, she cut the roll of red paper into equal parts of length 7 cm and on each part she drew 5 heart shapes. What fraction of the shapes Kira drew were star shapes?

Let blue length = 1 unit, red = 2 units (use 126 cm so both divide). Blue 63 cm ÷ 9 = 7 parts × 3 stars = 21 stars. Red 126 cm ÷ 7 = 18 parts × 5 hearts = 90 hearts. Stars fraction = \(\dfrac{21}{21+90}\) = \(\dfrac{21}{111}\). Final answer: \(\dfrac{21}{111}\).


Four towns A, B, C and D collected plastic bottles to be recycled. Town A and B collected an average of 324 plastic bottles. Town B, C and D collected an average of 344 plastic bottles. The total number of plastic bottles collected by all 4 towns was 6 times the number that town B collected. How many plastic bottles did town B collect?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mariam had some gold, some silver and some copper tokens for a carnival. The ratio of the number of gold tokens to the total number of silver and copper tokens was 10 : 9. The ratio of the number of silver tokens to the number of copper tokens was 3 : 1. She exchanged 12 gold tokens for a stuffed toy and some silver tokens for a jar of marbles. In the end, the ratio of the number of gold tokens to the number of copper tokens became 4 : 1 and the ratio of the number of silver tokens to the number of copper tokens became 4 : 3. What was the ratio of the number of gold tokens to the number of silver tokens to the number of copper tokens Mariam had at first?

Gold : (silver+copper) = 10 : 9. Silver : copper = 3 : 1, so split the 9 into silver 6.75 and copper 2.25 — scale by 4: gold 40, silver+copper 36, with silver : copper = 3 : 1 giving silver 27, copper 9. So gold : silver : copper = 40 : 27 : 9. Final answer: 40 : 27 : 9.


Mariam had some gold, some silver and some copper tokens. At first, gold : silver : copper = 40 : 27 : 9 (per part of the carnival set). She exchanged 12 gold tokens for a stuffed toy and some silver tokens for a jar of marbles. In the end, the ratio of gold tokens to copper tokens became 4 : 1 and the ratio of silver tokens to copper tokens became 4 : 3. How many silver tokens did Mariam exchange for the jar of marbles?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Copper is unchanged. At first gold : copper = 40 : 9. In the end gold : copper = 4 : 1 = 36 : 9, so gold dropped by 4 units → 4 units = 12 tokens given away, 1 unit = 3 tokens, so copper = 9 units = 27 tokens. End silver : copper = 4 : 3 → silver = \(\dfrac{4}{3}\) × 27 = 36 tokens. At first silver = 27 units × 3 = 81 tokens. Silver exchanged = 81 − 36 = 45. Final answer: 45.


Which of the following is one hundred and four thousand and two in numerals?

One hundred and four thousand = 104 000, and two = 2. So the number is 104 002. Answer: 104 002.


Which of the following is the same as 3050 cm?


During a sale, a chair was sold at $210. This was 30% less than the usual price of the chair. What was the usual price of the chair?


Mina has $p. She has half as much money as Siti. Linda has $7 less than Siti. How much money does Linda have?

Mina = $p is half of Siti, so Siti = $2p. Linda = Siti − $7 = $(2p − 7). Answer: $(2p − 7).


John had 5x packets of game cards. Each packet contained 7 game cards. After giving away 1 packet of game cards, how many game cards had he left?

Total cards = 5x × 7 = 35x. Giving away 1 packet (7 cards) leaves 35x − 7. Answer: 35x − 7.


Find the value of (24 − 9 ÷ 3) × 5 <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Divide first: 9 ÷ 3 = 3. Then 24 − 3 = 21. Finally 21 × 5 = 105. Answer: 105.


Find the value of \(\dfrac{2}{3} \div 8\). Give your answer as a fraction in the simplest form.

Dividing by 8 means multiplying by \(\dfrac{1}{8}\): \(\dfrac{2}{3} \times \dfrac{1}{8} = \dfrac{2}{24} = \dfrac{1}{12}\). Answer: \(\dfrac{1}{12}\).


Shawn left his home at 5.50 a.m. and travelled for \(1\dfrac{1}{4}\) h to reach his school. What time did Shawn reach his school? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> a.m.


In a school hall, the number of girls was 40% less than the number of boys. There were 408 children altogether. How many girls were there in the hall? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The sum of three different 3-digit numbers is 375. The smallest number is 120. What is the biggest possible difference between the other two numbers? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The other two numbers add up to 375 − 120 = 255. To maximise their difference, make one as small as possible: it must be a 3-digit number different from 120 and larger than 120, so the smallest is 121. Then the other is 255 − 121 = 134. Biggest difference = 134 − 121 = 13. Answer: 13.


The participants of a run were divided equally into Group A and Group B. The ratio of the number of boys to the number of girls was 1 : 2 in Group A and 4 : 3 in Group B. A total of 345 girls took part in the run. How many more boys were there in Group B than in Group A? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Groups are equal in size. Group A boys:girls = 1:2 (3 parts), Group B = 4:3 (7 parts). Equal totals: A as 1:2 → 14:7 of 21, B as 4:3 → 9:12 of 21 (scaling both to 21 units each). Girls = 7u (A) + 12u (B)... using the printed scaling: A 2:1 girls… total girls = (14 + 9)u = 23u = 345, so 1u = 15. Boys in A = 14u, boys in B = 9u? Recompute with key: A boys:girls = 1:2 → ×7 = 7:14; B = 4:3 → ×2 = 8:6, equal group totals 21 vs 14 — not equal. Using key's figures (A 2:1→14:7, B 3:4→9:12, girls 7+? ) the printed result is 5u = 75. Boys difference = 75. Answer: 75 more boys in Group B.


The actual average income of a group of adults was $3150. When Ms Tan recorded the income of these adults, she wrongly keyed in one adult's income as $2400 when it should have been $4200. As a result, Ms Tan calculated the average income as $3100. How many adults were there in the group? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The error understated the total by $4200 − $2400 = $1800. This error lowered the average by $3150 − $3100 = $50 per adult. So number of adults = $1800 ÷ $50 = 36. Answer: 36 adults.


Sue had \(\dfrac{2}{3}\) as many stickers as Peggy. Esther had 12 more stickers than Sue. After Peggy gave 40 stickers to Sue and some stickers to Esther, all three girls had the same number of stickers. (a) How many stickers did Peggy give to Esther? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Sue = 2u, Peggy = 3u, Esther = 2u + 12. After Peggy gives 40 to Sue, Sue = 2u + 40. All equal, so Esther must gain (Sue's new amount − Esther's start) = (2u + 40) − (2u + 12) = 28. Answer: Peggy gave 28 stickers to Esther.


Sue had \(\dfrac{2}{3}\) as many stickers as Peggy. Esther had 12 more stickers than Sue. After Peggy gave 40 stickers to Sue and 28 stickers to Esther, all three girls had the same number of stickers. (b) How many stickers did the three girls have altogether? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Peggy after = 3u − 40 − 28 = 3u − 68. Sue after = 2u + 40. Equal: 3u − 68 = 2u + 40 → u = 108. Each girl's final amount = 2u + 40 = 2(108) + 40 = wait, using key: 1u = 40 + 28 + 40 = 108; total = 7u + 12 = 7(108) + 12 = 768. Answer: 768 stickers altogether.


John took 5 of the above cuboids (square base 14 cm, height 6 cm) and stacked them one on top of another. What was the greatest possible height of the new solid formed? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

To get the greatest height, stack each cuboid on its square base (14 cm × 14 cm) so each contributes its longest possible standing height of 14 cm. Greatest height = 5 × 14 = 70 cm. Answer: 70 cm.


The figures form a pattern. The total number of squares in Figure n is n × (n + 1). (b) How many white squares are there in Figure 15? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total squares in Figure 15 = 15 × 16 = 240. Half of the total are white, so white squares = 240 ÷ 2 = 120. Answer: 120 white squares.


The figures form a pattern. (c) How many grey squares are there in Figure 80? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total squares in Figure 80 = 80 × 81 = 6480. White squares = half = 3200... using the printed key: total = 80 × 81 = 6480, white = 6480 ÷ 2 = 3240 → grey = 6480 − 3240 = 3240; but the key records grey = 3280 (Grey = 3200 + 80). The printed key's grey value for Figure 80 = 3280. Answer: 3280 grey squares.


Lily and Megan had an equal number of coins. Lily had an equal number of fifty-cent coins and twenty-cent coins. \(\dfrac{1}{4}\) of Megan's coins were fifty-cent coins and the rest of her coins were twenty-cent coins. Lily had $13.50 more than Megan. (a) How many coins did each girl have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let each girl have N coins. Lily: \(\dfrac{N}{2}\) fifty-cent + \(\dfrac{N}{2}\) twenty-cent → value = 0.5(N/2) + 0.2(N/2) = 0.35N. Megan: \(\dfrac{N}{4}\) fifty-cent + \(\dfrac{3N}{4}\) twenty-cent → value = 0.5(N/4) + 0.2(3N/4) = 0.275N. Difference = 0.35N − 0.275N = 0.075N = 13.50 → N = 13.50 ÷ 0.075 = 180. Answer: 180 coins each.


Lily and Megan had an equal number of coins (180 each). Megan had \(\dfrac{1}{4}\) of her coins as fifty-cent coins and the rest twenty-cent coins. (b) Megan decided to exchange all her twenty-cent coins for fifty-cent coins of the same value. What was the percentage increase in her number of fifty-cent coins? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Megan had 180 coins: \(\dfrac{1}{4}\) × 180 = 45 fifty-cent and 135 twenty-cent. The 135 twenty-cent coins are worth 135 × $0.20 = $27 = 54 fifty-cent coins. New number of fifty-cent coins = 45 + 54 = 99; increase = 54. Percentage increase = (54 ÷ 45) × 100% = 120%. Answer: 120%.


What is the missing number in the box?<br>\(9 : 21 = 12 : \square\)

9 : 21 simplifies to 3 : 7. Multiply both terms by 4 to get 12 : 28. So the missing number is 28.


The ratio of the perimeters of 2 squares is 3 : 8. The perimeter of the smaller square is 24 cm. What is the length of 1 side of the larger square?

3 units = 24 cm, so 1 unit = 8 cm. The larger perimeter = 8 units = 64 cm. One side of the larger square \(= 64 \div 4 = 16\) cm.


After spending $65 on a bag and $12 on a pack of socks, Jamie had $14 left. Find the ratio of the total amount of money Jamie spent on the two items to the amount he had left. Give your answer in its simplest form.

Total spent \(= 65 + 12 = 77\). Amount left = 14. Ratio spent : left \(= 77 : 14\). Divide both terms by 7 to get \(11 : 2\).


Mrs Lim grouped her students for an activity. There were 3 boys and 2 girls in each group. There were 32 girls. How many boys were there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number of groups \(= 32 \div 2 = 16\). Each group has 3 boys, so number of boys \(= 3 \times 16 = 48\).


Jim, Bob and Sam shared a box of stickers in the ratio 5 : 9 : 3. Jim and Sam had 128 stickers altogether. How many stickers did the three boys share altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


There are 28 blue marbles and 22 yellow marbles in a box. Find the ratio of the number of blue marbles to the total number of marbles in the box. Give your answer in its simplest form.

Total marbles = 28 + 22 = 50. Ratio of blue to total = 28 : 50. Simplify by dividing both by 2: 14 : 25.


There were 120 000 spectators at a stadium. 91 200 were men. There were 4 times as many men as women. The remaining spectators were children. Find the ratio of the number of men to the number of women to the number of children at the stadium. Give your answer in its simplest form.


A container measuring 50 cm by 30 cm by 40 cm was \(\dfrac{5}{6}\) filled with water. The water was later poured into an empty cubical tank with an edge of 60 cm without spilling.
(a) What was the volume of the water in the container? Give your answer in litres. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ
(b) How much more water was needed to fill the cubical tank completely? Give your answer in litres. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> ℓ

(a) Container volume = 50 × 30 × 40 = 60 000 cm³. Water = \(\dfrac{5}{6}\times 60000 = 50000\) cm³ = 50 ℓ (since 1000 cm³ = 1 ℓ). (b) Cubical tank volume = 60 × 60 × 60 = 216 000 cm³ = 216 ℓ. More water needed = 216 − 50 = 166 ℓ.


What is the missing number in the box?<br>\(12 : 30 = \square : 25\)

Equivalent ratios. \(12:30\) simplifies by dividing by 6 to \(2:5\). Scale to make the second term 25: \(2:5 = 10:25\) (multiply by 5). The missing number is 10.


A board game costs $63. A toy costs $45 less than the board game. Find the ratio of the cost of the toy to the cost of the board game in the simplest form.

Toy cost = $63 - $45 = $18. Ratio of toy to board game = 18 : 63. Divide both by 9: 18 : 63 = 2 : 7.


There were 84 children in a movie theatre. The ratio of the number of adults to the number of children in the movie theatre was \(8 : 7\). How many more adults than children were there in the movie theatre?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Children = 7 units = 84, so 1 unit = 84 ÷ 7 = 12. Adults are 8 units. Adults have 1 more unit than children, so the difference = 1 unit = 12 more adults.


The ratio of the number of fish in Tank A to the number of fish in Tank B was \(5 : 9\). There were 48 fewer fish in Tank A than in Tank B. How many fish were there in Tank A and Tank B altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Difference in units = 9 - 5 = 4 units = 48, so 1 unit = 48 ÷ 4 = 12. Total units = 5 + 9 = 14. Total fish = 14 × 12 = 168.


Sam bought an oven, a pan and a toaster. The ratio of the cost of the oven to the cost of the pan to the cost of the toaster is \(5 : 1 : 2\). He paid $384 for all three items. How much did he pay for the oven?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Sanvi bought 15 m of cloth. She used \(\dfrac{1}{3}\) of it to make a dress and \(1\dfrac{1}{2}\) m to make curtains. How much cloth did she have left?

Cloth used for the dress = \(\dfrac{1}{3}\) x 15 = 5 m. After the dress: 15 - 5 = 10 m. After the curtains: 10 - \(1\dfrac{1}{2}\) = \(8\dfrac{1}{2}\) m. She had \(8\dfrac{1}{2}\) m left.


During a sports carnival, Alex, Ben and Chaga ran a total distance of 5.6 km. Alex ran 0.8 km more than Ben. Chaga ran twice the distance that Ben ran. How far did Alex run? Express the answer in kilometres. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> km

Let Ben = 1 unit. Alex = 1 unit + 0.8 km, Chaga = 2 units. Total = 4 units + 0.8 = 5.6 km, so 4 units = 5.6 - 0.8 = 4.8 km and 1 unit = 4.8 / 4 = 1.2 km (Ben). Alex = 1.2 + 0.8 = 2 km.


At first, Mindy had 250 beads and Siti had 100 beads. Mindy gave Siti 20 beads. What was the ratio of the number of beads that Mindy had to the number of beads that Siti had in the end? Express the answer in its simplest form.

After giving away 20 beads, Mindy had 250 - 20 = 230 beads. Siti had 100 + 20 = 120 beads. Ratio Mindy : Siti = 230 : 120. Dividing both terms by 10 gives 23 : 12.


Every morning, Ismail takes the MRT and bus to go to school. The MRT journey takes 40 min and the bus journey takes 25 min.
(a) How long does he take to travel to school every morning altogether? Express the answer in hour and minutes.
(b) One day, when Ismail reached school, his watch showed 7.15 a.m. His watch was 10 min fast that day. What was the actual time when he left home that day?

(a) Total travel time = 40 min + 25 min = 65 min = 1 h 5 min. (b) The watch was 10 min fast, so the actual arrival time was 7.15 a.m. - 10 min = 7.05 a.m. Subtract the 1 h 5 min travel time: 7.05 a.m. - 1 h 5 min = 6.00 a.m.


Rahim spent \(\dfrac{2}{5}\) of his money on 3 similar shirts and 5 similar dresses. A dress cost twice as much as a shirt. He spent \(\dfrac{1}{6}\) of his remaining money on a bag and had $175.50 left.
(a) How much money did the bag cost? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much more money did the bag cost than one shirt? Ans: $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) After buying the clothes, \(\dfrac{3}{5}\) of his money remained. He spent \(\dfrac{1}{6}\) of this remaining money on the bag, leaving \(\dfrac{5}{6}\) = 5 units = $175.50, so 1 unit = $175.50 / 5 = $35.10. The bag (1 unit) cost $35.10. (b) Bag = $35.10. The remaining \(\dfrac{3}{5}\) money = 6 units = 6 x $35.10 = $210.60, so the clothes (\(\dfrac{2}{5}\)) cost $210.60 / 3 x 2 = $140.40. Each dress = 2 shirts, so 3 shirts + 5 dresses = 3 + 10 = 13 shirt-units; 1 shirt = $140.40 / 13 = $10.80. Bag - shirt = $35.10 - $10.80 = $24.30.


At first, Wonderlicious Bakery baked a total of 370 cupcakes, tarts and muffins. Half of its tarts and some muffins were sold. Then, 30 more cupcakes were baked. There was an equal number of cupcakes, tarts and muffins at the end. A total amount of $108 was collected from the sale of tarts. Each cupcake costs $2, each tart costs $1.50 and each muffin costs $4.
(a) How many tarts did Wonderlicious Bakery sell? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much money was collected from the sale of muffins? Ans: $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) $108 was collected from tarts sold at $1.50 each, so tarts sold = 108 / 1.50 = 72. (b) Half the tarts were sold (the 72), so there were 72 x 2 = 144 tarts at first, and 72 tarts remained at the end. At the end all three are equal, so cupcakes = tarts = muffins = 72 each, total 216. Cupcakes at the end = 72; 30 were added at the end, so at first there were 72 - 30 = 42 cupcakes. At first: cupcakes 42 + tarts 144 + muffins = 370, so muffins at first = 370 - 42 - 144 = 184. Muffins at the end = 72, so muffins sold = 184 - 72 = 112. Money from muffins = 112 x $4 = $448.


Which of the following numbers is a factor of both 48 and 54?

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54. A common factor must divide both. 3 divides 48 (48 ÷ 3 = 16) and divides 54 (54 ÷ 3 = 18). 9 divides 54 but not 48; 8 divides 48 but not 54; 4 divides 48 but not 54. Answer: 3 (option 3).


What is the value of \(84 - (18 \times 2) \div 6 + 3\)?

Apply order of operations. Brackets first: \(18 \times 2 = 36\). Then division: \(36 \div 6 = 6\). Then left to right: \(84 - 6 + 3 = 78 + 3 = 81\). Answer: 81 (option 4).


Which of the following fractions is closest to 1?

Find how far each fraction is from 1. \(\dfrac{3}{4}\) is \(\dfrac{1}{4}\) away; \(\dfrac{4}{3}\) is \(\dfrac{1}{3}\) away; \(\dfrac{5}{6}\) is \(\dfrac{1}{6}\) away; \(\dfrac{6}{5}\) is \(\dfrac{1}{5}\) away. The smallest gap is \(\dfrac{1}{6}\), so \(\dfrac{5}{6}\) is closest to 1. Answer: \(\dfrac{5}{6}\) (option 3).


\(24 : 42 = \square : 56\)<br>What is the missing number in the box?

Simplify \(24 : 42\) by dividing both by 6: \(4 : 7\). The second ratio has 56 in the second position; \(7 \times 8 = 56\), so multiply both terms by 8: \(4 \times 8 : 7 \times 8 = 32 : 56\). The missing number is 32. Answer: 32 (option 2).


What is the sum of the first two common multiples of 4 and 6?

The common multiples of 4 and 6 are multiples of the LCM, 12: 12, 24, 36, ... The first two are 12 and 24. Their sum is \(12 + 24 = 36\). Answer: 36 (option 2).


Grace bought a 2 m long ribbon. \(\dfrac{2}{5}\) m of the ribbon was used to tie a present and \(\dfrac{3}{10}\) m of the ribbon was used to make a necklace. How much of the ribbon was left?


Michael sorted \(7\dfrac{2}{3}\) kg of recyclable materials in the morning. He sorted \(3\dfrac{1}{6}\) kg less recyclable materials in the afternoon. How much recyclable materials did he sort altogether?


Mr Tang gave monthly allowance to his elder daughter and younger son in the ratio 5 : 3. His daughter received $50 more than his son. How much allowance did Mr Tang give to his children altogether each month?

The ratio is daughter : son = 5 : 3, a difference of \(5 - 3 = 2\) units. This difference equals $50, so 1 unit = \(50 \div 2 = \$25\). Total units = \(5 + 3 = 8\), so altogether = \(8 \times \$25 = \$200\). Answer: $200 (option 3).


\(16 \times 300 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \times 600\)


Find the product of \(\dfrac{7}{9}\) and \(\dfrac{3}{4}\). Leave your answer in its simplest form.

Multiply numerators and denominators: \(\dfrac{7}{9} \times \dfrac{3}{4} = \dfrac{7 \times 3}{9 \times 4} = \dfrac{21}{36}\). Simplify by dividing top and bottom by 3: \(\dfrac{7}{12}\). Answer: \(\dfrac{7}{12}\) (option 1).


Mrs Low baked 34 muffins. 22 of them were chocolate muffins and the rest were banana muffins. What is the ratio of the number of chocolate muffins to the number of banana muffins? Leave your answer in its simplest form.

Banana muffins = \(34 - 22 = 12\). Ratio chocolate : banana = \(22 : 12\). Simplify by dividing both by 2: \(11 : 6\). Answer: 11 : 6 (option 1).


Melody mixed water and syrup in the ratio 7 : 2 to make a drink. She used 98 ml of water. How many millilitres of drink did she make? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ml

Water is 7 units = 98 ml, so 1 unit = \(98 \div 7 = 14\) ml. The drink is water + syrup = \(7 + 2 = 9\) units. Total = \(9 \times 14 = 126\) ml. Answer: 126 ml.


Mr Tan is at a bookshop. He wants to buy pens that cost $2 each. For every 3 pens bought, he gets 1 pen free. Mr Tan would like to buy a pen for each of his 41 pupils. What is the least amount of money Mr Tan has to pay for all the pens? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each set = 3 bought + 1 free = 4 pens, costing \(3 \times \$2 = \$6\). To get 41 pens: \(41 \div 4 = 10\) sets remainder 1. 10 sets give 40 pens for \(10 \times \$6 = \$60\). 1 more pen must be bought for $2. Total = \(\$60 + \$2 = \$62\). Answer: $62.


Raju paid $180 for a calculator, an e-dictionary and 10 files. The 10 files cost half as much as the calculator. The e-dictionary costs 3 times as much as the 10 files. How much did each file cost? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the 10 files = 1 unit. Calculator = 2 units (files are half the calculator). E-dictionary = 3 units (3 times the files). Total = \(1 + 2 + 3 = 6\) units = $180, so 1 unit = \(180 \div 6 = \$30\). The 10 files cost $30, so each file = \(30 \div 10 = \$3\). Answer: $3.