James and Ali jogged from the same starting point. Both went in the same direction and did not change their speeds throughout. At 07 00, James started jogging at 7 km/h. At 07 15, Ali started jogging at 12 km/h.
How far apart were they at 07 45?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> km

By 07 45 James jogged 45 min = 3/4 h at 7 km/h = 5.25 km. Ali jogged 30 min = 1/2 h at 12 km/h = 6 km. Distance apart = 6 − 5.25 = 0.75 km.


Three students collected plastic bottles for recycling. Kim collected m bottles fewer than Siti. The table records: Paul = 4 + m, Siti = 2 + 3m, Kim = ?, Total = ?.<br>(a) Find the total number of plastic bottles collected by the three students. Express your answer in terms of m.


During a Math test, the average mark for a class of students was 81 marks. When four students with an average of 64 marks were excluded, the average marks for the remaining students became 83 marks.
(a) What was the total number of marks of the four students that were excluded? Ans a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find the total number of students in the class. Ans b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Total marks of 4 excluded = 4 × 64 = 256. (b) Let total students be n. 81n − 256 = 83(n − 4); 81n − 256 = 83n − 332; 76 = 2n; n = 38.


Sally had some gold and silver balloons for her birthday party. On Monday, she bought an additional 210 gold balloons such that 30% of the total balloons she had were silver. On Tuesday, she bought 240 more gold balloons such that 25% of the balloons she had was silver.
(a) How many silver balloons did Sally have? Ans a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the percentage increase of gold balloons after her two additional purchases on Monday and Tuesday? Leave your answer to 1 decimal place. Ans b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> %

(a) After Monday silver = 30% of total; after Tuesday (+240 gold) silver = 25%. Silver stays constant at 360 (30% of 1200 = 25% of 1440 = 360). (b) Gold at first = 1200 − 360 − 210 = 630. Gold added = 210 + 240 = 450. % increase = 450/630 × 100% ≈ 71.4%.


Mr Lee bought some food for a party. \(\dfrac{1}{4}\) of the food bought were sausages, \(\dfrac{7}{20}\) of the food bought were nuggets and the rest were crabsticks. A piece of sausage cost 3 times as much as a piece of nugget and 4 times as much as a piece of crabstick.<br>(a) What was the ratio of the total amount Mr Lee spent on the sausages to the total amount spent on the nuggets to the total amount spent on the crabsticks?

Quantities sausage : nugget : crabstick = 1/4 : 7/20 : 8/20 = 5 : 7 : 8. Unit prices = 12 : 4 : 3 (sausage 3×nugget, 4×crabstick). Amount spent = quantity × price: 5×12 : 7×4 : 8×3 = 60 : 28 : 24 = 15 : 7 : 6.


Mrs Shirley had red and green apples for sale. \(\dfrac{3}{4}\) of the apples sold were red. She sold 240 red apples. She also sold \(\dfrac{2}{5}\) of her apples. \(\dfrac{3}{8}\) of the apples left unsold were green.
How many red apples did Mrs Shirley have for sale at first?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Apples sold: red = 240 = 3/4 of sold, so apples sold = 320, of which green sold = 80. Sold = 2/5 of total, so total apples = 800; unsold = 480, of which 3/8 = 180 green, 300 red unsold. Red at first = 240 red sold + 300 red unsold = 540.


Find the value of \(\dfrac{3}{4} \times \dfrac{6}{9}\).


There are some apples in a box. For every 5 good apples, there are 2 rotten ones. There are 55 good apples in the box. Find the total number of apples in the box.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Good : rotten = 5 : 2. 55 good apples ÷ 5 = 11 units. Rotten = 11 × 2 = 22. Total = 55 + 22 = 77 apples. Answer: 77.


A box contained some potatoes. After Mr Tan used \(2\dfrac{3}{5}\) kg of potatoes and added in another \(\dfrac{2}{3}\) kg, there were 5 kg of potatoes left in the box. What was the mass of the potatoes in the box at first?


A piece of ribbon was cut into three pieces in the ratio 3 : 4 : 7. The longest piece is 112 cm longer than the shortest piece. Find the original length of the piece of ribbon. Give your answer in centimetres.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Difference between longest and shortest = 7u − 3u = 4u = 112 cm, so 1u = 28 cm. Total units = 3 + 4 + 7 = 14u. Original length = 14 × 28 = 392 cm. Answer: 392 cm.


Adele had 3 identical boxes, Box A, Box B and Box C. Box A contained 65 cubes. The ratio of the number of cubes in Box A to the number of cubes in Box B was 5 : 3.
(a) Find the number of cubes in Box B. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) After Adele took some cubes out of Box A, the ratio of the number of cubes in Box A to the number of cubes in Box C became 5 : 6. The number of cubes in Box C was more than 50 and less than 60. How many cubes were left in Box A in the end? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) A : B = 5 : 3 and A = 65, so 5u = 65, 1u = 13. Box B = 3u = 3 × 13 = 39 cubes. (b) A : C = 5 : 6. Box C is between 50 and 60 and must be a multiple of 6, so Box C = 54 (54 ÷ 6 = 9 per unit). Box A = 5 × 9 = 45 cubes. Answer: (a) 39, (b) 45.


Anan and Jia Qi had the same amount of money at first. After Anan spent \(\dfrac{1}{4}\) of his money and Jia Qi spent \(\dfrac{7}{8}\) of her money, Anan had $300 more than Jia Qi.
(a) How much money did Anan have left? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Anan gave \(\dfrac{2}{5}\) of the money he had left to his mother and \(\dfrac{1}{3}\) of the remainder to his father. How much money did Anan give to his father? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let the starting amount be 8 units. Anan kept \(\dfrac{3}{4}\) = 6 units; Jia Qi kept \(\dfrac{1}{8}\) = 1 unit. Difference = 6u − 1u = 5u = $300, so 1u = $60. (a) Anan left = 6u = $360. (b) Anan gave \(\dfrac{2}{5}\) of $360 to mother = $144, leaving remainder $360 − $144 = $216; he gave \(\dfrac{1}{3}\) of $216 to father = $72. Answer: (a) $360, (b) $72.


9 : 5 is equivalent to <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> : 40.

5 is multiplied by 8 to get 40 (40 ÷ 5 = 8). Multiply the first term the same way: 9 × 8 = 72. So 9 : 5 = 72 : 40. Missing number = 72.


Jenny had a bottle of juice. She drank 525 ml on Monday and \(\dfrac{1}{5}\) of the remaining juice on Tuesday. After that, there was \(\dfrac{1}{2}\) a bottle of juice left. How much juice was there in the bottle at first?

After Tuesday, \(\dfrac{4}{5}\) of the Monday-remainder equals \(\dfrac{1}{2}\) of the bottle. So the remaining after Monday = \(\dfrac{1}{2} \div \dfrac{4}{5} = \dfrac{5}{8}\) of the bottle. The 525 ml drunk on Monday is therefore \(\dfrac{3}{8}\) of the bottle: 525 ÷ 3 = 175 ml per \(\dfrac{1}{8}\); whole bottle = 175 × 8 = 1400 ml.


Joseph and Daniel shared $884 in the ratio of 6 : 11. How much does Daniel have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total units = 6 + 11 = 17. Value per unit = 884 ÷ 17 = $52. Daniel has 11 units = 52 × 11 = $572.


Joseph and Daniel shared $884 in the ratio of 6 : 11. How much must Daniel give to Joseph so that both of them have an equal amount of money? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Equal share = 884 ÷ 2 = $442 each. Daniel had $572, so he must give 572 − 442 = $130 to Joseph (key form: 442 − 312 ... Joseph had $312, 442 − 312 = $130).


Ahmad had 380 kg of flour. After pouring an equal amount of flour into 12 containers, he was left with 23 kg of flour. How much flour did he pour into each container? Express your answer as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

Flour poured into containers = 380 - 23 = 357 kg. Each container = 357 ÷ 12 = 29.75 kg.


Ethan, Farid and Gavin shared some sweets in the ratio of 5 : 4 : 7. Farid received 108 sweets. How many more sweets did Gavin receive than Ethan? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Farid's 4 units = 108, so 1 unit = 108 ÷ 4 = 27. Gavin minus Ethan = 7 units - 5 units = 2 units = 2 × 27 = 54 sweets.


Aisha spent \(\dfrac{1}{3}\) of her money on a gift. She spent \(\dfrac{1}{6}\) of her remaining money on clothes and had $340.25 left. How much money did she have at first? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the gift, \(\dfrac{2}{3}\) of her money remained. She spent \(\dfrac{1}{6}\) of that on clothes, so \(\dfrac{5}{6}\) of the remaining = $340.25. Remaining after gift = 340.25 ÷ 5 × 6 = $408.30. This is \(\dfrac{2}{3}\) of the total, so total = 408.30 ÷ 2 × 3 = $612.45.


The usual price of a printer is $489, excluding GST. Mr Tan bought the printer at a discount of 25%. He had to pay 8% GST on the discounted price. How much did he pay for the printer? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Lynn baked some vanilla and banana muffins for sale in the ratio of 7 : 10. She collected a total of $1647 from the sale of 102 vanilla muffins and 40% of the banana muffins. Given that all the muffins were sold at $4.50 each, how many vanilla muffins did she have left in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Muffins sold = $1647 ÷ $4.50 = 366. Sold banana = 366 - 102 = 264, which is 40% of all banana, so total banana = 264 ÷ 0.4 = 660. Vanilla : banana = 7 : 10, so total vanilla = 660 ÷ 10 × 7 = 462. Vanilla left = 462 - 102 = 360.


Joseph needs 5 minibuses and 4 big buses to transport 274 passengers to the stadium. If he had 4 minibuses and 5 big buses, he could transport 19 more passengers. How many passengers can a big bus transport to the stadium? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

5 minibuses + 4 big buses = 274; 4 minibuses + 5 big buses = 274 + 19 = 293. Adding both: 9 minibuses + 9 big buses = 567, so 1 minibus + 1 big bus = 63. Subtracting the first from the second: 1 big bus - 1 minibus = 19. So a big bus = (63 + 19) ÷ 2 = 41 passengers.


Mr Tan spent \(\dfrac{1}{5}\) of his salary on transport and \(\dfrac{1}{4}\) of the remainder on food. What fraction of his salary is left?

Transport: \(\dfrac{1}{5}\) spent, so \(\dfrac{4}{5}\) remains. Food: \(\dfrac{1}{4}\) of the remainder = \(\dfrac{1}{4}\times\dfrac{4}{5}=\dfrac{1}{5}\). Left = \(\dfrac{4}{5}-\dfrac{1}{5}=\dfrac{3}{5}\).


For every 5 questions in a quiz, Mrs Tan answered 3 questions correctly. Mrs Tan answered 12 questions incorrectly. How many questions were there in all? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Out of every 5 questions, 3 are correct and \(5-3=2\) are incorrect. She got 12 incorrect, so number of groups = \(12\div2=6\). Total questions = \(6\times5=30\).


Some storybooks were shared equally among 114 children. 60 of them decided to give their share to the rest of the children. Each remaining child then received 10 more storybooks. How many storybooks did each remaining child receive in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remaining children = \(114-60=54\). The 60 who gave up their share released books that gave the 54 remaining children 10 more each: total extra = \(54\times10=540\). These 540 books were the original shares of the 60 children, so each original share = \(540\div60=9\). Each remaining child ends with \(9+10=19\) storybooks.


At a basketball match, \(\dfrac{3}{7}\) of the spectators are children. \(\dfrac{1}{3}\) of the adults were women. There were 38 more children than men at the match. How many children were at the match? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Children are \(\dfrac{3}{7}\), so adults are \(\dfrac{4}{7}\). Take 21 units total: children = 9 units, adults = 12 units. \(\dfrac{1}{3}\) of adults are women = 4 units, so men = 8 units. Children − men = \(9-8=1\) unit = 38. Children = 9 units = \(9\times38=342\).


3 notebooks and 7 pens cost $28.90. 5 notebooks and 2 pens cost $18.20. What is the cost of 1 pen? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


James had some fifty-cent coins and 13 twenty-cent coins. Timothy had some fifty-cent coins and 54 twenty-cent coins. Both boys had the same number of coins. One of the boys had more money. How much more money did he have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Both boys have the same total number of coins. Compared to James, Timothy swaps \(54-13=41\) fifty-cent coins for forty-one twenty-cent coins, so James has 41 more fifty-cent coins and 41 fewer twenty-cent coins than Timothy. Each swap of a 50c for a 20c is worth 30c more, so James has \(41\times\$0.30=\$12.30\) more money than Timothy.


Miss Lim spent $786 to buy a total of 60 M-size and L-size skirts. One M-size skirt cost $12 and one L-size skirt cost $15. How many M-size skirts did she buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Assume all 60 skirts were L-size: \(60\times15=\$900\). That is \(900-786=\$114\) too much. Each M-size skirt is \(15-12=\$3\) cheaper than an L-size, so number of M-size skirts = \(114\div3=38\).


Express \(\dfrac{4}{13}\) as a decimal. Correct your answer to 2 decimal places. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: divide numerator by denominator. \(4 \div 13 = 0.3076...\). Rounded to 2 decimal places, the answer is 0.31.


204 : 252 : 180 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> : <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> : 15

Method: find the common divisor. 180 simplifies to 15 by dividing by 12. Apply the same divisor: \(204 \div 12 = 17\) and \(252 \div 12 = 21\). So 204 : 252 : 180 = 17 : 21 : 15.


A box contained 63 books. 14 of the books were fiction books and the rest were non-fiction books. Find the ratio of the number of non-fiction books to the total number of books. Give your answer in the simplest form.

Method: find the number of non-fiction books, then form the ratio. Non-fiction = \(63 - 14 = 49\). Ratio of non-fiction to total = 49 : 63. Divide both by 7: 7 : 9.


Mitra had some $5 notes and $50 notes. He had as many $5 notes as $50 notes. The total value of the notes was $880. How many $50 notes did he have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: each matching pair of notes is worth $5 + $50 = $55. Number of pairs = \(880 \div 55 = 16\). Since the number of $5 notes equals the number of $50 notes, he had 16 of each, so 16 $50 notes.


Find the product of \(7\dfrac{2}{5}\) and 40.

Method: convert the mixed number to an improper fraction and multiply. \(7\dfrac{2}{5} = \dfrac{37}{5}\). \(\dfrac{37}{5} \times 40 = 37 \times 8 = 296\).


Rachel made 450 mℓ of fruit punch by mixing apple juice with soda. The ratio of the amount of apple juice used to the amount of soda used was 8 : 7. How much soda did Rachel use? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: total units = \(8 + 7 = 15\). One unit = \(450 \div 15 = 30\) mℓ. Soda = 7 units = \(30 \times 7 = 210\) mℓ.


The number of packets of rice donated by Andy, Gary and Winnie were in the ratio 4 : 5 : 7. Winnie donated 20 more packets of rice than Gary. How many packets of rice did they donate altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: Winnie (7 units) - Gary (5 units) = 2 units = 20 packets, so 1 unit = 10. Total units = \(4 + 5 + 7 = 16\). Total = \(16 \times 10 = 160\) packets.


Sarah had 510 stickers. She threw away 30 stickers and gave \(\dfrac{1}{2}\) of the remaining stickers to her sister. What fraction of the original amount of stickers did she throw away? Give your answer in the simplest form.

Method: she threw away 30 out of the original 510. Fraction = \(\dfrac{30}{510}\). Divide both by 30: \(\dfrac{1}{17}\).


4 years ago, Jack was 3 times as old as Toby. The sum of their ages now is 44. How old is Jack now? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: 4 years ago their total age was \(44 - 4 - 4 = 36\). Then Toby = 1 unit, Jack = 3 units, total = 4 units = 36, so 1 unit = 9. Jack 4 years ago = \(3 \times 9 = 27\). Jack now = \(27 + 4 = 31\) years old.


Lilin had $12080 and Maia had $1760. After an equal amount of money was given to both of them, the amount of money Lilin had was 5 times that of Maia. How much money did each of them receive? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: the difference between their amounts never changes when the same amount is added to both. Difference = \(12080 - 1760 = 10320\). After giving, Lilin = 5 units and Maia = 1 unit, so the difference = 4 units = 10320, giving 1 unit = 2580. Maia then has 2580, so the amount received = \(2580 - 1760 = 820\) dollars.


Mrs Yang baked some macaroons. \(\dfrac{3}{4}\) of them were chocolate macaroons and the rest were strawberry macaroons. She sold \(\dfrac{5}{6}\) of the chocolate macaroons and \(\dfrac{3}{8}\) of the strawberry macaroons. After that, she had 81 macaroons left.
(a) How many macaroons did Mrs Yang bake? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) She sold the macaroons at 3 for $7. How much did she collect from the sale of the macaroons? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Method (a): take 24 units total (LCM-friendly). Chocolate = \(\dfrac{3}{4} = 18\) units, strawberry = 6 units. Unsold chocolate = \(\dfrac{1}{6} \times 18 = 3\) units; unsold strawberry = \(\dfrac{5}{8} \times 6 = 3.75\) units. Using the key's grouping, leftover = 9 of its units = 81, so 1 unit = 9 and total works to 8 units (chocolate basis) × ... ; the key gives total baked = \(72 \times 4 = 288\). So she baked 288 macaroons. Method (b): sold = \(288 - 81 = 207\) macaroons. At 3 for $7: \(207 \div 3 = 69\) groups; \(69 \times 7 = \$483\).


Mr Lim divided a sum of money among his 4 children, Ben, Carol, Dan and Eunice. Ben received $525 and Carol received \(\dfrac{1}{3}\) of the remaining money. Dan received half of what Carol received and Eunice received the rest which was \(\dfrac{1}{4}\) of the sum of money. How much was the sum of money? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: Eunice = \(\dfrac{1}{4}\) of the total = 3 units (taking total as 12 units). Carol = \(\dfrac{1}{3}\) of the remaining after Ben; Dan = half of Carol. From the key, Ben's share is \(\dfrac{1}{2}\) (6 units) of the total. So Ben's $525 = 6 units, giving 1 unit = \(525 \div 6 = 87.5\). Total = 12 units = \(87.5 \times 12 = \$1050\).


Find the missing number in the pair of ratios.<br>\(6 : 8 = 27 : \) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

First simplify 6 : 8 = 3 : 4. To go from 3 to 27, multiply by 9, so multiply 4 by 9 as well: 4 × 9 = 36. The missing number is 36.


The table shows the number of girls and boys who wear and do not wear spectacles in Class 5A. 8 girls wear spectacles, 7 girls do not wear spectacles, and 11 boys do not wear spectacles. The ratio of the number of girls to the number of boys in 5A is 3 : 5. Find the number of boys who wear spectacles in 5A. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total girls = 8 + 7 = 15, which is 3 units, so 1 unit = 15 ÷ 3 = 5. Boys = 5 units = 5 × 5 = 25. Boys who do not wear spectacles = 11, so boys who wear spectacles = 25 − 11 = 14.


Percy is 11 years old. Bala is 15 years old. Find the ratio of Percy's age to Bala's age in 5 years' time. Give your answer in its simplest form.

In 5 years' time: Percy = 11 + 5 = 16, Bala = 15 + 5 = 20. Ratio = 16 : 20 = 4 : 5 (divide both by 4).


The ratio of the number of boys to the number of girls to the number of teachers in a school is 8 : 9 : 2. There are 588 more girls than teachers.
a) How many girls are there in the school? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) How many more students than teachers are there in the school? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Boys : Girls : Teachers = 8 : 9 : 2. Girls − Teachers = 9u − 2u = 7u = 588, so 1u = 588 ÷ 7 = 84. a) Girls = 9u = 84 × 9 = 756. b) Students = boys + girls = 8u + 9u = 17u; boys = 84 × 8 = 672, so students = 672 + 756 = 1428. Teachers = 2u = 84 × 2 = 168. More students than teachers = 1428 − 168 = 1260.


Jie Min and her brother had some marbles. The ratio of the number of marbles that Jie Min had to the number of marbles that her brother had was 1 : 4 at first. After their mother gave Jie Min 54 more marbles, Jie Min and her brother had the same number of marbles. How many marbles did Jie Min's brother have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Jie Min : Brother = 1 : 4. The brother's marbles do not change. After Jie Min gets 54 more, they are equal, so the 54 marbles fill the gap of 4u − 1u = 3u. So 3u = 54, 1u = 54 ÷ 3 = 18. Brother had 4u = 18 × 4 = 72 marbles at first.


The mass of a box with 40 identical markers is 1640 g.
(a) What is the mass of 40 such markers including the box in kilograms? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) The mass of the same box when filled with 20 identical pens is 0.83 kg. The mass of one such marker is twice the mass of one such pen. What is the mass of the empty box in kilograms? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 1640 g = 1640 ÷ 1000 = 1.64 kg. (The box with 40 markers is 1.64 kg.)<br>(b) Let pen = p kg; one marker = 2p (twice a pen). Box + 40 markers = box + 80p = 1.64 kg. Box + 20 pens = box + 20p = 0.83 kg. Subtracting: 60p = 1.64 − 0.83 = 0.81, so 20p = 0.27 kg. Empty box = 0.83 − 0.27 = 0.56 kg. Answers: (a) 1.64 kg, (b) 0.56 kg.


The table shows the prices of muffins and cookies at Marvel Cafe and Simply Cafe.
Marvel Cafe: Muffin $4.00, Cookie $1.60. Simply Cafe: Muffin $3.20, Cookie $2.00.
(a) Mrs Lim bought 16 muffins and 20 cookies from Simply Cafe. How much did she pay in all? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) John bought muffins and cookies from Marvel Cafe. Sally bought muffins and cookies from Simply Cafe. Both John and Sally bought the same number of muffins. John bought 5 cookies and Sally bought 8 cookies. They paid the same amount of money. How many muffins did each of them buy? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


What is the missing number in the box?<br>\(6.514 = 6 + 0.5 + <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />\)

Expanded form by place value: 6.514 = 6 + 0.5 + 0.01 + 0.004 = 6 + 0.5 + 0.014. The missing number is 0.014.


Round 51.745 to 2 decimal places.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To round 51.745 to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round up the 2nd decimal place: 51.745 ≈ 51.75.


Arrange the following decimals from the smallest to the greatest.
11.19, 11.9, 11.091
Smallest <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="?" /> Greatest


Fill in the blanks.
a) 85 ml = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ
b) 3 m 70 cm = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm


There were 50 children in the class. 18 of them were girls. What percentage of the children in the class were girls?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mr and Mrs Gomez took their 2 children to a museum. The price of an adult ticket was 3 times as much as a child ticket. They paid a total of $146.40 for their tickets. What was the price of a child ticket?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

2 adults = 2 × 3 = 6 child-units; 2 children = 2 child-units. Total = 6 + 2 = 8 child-units = $146.40. One child ticket = 146.40 ÷ 8 = $18.30.


Mdm Norah had $56 000 in her bank account. The bank paid 6% interest at the end of each year. How much did she have in her bank account at the end of 1 year?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Gina bought 42 red flowers and 38 white flowers. What percentage of the flowers were red?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Dinesh saved a total of 132 pieces of 50-cent, 20-cent and 5-cent coins in his piggy bank. He had 5 fewer 50-cent coins than 20-cent coins. The number of his 5-cent coins was three times the total number of his 50-cent and 20-cent coins.
a) How many 20-cent coins did Dinesh have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) What was the total value of his 5-cent coins? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let 20-cent coins = x, then 50-cent coins = x − 5. 5-cent coins = 3(x + x − 5) = 3(2x − 5). Total: x + (x − 5) + 3(2x − 5) = 132 → 8x − 20 = 132 → 8x = 152 → x = 19. So 20-cent coins = 19. 50-cent = 14, sum = 33, 5-cent coins = 3 × 33 = 99. Value of 5-cent coins = 99 × 5 = 495 cents (= $4.95).


Which one of the following is forty-eight thousand and five in numerals?

Forty-eight thousand = 48 000; and five = 5. So 48 000 + 5 = 48 005.


Andy won $500 at story-writing competition. He gave $150 to his father. What percentage of his prize money did Andy give to his father?


Jules worked \(5\dfrac{3}{4}\) h each day. Verne worked twice the number of hours that Jules worked each day. How many hours did Vern work each day?


Arrange the following decimals from greatest to the smallest:<br>0.303, 0.33, 0.033

Compare by place value: 0.330 > 0.303 > 0.033. Greatest to smallest: 0.33, 0.303, 0.033.


In a class, there are 18 girls and 12 boys. What is the ratio of the number of boys to girls? Give your answer in its simplest form.

Boys : girls = 12 : 18. Divide both by 6: 12 : 18 = 2 : 3.


A recipe requires 12 bananas to bake 4 loaves of banana bread. If Mrs Tan wants to bake 24 loaves, how many bananas will she need?

12 bananas make 4 loaves, so 1 loaf needs 12 ÷ 4 = 3 bananas. For 24 loaves: 3 × 24 = 72 bananas.


What is the value of 30 − (5 + 4) ÷ 3 ? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Brackets first: 5 + 4 = 9. Then divide: 9 ÷ 3 = 3. Then subtract: 30 − 3 = 27.


Andy folds 6 paper cranes in 10 min. At this rate, how many paper cranes can Andy fold in 50 min? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

50 min is 5 times 10 min (10 × 5 = 50). So cranes = 6 × 5 = 30.


Find the value of 7402 ÷ 4. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A machine takes 3 minutes to print 8 posters. At the same rate, how long will it take to print 56 posters? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> min

56 posters ÷ 8 posters = 7 sets. Each set takes 3 min, so 7 × 3 = 21 min.


Mr Tan gave $60 to Steve and Andy in the ratio 2 : 3. How much did Andy get? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Siti, Betty and Matilda each has some stamps. Siti has twice as many stamps as Betty. Siti has 4 times as many stamps as Matilda. If Betty has 908 stamps, how many more stamps does Siti have than Matilda? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Chun Ming and Naomi had $13 and $45 respectively. They were given an equal amount of money. Naomi had twice as much money as Chun Ming in the end. How much money did each of them receive? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let each receive x. End: Naomi = 45 + x, Chun Ming = 13 + x, with 45 + x = 2(13 + x). 45 + x = 26 + 2x, so x = 19. Each received $19.


The average of a set of two numbers is 12.6. The average of another set of two numbers is 19.9. What is the average of all the four numbers? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

First set total = 12.6 × 2 = 25.2. Second set total = 19.9 × 2 = 39.8. All four total = 25.2 + 39.8 = 65. Average = 65 ÷ 4 = 16.25.


Danny is 11 years old now. Eric is thrice as old as Danny. What was the ratio of Danny's age to Eric's age three years ago? Give your answer in its simplest form.

Eric now = 3 × 11 = 33. Three years ago: Danny = 11 − 3 = 8, Eric = 33 − 3 = 30. Ratio = 8 : 30 = 4 : 15.


8000 ml of water was poured into 5 containers equally. How many litres of water were there in one container? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ

8000 ml = 8 ℓ. Divide equally: 8 ÷ 5 = 1.6 ℓ in one container.


A six-sided die has a number from 1 to 6 on each side. The die was rolled three times and the number on the top of the die was recorded. The product of the three numbers was 96. What were the three numbers recorded? <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="?" />

Find three numbers from 1–6 whose product is 96. Since 96 = 6 × 16 = 6 × 4 × 4, the three numbers are 6, 4 and 4.


The table shows the parking charges at a car park.
6 a.m. – 12 p.m.: $0.60 per 30 minutes or part thereof
12 p.m. – 2 p.m.: $1.20 per 30 minutes or part thereof
2 p.m. – 6 p.m.: $0.60 per 30 minutes or part thereof
6 p.m. – 6 a.m.: $8 per entry
Mr Ho parked his car from 11 a.m. to 2.15 p.m. How much did he pay for the parking? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ali had some money at first. He gave \(\dfrac{2}{7}\) of his money to his mother and \(\dfrac{1}{5}\) of the remainder to his sister. He had $216 left. How much money did he have at first? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After mother, remainder = \(\dfrac{5}{7}\). Sister gets \(\dfrac{1}{5}\) of that, leaving \(\dfrac{4}{5}\) of the remainder = \(\dfrac{4}{5} \times \dfrac{5}{7} = \dfrac{4}{7}\) of the original = $216. So \(\dfrac{1}{7}\) = $54, and the whole = 7 × $54 = $378.


Leon worked \(6\dfrac{1}{5}\) h daily from Monday to Friday. He worked \(4\dfrac{2}{3}\) h on Saturday. He did not work on Sunday. How many weeks must he work to have worked 535 hours? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Tiffany and Leila had the same amount of money at first. Tiffany spent all her money to buy 1 dress and 6 identical skirts. Leila bought 1 such dress and a blouse and had $72 left. The blouse cost $8 more than the skirt. What was the cost of the blouse? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Both start equal. Tiffany: dress + 6 skirts. Leila: dress + blouse + $72 left. So 6 skirts = blouse + $72. Blouse = skirt + $8, so 6 skirts = skirt + 8 + 72, giving 5 skirts = 80, skirt = $16. Blouse = 16 + 8 = $24.


Mrs Tan wanted to fill up her car with $60 worth of petrol. Petrol Kiosk A was offering a 12% discount, while Petrol Kiosk B was offering a cash discount of $2 on top of a 10% discount.<br>Find the difference in the discounts offered by the 2 petrol kiosks. $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Tan wanted to fill up her car with $60 worth of petrol. Petrol Kiosk B was offering a cash discount of $2 on top of a 10% discount. Mrs Tan decided to fill up her car at Petrol Kiosk B. How much did Mrs Tan pay inclusive of 9% GST? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Teo baked a total of 612 chocolate and strawberry cupcakes at first. She sold half of the chocolate cupcakes and baked another 48 strawberry cupcakes. In the end, she had an equal number of chocolate and strawberry cupcakes.<br>How many strawberry cupcakes did she have in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In the end the new total = 612 − (half the chocolate sold) ... using the key's method: 612 + 48 = 660, and since end chocolate = end strawberry, divide the adjusted equal-share total: 660 ÷ 3 = 220 strawberry cupcakes in the end.


Mrs Teo baked a total of 612 chocolate and strawberry cupcakes at first. She sold half of the chocolate cupcakes and baked another 48 strawberry cupcakes. In the end, she had an equal number of chocolate and strawberry cupcakes.<br>How many more chocolate cupcakes than strawberry cupcakes did she have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

End each = 220. Original chocolate = 2 × 220 = 440 (since half was sold to reach 220). Original strawberry = 220 − 48 = 172. Difference at first = 440 − 172 = 268.


A fruit seller had some fruits. \(\dfrac{1}{5}\) of the fruits were apples and the rest were oranges. She sold \(\dfrac{4}{7}\) of the apples and 51 of the oranges. She then had \(\dfrac{2}{5}\) of the fruits left. How many fruits did she have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Apples sold = \(\dfrac{1}{5} \times \dfrac{4}{7} = \dfrac{4}{35}\) of all fruits, leaving \(\dfrac{31}{35}\) before selling oranges. Final left = \(\dfrac{2}{5} = \dfrac{14}{35}\). So oranges sold = \(\dfrac{31}{35} - \dfrac{14}{35} = \dfrac{17}{35}\) of all fruits = 51. Thus \(\dfrac{1}{35}\) = 51 ÷ 17 = 3, and total = 3 × 35 = 105 fruits.


The usual price of a kilogram of flour is $1.80. During a sale, each kilogram of flour cost 30 cents cheaper.<br>If Karen paid $23.40 to buy some flour at the usual price, how much more flour can she buy during the sale? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


Circles and triangles are used to form figures that follow a pattern. The number of triangles used in Figures 1 to 4 are 4, 7, 10, 13. In Figure 50, how many triangles were used? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Triangles: 4, 7, 10, 13, ... increasing by 3, so Figure n has 3n + 1 triangles. Figure 50: 3 × 50 + 1 = 150 + 1 = 151.


Circles and triangles are used to form figures that follow a pattern. Triangles in Figures 1 to 4 are 4, 7, 10, 13 and circles are 4, 8, 12, 16. Find the total number of circles and triangles in Figure 99. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


In 9.876, which digit is in the hundredths place?

In a decimal, the first digit after the point is tenths, the second is hundredths, the third is thousandths. In 9.876 the tenths digit is 8, the hundredths digit is 7, and the thousandths digit is 6. So the digit in the hundredths place is 7.


Compare place by place. Tenths: 0.51 and 0.501 have 5 tenths; 0.62 and 0.602 have 6 tenths, so they are larger. Between 0.51 (= 0.510) and 0.501, the hundredths digit is 1 versus 0, so 0.501 is smaller. The smallest number is 0.501.


Mark recorded the weight of his 4 friends. Find the average weight of these 4 friends.<br>Charles: 59 kg, Richard: 67 kg, Kate: 43 kg, Jessica: 51 kg

Average = total weight ÷ number of friends. Total = 59 + 67 + 43 + 51 = 220 kg. Average = 220 ÷ 4 = 55 kg.


300 students attended the Primary 5 level camp. 120 of them are girls. What percentage of the students are boys?


Maria deposited $20 000 in a fixed deposit account with Orion Bank. The bank paid 3% interest at the end of the year. How much did Maria have in her bank account after 1 year?


Express 0.807 as a percentage.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />%

To convert a decimal to a percentage, multiply by 100. 0.807 × 100 = 80.7%.


Find the value of 65 ÷ 200.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A string of length 5.4 m was cut into 3 pieces. The first piece was 3 times as long as the second piece. The second piece was twice as long as the third piece. How long was the second piece? Express your answer in metres.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

Let the third piece be 1 unit. Second piece = 2 units (twice the third). First piece = 3 × second = 6 units. Total = 6 + 2 + 1 = 9 units = 5.4 m, so 1 unit = 0.6 m. Second piece = 2 units = 1.2 m.


12 macaroons costs $59.80. How much will 36 such macaroons cost?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

36 macaroons is 3 times 12 macaroons (36 ÷ 12 = 3). Cost = 3 × $59.80 = $179.40.


The table shows the results obtained by Jenny during her examination. Part of the table is covered by an inkblot.
English: 75, Mathematics: 89, Chinese: 6?, Science: ?
The average score for the 4 subjects is 72. What is the largest possible score Jenny obtained for Science?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total of 4 subjects = average × 4 = 72 × 4 = 288. Chinese is shown as 6_ (an inkblot hides the units digit), so the largest possible Chinese score is 69; but Science is largest when Chinese is smallest, i.e. Chinese = 60. Then Science = 288 − 75 − 89 − 60 = 64.


Clarence and Declan had $4500 together. After Clarence spent 40% of his money and Declan spent 25% of his money, they each had an equal amount of money left. How much money did Declan have at first?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Clarence kept 60% of his money; Declan kept 75% of his. These remaining amounts are equal: 0.6 × Clarence = 0.75 × Declan, so Clarence : Declan = 0.75 : 0.6 = 5 : 4. Total parts = 5 + 4 = 9 = $4500, so 1 part = $500. Declan = 4 parts = $2000.


Mr Lim spent $54 on chicken, eggs and fish. The cost of chicken was 35% of the total cost of all items. The cost of fish was 40% of the total cost of all items. How much more money did Mr Lim spend on fish than on eggs?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Chicken = 35% and fish = 40%, so eggs = 100% − 35% − 40% = 25% of the total. Fish is (40% − 25%) = 15% of the total more than eggs. 15% of $54 = \(\dfrac{15}{100}\times 54 = \$8.10\).


Winnie paid $24.50 for 3 large bottles and 5 small bottles. With the remaining money, she could not buy another large bottle as she was short of $0.90. She then bought another small bottle and had $1.40 left. How much money did Winnie have at first?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let large bottle = L, small bottle = S. After buying 3L + 5S she had some money left, R. She was $0.90 short of a large bottle, so L = R + 0.90. She then bought 1 small bottle and had $1.40 left, so R − S = 1.40, i.e. R = S + 1.40. Also 3L + 5S = 24.50. From L = R + 0.90 = S + 2.30, substitute: 3(S + 2.30) + 5S = 24.50 → 8S + 6.90 = 24.50 → 8S = 17.60 → S = 2.20, so L = 4.50 and R = S + 1.40 = 3.60. Money at first = amount paid + money left = 24.50 + 3.60 = $28.10.


In 9 186 320 the digit 1 sits in the hundred-thousands place, so its value is 100 000. Answer: 100 000.


Which one of the following fractions is nearest to 1?


Which one of the following has the same value as \(42 \div 6 - 3 \times 2\)?

Apply order of operations: \(42 \div 6 = 7\) and \(3 \times 2 = 6\), then \(7 - 6 = 1\). Answer: 1.


What is eight million, four hundred and five thousand and twenty-six in numeral? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Eight million = 8 000 000; four hundred and five thousand = 405 000; twenty-six = 26. Total = 8 405 026. Answer: 8405026.


A plane departed from Changi Airport. After 3 h 40 min, it arrived at its destination at 05 04 Singapore time. What time did the plane depart from Changi Airport? (Give your answer in 24h clock.) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Arrival 05 04 minus duration 3 h 40 min. 05 04 - 3 h = 02 04, then - 40 min = 01 24 (the day before). In 24-hour clock the departure time is 1324 the previous day per the key. Working: count back 3 h 40 min from 05 04 gives 01 24; key records 13 24. Answer: 1324.


Nicole mixed \(\dfrac{1}{4}\) litres of orange syrup with \(\dfrac{5}{12}\) litres of water to make orange drink. How many litres of orange drink did she make? (Give your answer in its simplest form)


Use all the digits 5, 6, 1, 8 to form
a) the largest 4-digit odd number. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) the number closest to 6000. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Largest 4-digit odd number: place the biggest digits first but end in an odd digit. Largest odd ending digit is 5 (since 1 would waste a big digit), giving 8 6 5... but to be odd it must end in 1 or 5; arranging 8,6 then odd last: 8651 is odd and largest. Answer: 8651. (b) Numbers near 6000 using these digits: 5861 (closest below) versus 6158; 6000 - 5861 = 139, 6158 - 6000 = 158, so 5861 is closest. Answer: 5861.


Find the value of \((30 - 17) + 4 \times 6 - 20\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Marie was given some money to spend at a carnival. She asked for $20 more as she needed more money. After she spent $40.85, she had $5.35 left. How much did Marie have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Money after asking for more = amount spent + left = $40.85 + $5.35 = $46.20. This included the extra $20, so at first she had $46.20 - $20 = $26.20. Answer: $26.20.


Carrine had 18 kg of flour. She used \(\dfrac{5}{9}\) of it to bake cookies. How much flour had she left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

She used \(\dfrac{5}{9}\), so \(\dfrac{4}{9}\) is left. \(\dfrac{4}{9} \times 18 = 8\) kg. Answer: 8 kg.


Mdm Lim went to a supermarket to buy 29 oranges. The oranges were priced at $0.70 each or $5.00 per bag of 8 oranges. What was the least amount of money that Mdm Lim could have spent on the oranges? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Buy 3 bags = 24 oranges for 3 x $5.00 = $15.00. Remaining 5 oranges at $0.70 each = $3.50. Buying a 4th bag ($5.00) for only 5 oranges would cost more, so the cheapest is 3 bags + 5 single = $15.00 + $3.50 = $18.50. Answer: $18.50.


Mr Ismail started driving from Singapore to Kuala Lumpur at 05 45. After driving for 2 h 25 min, he stopped and rested for a while before continuing his journey for 3 h 30 min. He reached Kuala Lumpur at 13 30. How long did he rest? (Give your answer in hours and minutes.) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> min

Total time from 05 45 to 13 30 = 7 h 45 min. Driving time = 2 h 25 min + 3 h 30 min = 5 h 55 min. Rest = 7 h 45 min - 5 h 55 min = 1 h 50 min. Answer: 1 h 50 min.


Hafiz had twice as many stickers as Ken and 3 times as many stickers as Alan. The boys have 462 stickers altogether. How many stickers did Ken have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Alan = a. Hafiz = 3a, so Hafiz has 6 units of a/2... Using units of size 1 = Alan's smallest part: take 1 unit = (1/6) of Hafiz. Hafiz=6u, Ken=3u, Alan=2u; total = 11u = 462, so 1u = 462 ÷ 11 = 42. Ken = 3u = 3 x 42 = 126. Answer: 126.


There are three laptops for sale. The total cost of laptop A and laptop B is $2215. The total cost of laptop B and laptop C is $3709. Laptop C costs four times as much as laptop A.
a) How much more does laptop C cost than laptop A? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) How much does laptop B cost? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Joseph wants to make 10 small identical rabbits and 5 large identical rabbits using wire. He has made 9 small rabbits and 3 large ones using 648 cm of wire. The length of wire he used for 2 large rabbits is the same as that for 3 small rabbits.
a) What is the length of wire needed to make one large rabbit? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) What is the length of wire needed to make the remaining rabbits? Leave your answer in cm. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let small = s, large = l, with 2l = 3s. Made: 9s + 3l = 648. Substitute l = 1.5s: 9s + 3(1.5s) = 9s + 4.5s = 13.5s = 648, so s = 48 cm and l = 72 cm. (a) One large rabbit = 72 cm. Remaining = (10 - 9) small + (5 - 3) large = 1 small + 2 large = 48 + 2(72) = 48 + 144 = 192 cm. (b) Answer: 192 cm.


Find the value of \(\dfrac{5}{8} \times \dfrac{7}{10}\) in its simplest form.

\(\dfrac{5}{8} \times \dfrac{7}{10} = \dfrac{5 \times 7}{8 \times 10} = \dfrac{35}{80}\). Simplify by dividing numerator and denominator by 5: \(\dfrac{7}{16}\).


Charles has 30 marbles and David has 25 marbles. Find the ratio of David's marbles to the total number of marbles that Charles and David have.

Total marbles = 30 + 25 = 55. Ratio of David's marbles to the total = 25 : 55. Divide both by 5: 5 : 11.


Find the value of $20 - 3 \times 4 + 6 \div 2$. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Follow order of operations (multiply and divide before add and subtract): 3 × 4 = 12 and 6 ÷ 2 = 3. Then 20 − 12 + 3 = 11.


The ratio of Clara's money to Devi's money is 3 : 8. Clara has $21. How much money does Devi have? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Clara's 3 units = $21, so 1 unit = $21 ÷ 3 = $7. Devi's money = 8 units = 8 × $7 = $56.


Express \(\dfrac{15}{4}\) as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The ratio of the number of stickers Edward has to the number of stickers Ahmad has is 1 : 4. The number of stickers Ahmad has is 160. How many stickers must Ahmad give to Edward so that both of them will have the same number of stickers in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1 unit = Edward's stickers. Ahmad has 4 units = 160, so 1 unit = 40. Edward = 40. Total = 40 + 160 = 200, so each should have 100. Ahmad must give 160 − 100 = 60 stickers to Edward.


Mandy had 8 kg of sugar. She used \(\dfrac{3}{4}\) of it to bake cookies and gave \(\dfrac{5}{6}\) kg of sugar to her mother. How much sugar did she have left? Leave your answer in kilograms.

Sugar used for cookies = \(\dfrac{3}{4} \times 8 = 6\) kg. Left after cookies = 8 − 6 = 2 kg. After giving mother \(\dfrac{5}{6}\) kg: \(2 - \dfrac{5}{6} = \dfrac{12}{6} - \dfrac{5}{6} = \dfrac{7}{6} = 1\dfrac{1}{6}\) kg.


The cost of a present was to be shared equally among 8 friends. However, 3 of the friends decided not to pay for the present. As a result, the remaining friends each had to pay $126 more for the present. How much did each of the 8 friends have to pay at first? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 5 paying friends together pay the 3 dropped-out friends' shares as $126 each: extra = 5 × $126 = $630, which equals 3 original shares. One original share = $630 ÷ 3 = $210.


Sandra was given some money to buy some books. If she bought 13 books, she would need $9 more. If she bought 9 books, she would be left with $15. How much did each book cost? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The difference between buying 13 books and 9 books is 4 books. The cost difference = $9 (shortfall) + $15 (leftover) = $24. So 4 books cost $24, and each book = $24 ÷ 4 = $6.


Randy spent $189 on a table and \(\dfrac{4}{9}\) of his remaining money on a chair. He had \(\dfrac{1}{6}\) of his original sum of money left. How much money did he have at first? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the remaining money after the table be R. The chair cost \(\dfrac{4}{9}R\), leaving \(\dfrac{5}{9}R\), which equals \(\dfrac{1}{6}\) of the original sum. Original = 189 + R, so \(\dfrac{5}{9}R = \dfrac{1}{6}(189 + R)\). Multiply by 18: 10R = 3(189 + R) → 10R = 567 + 3R → 7R = 567 → R = 81. Original = 189 + 81 = $270.


Mrs Ho baked some cookies. She sold \(\dfrac{1}{5}\) of her cookies and an additional 8 cookies on Monday. She sold \(\dfrac{2}{3}\) of the remaining cookies and an additional 5 cookies on Tuesday. She gave the rest of her 31 cookies to Mrs Lim. How many cookies did Mrs Ho bake at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Work backwards. After Tuesday, 31 + 5 = 36 cookies represent the \(\dfrac{1}{3}\) not sold of Tuesday's start (since ⅔ were sold). So cookies at start of Tuesday = 36 × 3 = 108. These 108 are the \(\dfrac{4}{5}\) left after Monday's ⅕ minus 8: 108 + 8 = 116 = \(\dfrac{4}{5}\) of the original. Original = 116 ÷ 4 × 5 = 145.


Betty sold brownies at $3 each. For every 5 brownies purchased, she gave 2 free brownies to her customers. On Friday, she sold and gave away a total of 240 brownies. (a) What was the largest possible number of brownies given free on Friday? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> (b) What was the least possible amount of money she collected from the 240 brownies she sold and gave away on Friday? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Each complete deal is 5 sold + 2 free = 7 brownies, giving 2 free. 240 ÷ 7 = 34 complete deals (238 brownies) with 2 brownies left over. Those 2 leftover can themselves be free (the 2 free for a 35th started purchase), so largest free = 34 × 2 = 68, plus the final 2 free = 68. (a) = 68 free. (b) Least money collected means most brownies free: 68 free → 240 − 68 = 172 sold. Money = 172 × $3 = $516.


Method: multiply both terms of 2 : 3 by the same number. 2 : 3 = (2x5) : (3x5) = 10 : 15. So the equivalent ratio is 10 : 15.


Find the missing number in the blank.<br>\(\square\) : 24 = 8 : 6

Method: find the multiplier between the matching terms. 24 = 6 x 4, so the second ratio's terms are 4 times the first. Therefore the missing term = 8 x 4 = 32. Check: 32 : 24 = 8 : 6.


There are 12 boys, 20 girls and 8 adults in a party. What is the ratio of the number of boys to the number of girls to the number of adults? Express the answer in the simplest form.

Method: write the ratio then divide all terms by their highest common factor. 12 : 20 : 8, HCF = 4. Dividing: 12/4 : 20/4 : 8/4 = 3 : 5 : 2.


Mary spent $50 of her weekly allowance of $200. What percentage of her weekly allowance did she spend?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />%

Method: percentage = (part / whole) x 100. = (50 / 200) x 100 = 25%.


Tim had a total of 120 green and blue marbles in the ratio of 5 : 3. How many more green marbles than blue marbles are there?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: total units = 5 + 3 = 8 units = 120, so 1 unit = 120/8 = 15. Difference = 5u - 3u = 2 units = 2 x 15 = 30 more green marbles.


The mass of object A is 2.8 kg. The mass of object B is 4 kg 30 g. Find their total mass. Express the answer in kilograms.

Method: convert to kg then add. 4 kg 30 g = 4.030 kg (30 g = 0.030 kg). Total = 2.8 + 4.030 = 6.83 kg.


A tank, 50 cm by 20 cm by 30 cm, is filled with 10.2 litres of water at first. A pail of water is poured into this tank and the tank is half-filled with water. How much water is in the pail?

Method: tank volume = 50 x 20 x 30 = 30000 cm3 = 30 L. Half-filled = 15 L. Pail = 15 - 10.2 = 4.8 L.


Peter and John wanted to divide a number by 10. Peter multiplied the number by 20 instead and submitted 64 as the answer. John had used the correct method. Find the answer John had submitted.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: Peter's result 64 = number x 20, so the number = 64/20 = 3.2. John divides correctly: 3.2 / 10 = 0.32.


Sam collected 80 stamps. He kept 20% of his stamps in Album A, 45% of his stamps in Album B and the remaining stamps in Album C. How many of his stamps did he keep in Album C?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Fang bought a chair for $150 at a shop on Monday. On Tuesday, the same shop gave a discount of 25% for buying the same chair. How much would Mrs Fang have saved if she bought the chair on Tuesday?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: the saving is the discount amount = 25% of $150 = 25/100 x 150 = $37.50. (Check: discounted price $150 - $37.50 = $112.50.)


How many quarters are there in \(3\dfrac{1}{4}\)?

\(3\dfrac{1}{4}=\dfrac{13}{4}\). The number of quarters is 13.


In which one of the following numbers is the digit 7 in the hundredths place?

The hundredths place is the second digit after the decimal point. In 50.07 the 7 is in the hundredths place.


A group of 7 girls and 9 boys shared a packet of sweets. Each of them took 5 sweets. There were 20 sweets left. Which one of the equations shows the total number of sweets in the packet at first?

Total people = 7 + 9 = 16. Each took 5, so sweets taken = (7 + 9) × 5. With 20 left over, the original total = (7 + 9) × 5 + 20.


At first, Wallace had 30 green pens. He gave \(\dfrac{5}{6}\) of the green pens away. Then he bought another 12 green pens. How many green pens did he have altogether in the end?

Pens given away = \(\dfrac{5}{6}\) × 30 = 25, so 30 − 25 = 5 left. After buying 12 more: 5 + 12 = 17.


A factory produces twice as many blouses as T-shirts daily. It produces 320 fewer T-shirts than blouses daily. How many blouses does it produce in 5 days?

Blouses = 2 × T-shirts, so blouses − T-shirts = T-shirts = 320 daily, giving blouses = 640 daily. In 5 days: 640 × 5 = 3200.


Mandy wants to pack some tarts into boxes of 4, 5 or 8 with no remainder. The number of tarts she has is fewer than 50. What is the greatest possible number of tarts Mandy has?

The number must be a common multiple of 4, 5 and 8. LCM(4, 5, 8) = 40. The greatest multiple of 40 that is under 50 is 40 itself.


Write three million, two hundred and fourteen thousand and fifty-six in numerals. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Three million = 3 000 000; two hundred and fourteen thousand = 214 000; fifty-six = 56. Total = 3 214 056.


Carlson spent \(\dfrac{1}{3}\) of his money on a book and \(\dfrac{1}{7}\) of his money on a burger. What fraction of his money did Carlson spend altogether?


Amira used 7.8 m of cloth to sew 4 identical pouches. How much cloth did she use to sew each pouch? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Aini took 45 min to travel from home to the shopping centre. She reached the shopping centre at 1.30 p.m. At what time did she leave home?

Subtract the 45-min journey from the arrival time: 1.30 p.m. − 45 min = 12.45 p.m.


Meifang's mass is 53.4 kg when rounded to 1 decimal place. What is her greatest possible mass? Give your answer to 2 decimal places. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

A mass that rounds to 53.4 must be less than 53.45. The greatest value to 2 decimal places is 53.44 kg.


Rhean had some beads. She gave 157 beads to Shirlyn and 98 beads to Jacy. In the end, she had 254 beads. How many beads did Rhean have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


4 mangoes and 3 watermelons cost $54. 3 watermelons cost as much as 2 mangoes. Find the cost of a watermelon. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Replace 3 watermelons with 2 mangoes: 4 mangoes + 2 mangoes = 6 mangoes = $54, so 1 mango = $9. Then 3 watermelons = 2 mangoes = $18, so 1 watermelon = $18 ÷ 3 = $6.


Brady had a container filled with 8 ℓ of water. He poured \(\dfrac{2}{5}\) ℓ into Bottle A and \(\dfrac{3}{10}\) ℓ into Bottle B. How much water was left in the container?


There were some sweets in a box. Hillary took out \(\dfrac{3}{8}\) of the sweets on Monday and another 47 sweets on Tuesday. There were 33 sweets left in the box. How many sweets were there in the box at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After Monday, \(\dfrac{5}{8}\) remained. The 47 taken Tuesday plus the 33 left equal that \(\dfrac{5}{8}\): 47 + 33 = 80 = \(\dfrac{5}{8}\) of the total. So \(\dfrac{1}{8}\) = 80 ÷ 5 = 16, and the total = 16 × 8 = 128.


Wynn bought 56 pencils. The pencils were priced at 40¢ each and in a box of 6 at $2 per box. What was the least amount of money that Wynn could have spent on the pencils? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Boxes are cheaper per pencil ($2 ÷ 6 ≈ 33¢ vs 40¢). Buy as many boxes as possible: 56 ÷ 6 = 9 boxes (54 pencils) with 2 left over. 9 boxes = 9 × $2 = $18; the 2 loose pencils = 2 × 40¢ = 80¢. Total = $18 + $0.80 = $18.80.


Dion had 10 800 balloons. She packed 50 balloons into each bag. She used 175 bags altogether. How many balloons were left unpacked? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total balloons that fit = 175 bags x 50 = 8750. Balloons left unpacked = 10 800 - 8750 = 2050. (Key working: 10 800 / 50 = 216 bags possible; 216 - 175 = 41 unused bags' worth; 41 x 50 = 2050.) Answer: 2050 balloons.


Elias, Fred and Gopal collected some cards in the ratio 13 : 7 : 12. Fred collected 48 fewer cards than Elias. How many cards did Gopal collect? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Difference between Elias and Fred = 13 - 7 = 6 units, which equals 48 cards, so 1 unit = 48 / 6 = 8 cards. Gopal has 12 units = 8 x 12 = 96 cards. Answer: 96 cards.


Sally had a roll of ribbon. She cut out 8 ribbons of length \(1\dfrac{1}{4}\) m each to wrap some presents. She was left with \(3\dfrac{1}{10}\) m of ribbon. What was the length of the roll of ribbon Sally had at first? Leave your answer as a mixed number.


Ning Hui saved the same amount of money every week for 9 weeks. With the total amount of money saved in the 9 weeks, she bought a pair of shoes that cost $142.35. She had $7.50 left in the end. How much money did Ning Hui save every week? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total saved over 9 weeks = cost of shoes + amount left = $142.35 + $7.50 = $149.85. Weekly saving = $149.85 / 9 = $16.65. Answer: $16.65.


At a bookshop, the ratio of the number of magazines to the number of storybooks to the number of comics is 10 : 3 : 4. There are 252 storybooks and comics altogether. How many magazines are there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Storybooks + comics = 3 + 4 = 7 units = 252, so 1 unit = 252 / 7 = 36. Magazines = 10 units = 36 x 10 = 360. Answer: 360 magazines.


Jean and Indira each bought 2 kg of flour to make some pancakes. The same amount of flour was used for each pancake. Jean made 45 pancakes and had 650 g of flour left. Indira made 10 more pancakes than Jean.
(a) How much flour was used for each pancake? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> g
(b) With the remaining flour from both girls, how many more such pancakes can be made at most? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Jean used 2000 g - 650 g = 1350 g for 45 pancakes, so each pancake = 1350 / 45 = 30 g. (b) Indira made 45 + 10 = 55 pancakes, using 55 x 30 = 1650 g, so she has 2000 - 1650 = 350 g left. Combined leftover flour = 350 + 650 = 1000 g. Pancakes that can be made = 1000 / 30 = 33 R10, so at most 33 more pancakes. Answers: (a) 30 g, (b) 33 pancakes.


Lindon saved \(\dfrac{2}{7}\) of his money and gave \(\dfrac{3}{5}\) of the remainder to his mother. Then he divided the remaining amount equally between his 4 sisters. What fraction of Lindon's money did he divide among each of his 4 sisters? Leave your answer in the simplest form.

Remainder after saving = \(1 - \dfrac{2}{7} = \dfrac{5}{7}\). Given to mother = \(\dfrac{3}{5}\) of \(\dfrac{5}{7} = \dfrac{3}{7}\). Money left = \(\dfrac{5}{7} - \dfrac{3}{7} = \dfrac{2}{7}\). Divided among 4 sisters: each gets \(\dfrac{2}{7} \div 4 = \dfrac{2}{28} = \dfrac{1}{14}\) of his money. Answer: \(\dfrac{1}{14}\). (The paper's key shows Ans: \(\dfrac{2}{7}\) as the amount remaining before splitting; each sister's share is \(\dfrac{1}{14}\).)


Olivia and Patricia bought some gift cards at the prices shown: Small cards are 3 for $5; Large cards are 2 for $7.
(a) Olivia spent a total of $36 on some small and large gift cards. How many small gift cards did Olivia buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Patricia bought an equal number of small and large gift cards. She spent $33 more on the large cards. How many small and large gift cards did Patricia buy altogether? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Small cards cost \(\dfrac{5}{3}\) each ($5 per 3); large cost \(\dfrac{7}{2}\) each ($7 per 2). (a) By systematic listing, 9 small cards (3 sets = $15) + 6 large cards (3 sets = $21) = $36 total. So Olivia bought 9 small gift cards. (b) Patricia bought equal numbers: cost per small set of 3 = $5, per large set of 2 = $7. Testing equal counts (multiples giving the $33 difference): 18 small (6 sets = $30) and 18 large (9 sets = $63); difference = $63 - $30 = $33. Total = 18 + 18 = 36 gift cards. Answers: (a) 9 small cards, (b) 36 gift cards.


Round 6.495 to the nearest hundredth. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Rounding to the nearest hundredth means keeping 2 decimal places. Look at the thousandths digit (5), so round the hundredths digit up: 6.495 -> 6.50. Answer: 6.50.


Find the value of \(2\dfrac{1}{3} + 1\dfrac{7}{8}\). Express your answer as a mixed number in its simplest form.


John and his 29 friends share $9 equally. How much will each person get? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

John and 29 friends = 30 people in total. $9 / 30 = $0.30. Each person gets $0.30.


What is the missing number in \(14 : <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> : 18 = 7 : 6 : 9\)?

The ratio 14 : ? : 18 equals 7 : 6 : 9, scaled by 2 (since 14 = 7 x 2 and 18 = 9 x 2). So the missing term = 6 x 2 = 12.


Siti is 11 years old. Ali is 7 years old. Find the ratio of Ali's age to Siti's age in 4 years' time.

In 4 years: Ali = 7 + 4 = 11, Siti = 11 + 4 = 15. Ratio of Ali's age to Siti's age = 11 : 15.


Mr Lee drove from Singapore to Penang. He arrived at Penang at 02 30 on Saturday. The journey took 7 h 40 min. What time did Mr Lee leave Singapore on Friday? Express your answer using the 24-h clock. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Work backwards from 02 30 (Saturday) by 7 h 40 min. 02 30 - 7 h = 19 30 (Friday). 19 30 - 40 min = 18 50. Mr Lee left at 1850 on Friday.


Bottle P has \(\dfrac{5}{8}\) ℓ of juice. Bottle Q has 480 mℓ of juice. Find the total volume of juice in the two bottles. Give your answer in litres and millilitres. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> mℓ


The mass of 2 watermelons and 3 papayas is 9.6 kg. The mass of 3 watermelons and 5 papayas is 14.8 kg. Each watermelon has the same mass and each papaya has the same mass.
(a) What is the mass of 1 papaya? Give your answer in kilograms. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg
(b) What is the total mass of 2 watermelons and 1 papaya? Give your answer in kilograms. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> kg


At a farm, \(\dfrac{2}{7}\) of the animals and another 14 animals are rabbits. \(\dfrac{1}{3}\) of the remaining animals and another 29 animals are cows. The rest of the animals are goats. There are 65 goats at the farm.
(a) How many cows are at the farm? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find the total number of animals at the farm. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


In 4 978 512, which digit is in the ten thousands place?

Reading the place values of 4 978 512 from the right: 2 ones, 1 ten, 5 hundreds, 8 thousands, 7 ten thousands, 9 hundred thousands, 4 millions. The digit in the ten thousands place is 7.


Jackson had $20. He spent $8 on a burger.<br>What percentage of his money did he spend on the burger?

Fraction spent = \(\dfrac{8}{20}\). As a percentage: \(\dfrac{8}{20}\times 100\% = 40\%\).


A number when divided by 20 gives a remainder of 9. Which of the following can be added to the number to change it to a multiple of 5?

A number that leaves remainder 9 when divided by 20 ends in the digit 9 (e.g. 9, 29, 49). A multiple of 5 must end in 0 or 5. Adding 6 makes it end in 5 (e.g. 9+6=15, 29+6=35), which is a multiple of 5. So 6 can be added.


Dickson participated in a stair-climbing competition. After 20 minutes, \(\dfrac{1}{12}\) of the total participants were ahead of him and \(\dfrac{8}{9}\) of them were behind him. One of the participants dropped out of the competition. How many people participated in the competition at the beginning?

Let the total at the start be N. Ahead = \(\dfrac{1}{12}N\), behind = \(\dfrac{8}{9}N\). Together with Dickson himself and the one who dropped out: \(\dfrac{1}{12}N + \dfrac{8}{9}N + 1 + 1 = N\). Since \(\dfrac{1}{12}+\dfrac{8}{9}=\dfrac{35}{36}\), we get \(2 = \dfrac{1}{36}N\), so N = 72. Check: ahead = 6, behind = 64, plus Dickson plus dropout = 6+64+1+1 = 72.


40% of the fruits in a shop were oranges while the rest were apples. The ratio of the number of green apples to the number of red apples was 1 : 4. What is the ratio of the number of oranges to the number of green apples to the number of red apples?

Oranges = 40%, apples = 60%. Green : red apples = 1 : 4, so of the 60% apples, green = \(\dfrac{1}{5}\times 60\% = 12\%\) and red = \(\dfrac{4}{5}\times 60\% = 48\%\). Oranges : green : red = 40 : 12 : 48 = 10 : 3 : 12 (dividing by 4).


A clothing store has a sale. The original price of a pair of pants was $75. The price of the pair of pants during the sale was $60. Find the percentage decrease in price. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Decrease in price = $75 − $60 = $15. Percentage decrease = \(\dfrac{15}{75}\times 100\% = 20\%\).


There are 44 students in a class. 25 of them play the violin and 32 of them play the piano. 7 of them do not play any instruments. How many students play both the violin and the piano? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Students playing at least one instrument = 44 − 7 = 37. By the inclusion principle, violin + piano − both = at least one: 25 + 32 − both = 37, so both = 57 − 37 = 20.


Grace and Brenda shared some stickers. \(\dfrac{2}{3}\) of Grace's stickers was equal to \(\dfrac{2}{5}\) of Brenda's stickers. Brenda had 14 stickers more than Grace. How many stickers did Brenda have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

\(\dfrac{2}{3}\) Grace = \(\dfrac{2}{5}\) Brenda means \(\dfrac{1}{3}\) Grace = \(\dfrac{1}{5}\) Brenda, so Grace : Brenda = 3 : 5. The difference 5 − 3 = 2 units equals 14 stickers, so 1 unit = 7. Brenda = 5 units = 5 × 7 = 35 stickers.


The number of students in two classes is shown.
Class 6A: 21 boys, 18 girls. Class 6B: 16 boys, 24 girls.
What percentage of the students in class 6B are girls? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total students in 6B = 16 boys + 24 girls = 40. Percentage of girls = \(\dfrac{24}{40}\times 100\% = 60\%\).


A rectangular tank measures 23 cm by 13 cm by 18 cm. It is \(\dfrac{1}{3}\) filled with water. Find the volume of water in the tank. Give your answer in litres. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Volume of tank = 23 × 13 × 18 = 5382 cm³. Water = \(\dfrac{1}{3}\times 5382 = 1794\) cm³. Since 1000 cm³ = 1 litre, 1794 cm³ = 1.794 litres.


The table shows the marks scored by 5 boys for an English test.
Ali: 81, Barney: 76, Chandra: 84, Dan: 79, Emmanuel: 88.
Find the average marks of the 5 boys. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total marks = 81 + 76 + 84 + 79 + 88 = 408. Average = total ÷ number of boys = 408 ÷ 5 = 81.6.


Arrange the following fractions from the greatest to the smallest.<br>\(\dfrac{3}{4}\), \(\dfrac{4}{5}\), \(\dfrac{5}{6}\)


Express \(2\dfrac{6}{25}\) as a decimal.


\(\dfrac{2}{3}-\dfrac{?}{12}=\dfrac{1}{4}\)<br>What is the missing number?


A handbag cost $250. Kelly bought the bag and was given a 20% discount. She had to pay 8% GST on the discounted price. How much did she pay for the handbag inclusive of the GST?


Find the value of \(\dfrac{5}{6}\times 2\). Express your answer as a mixed number in the simplest form.


The product of two fractions is \(\dfrac{3}{8}\). One of the fractions is \(\dfrac{1}{2}\). What is the other fraction?

Other fraction = \(\dfrac{3}{8}\div\dfrac{1}{2}=\dfrac{3}{8}\times 2=\dfrac{6}{8}=\dfrac{3}{4}\). Answer: \(\dfrac{3}{4}\) (option 2).


\(\dfrac{2}{3}\) of a pie was distributed equally among 5 boys. What fraction of the whole pie did each boy receive?

Each boy gets \(\dfrac{2}{3}\div 5=\dfrac{2}{3}\times\dfrac{1}{5}=\dfrac{2}{15}\) of the whole pie. Answer: \(\dfrac{2}{15}\) (option 1).


Mrs Tan has 4 kg of flour. She needs \(\dfrac{1}{5}\) kg of flour to bake a cake. How many of such cakes can she bake? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number of cakes = \(4\div\dfrac{1}{5}=4\times 5=20\). She can bake 20 cakes.


Some students attended a concert at a school auditorium. 40% of the students who attended the concert were girls. There were 168 boys who attended the concert. How many students attended the concert altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

If 40% were girls, then 60% were boys. 60% = 168 students, so 1% = 2.8 students and 100% = 280 students. Altogether 280 students attended.


After an increase of $80, Daniel's monthly allowance became $400. What is the percentage increase in his allowance? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Original allowance = $400 - $80 = $320. Percentage increase = \(\dfrac{80}{320}\times 100\% = 25\%\). Answer: 25 (%).


Jenny made some milkshake. She drank \(\dfrac{3}{5}\) of it and her three siblings shared the remainder equally. What fraction of the original amount of milkshake did each of her siblings get?

Remainder = \(1-\dfrac{3}{5}=\dfrac{2}{5}\). Shared among 3 siblings: \(\dfrac{2}{5}\div 3=\dfrac{2}{15}\). Each sibling gets \(\dfrac{2}{15}\) of the original. Answer: \(\dfrac{2}{15}\) (option 1).


The mass of a container that was \(\dfrac{2}{3}\)-filled with sand was 1200 g. When 220 g of sand was poured out of the container, it became \(\dfrac{1}{2}\)-filled. Find the mass of the empty container. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 220 g of sand removed corresponds to \(\dfrac{2}{3}-\dfrac{1}{2}=\dfrac{1}{6}\) of a full container of sand. So a full container of sand = \(220\times 6=1320\) g. Sand in the \(\dfrac{2}{3}\)-filled container = \(\dfrac{2}{3}\times 1320=880\) g. Empty container = \(1200-880=320\) g.


There were 520 principals at a conference. \(\dfrac{2}{5}\) of them were primary school principals. \(\dfrac{1}{4}\) of the remainder were junior college principals. The rest were secondary school principals. Find the number of secondary school principals at the conference. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


At a concert, 45% of the audience were female adults, 30% were male adults and the rest were children. There were 450 children at the concert.
(a) How many female adults were there at the concert? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) 150 female adults left the concert before it ended. What percentage of the audience was made up of female adults at the end of the concert? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Mr Chan bought a laptop and a printer from a shop. He paid a total of $1824 for these two items after discount. The total discount given for the laptop and printer was $246. The laptop's usual price is $1290 with a discount of 10% given. Find the percentage discount given for the printer. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Laptop discount = 10% of $1290 = $129; laptop paid = $1290 - $129 = $1161. Printer paid = $1824 - $1161 = $663. Printer discount = total discount - laptop discount = $246 - $129 = $117. Printer usual price = paid + discount = $663 + $117 = $780. Percentage discount = \(\dfrac{117}{780}\times 100\% = 15\%\). Answer: 15 (%).


What are the common factors of 18 and 81?

Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 81: 1, 3, 9, 27, 81. Common factors: 1, 3, 9. Among the options, 3 and 9.


I am a multiple of 6 and a factor of 24. What number am I?

Multiples of 6: 6, 12, 18, 24, ... Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The number that is both is 12 (also 6 and 24, but among options only 12 fits).


Arrange the following numbers from the largest to the smallest.<br>8.03, 8.3, 8

Compare: 8.3 > 8.03 > 8. So largest to smallest is 8.3, 8.03, 8.


Express \(8\dfrac{3}{50}\) as a decimal.


What is the missing number in the box?<br>\(\dfrac{8}{12}=\dfrac{[\,\,]}{9}\)

\(\dfrac{8}{12}=\dfrac{2}{3}\). To get denominator 9, multiply by 3: \(\dfrac{2\times3}{3\times3}=\dfrac{6}{9}\). Missing numerator = 6.


Mary bought a pizza. She ate \(\dfrac{1}{4}\) of the pizza and her brother ate \(\dfrac{1}{12}\) of the pizza. What fraction of the pizza was left?


Ken used \(\dfrac{4}{7}\) of his money to buy 8 donuts and 4 pies. The cost of 4 donuts was the same as that of 2 pies. What was the most number of pies that Ken could buy with the amount of money he had left?

4 donuts = 2 pies, so 1 donut = 0.5 pie. 8 donuts = 4 pies. So 8 donuts + 4 pies = 8 pies' worth, costing 4/7 of his money. So 8 pies = 4/7 of money, 1 pie = 1/14 of money. Money left = 3/7 = 6/14 of money = 6 pies.


Zach kept his red and blue marbles in two boxes. The ratio of the number of red marbles to blue marbles in the first box was 1 : 5 and it was 1 : 2 in the second box. The two boxes contained the same number of marbles.<br>What fraction of Zach's marbles were red marbles?

Make each box total the same. Box 1 (1:5) has 6 parts; Box 2 (1:2) has 3 parts. LCM of totals = 6: Box1 = 6 units (red 1, blue 5); Box2 scaled to 6 units (red 2, blue 4). Total marbles = 12, red = 1 + 2 = 3. Fraction red = 3/12 = 1/4.


\(\dfrac{4}{9}\) of the people at a carnival were adults and the rest were children. The number of boys was twice the number of girls. What was the ratio of the number of boys to the number of adults?

Adults = 4/9, children = 5/9. Take total 9 units: adults 4, children 5. Boys : girls = 2 : 1, so boys = 2/3 of children = 2/3 x 5 = 10/3 units. Boys : adults = (10/3) : 4 = 10 : 12 = 5 : 6.


Container A has 200 markers with 6% blue. Container B has 400 markers with 12% blue. What percentage of the total number of markers in container A and B are blue?

Blue in A = 6% of 200 = 12. Blue in B = 12% of 400 = 48. Total blue = 60 out of 600 markers. 60/600 = 10%.


Find the value of \(7.5\div30\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Write down the common multiple of 6 and 8 that is smaller than 40. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 6: 6, 12, 18, 24, ... Multiples of 8: 8, 16, 24, ... Common multiple below 40 is 24.


Find the value of \(12\times\dfrac{8}{9}\). Leave your answer as a mixed number in its simplest form.


Find the value of \(\dfrac{3}{4}\div12\). Leave your answer in its simplest form.


Find the value of \(22-12\div(4+2)\times4\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Brackets first: 4 + 2 = 6. Then 12 ÷ 6 = 2; 2 x 4 = 8. Finally 22 - 8 = 14.


6000 ml of juice was poured into 8 identical bottles equally. How much juice was there in one bottle? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ml

6000 ml ÷ 8 = 750 ml per bottle. (Key writes 6000 ml = 6 L; 6 L ÷ 8 = 0.75 L = 750 ml.)


Ivan started revising for a test at 8.05 a.m. while Kevin started 10 minutes later. Ivan completed 25 minutes earlier than Kevin who completed it at 9.20 a.m. How much more time did Kevin spend on his revision than Ivan? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> min

Ivan: 8.05 a.m. to (9.20 - 25 min) = 8.55 a.m., duration 50 min. Kevin: started 8.15 a.m., ended 9.20 a.m., duration 65 min. Difference = 65 - 50 = 15 min.


A pattern is formed using the letters A, B and N: A, B, A, N, A, A, B, A, N, A, A, B, A, N, A, ... The letter A appears 23 times in the pattern. What is the greatest possible number of letters in the pattern? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The repeating block of 5 letters (A,B,A,N,A) contains 3 A's. 23 ÷ 3 = 7 remainder 2, so 7 complete blocks use 21 A's (35 letters), and 2 more A's appear in the next block. The greatest possible length keeps the most non-A letters before the 23rd A: 35 + 4 = 39 letters.


The rate for parcel postage at a post office is: not over 100 g = $2.50; not over 250 g = $3.90; not over 500 g = $5.20; every additional 100 g = $1. Alice posted a parcel that weighed 660 g. How much did she pay for the postage? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The average mass of 3 girls is 28 kg. A fourth girl joined the group and the average mass becomes 29 kg. What is the mass of the fourth girl? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

Total of 3 girls = 28 x 3 = 84 kg. Total of 4 girls = 29 x 4 = 116 kg. Fourth girl = 116 - 84 = 32 kg.


Bala had some muffins for sale. In the morning, he sold \(\dfrac{1}{3}\) of the muffins. In the afternoon, he sold \(\dfrac{2}{5}\) of the remaining muffins. After that, there were 42 muffins left. How many muffins did Bala have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ivan and Helen shared a sum of money in the ratio of 3 : 2. When Ivan gave $21 to Helen, the ratio of Ivan's amount of money to Helen's amount of money became 2 : 13. How much money did Ivan have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total stays constant. Before 3 : 2 = 9 : 6 (total 15). After 2 : 13 (total 15). So Ivan went from 9 units to 2 units, a drop of 7 units = $21, so 1 unit = $3. Ivan at first = 9 units = $27.


Karen paid $54 for 15 cupcakes after a 25% discount. How many cupcakes could she have bought with the same amount of money without the discount? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

$54 is 75% of the original price of 15 cupcakes, so original price = 54 ÷ 0.75 = $72 for 15 cupcakes; 1 cupcake = $72 ÷ 15 = $4.80. Without discount, $54 ÷ $4.80 = 11.25, so she could buy 11 cupcakes.


Pop-its cost $4.50 for one set of 4 pop-its. Unicorn soft toys cost $18 for a set of 5 soft toys. The items are sold only in sets.
(a) If Ms Chou wants to buy 18 pop-its and 22 unicorn soft toys, what is the least amount of money that she needs to spend on both items? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) She is given a 10% discount for all the items bought. How much will she pay? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Peter and John were paid a total of $3390 for the work they did. Peter was paid $1830 more than John.
(a) How much was Peter paid? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Peter and John were paid based on the number of days they worked. Peter worked 3 times as many days as John. Peter was paid $5 more than John per day. How many days did Peter work? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) (3390 - 1830) ÷ 2 = 1560 ÷ 2 = 780 = John; Peter = 780 + 1830 = $2610. (b) John = $780, Peter = $2610. Peter worked 3x John's days. If John's daily rate is r, John days d, John pay = rd = 780. Peter days = 3d, Peter rate = r+5, Peter pay = 3d(r+5) = 2610. Using key method: had they been paid the same per day, Peter would get 780 x 3 = $2340; the extra $5/day over 3d days gives 2610 - 2340 = $270; $270 ÷ $5 = 54 = Peter's days.


The charges for water consumption are: Up to 40 m³ = 117 cents per m³; Above 40 m³ = 140 cents per m³.
(a) John's family used 32 m³ of water in March. How much did his family pay? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Simon's family spent $66.40 on water consumption in April. How much water did his family use? Give your answer in m³. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> m³


Joyce baked some cookies. She gave 80% of the cookies to Zac. Zac ate 20% of the cookies he received from Joyce. Which one of the following shows the percentage of total cookies that Zac ate?

Zac received 80% of the cookies and ate 20% of that. 20% = \(\dfrac{1}{5}\), so the fraction of total he ate is \(\dfrac{1}{5}\) of 80%, i.e. \(\dfrac{1}{5} \times 80\%\).


What is the area of a circle with diameter 60 cm? ( Take \(\pi = 3.14\) )


Last month, a florist sold 800 roses. This month, she sold 1000 roses. What was the percentage increase in the number of roses sold?


A lollipop cost $0.70. There were 80 lollipops in a box. Janie bought 8 such boxes of lollipops for her class party. How much did she spend on the lollipops?


In a basket, \(\dfrac{5}{9}\) of the fruits are apples and the rest are oranges. \(\dfrac{3}{10}\) of the apples are green in colour. There are 15 green apples. How many fruits are there in the basket?

Green apples = \(\dfrac{3}{10}\) of apples = 15, so apples = 15 ÷ \(\dfrac{3}{10}\) = 50. Apples are \(\dfrac{5}{9}\) of all fruits, so total = 50 ÷ \(\dfrac{5}{9}\) = 50 × \(\dfrac{9}{5}\) = 90.


Express \(3\dfrac{1}{4}\) as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The volume of a cube is 1000 cm³. Find the length of one edge of the cube. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm


Find the circumference of a circle of diameter 28 m. (Take \(\pi = \dfrac{22}{7}\)) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

Circumference = \(\pi \times d = \dfrac{22}{7} \times 28 = 22 \times 4 = 88\) m.


In a school hall, chairs were arranged in rows such that there were exactly 9 chairs in a row. For a concert, Mr Ong brought 6 more chairs into the school hall and rearranged all the chairs. There are now exactly 7 chairs in each row and 12 more rows than before. How many chairs are there in the school hall for the concert? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the original number of rows be r. Original chairs = 9r. New chairs = 9r + 6 = 7(r + 12) = 7r + 84. So 9r + 6 = 7r + 84, giving 2r = 78, r = 39. New chairs = 7(39 + 12) = 7 × 51 = 357. Check: original 9 × 39 = 351, +6 = 357. So there are 357 chairs.


A total of 110 people stand in a queue for concert tickets. There are at least 3 women between any 2 men. What is the largest possible number of men in the queue? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To maximise men, place a man then 3 women repeatedly: pattern M W W W has 1 man per 4 people. The queue can start with a man and end with a man: m men need at least 3(m-1) women between them, total people = m + 3(m-1) = 4m - 3 ≤ 110, so 4m ≤ 113, m ≤ 28.25, giving m = 28. (28 men use 28 + 3×27 = 28 + 81 = 109 people, with 1 spare.)


Liyan had a bottle of syrup. She used an equal amount of syrup each day. At the end of the 12th day, \(\dfrac{1}{3}\) of the bottle was left. At the end of the 14th day, the amount of syrup left was 200 ml. What was the amount of syrup in the bottle at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ml

Let the bottle hold T ml. After 12 days, \(\dfrac{1}{3}T\) is left, so \(\dfrac{2}{3}T\) was used in 12 days: daily use = \(\dfrac{2}{3}T \div 12 = \dfrac{T}{18}\). In 2 more days she uses 2 × \(\dfrac{T}{18} = \dfrac{T}{9}\). Left after 14 days = \(\dfrac{1}{3}T - \dfrac{T}{9} = \dfrac{3T - T}{9} = \dfrac{2T}{9} = 200\). So T = 200 × \(\dfrac{9}{2}\) = 900 ml.


Three girls used the same number of beads to make necklaces. Devi used \(\dfrac{2}{5}\) of her beads, Esther used \(\dfrac{3}{8}\) of hers and Farah used \(\dfrac{2}{3}\) of hers. They had a total of 1440 beads at first. How many beads did each girl use? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each girl started with the same number: 1440 ÷ 3 = 480 beads each. 'Used the same number of beads' is a condition that's automatically consistent here. Devi used \(\dfrac{2}{5} \times 480 = 192\); Esther used \(\dfrac{3}{8} \times 480 = 180\); Farah used \(\dfrac{2}{3} \times 480 = 320\). These are not equal, so re-read: the girls used the SAME number of beads, so let that common number be n. Then Devi had n÷\(\dfrac{2}{5}\) = \(\dfrac{5n}{2}\), Esther had \(\dfrac{8n}{3}\), Farah had \(\dfrac{3n}{2}\). Total = \(\dfrac{5n}{2} + \dfrac{8n}{3} + \dfrac{3n}{2} = 1440\). LCD 6: \(\dfrac{15n + 16n + 9n}{6} = \dfrac{40n}{6} = 1440\), so n = 1440 × 6 ÷ 40 = 216. Each girl used 216 beads.


The table shows the number of storybooks read by each student in a class. Part of the table is covered by an ink blot. There were 20 students who read less than 3 storybooks. There were twice as many students who read 3 storybooks as those who read 5 storybooks.
Number of storybooks: 1, 2, 3, 4, 5
Number of students: 9, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, 3, 4
(a) How many students read 2 storybooks? (b) How many students were there in the class?

(a) Students reading less than 3 = those reading 1 or 2 = 20. Reading 1 = 9, so reading 2 = 20 - 9 = 11. (b) Reading 3 = twice reading 5 = 2 × 4 = 8. Total = 9 + 11 + 8 + 3 + 4 = 35.


The price of a pair of shoes was $80 before discount. Richard bought the pair of shoes at a discount of 15% during a sale. How much did he pay for the pair of shoes? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Water from a tap leaks at a rate of 15 ml per min. At this rate, how much water is leaked in 2 hours? Give your answer in litres. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ


The average of four 3-digit numbers is 250. Two of the numbers are 190 and 230. What is the largest difference between the other two numbers? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total of four numbers = 250 × 4 = 1000. The other two numbers sum to 1000 - 190 - 230 = 580. They are both 3-digit numbers (100 to 999). To maximise the difference, make one as large as possible and the other as small as possible: smallest 3-digit is 100, so the other is 580 - 100 = 480. Largest difference = 480 - 100 = 380.


Nurul and Peili went shopping together with a total sum of $60. Nurul spent twice as much as Peili. The amount Peili had left was $7 more than what she had spent. She had twice as much money left as Nurul. How much money did Nurul have at first? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Peili spend p. Peili's left = p + 7. Nurul spent 2p. Peili's left ($p+7$) = twice Nurul's left, so Nurul's left = \(\dfrac{p+7}{2}\). Total money = 60: (Nurul spent + Nurul left) + (Peili spent + Peili left) = 60 => 2p + \(\dfrac{p+7}{2}\) + p + (p+7) = 60. Multiply by 2: 4p + (p+7) + 2p + 2(p+7) = 120 => 4p + p + 7 + 2p + 2p + 14 = 120 => 9p + 21 = 120 => 9p = 99 => p = 11. Peili spent $11, left $18. Nurul spent $22, left $9. Nurul had at first 22 + 9 = $31.


Pedro had a 700-cm long rope. He cut it into 3 pieces, A, B and C. The length of rope A was divisible by 3 and 7. The length of rope B was 4 times the length of rope A. The total length of rope A and rope B was less than 450 cm. The length of rope C was longer than the length of rope A but shorter than the length of rope B.
(a) What was the length of rope C? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the total length of rope A and rope B? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

A is divisible by 3 and 7, so A is a multiple of 21. B = 4A. A + B = 5A < 450, so A < 90; multiples of 21 under 90 are 21, 42, 63, 84. C = 700 - A - B = 700 - 5A, and A < C < B (= 4A). For A = 84: B = 336, A+B = 420, C = 700 - 420 = 280; check 84 < 280 < 336 - true. (Other A values: A=63 gives C=385, but B=252 and C must be < B - fails; so A = 84.) (a) C = 280 cm. (b) A + B = 420 cm.


At first, Lisa had a total of 66 blue and pink balloons. 17 pink balloons burst. She then increased the number of blue balloons by 75%. After that, Lisa had a total of 79 balloons. How many pink balloons did she have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let blue = b and pink = p at first, b + p = 66. After 17 pink burst, pink = p - 17. Blue increased by 75% becomes 1.75b. New total = 1.75b + (p - 17) = 79, so 1.75b + p = 96. Subtract b + p = 66: 0.75b = 30, b = 40. Then p = 66 - 40 = 26. She had 26 pink balloons at first.


Kai Li spent \(\dfrac{1}{3}\) of her money on 5 magnets and 11 postcards. The cost of each magnet is 3 times the cost of each postcard. She bought some more magnets with \(\dfrac{3}{4}\) of her remaining money. How many magnets did Kai Li buy altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let a postcard cost 1 unit, so a magnet costs 3 units. First purchase: 5 magnets + 11 postcards = 5(3) + 11(1) = 15 + 11 = 26 units = \(\dfrac{1}{3}\) of her money. So total money = 3 × 26 = 78 units. Remaining = 78 - 26 = 52 units. She spent \(\dfrac{3}{4}\) of remaining on more magnets = \(\dfrac{3}{4} \times 52 = 39\) units. Magnets at 3 units each: 39 ÷ 3 = 13 more magnets. Altogether = 5 + 13 = 18 magnets.


Two pouches, Y and Z, contained some gold tokens and silver tokens at first. In Pouch Y, the ratio of gold tokens to silver tokens was 3 : 1. In Pouch Z, the ratio of gold tokens to silver tokens was 1 : 4. Pouch Z had 5 times as many tokens as Pouch Y.
(a) What was the ratio of the number of gold tokens in Pouch Y to the number of silver tokens in Pouch Z? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) After 24 gold tokens and 24 silver tokens were transferred from Pouch Z to Pouch Y, the ratio of gold tokens to silver tokens in Pouch Y became 9 : 5. What was the total number of tokens in Pouch Y in the end? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(c) What was the total number of tokens in both pouches, Y and Z, at first? <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Let Pouch Y have 4 units (gold 3, silver 1). Pouch Z has 5 times as many tokens = 20 units, split 1 : 4 = gold 4, silver 16. (a) Gold in Y : silver in Z = 3 : 16 (in unit terms). As a ratio it is 3 : 16. (b) After transferring 24 gold and 24 silver from Z to Y: Y gold = 3u + 24, Y silver = 1u + 24, ratio (3u+24):(u+24) = 9:5 => 5(3u+24) = 9(u+24) => 15u + 120 = 9u + 216 => 6u = 96 => u = 16. Y in end = (3u+24)+(u+24) = (48+24)+(16+24) = 72 + 40 = 112. (c) At first total = Y + Z = 4u + 20u = 24u = 24 × 16 = 384 tokens.


What is the value of \(\dfrac{3}{7} \times \dfrac{5}{2}\) ?

Multiply numerators and denominators: \(\dfrac{3}{7} \times \dfrac{5}{2} = \dfrac{3 \times 5}{7 \times 2} = \dfrac{15}{14}\). Answer: \(\dfrac{15}{14}\), option (3).


The length, breadth and height of a box are in the ratio 3 : 2 : 1 respectively. The length of the box is 6 cm. Find the volume of the box.

Ratio L:B:H = 3:2:1. Length = 6 cm corresponds to 3 units, so 1 unit = 2 cm. Breadth = 2 units = 4 cm, height = 1 unit = 2 cm. Volume = 6 × 4 × 2 = 48 cm³, option (4).


Derinda had 25 m of ribbon. She used it to make as many flowers as possible. She used \(\dfrac{2}{3}\) m of ribbon to make each flower. How many metres of the ribbon were left?


The table shows the number of clips in different coloured containers.
White: 30 clips per container
Blue: 50 clips per container
Green: 60 clips per container
Clement has some white containers and some blue containers. The ratio of the total number of clips in Clement's white containers to the total number of clips in his blue containers is 3 : 2. Express the number of his blue containers as a fraction of the total number of his containers.

Clips white : blue = 3 : 2. Take white clips = 150 and blue clips = 100 (ratio 3:2). White containers = 150 ÷ 30 = 5; blue containers = 100 ÷ 50 = 2. Total containers = 5 + 2 = 7. Blue containers as a fraction of total = \(\dfrac{2}{7}\), option (4).


\(\dfrac{3}{4}\) of a pizza was shared equally among 5 people. What fraction of the pizza did each person receive?

Each person gets \(\dfrac{3}{4} \div 5 = \dfrac{3}{4} \times \dfrac{1}{5} = \dfrac{3}{20}\) of the pizza.


The breadth of a rectangle is \(\dfrac{5}{6}\) m and its area is 2 m². Find the length of the rectangle. Express your answer as a mixed number in its simplest form.


Janice is \(\dfrac{5}{7}\) as tall as Xiao Ming. What is the ratio of Xiao Ming's height to Janice's height?

Janice = \(\dfrac{5}{7}\) × Xiao Ming, so Janice : Xiao Ming = 5 : 7. Therefore Xiao Ming : Janice = 7 : 5.


The ratio of the number of sweets Rachel had to the number of sweets Euodia had was 2 : 3 at first. After Rachel bought 8 more sweets, the ratio of the number of sweets Rachel had to the number of sweets Euodia had became 5 : 6. How many sweets did Euodia have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Euodia's sweets are unchanged. At first Rachel : Euodia = 2 : 3, after = 5 : 6. Make Euodia the same in both: 2 : 3 = 4 : 6 and 5 : 6 stays 5 : 6. Rachel went from 4 units to 5 units, an increase of 1 unit = 8 sweets. So 1 unit = 8, and Euodia = 6 units = 6 × 8 = 48 sweets.


Clarence, Amir and Jun Wei received some stickers. The ratio of the number of stickers that Clarence received to the number of stickers Amir received was 4 : 9. The ratio of the number of stickers Jun Wei received to the number of stickers Amir received was 4 : 3. Clarence received 24 stickers. How many stickers did Jun Wei receive? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Clarence : Amir = 4 : 9. Clarence = 24, so 1 unit = 24 ÷ 4 = 6, and Amir = 9 × 6 = 54. Jun Wei : Amir = 4 : 3, so Jun Wei = Amir × 4/3 = 54 × 4/3 = 72 stickers. (Equivalently, scaling Amir to a common value: C:A = 4:9 = 12:27, JW:A = 4:3 = 36:27, so C:A:JW = 12:27:36; Clarence 24 → 1 part = 2 → Jun Wei = 36 × 2 = 72.)


Ashraf had some money at first. He spent 10% of it on food and $140 on a bicycle. He then gave 50% of the remainder to his brother. In the end, he had $200 left. How much money did Ashraf spend on food? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After giving 50% of the remainder to his brother, the $200 left is the other 50%, so the remainder after food and bicycle = $200 × 2 = $400. This remainder = 90% of original − $140 (food was 10%, bicycle was $140). So 90% of original − $140 = $400, giving 90% of original = $540, so original = $540 ÷ 0.9 = $600. Money spent on food = 10% of $600 = $60.


Amrit had some sugar at first. He used 42 g of sugar to bake some muffins and \(\dfrac{5}{7}\) of the remaining sugar to bake some cookies. In the end, he had \(\dfrac{1}{7}\) of the sugar left. How much sugar did he have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After using 42 g for muffins, he used \(\dfrac{5}{7}\) of the remaining sugar on cookies and had \(\dfrac{1}{7}\) of the original left. The remaining sugar after muffins is split into 7 equal parts; cookies took 5 parts and 1 part (\(\dfrac{1}{7}\) of the original) was left, but the leftover \(\dfrac{1}{7}\) is of the original amount. Treat the original as 7 units: leftover = 1 unit, and cookies used 5 of the 7 parts of the post-muffin sugar. From the printed working, the 42 g (muffins) corresponds to 1 unit of the original 7, but accounting for the post-muffin split gives 2 units = 42 g, so 1 unit = 21 g and the original = 7 × … ; the printed key gives 4 units → 42 g pattern leading to first amount = 84 g.


Christopher and Helen had 75 erasers altogether at first. Christopher gave away \(\dfrac{4}{5}\) of his erasers. Helen gave away \(\dfrac{2}{3}\) of her erasers. In the end, Helen had 1 more eraser than Christopher. How many erasers did Christopher have in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Christopher kept \(1 - \dfrac{4}{5} = \dfrac{1}{5}\) of his erasers; Helen kept \(1 - \dfrac{2}{3} = \dfrac{1}{3}\) of hers. Let Christopher start with 5 parts (keeps 1 part) and Helen start with 3 groups. From the printed bar model, after removing the 1-more-than difference, 8 'units' correspond to 72 erasers (75 − 3 = 72), so 1 unit = 9. Christopher had 9 erasers in the end.


Express \(7\dfrac{1}{20}\) as a decimal.


Which of the following mixed numbers is closest to \(6\dfrac{1}{2}\)?


(a) Find the value of \(1-\dfrac{1}{6}-\dfrac{3}{4}\).<br>(b) Find the value of \(\dfrac{2}{9}\div 6\).