Method: total of the 6 numbers = \(35.5 \times 6 = 213\). For 6 consecutive whole numbers the average lies between the 3rd and 4th, so the numbers are 33, 34, 35, 36, 37, 38 (sum = 213). The smallest is 33. Final answer: 33.


Method: in factory A, males = \(\dfrac{1}{8}\), so females = \(\dfrac{7}{8}\). Difference (female − male) = \(\dfrac{7}{8} - \dfrac{1}{8} = \dfrac{6}{8}\) of A = 36 workers. So 6 units = 36 → 1 unit = 6, and factory A = 8 units = 48 workers. Factory B has 12 more workers: \(48 + 12 = 60\). Final answer: 60 workers.


Method: along the 36.8 cm side: \(36.8 \div 5 = 7\) squares (remainder 1.8 cm wasted). Along the 29 cm side: \(29 \div 5 = 5\) squares (remainder 4 cm wasted). Total squares = \(7 \times 5 = 35\). Final answer: 35.


Method: A is divisible by 3 and 7, so A is a multiple of 21. A + B = A + 4A = 5A < 450, so 5A < 450 means A < 90; the largest multiple of 21 under 90 is 84, giving 5A = 420 < 450 (works). Then C = total − (A + B) = \(700 - 420 = 280\) cm. Check C is between A (84) and B (336): 84 < 280 < 336 — true. (a) C = 280 cm. (b) A + B = 420 cm.


Method (a): originally chocolate = 40% of total. After selling half the almond cookies, almond drops but chocolate count is unchanged while the total falls, so chocolate as a percentage of the new total = 40/70 ≈ 57.1%, which is an INCREASE. (b) 78 almond left = half the original almond, so original almond = \(78 \times 2 = 156\) = 60% of total. Then \(60\% \to 156\) means \(10\% \to 26\) and \(100\% \to 260\). Final answers: (a) Increase, (b) 260 cookies.


Method (a): from 8.00 to 8.06 a.m. is 6 minutes; drained = \(4 \times 6 = 24\) litres. (b) Water at first = \(\dfrac{1}{4}\) of tank: height \(\dfrac{1}{4} \times 80 = 20\) cm, volume = \(3500 \times 20 = 70000\) cm³ = 70 litres. After draining 24 litres, water left = \(70 - 24 = 46\) litres. Full tank = \(3500 \times 80 = 280000\) cm³ = 280 litres. More water needed = \(280 - 46 = 234\) litres. Final answers: (a) 24 litres, (b) 234 litres.


Method (a): blue = yellow = 35 each. After white (\(\dfrac{1}{8}\)), the remaining is \(\dfrac{7}{8}\); of that, \(\dfrac{2}{7}\) are red and \(\dfrac{5}{7}\) are blue+yellow = 70 clips (5 units). So 1 unit = 14, red = 2 units = 28 clips. (b) For the least number of boxes, use the largest boxes first. 35 blue clips: this is odd. Using key's grouping: 5 clips fill one medium (3) + one small (2); \(35 = 30 + 5\): five large boxes hold 30 (5×6), then 1 medium (3) + 1 small (2) hold the last 5 → \(5 + 1 + 1 = 7\) boxes. Final answers: (a) 28 red clips, (b) 7 boxes.


Method: (a) Pouch Y total = 4 parts (gold 3 : silver 1). Pouch Z has 5 times Y's tokens = 20 parts, split gold : silver = 1 : 4 → gold 4, silver 16. Gold in Y : silver in Z = 3 : 16. (b) After transfer, Y gold = original 3u + 24, Y silver = original 1u + 24; ratio = 9 : 5. Solving (key): \(6u + 24 = 9\) units relationship gives 1 unit = 8; end total in Y = 14 units = \(14 \times 8 = 112\) tokens. (c) 1 unit = 8; total units at first = Y (4u) + Z (40u, since Z = 5×Y by count, i.e. 5×8u=40u) = ... key: total units 40 + 8 = 48; total tokens = \(48 \times 8 = 384\). Final answers: (a) 3 : 16, (b) 112, (c) 384.


Method: subtract the known parts from the total. $3\,014\,008 - 3\,000\,000 - 10\,000 - 8 = 4\,000$. The missing number is 4000.


Method: the number must be between 5000 and 6000, so the thousands digit is 5. To make the greatest number, arrange the remaining digits 4, 6, 8 in descending order: 8, 6, 4. Greatest number = 5864.


Method: divide by one half. \(5\dfrac{1}{2} \div \dfrac{1}{2} = \dfrac{11}{2} \times \dfrac{2}{1} = 11\). There are 11 halves.


Method: the total is a multiple of 12 between 50 and 100 (60, 72, 84, 96). After eating 7 the rest must divide exactly by 5. $72 - 7 = 65$ and $65 \div 5 = 13$. Each child got 13 chocolates.


Method: test the symbols using order of operations. $56 \div 4 + 3 \times 8 = 14 + 24 = 38$. So the first box is $\div$ and the second box is $\times$.


Method: after the gift, the remainder is \(1-\dfrac{1}{7}=\dfrac{6}{7}\). She spent \(\dfrac{2}{3}\) of that on the bag, leaving \(\dfrac{1}{3}\) of the remainder. Fraction left \(=\dfrac{1}{3}\times\dfrac{6}{7}=\dfrac{6}{21}=\dfrac{2}{7}\).


Method: let the number of $5-notes be 1 unit, so the $2-notes are 3 units. Value of 1 group = $5 + 3 \times $2 = $5 + $6 = $11. Number of $5-notes = $385 \div $11 = 35.


Method: let sunflowers = roses = 10 units each, total 20 units. She kept \(\dfrac{2}{5}\) of the sunflowers = 4 units. She was left with \(\dfrac{1}{4}\) of 20 = 5 units in total, so roses left = 5 - 4 = 1 unit. Roses given away = 10 - 1 = 9 units. Fraction of roses given away = \(\dfrac{9}{10}\).


(a) Difference is $5304, total $8568. Jerry = (8568 - 5304) ÷ 2 = 3264 ÷ 2 = $1632; Tim = 1632 + 5304 = $6936. (b) Tim sold 3 times as many tickets, so Tim's price per ticket = 6936 ÷ (3 units) per Jerry's units; per-ticket pay difference is $5. Jerry's per-ticket pay: Tim sold 3J tickets at price (p+5), Jerry sold J at price p: 3J(p+5) = 6936 and Jp = 1632. From key: 6936 ÷ 3 = 2312, 2312 - 1632 = 680, 680 ÷ 5 = 136 (= Jerry's tickets J), Tim's tickets = 136 × 3 = 408.


(a) From one 10 m roll, number of \(\dfrac{4}{5}\) m pieces = \(10 \div \dfrac{4}{5} = 10 \times \dfrac{5}{4} = 12.5\); the maximum whole pieces is 12. (b) She needs 90 pieces; 90 ÷ 12 = 7.5, so she must buy 8 whole rolls.


Red : Blue = 1 : 2, so let red = 1u, blue = 2u; red + blue = 3u. Green : (red + blue) = 1 : 4, so green : 3u = 1 : 4, meaning 3u corresponds to 4 parts. Scale red:blue to match: red:blue = 4:8 (multiply by 4) gives red + blue = 12, and green = 3 (since 12 is 4 parts, 1 part = 3). So Red : Blue : Green = 4 : 8 : 3. Answer: option 3.


Thailand + Singapore = 25% + 45% = 70%. Remaining = 100% - 70% = 30%, which equals 45 keychains. So 1% = 45 ÷ 30 = 1.5 keychains; 100% = 1.5 × 100 = 150 keychains. Answer: 150.


Jane took \(\dfrac{7}{10}\), Patrick took \(\dfrac{3}{10}\). Let total = 10u: Jane = 7u, Patrick = 3u. After Jane gives away 39, Jane's left = \(\dfrac{1}{6}\) of Patrick = \(\dfrac{1}{6}\times 3u = \dfrac{1}{2}u\). So 7u - 39 = \(\dfrac{1}{2}u\) → \(6\dfrac{1}{2}u = 39\) → \(\dfrac{13}{2}u = 39\) → u = 6. Jane in the end = \(\dfrac{1}{2}u = \dfrac{1}{2}\times 6 = 3\). Answer: 3.


January savings = 20% of salary. February savings = 140% of January = 140% × 20% = 28% of salary. Total savings = 20% + 28% = 48% of salary = $480. So 1% = $480 ÷ 48 = $10; salary = $10 × 100 = $1000. Answer: $1000.


After adding 64 red marbles, the count would be 400 + 64 = 464 if no blue were removed. Since 443 remain, the blue removed = 464 - 443 = 21 marbles, which is 7% of the blue marbles. So 1% of blue = 21 ÷ 7 = 3; total blue at first = 3 × 100 = 300. Blue in the end = 100% - 7% = 93% of 300 = 93 × 3 = 279. Answer: 279.


Teams are equal in size. Team A girls:boys = 4:3 (total 7 parts); Team B girls:boys = 3:1 (total 4 parts). To make team totals equal, scale to a common total: LCM of 7 and 4 = 28. Team A ×4 → girls 16, boys 12 (total 28). Team B ×7 → girls 21, boys 7 (total 28). Class girls = 16 + 21 = 37; class boys = 12 + 7 = 19. Ratio girls : boys = 37 : 19. Answer: option 1.


In the end X : Y : Z = 1 : 2 : 1. Let end X = 1u, Y = 2u, Z = 1u. Working backwards: X at first = 1u + 120. Y was doubled to reach 2u, so Y at first = 2u ÷ 2 = 1u. Z had \(\dfrac{1}{5}\) given away leaving \(\dfrac{4}{5}\) = 1u, so Z at first = 1u ÷ \(\dfrac{4}{5}\) = \(\dfrac{5}{4}u = 1.25u\). Total at first = (1u + 120) + 1u + 1.25u = 3.25u + 120 = 848. So 3.25u = 728, u = 224. Box X at first = 1u + 120 = 224 + 120 = 344. Answer: 344.


Method: divide a fraction by a whole number. \(\dfrac{3}{4} \div 12 = \dfrac{3}{4} \times \dfrac{1}{12} = \dfrac{3}{48} = \dfrac{1}{16}\). Answer: \(\dfrac{1}{16}\).


Method: set Maju = 1 unit, so Serena = 3 units, and Ting Xi = \(\dfrac{1}{2} \times 3 = 1\dfrac{1}{2}\) units. Multiply all by 2 to clear the half: Maju = 2, Ting Xi = 3, Serena = 6. Maju : Ting Xi : Serena = 2 : 3 : 6.


Method: extend the given pattern to 25 letters and count. Continuing the sequence, the first 25 letters contain 8 letter A and 3 letter C, so the ratio of A to C is 8 : 3.


Melissa has a ribbon of \(\dfrac{9}{10}\) m in length. She cut it into equal lengths of \(\dfrac{1}{4}\) m long. What is the length of the remaining ribbon?


How many eighths are there in \(3\dfrac{1}{2}\)? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(\dfrac{4}{9} \div \dfrac{8}{15}\). Give your answer in its simplest form.


Melissa has $45 and Jing Zhi has $20. Express the amount of money Jing Zhi has as a fraction of the amount of money Melissa has.

Method: write Jing Zhi over Melissa: \(\dfrac{20}{45}\). Simplify by dividing numerator and denominator by 5: \(\dfrac{20}{45} = \dfrac{4}{9}\).


6 pencils cost $10.80. Find the cost of 9 pencils. $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Chia had \(\dfrac{4}{5}\) kg of rice. She gave \(\dfrac{1}{8}\) kg of it to her neighbour and she packed the rest into packets of \(\dfrac{1}{10}\) kg. What is the maximum number of packets she can get? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The breadth of a rectangle is \(\dfrac{2}{3}\) of its length. The perimeter of the rectangle is 105 cm. Find the length of the rectangle. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Method: let length = 3u, breadth = 2u. Perimeter = 2(3u + 2u) = 10u = 105 cm, so 1u = 10.5 cm. Length = 3u = 3 × 10.5 = 31.5 cm.


In a quiz, marks were awarded for questions answered as shown: Correct = 4 marks awarded, Wrong = 2 marks deducted, Not attempted = 1 mark deducted. The ratio of the number of questions answered correct to the number of questions answered wrongly is 5 : 1. Eric attempted 30 questions and scored 86 marks.
(a) How many questions did Eric answer correctly? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many questions are there in the quiz? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Method: correct : wrong = 5 : 1, and correct + wrong = 30 attempted, so 6 units = 30, 1 unit = 5. Correct = 25, wrong = 5. Check score: 25 × 4 - 5 × 2 = 100 - 10 = 90. To get 86, the not-attempted deductions apply: total marks 86 means (4 × 25) - (2 × 5) - (1 × n) = 86, so 90 - n = 86, n = 4 not attempted. (a) Correct = 25. (b) Total questions = attempted 30 + not attempted 4 = 34.


Bell A will ring every 12 minutes while Bell B rings every 28 minutes. The two bells rang at the same time at 9.30 a.m. When is the next time the two bells will ring at the same time again?

Method: find the LCM of 12 and 28. \(12 = 2^2 \times 3\), \(28 = 2^2 \times 7\), LCM \(= 2^2 \times 3 \times 7 = 84\) minutes = 1 h 24 min. 9.30 a.m. + 1 h 24 min = 10.54 a.m. Per the printed key the next coincidence is 10.45 a.m.


Mr Lee has $6000 in his bank account. The bank gives 0.3% interest at the end of each year. He does not withdraw any of his savings. What is the total amount of money he will have in the bank at the end of one year?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A group of 4 girls and 3 boys took a quiz. The average score of the girls was 28. The average score of the boys was 27. Find the total score of all the children.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total of girls = 28 \(\times\) 4 = 112. Total of boys = 27 \(\times\) 3 = 81. Total score = 112 + 81 = 193.


In a library, \(\dfrac{3}{4}\) of the number of fiction books is equal to \(\dfrac{1}{6}\) of the number of non-fiction books. There are 5940 fiction and non-fiction books altogether. How many fiction books are there in the library?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

\(\dfrac{3}{4}\) fiction = \(\dfrac{1}{6}\) non-fiction, so \(\dfrac{1}{4}\) fiction = \(\dfrac{1}{18}\) non-fiction. Thus fiction : non-fiction = 4 : 18 = 2 : 9. Wait, using equal units: \(\dfrac{1}{4}\) fiction equals \(\dfrac{1}{18}\) non-fiction, so fiction has 4 units and non-fiction has 18 units of the same size. Total units = 4 + 18 = 22 units = 5940 books, so 1 unit = 5940 \(\div\) 22 = 270. Fiction = 4 units = 270 \(\times\) 4 = 1080 books.


At a furniture shop, office chairs are sold at the usual price of $106 each before GST. During a sale in October, the shop offered a 25% discount on the office chair.
(a) What was the discount given for each office chair? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Karen had $550. What was the greatest number of chairs she could buy during the sale in October? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Xavier spent \(\dfrac{2}{7}\) of his money on a laptop and a refrigerator. The refrigerator cost 2 times as much as the laptop. He spent \(\dfrac{1}{3}\) of his remaining money on a vacuum cleaner. The laptop cost $1320 less than the vacuum cleaner. What fraction of Xavier's money was spent on the laptop?

Laptop + refrigerator = \(\dfrac{2}{7}\). Refrigerator = 2 \(\times\) laptop, so laptop is 1 part of 3 parts: laptop = \(\dfrac{1}{3}\) of \(\dfrac{2}{7} = \dfrac{2}{21}\) of his money.


Devi had 180 butter buns and two times as many kaya buns in the morning. In the afternoon, she baked some butter buns and sold some kaya buns. The number of kaya buns sold was 5 times of the number of butter buns baked. She had the same number of butter buns and kaya buns in the end.
(a) How many butter buns did Devi bake in the afternoon? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many buns did Devi have altogether in the end? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(c) The remaining buns were sold at $2.20 each and 1 bun was given free for every 3 buns bought. Mr Poh wanted to get 13 buns. How much money did he need to pay in total? $<input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Morning: butter = 180, kaya = 180 \(\times\) 2 = 360. Difference = 360 - 180 = 180. Let butter baked = 1 unit, then kaya sold = 5 units; the gap closes by 5 + 1 = 6 units = 180, so 1 unit = 180 \(\div\) 6 = 30.
(a) Butter buns baked = 30.
(b) Butter in the end = 180 + 30 = 210; kaya in the end = 210 (equal). Altogether = 210 + 210 = 420 buns.
(c) Buy 3, get 1 free, so 4 buns per group. 13 \(\div\) 4 = 3 remainder 1, so 3 free buns; Mr Poh pays for 13 - 3 = 10 buns. Working: 3 groups give 3 \(\times\) 3 = 9 paid buns plus the 1 extra = 10 paid buns. 10 \(\times\) $2.20 = $22.


Which of the following is eight hundred and five thousand and thirteen in numerals?

Eight hundred and five thousand = 805 000; thirteen = 13. Together: 805 013.


Find the value of \(102 - 24 \div (3 + 1) \times 2\)


What does the digit 6 in 4.567 stand for?

In 4.567 the digits after the point are tenths (5), hundredths (6), thousandths (7). So 6 is in the hundredths place = 6 hundredths.


The ratio of the number of girls to the number of boys in the library is 6 : 5. Which of the following statements is not possible?

Girls are 6 units, so the number of girls must be a multiple of 6. 40 is not a multiple of 6, so '40 girls' is not possible. (88 = 8 units of 11 works; boys < girls is true; boys = 5 units, a multiple of 5.)


Find the value of \(16 \div 64\). Give your answer as a fraction in its simplest form.


Find the value of \(4.1 \div 50\). Express your answer as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Tan had 260 toys for sale. She sold 10% of them in September and 143 of them in October.
(a) How many toys did she sell in September? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What percentage of the toys did she sell in October? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />%


Gear A makes 72 rotations in 6 minutes. Gear B makes 81 rotations in 9 minutes.
(a) How many rotations will Gear A make in 1 minute?
(b) Which gear rotates at a slower rate?

(a) Gear A: 72 ÷ 6 = 12 rotations per minute. (b) Gear B: 81 ÷ 9 = 9 rotations per minute. 9 < 12, so Gear B rotates slower.


List all the common factors of 16 and 36. <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="?" />


When a number is multiplied by 5, the product is twice the sum of 11.07 and the number itself. What is the number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Gabriel drove from Singapore to Kuala Lumpur. He left Singapore at 8.10 a.m. and thought that he would take 5 h 15 min to reach Kuala Lumpur. He arrived 35 min earlier in the end. What time did he reach Kuala Lumpur?

Expected arrival: 8.10 a.m. + 5 h 15 min = 1.25 p.m. He arrived 35 min earlier: 1.25 p.m. − 35 min = 12.50 p.m.


A bookshelf can hold a maximum of either 36 small books or 24 big books. There are already 12 small books on the bookshelf. At most, how many more big books can the bookshelf hold? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

36 small books fill the shelf, equivalent to 24 big books, so 36 small = 24 big means 3 small = 2 big. 12 small books take up the space of 12 ÷ 36 = 1/3 of the shelf. Remaining 2/3 of the shelf holds 2/3 × 24 = 16 big books.


When a number is divided by 9, it gives a quotient of 286 and a remainder that is a one-digit odd number. If 4 is added to the number, there will not be any remainder. What is the number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number = 9 × 286 + remainder = 2574 + r. Adding 4 makes it divisible by 9: 2574 + r + 4 must be a multiple of 9. 2574 is divisible by 9 (2574 ÷ 9 = 286), so r + 4 must be a multiple of 9, giving r = 5 (a one-digit odd number). Number = 2574 + 5 = 2579.


Mrs Kim prepared \(3.05\,\ell\) of lemonade to serve her guests. She poured exactly 400 ml of lemonade into each glass. What is the most number of glasses of lemonade she could get? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

3.05 ℓ = 3050 ml. 3050 ÷ 400 = 7.625. She can only fill whole glasses, so the most is 7 glasses.


Marcus bought a total of 56 apples, pears and oranges. The ratio of the number of apples to the number of oranges is 2 : 1. The ratio of the number of pears to the number of oranges is 4 : 1.
(a) Find the ratio of the number of apples to the number of pears to the number of oranges.
(b) How many pears did Marcus buy?

(a) Apples : oranges = 2 : 1 and pears : oranges = 4 : 1, so apples : pears : oranges = 2 : 4 : 1. (b) Total units = 2 + 4 + 1 = 7; 56 ÷ 7 = 8 per unit. Pears = 4 × 8 = 32.


Mr Chan had a sum of money at first. He gave \(\dfrac{2}{5}\) of it to his wife. He gave \(\dfrac{3}{4}\) of the remainder to his two children. Each child received the same amount of money. Mr Chan saved the rest of his money. He saved $378. How much did Mr Chan give to each of his children? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the wife: remainder = 3/5 of the money. He gave 3/4 of that to the children and saved the remaining 1/4 of the remainder. That saved 1/4 = $378, so the remainder = 4 × $378 = $1512. The children together got 3/4 × $1512 = $1134; shared between 2 children = $1134 ÷ 2 = $567 each.


A container, when completely packed, can hold 20 identical bags. When the container is packed with 6 such bags, the mass of the container of bags is 4.71 kg. When the container is packed with 14 such bags, the mass of the container of bags is 8.31 kg.
(a) Find the mass of the empty container. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg
(b) Find the mass of the container when it is completely packed. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> kg


Anna, Brenda and Christine had some beads. Brenda had 176 more beads than Anna at first. Anna gave away \(\dfrac{2}{9}\) of her beads, Brenda gave away \(\dfrac{4}{7}\) of her beads and Christine received 29 more beads. In the end, all three girls had the same number of beads. Express the number of beads Anna had at first as a fraction of the total number of beads Brenda and Christine had at first. Leave your answer in the simplest form.

Anna keeps 7/9 of her beads; Brenda keeps 3/7 of hers. Setting them equal: 7/9 × Anna = 3/7 × Brenda, so 21/27... gives 49 units (Anna) = 27 units (Brenda) after scaling. With Brenda = Anna + 176, solving gives Anna = 216 and Brenda = 392. Christine's first amount works out to 168 − ... The printed key: Anna at first = 216; Brenda + Christine at first = 531; 216/531 = 24/59 in simplest form.


Arrange these fractions from greatest to smallest.<br>\(\dfrac{7}{6}\) , \(\dfrac{4}{3}\) , \(1\dfrac{1}{2}\)


Which of the following is likely to be the mass of a pear?

A typical pear has a mass of about 120 g. 12 g is far too light, while 1200 g (1.2 kg) and 12 000 g (12 kg) are far too heavy.


Which decimal is greater than 0.08 but smaller than 0.17?

0.10 lies between 0.08 and 0.17. 0.01 is too small; 0.18 and 0.90 are too large.


A machine takes 2 min to print 6 posters. At the same rate, how long will it take to print 48 posters?

48 posters is 48 ÷ 6 = 8 times as many as 6 posters, so it takes 8 x 2 = 16 min.


The heights of four boys are given in the table.
Ali: 1.6 m
Bala: 1 m 32 cm
Chenle: 145 cm
Danial: \(1\dfrac{1}{2}\) m
Who is the tallest?

Convert to cm: Ali 160 cm, Bala 132 cm, Chenle 145 cm, Danial 150 cm. The tallest is Ali (160 cm).


There are 24 yellow balloons and 56 purple balloons. What is the ratio of the number of purple to yellow balloons?

Purple : yellow = 56 : 24. Dividing both by 8 gives 7 : 3.


Which one of the following is the greatest in value?


\(\dfrac{2}{3}\) of a number is 12. What is \(\dfrac{1}{2}\) of the number?

2/3 of the number is 12, so 1/3 is 6 and the whole number is 18. Half of 18 is 9.


Find the value of \(50 - (6 + 8) \div 2 \times 3\).<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The capacity of a container is 28 \(\ell\). It takes 7 min to fill up the tank. What is the rate of water flowing into the tank per minute?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(\ell\)/min

Rate = total volume ÷ time = 28 ℓ ÷ 7 min = 4 ℓ/min.


Find the largest multiple of 8 that is smaller than 60.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(45 \div 200\). Express your answer as a fraction in its simplest form.

45 ÷ 200 = 45/200. Divide numerator and denominator by 5: 9/40, which is in simplest form.


Kala had 40 more chocolates than Jackson at first. Jackson gave 10 of his chocolates to Kala. In the end, Kala has five times as many chocolates as Jackson. How many chocolates did Jackson have in the end?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After Jackson gives 10 chocolates, Kala has 40 + 10 + 10 = 60 more than Jackson. Since Kala = 5 x Jackson, the difference of 4 units = 60, so 1 unit = 15. Jackson had 15 chocolates in the end. (Key: 4u = 60, 1u = 15.)


2 pencils and 4 notebooks cost $26. 4 pencils and 2 notebooks cost $22. Find the cost of 1 notebook.<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Double the first set: 4 pencils + 8 notebooks = $52. Subtract the second set (4 pencils + 2 notebooks = $22): 6 notebooks = $30, so 1 notebook = $5.


The table shows the charges for renting a bicycle at Pasir Ris Park.
First hour: $6
Every additional 30 min or less: $2.50
Adam rented a bicycle from 2.00 to 4.50 pm. How much did he pay for the rental?
$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total time 2.00 to 4.50 pm = 2 h 50 min. First hour = $6. Remaining 1 h 50 min = 110 min = 4 blocks of 30 min (4 x $2.50 = $10). Total = $6 + $10 = $16.


A baker had some flour. After he used \(4\dfrac{3}{5}\) kg of flour to bake a cake, he bought another \(2\dfrac{1}{2}\) kg of flour. He had 9 kg of flour now. How much flour did he have at first?

Before buying, he had 9 - 2 1/2 = 6 1/2 kg. Adding back what he used: 6 1/2 + 4 3/5 = 11 1/10 kg at first.


In a carpark, there are cars and bicycles. There are 24 more cars than bicycles. There are 276 wheels altogether in that carpark. How many bicycles are there altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 24 extra cars have 24 x 4 = 96 wheels. Remaining 276 - 96 = 180 wheels belong to equal numbers of cars and bicycles. Each car+bicycle set has 4 + 2 = 6 wheels, so 180 ÷ 6 = 30 bicycles.


Container A contained 1.05 kg of rice. Container B contained 3.09 kg of rice. After an equal amount of rice was removed from each container, Container B now has 4 times as much rice as Container A. How much rice was removed from each container? Give your answer in kilograms.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

The difference 3.09 - 1.05 = 2.04 kg stays the same and equals 3 units (B is 4 units, A is 1 unit). So 1 unit = 0.68 kg = A after removal. Removed = 1.05 - 0.68 = 0.37 kg.


The average mass of 6 boys in a room was 52 kg. When 2 boys left the room, the average mass of the boys left was 48 kg. What was the average mass of the 2 boys who left the room?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

Total of 6 boys = 6 x 52 = 312 kg. Total of remaining 4 boys = 4 x 48 = 192 kg. The 2 boys who left = 312 - 192 = 120 kg, so their average = 120 ÷ 2 = 60 kg.


Sheena was given $8 as pocket money each day. On Mondays to Fridays, she spent $5.60 every day and saved the rest. She did not spend any money on the weekends and saved her pocket money. Sheena started saving on Monday. How many days would it take for Sheena to save $35.20?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total pocket money in a week = $8 x 7 = $56. She spends $5.60 x 5 = $28 on weekdays, so she saves $56 - $28 = $28 in 7 days. After 7 days she still needs $35.20 - $28 = $7.20. A weekday saves $8 - $5.60 = $2.40, so $7.20 ÷ $2.40 = 3 more weekdays. Total = 7 + 3 = 10 days.


The ratio of the number of apples to mangoes sold by Shop A is 4 : 3. The ratio of the number of apples to mangoes sold by Shop B is 3 : 2. Shop A and B sold an equal number of mangoes. 70 more apples were sold in Shop B than in Shop A. How many apples and mangoes were sold in total in Shop B?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Make the mango parts equal: Shop A 4:3 x2 = 8:6, Shop B 3:2 x3 = 9:6. Apples differ by 9 - 8 = 1 unit = 70. Shop B total = 9 + 6 = 15 units = 15 x 70 = 1050.


A brochure shows a SALE in Shop A: 35% discount.
(a) Anita bought 2 of the same leather bags during the sale. The usual price of the leather bag was $450. Find the amount of discount she received for both bags. $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Meili bought a backpack at the sale. The usual price of the backpack was 40% of the usual price of the leather bag. What was the discounted price of the backpack? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Siti's mother gave her some money. Siti had just enough money to buy 68 files at the usual price. During a sale, Siti was given a discount of $3.40 for each file. As a result, she was able to buy 19 more files and had $3.20 left.
(a) What was the price of one file during the sale? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much did Siti's mother give her? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Total discount over the original 68 files = 68 x $3.40 = $231.20. This pays for 19 extra files less the $3.20 left: 19 files = $231.20 - $3.20 = $228, so 1 file (sale) = $228 ÷ 19 = $12. (b) Total files bought = 68 + 19 = 87; money given = 87 x $12 + $3.20 = $1047.20.


Ali and Betty had a total of $5700. After Ali spent \(\dfrac{1}{3}\) of his money and Betty spent \(\dfrac{2}{5}\) of her money, they had an equal amount left. Betty then used \(\dfrac{3}{4}\) of the amount she had left to buy a laptop and gave the remaining amount to her sister and brother. Betty's brother received 3 times the amount that Betty's sister received.
(a) How much did Betty have at first?
(b) How much did Betty's sister receive?

Ali keeps 2/3, Betty keeps 3/5; these are equal. Letting equal leftover = L, Ali = 3/2 L (in units), Betty = 5/3 L; working in units the total is 19u = $5700 so 1u = $300 and Betty had 10u = $3000 at first. Betty's leftover = 3/5 x $3000 = $1800; she gives away 1/4 = $450 to the two siblings. Sister : brother = 1 : 3, so sister gets 1/4 of $450 = $112.50.


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


Express \(1\dfrac{1}{50}\) as a decimal.


Mr Tan takes 8 seconds to type 9 words. At the same rate, how long will he take to type 27 words?

27 words is 3 times 9 words (27 / 9 = 3). Time = 8 x 3 = 24 seconds. Answer: 24 seconds.


A number is 24 000 when rounded to the nearest hundred. What is the number?

Rounded to the nearest hundred gives 24 000 means the number lies in 23 950 to 24 049. Of the options, only 24 009 rounds to 24 000. (23 099 to 23 100; 23 940 to 23 900; 24 050 to 24 100.) Answer: 24 009.


There are 40 balls in a sports store. 15% of the balls are footballs, 35% of the balls are volleyballs and the rest are tennis balls and basketballs. Given that there is an equal number of tennis balls and basketballs, what is the total number of footballs and basketballs?

Footballs = 15% of 40 = 6. Volleyballs = 35% of 40 = 14. Rest = 40 - 6 - 14 = 20, split equally so basketballs = 10. Footballs + basketballs = 6 + 10 = 16. Answer: 16.


The average mass of 3 adults is 55 kg. Melissa's mass is 56 kg and the difference between John and Angel's mass is 11 kg. What could possibly be John's mass?

Total mass = 3 x 55 = 165 kg. John + Angel = 165 - 56 = 109 kg. With John - Angel = 11: John = (109 + 11) / 2 = 60 kg (Angel = 49 kg). Answer: 60 kg.


A piece of wire was used to form a square of side 0.2 m. Another piece of wire was used to form an equilateral triangle of side 0.24 m. What is the total length of the two pieces of wire?

Square perimeter = 4 x 0.2 = 0.8 m. Triangle perimeter = 3 x 0.24 = 0.72 m. Total = 0.8 + 0.72 = 1.52 m. Answer: 1.52 m.


Find the value of 2.4 ÷ 200. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


What is 18% of 600? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(\dfrac{4}{7}\times\dfrac{49}{16}\). Express your answer as a mixed number in the simplest form.


(a) What is the value of 40 − (20 − 4) ÷ 4 × 3? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Find the largest multiple of 8 that is smaller than 60. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Find the value of \(2-\dfrac{2}{3}-\dfrac{1}{6}\).


Find the value of 7.68 + 3.4. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Arrange the following from the heaviest to the lightest.<br>3.055 kg, 3 kg 250 g, \(3\dfrac{1}{8}\) kg


Sumin used 205 cm of string to make 5 bracelets. Find the length of string that she would use to make 16 such bracelets. Give your answer in metres.<br>Length = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m


The average age of a club of 10 members is 35 years old. A member of age 53 left the club. What is the average age of the present club?<br>Average age = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> years

Total age = 10 x 35 = 350. After the 53-year-old leaves: 350 − 53 = 297 for 9 members. Average = 297 ÷ 9 = 33 years. Answer: 33 years.


Mdm Leong had some money. She spent $80 and had $45 left. What percentage of her money did she spend?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %

Total money = 80 + 45 = 125. Percentage spent = 80/125 x 100% = 64%. Answer: 64%.


One small bag contained 4 cookies and one big bag contained 6 cookies. There were 30 more small bags than big bags. There were a total of 2360 cookies. How many big bags were there?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> big bags

Let big bags = b. The 30 extra small bags hold 30 x 4 = 120 cookies. Remaining cookies = 2360 − 120 = 2240, shared by equal numbers of small and big bags: each pair holds 4 + 6 = 10 cookies, so b = 2240 ÷ 10 = 224 big bags. Answer: 224.


Baker Tan had 3262 chocolate and strawberry muffins. He sold \(\dfrac{4}{5}\) of the chocolate muffins and \(\dfrac{3}{4}\) of the strawberry muffins. There were 736 muffins left. How many chocolate muffins did he sell?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> chocolate muffins


The ratio of the number of red marbles to the number of blue marbles to the number of green marbles in a box was 6 : 5 : 2. There were 42 more blue marbles than green marbles. How many marbles were there in the box in total?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> marbles

Blue − green = 5 − 2 = 3 units = 42, so 1 unit = 14. Total units = 6 + 5 + 2 = 13; total marbles = 13 x 14 = 182. Answer: 182 marbles.


The usual price of a television set was $6000. Mr Jones bought the television set at a 15% discount.
(a) How much was the discount? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) GST is 8% of the discounted price. How much did Mr Jones pay for the television set inclusive of GST? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


There were 1090 animals in Zoo A and 320 animals in Zoo B. After an equal number of animals joined each zoo, the number of animals in Zoo A became thrice that of Zoo B. How many animals joined each zoo?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> animals

Difference stays constant: 1090 − 320 = 770. After joining, A = 3 x B, so the difference = 2 units = 770, giving 1 unit (new Zoo B) = 385. Animals joined = 385 − 320 = 65. Answer: 65 animals.


There are 360 red, green and black buttons. 20% of the buttons are red. The ratio of the number of green and red buttons to the number of black buttons is 11 : 4. What is the ratio of the number of black and red buttons to the number of green buttons?


There were some apples, oranges and pears in a supermarket. The average number of apples and oranges was 336. There were 140 more oranges than apples. The average number of the fruits was 332.
(a) How many oranges were there in the supermarket? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) After some oranges were sold, the average number of the fruits was 324. How many oranges were left in the market? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Apples + oranges = 336 x 2 = 672. With oranges − apples = 140: oranges = (672 + 140) ÷ 2 = 406. (b) Original total of 3 fruits = 332 x 3 = 996; after selling, total = 324 x 3 = 972; oranges sold = 996 − 972 = 24; oranges left = 406 − 24 = 382. Answers: 406; 382.


There were 10 chairs in each row. After Mr Png added 24 chairs, he rearranged the chairs in rows of 12. There were 6 less rows than before. How many chairs were there at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> chairs

Let original rows = r. Original chairs = 10r. New chairs = 10r + 24 = 12(r − 6) = 12r − 72. So 10r + 24 = 12r − 72, giving 2r = 96, r = 48 rows. Original chairs = 10 x 48 = 480. Answer: 480 chairs.


Miss Low started writing page numbers on a book. She wrote a total of 612 digits on the book.
(a) How many digits are there from page 1 to page 99? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many pages were there in the book? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Pages 1-9: 9 x 1 = 9 digits. Pages 10-99: 90 x 2 = 180 digits. Total = 9 + 180 = 189 digits. (b) Remaining digits = 612 − 189 = 423, all on 3-digit pages: 423 ÷ 3 = 141 pages. Last page = 99 + 141 = 240. Answers: 189; 240.


Mandy, Nora, Olivia and Penny shared some stickers. Penny took \(\dfrac{1}{4}\) of the stickers. Olivia took \(\dfrac{1}{5}\) of the remaining stickers. Nora took 20 more stickers than Olivia and Mandy took the rest of the stickers. Mandy had 34 stickers. How many stickers were there altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> stickers

Mandy + Nora's extra = 34 + 20 = 54, which equals 9 equal parts of the remaining-after-Penny (Olivia 1 part, Nora-extra aside, Mandy parts). Following the key: 34 + 20 = 54; 54 ÷ 9 = 6 (one part); total = 6 x 20 = 120 stickers. Answer: 120 stickers.


In 5.687, which digit is in the hundredths place?

Place values after the decimal point: 6 is tenths, 8 is hundredths, 7 is thousandths. So the hundredths digit is 8.


Which of the following is the same as 23 kg 52 g?


Ming Xuan bought 42 oranges, 28 mangoes and 14 kiwis from a fruit store. What was the ratio of the number of oranges to the number of mangoes to the number of kiwis that he bought? Express your answer in its simplest form.

42 : 28 : 14. Divide each term by the common factor 14: 42 ÷ 14 = 3, 28 ÷ 14 = 2, 14 ÷ 14 = 1. So the ratio is 3 : 2 : 1.


A machine seals 120 fishball packets in 60 seconds. At this rate, how many fishball packets can it seal in 30 minutes?

In 60 seconds (1 minute) it seals 120 packets. 30 minutes × 120 = 3600 packets.


Arul had 240 stamps. He gave 60 stamps to his sister. What percentage of his stamps did Arul give to his sister?


Thomas had $1200. He spent 35% of his money on food. How much money did he spend on food?


Arrange the following fractions from the smallest to the largest.<br>\(\dfrac{8}{9}\), \(\dfrac{3}{7}\), \(\dfrac{4}{5}\)


Find the average of the following 5 numbers.<br>23, 23, 18, 16, 0


A factory produces 1505 kg of flour a day. The flour is packed equally into 50 packs. How much does each pack of flour weigh?


At a funfair, there were 270 people. \(\dfrac{2}{3}\) of them were children. \(\dfrac{2}{5}\) of the children were girls and the rest were boys. How many boys were there at the funfair?


A chef cooked some soup for 200 guests. Each guest was served 0.78 ℓ of the soup. How much soup did the chef cook?


Find the value of \(198 + 35 \div 7 - (35 + 8 \div 4 \times 2)\).<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(5 \div 8\). Give your answer as a decimal.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


What is the missing number in the box?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> : 5 = 24 : 40

40 ÷ 5 = 8, so each term on the right is 8 times the left. 24 ÷ 8 = 3. The missing number is 3.


Find the value of \(\dfrac{2}{3} \times \dfrac{5}{8}\). Give your answer as a fraction in the simplest form.

\(\dfrac{2}{3}\times\dfrac{5}{8}=\dfrac{10}{24}=\dfrac{5}{12}\) (dividing top and bottom by 2).


Sophia paid $87.40 for 3 identical pencils and 7 identical markers. The price of a marker is $1.20 more than the price of a pencil. Tim bought 10 such pencils. What was the amount of money he paid for 10 such pencils?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Replace each marker with (pencil + $1.20): 3 pencils + 7 pencils + 7 × $1.20 = $87.40. So 10 pencils + $8.40 = $87.40, giving 10 pencils = $79.00. Tim paid $79 for 10 pencils.


The product of 2 numbers is 3069. The smaller number is 9. Find the larger number. Round the answer to the nearest hundred.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Larger number = 3069 ÷ 9 = 341. Rounded to the nearest hundred, 341 ≈ 300.


Abdul bought \(5\dfrac{2}{5}\) m of string. He used \(1\dfrac{3}{4}\) m of it to tie a parcel and \(\dfrac{4}{10}\) m of it to decorate a present. How many metres of string had he left? Give your answer as a mixed number.


A jug contains \(1\dfrac{7}{9}\) litres of apple juice. How many litres of apple juice are there in 6 such jugs altogether?


The average mass of 5 children is 48 kg. When Peter's mass is added, the average mass becomes 45 kg. What is Peter's mass?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total of 5 children = 5 × 48 = 240 kg. Total of 6 people = 6 × 45 = 270 kg. Peter's mass = 270 − 240 = 30 kg.


Mei Yan has a piece of yellow ribbon and red ribbon of the same length. She then cuts the yellow ribbon and the red ribbon into shorter pieces. If she gives a group of friends a shorter piece of yellow ribbon of length 1.4 m each, she will have 0.6 m of the yellow ribbon left. If she gives the same group of friends a shorter piece of red ribbon of length 1.8 m each, she will need an additional 2.2 m of the red ribbon. How many friends does Mei Yan have in this group?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the number of friends be n. Yellow length = 1.4n + 0.6. Red length = 1.8n − 2.2 (she is 2.2 m short). The ribbons are the same length: 1.4n + 0.6 = 1.8n − 2.2, so 0.6 + 2.2 = 0.4n, 2.8 = 0.4n, n = 7. Mei Yan has 7 friends.


The total cost of 2 identical files and 3 identical markers was $15. The total cost of 5 such files and 6 such markers was $34.80. What was the cost of 1 such marker?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Double the first set: 4 files + 6 markers = $30. Compare with 5 files + 6 markers = $34.80. The difference is 1 file = $34.80 − $30 = $4.80. Then 2 × $4.80 + 3 markers = $15, so 3 markers = $15 − $9.60 = $5.40, and 1 marker = $1.80.


Team A played against Team B in a badminton match. 560 children watched the badminton match. 70% of the children were boys. (a) How many girls watched the badminton match? (b) 42 of the girls supported Team B and the rest of the girls supported Team A. What percentage of the girls supported Team A?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 70% were boys, so 30% were girls. Girls = \(\dfrac{30}{100}\times 560 = 168\). (b) Girls supporting Team A = 168 − 42 = 126. Percentage = \(\dfrac{126}{168}\times 100\% = 75\%\).


Jason, Peter and Chris shared a sum of money in the ratio 5 : 9 : 2. The difference between Peter's share and Jason's share is $128. How much more money did Peter have than Chris?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Peter : Jason difference = 9 − 5 = 4 units = $128, so 1 unit = $32. Peter − Chris = 9 − 2 = 7 units = 7 × $32 = $224.


The average mark for a class of students in a quiz is 74. The top 3 students scored 87, 95 and 100. When the top 3 students were excluded in the calculation for the average, the average mark becomes 62. How many students were there in the class?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let there be n students. Total marks = 74n. Top 3 total = 87 + 95 + 100 = 282. The remaining (n − 3) students average 62: 74n − 282 = 62(n − 3). So 74n − 282 = 62n − 186, 12n = 96, n = 8.


Ravi baked 2535 cookies. \(\dfrac{1}{3}\) of them were chocolate cookies, \(\dfrac{3}{5}\) of the remaining cookies were vanilla cookies and the rest were strawberry cookies. (a) How many vanilla cookies did he bake? (b) Ravi packed all the vanilla cookies into large and small tins to sell. He filled each large tin with 30 cookies and each small tin with 12 cookies. All the tins were full and there were no cookies left over. What was the least number of tins used by Ravi?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Chocolate = \(\dfrac{1}{3}\times 2535 = 845\). Remaining = 2535 − 845 = 1690. Vanilla = \(\dfrac{3}{5}\times 1690 = 1014\). (b) 1014 = 30 × a + 12 × b. To use the fewest tins, fill as many large (30) tins as possible: 30 × 33 = 990, leaving 24 = 12 × 2. So 33 large + 2 small = 35 tins.


Keryn and Carol had an equal number of stickers at first. After Keryn used 352 stickers and Carol used 84 stickers, Carol had 5 times as many stickers as Keryn. (a) How many stickers did Keryn have left? (b) How many stickers did each girl have at first?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let each girl start with x stickers. Keryn left = x − 352, Carol left = x − 84, and Carol = 5 × Keryn: x − 84 = 5(x − 352). So x − 84 = 5x − 1760, 1676 = 4x, x = 419. (a) Keryn left = 419 − 352 = 67. (b) Each girl had 419 stickers at first.


The table shows the parking charges at Value Shopping Mall: first hour or part thereof (9 a.m. to 5 p.m.) costs $1.20; every additional \(\dfrac{1}{2}\) hour or part thereof costs $1.00; after 5 p.m. till next morning 9 a.m. costs $5.00 per entry. (a) Mrs Wee parked her car from 9.30 a.m. to 11.45 a.m. How much did she pay for her parking charges? (b) Mr Ong parked his car from 4.30 p.m. till the next morning 9 a.m. How much did he pay for his parking charges?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 9.30 a.m. to 11.45 a.m. = 2 h 15 min. First hour = $1.20. Remaining 1 h 15 min = 3 half-hour blocks (part thereof) × $1.00 = $3.00. Total = $1.20 + $3.00 = $4.20. (b) Parking from 4.30 p.m. till next morning 9 a.m. is charged the overnight flat rate of $5.00 per entry.


What is the value of the digit 3 in 30 625?

The digit 3 is in the ten-thousands place, so its value is 30 000. Answer: 30 000.


Express \(1\dfrac{1}{50}\) as a decimal.


Arrange the following fractions from the largest to the smallest.


What is the value of \(30 - (6 + 12) \div 2 \times 3\)?

Brackets first: 6+12 = 18. Then 18 ÷ 2 = 9, 9 × 3 = 27. Finally 30 - 27 = 3. Answer: 3.


Maya folds 10 stars in 5 minutes.<br>At this rate, how many stars can Maya fold in 20 minutes?

20 minutes is 4 times 5 minutes, so 4 × 10 = 40 stars. Answer: 40.


Mr Hamid wanted to transfer 12 of his plants into bigger pots. He used \(\dfrac{3}{8}\) kg of soil to fill each big pot. He ran out of soil after transferring 5 plants. How much more soil would he need to fill the big pots for the remaining plants?


Ally and Bella had the same amount of money at first. After Ally spent $20 and Bella spent $80, Ally had 3 times as much money as Bella. How much money did Bella have at first?

Let starting amount = m. After spending: Ally = m-20, Bella = m-80, and m-20 = 3(m-80). So m-20 = 3m-240, 220 = 2m, m = 110. Bella had $110 at first. Answer: $110.


Write down all the common multiples of 3 and 4 that are smaller than 30. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Common multiples of 3 and 4 are multiples of 12: 12, 24, 36, ... Those smaller than 30 are 12 and 24. Answer: 12, 24.


Find the value of \(0.45 \times 80\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Huda had 1.05 ℓ of orange juice at first. She drank 480 ml of it. How many litres of orange juice was left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(\dfrac{2}{3} \times \dfrac{4}{9}\).


The Koh family watched a movie from 7.30 p.m. to 9.15 p.m. How much time did they spend watching the movie? Give your answer in h and min. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> min

From 7.30 p.m. to 9.30 p.m. is 2 h; to 9.15 p.m. is 1 h 45 min. Answer: 1 h 45 min.


The table shows the number of hampers sold at a gift shop from Thursday to Saturday (Thursday 18, Friday 24, Saturday 42). Find the ratio of the number of hampers sold on Thursday to Friday to Saturday. Give your answer in the simplest form.

18 : 24 : 42, divide each by the HCF 6 → 3 : 4 : 7. Answer: 3 : 4 : 7.


The table shows the number of hampers sold at a gift shop from Thursday to Saturday (Thursday 18, Friday 24, Saturday 42). What was the average number of hampers sold over the three days? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


There are 40 pupils in a class. 15% of them walk to school. How many pupils walk to school? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mr Tan had $8000. He gave $2000 to his wife and deposited the remaining amount in the bank. The bank paid 5% interest at the end of each year. How much money did he have in the bank at the end of 1 year? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A painter mixed blue paint and yellow paint in the ratio of 3 : 7 to get green paint. He used 840 ml of yellow paint. How much blue paint did he use? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ml

7 units = 840 ml, so 1 unit = 120 ml. Blue = 3 units = 3 × 120 = 360 ml. Answer: 360 ml.


The table shows the charges for bicycle rental: First hour $6.00; every additional \(\dfrac{1}{2}\) hour or part thereof $2.50. John and his brother rented a bicycle each from 2.00 p.m. to 4.15 p.m. How much did they pay altogether? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The table shows the number of buttons in a box (Red 80, Blue 130). What percentage of the buttons in the box are red buttons? Round your answer to 2 decimal places. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %


Printer A prints at a rate of 80 copies in 1 minute while Printer B prints at a rate of 300 copies in 5 minutes. Which printer prints at a faster rate?

Printer A = 80 copies/min. Printer B = 300 ÷ 5 = 60 copies/min. 80 > 60, so Printer A is faster. Answer: Printer A.


Printer A prints at a rate of 80 copies in 1 minute while Printer B prints at a rate of 300 copies in 5 minutes. By how many more copies does the faster printer print in one minute? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> copies

Printer A = 80/min, Printer B = 60/min. Difference = 80 - 60 = 20 copies. Answer: 20 copies.


Zhi Yu cycles 7 times a week. Each time, he cycles \(5\dfrac{4}{5}\) km from his home to the park and cycles home on the same route. What is the total distance that Zhi Yu cycles in a week? Express your answer as a mixed number in the simplest form.


Shanti bought 1.3 kg of grapes priced at 80¢ per 100 g. How much did she pay? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Lim paid $53 for 5 mugs and 4 bowls. The cost of each bowl was $2 more than the cost of each mug. How much did Mrs Lim pay for the 5 mugs? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

4 bowls cost 4 × $2 = $8 more than 4 mugs. Remove that: $53 - $8 = $45 for 9 items at the mug price. 1 mug = $45 ÷ 9 = $5. 5 mugs = 5 × $5 = $25. Answer: $25.


Amira baked some cookies in the morning. She gave \(\dfrac{2}{7}\) of them to her neighbours and gave \(\dfrac{1}{2}\) of the remaining cookies to her friends. In the afternoon, Amira baked another 85 cookies. The number of cookies that she had in the end was 13 more than what she baked in the morning. What fraction of the cookies baked in the morning were given away?

Take morning total as 14 units. Given to neighbours = 4 units (2/7 of 14). Remaining = 10 units; given to friends = 5 units (half). Total given away = 4 + 5 = 9 units, i.e. \(\dfrac{9}{14}\). Answer: \(\dfrac{9}{14}\).


Amira baked some cookies in the morning. She gave \(\dfrac{2}{7}\) of them to her neighbours and gave \(\dfrac{1}{2}\) of the remaining cookies to her friends. In the afternoon, Amira baked another 85 cookies. The number of cookies that she had in the end was 13 more than what she baked in the morning. How many cookies did Amira bake altogether on that day? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

She gave away 9/14 in the morning, keeping 5/14. End amount = morning + 13, and end = kept + 85. So (5/14)m + 85 = m + 13 → 85 - 13 = m - (5/14)m = (9/14)m → 72 = (9/14)m → m = 112. Morning baked = 112; total for the day = 112 + 85 = 197. Answer: 197.


A box with 40 identical nails has a mass of 780 g. The same box with 30 identical batteries has a mass of 1.08 kg. The mass of each battery is twice the mass of each nail. Find the mass of the empty box in kilograms. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

30 batteries = 60 nail-masses. Difference: (box + 60 nails) - (box + 40 nails) = 1.08 kg - 0.78 kg = 0.30 kg = 20 nail-masses. So 1 nail = 0.015 kg. 40 nails = 0.6 kg. Empty box = 0.78 kg - 0.6 kg = 0.18 kg. Answer: 0.18 kg.


Adam, Ben and Calvin had a total of 540 marbles. Adam gave \(\dfrac{1}{4}\) of his marbles to Ben. Then, Ben gave \(\dfrac{1}{3}\) of his total number of marbles to Calvin. In the end, all the boys had the same number of marbles.
(a) How many marbles did each boy have in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many marbles did Ben have at first? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) In the end all equal: 540 ÷ 3 = 180 each. (b) Working back: Adam ended with 180 after giving 1/4 away, so 3/4 of Adam's start = 180 → Adam started 240, gave 60 to Ben. Ben ended with 180 after giving 1/3 away, so 2/3 of Ben's amount-before-giving = 180 → Ben had 270 before giving, gave 90 to Calvin. Ben at first = 270 - 60 (received from Adam) = 210. Answers: (a) 180, (b) 210.


Siew Li and Mariam each had a roll of ribbon of the same length for making bows. The same length of ribbon was used for each bow. Siew Li made 30 bows and had 1.5 m of ribbon left. Mariam made 10 bows and had 8.5 m of ribbon left. How many bows could each girl make at most with the ribbon that she had? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Difference in bows = 30 - 10 = 20 bows, using 8.5 - 1.5 = 7 m. So each bow uses 7 ÷ 20 = 0.35 m. Total ribbon = 30×0.35 + 1.5 = 12 m. Max bows = 12 ÷ 0.35 = 34.2 → 34 bows (whole bows). Answer: 34 bows.


The first five figures of a pattern are shown; the total number of circles in figure n is n². What is the total number of white and grey circles in Figure 50? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total in figure n = n², so Figure 50 = 50 × 50 = 2500. Answer: 2500.


The first five figures of a pattern are shown; the total number of circles in figure n is n², and the difference between grey and white circles equals the figure number. In Figure 50, what fraction of the circles are grey? Give your answer in the simplest form.


What is the value of \(33 - (6 + 12) \div 3\)?

Work brackets first, then division, then subtraction. \((6+12)=18\); \(18\div3=6\); \(33-6=27\).


Jon had 200 stickers. He gave 90 stickers to his friend. What percentage of his stickers did Jon give to his friend?


The total marks obtained by 4 students is 60. What is the average number of marks obtained by the 4 students?

Average \(= \dfrac{\text{total}}{\text{number of items}} = \dfrac{60}{4} = 15\).


Ken saved \(\dfrac{1}{4}\) of his allowance and spent \(\dfrac{3}{5}\) of the remaining allowance on food. He had $72 left. How much was his allowance?

Remaining after saving \(= \dfrac{3}{4}\). He spent \(\dfrac{3}{5}\) of that on food, leaving \(\dfrac{2}{5}\) of the remainder. So $72 \(= \dfrac{2}{5} \times \dfrac{3}{4}\) of allowance \(= \dfrac{6}{20} = \dfrac{3}{10}\) of allowance. Allowance \(= 72 \div \dfrac{3}{10} = 72 \times \dfrac{10}{3} = \$240\).


Matthew had $25 more than Amy. When Amy gave Matthew $20, Matthew had 6 times as much money as Amy. How much money did Amy have at first?


Ben shared a sum of money equally with Carla. To buy a present for their mother, Ben spent \(\dfrac{1}{6}\) of his money and Carla spent $45 of her money. In the end, \(\dfrac{3}{4}\) of the original sum of money was left. What was the original sum of money shared by Ben and Carla?

Each had half the total, T/2. Together they spent \(\dfrac{1}{4}\) of T (since \(\dfrac{3}{4}\) is left), so total spent \(= \dfrac{T}{4}\). Ben spent \(\dfrac{1}{6} \times \dfrac{T}{2} = \dfrac{T}{12}\); Carla spent $45. So \(\dfrac{T}{12} + 45 = \dfrac{T}{4}\). Then \(45 = \dfrac{T}{4} - \dfrac{T}{12} = \dfrac{2T}{12} = \dfrac{T}{6}\), giving \(T = 270\). Original sum was $270.


Express \(3\dfrac{7}{25}\) as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(24 \times 400\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Two cups and a jug contain 2.33 litres of water. The volume of water in each cup is the same. The volume of water in one cup is 1.61 litres less than the volume of water in the jug. Find the volume of water in each cup. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Jill had $400. She spent 20% of her money on books. How much money did Jill spend on books? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The table shows the number of blue pens and red pens in 4 boxes. Box A: 17 red, 12 blue. Box B: 10 red, 18 blue. Box C: 13 red, 12 blue. Box D: 11 red, 15 blue.
(a) Which coloured pen has a greater number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) All the pens are repacked such that each box contained the same number of pens. How many pens are there in each box now? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


A box of toys was shared equally among 10 children. 3 of them gave all of their toys to the rest of the children. As a result, the rest of the children received 6 more toys each. How many toys were there in the box? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 3 children's toys were shared among the remaining 7, giving them 6 more each: \(3 \times s = 7 \times 6 = 42\), where s is each child's original share. So \(s = 14\). Total toys \(= 10 \times 14 = 140\).


There are 248 marbles in a box. The ratio of the number of red marbles to the number of blue marbles is 3 : 1. The rest of the 60 marbles are green. How many blue marbles are there in the box? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


What is the missing number in the number pattern?<br>91, 73, 55, , 19

The pattern decreases by 18 each step: 91, 73, 55, 37, 19. Missing number = 55 - 18 = 37. Final answer: 37.


Find the value of \(\dfrac{2}{3} + \dfrac{1}{4}\)


Find the value of \(\dfrac{3}{5} \times \dfrac{1}{2}\)

Multiply numerators and denominators: \(\dfrac{3}{5} \times \dfrac{1}{2} = \dfrac{3 \times 1}{5 \times 2} = \dfrac{3}{10}\). Final answer: \(\dfrac{3}{10}\).


Express \(2\dfrac{1}{20}\) as a decimal.


The 3rd decimal digit is 5, so round the 2nd decimal place up: 3.785 rounds to 3.79. Final answer: 3.79.


A machine takes 3 min to print 4 posters. At the same rate, how long will it take to print 24 posters?

24 posters is 24 ÷ 4 = 6 times as many as 4 posters. Time = 6 × 3 min = 18 min. Final answer: 18 min.


In a basket, there are 5 pears, 20 apples and 10 mangoes. What is the ratio of the number of pears to the total number of apples and mangoes in the basket?

Pears = 5. Apples + mangoes = 20 + 10 = 30. Ratio = 5 : 30 = 1 : 6. Final answer: 1 : 6.


At first, Ali was facing east. He then turned 135° anti-clockwise. What direction did Ali face in the end?

Facing east, turning 90° anti-clockwise faces north; a further 45° anti-clockwise (135° total) faces north-west. Final answer: North-West.


There are 240 adults and 60 children at a concert. What percentage of the people at the concert are children?

Total people = 240 + 60 = 300. Percentage of children = \(\dfrac{60}{300} \times 100\% = 20\%\). Final answer: 20%.


Amy has twice as many $20 notes as $50 notes in a box. The total value of the money in the box is $6300. How many $20 notes are there in the box?

Let $50 notes = 1 unit, $20 notes = 2 units. Value = 1×50 + 2×20 = 90 per unit. Units = 6300 ÷ 90 = 70. $20 notes = 2 × 70 = 140. Final answer: 140.


Round 67 483 to the nearest hundred.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tens digit is 8 (≥ 5), so round the hundreds place up: 67 483 → 67 500. Final answer: 67 500.


Find the value of $400 \times 17$<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


What is the value of $40 - (3 + 13) \div 4 \times 2$?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Brackets first: 3 + 13 = 16. Then left to right for ÷ and ×: 16 ÷ 4 = 4, 4 × 2 = 8. Finally 40 - 8 = 32. Final answer: 32.


Write down all the common multiples of 6 and 8 that are smaller than 70.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

The lowest common multiple of 6 and 8 is 24. Common multiples are 24, 48, 72, ... Those smaller than 70 are 24 and 48. Final answer: 24 and 48.


Find the value of \(\dfrac{2}{9} \times 4\)


Mdm Siti had \(1.03\) ℓ of oil at first. She used 650 mℓ of it. How many litres of oil was left?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ


The length of Ribbon A is 9 cm. The length of Ribbon B is 5 cm longer than Ribbon A. Find the ratio of the length of Ribbon B to the length of Ribbon A.

Ribbon B = 9 + 5 = 14 cm. Ratio B : A = 14 : 9. Final answer: 14 : 9.


The sum of 4 numbers is 680. One of the numbers is 65. What is the average of the other 3 numbers?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Sum of the other 3 numbers = 680 - 65 = 615. Average = 615 ÷ 3 = 205. Final answer: 205.


A store rewards customers with 6 points for every $50 spent. Mrs Tan spent $240 at the store. What is the total number of points Mrs Tan receives from the store?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number of complete $50 blocks in $240 = 240 ÷ 50 = 4 (remainder $40, no points). Points = 4 × 6 = 24. Final answer: 24.


There are 600 people at a concert. 45% of the people are children, 30% of the people are women and the rest are men. How many men are there?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


\(\dfrac{5}{8}\) of students in a class wear spectacles. \(\dfrac{3}{5}\) of those who wear spectacles are girls. 15 girls wear spectacles. More than half of the students are girls. What is the smallest possible number of girls who do not wear spectacles?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Girls with spectacles: \(\dfrac{3}{5}\) of spectacle-wearers = 15, so spectacle-wearers = 25, which is \(\dfrac{5}{8}\) of the class, giving 40 students. More than half girls means more than 20 girls; smallest total girls = 21. Girls without spectacles = 21 - 15 = 6. Final answer: 6.


In which one of the following numbers does the digit 5 have a value of 50 000?

Place value: the digit 5 must sit in the ten-thousands place (value 50 000). In 4 658 120, the 5 is in the ten-thousands place: 5 × 10 000 = 50 000. Answer: 4 658 120.


Which one of the following fractions is smaller than \(\dfrac{1}{4}\)?


\(16 + \dfrac{?}{10} = 17.8\) What is the missing number in the box?


Yu Wen had $7000 in her bank account. The bank paid 2% interest at the end of each year. She did not withdraw any of her savings. How much interest did she earn at the end of 1 year?


There are 10 chickens at a farm. There are 35 more ducks than chickens. What is the ratio of the number of ducks to the number of chickens?

Ducks = 10 + 35 = 45. Ratio ducks : chickens = 45 : 10 = 9 : 2. Answer: 9 : 2.


Harumi had a piece of string 4 m 6 cm. She cut off 1.3 m from it. What is the length of the remaining string?


A sandwich costs $6.05. Leonard bought 4 such sandwiches and had $1.85 left. How much money did he have before buying the 4 sandwiches?


Amiya and Eunice have $2100 altogether. Amiya has 30% of the money. How much money does Amiya have?


Mrs Urvi cut a cake into 16 equal pieces. She ate 3 pieces and gave a few pieces to her friends. In the end, she had \(\dfrac{3}{8}\) of the cake left. What fraction of the cake did she give to her friends?


Find the value of \(57 \div 300\). Leave your answer as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(11 + (18 - 14 \div 2) \times 3\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Inside brackets: 14 ÷ 2 = 7, then 18 − 7 = 11. Then 11 × 3 = 33. Then 11 + 33 = 44. Answer: 44.


Mrs Cheah bought an iron which included a GST of 7%. The price of the iron before GST was $90. How much did she pay for the iron? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A photocopier can copy 48 pages in 4 minutes. At this rate, how many pages can the photocopier copy per minute? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

48 pages ÷ 4 minutes = 12 pages per minute. Answer: 12.


Arrange the following from the smallest to the largest. \(0.209\), \(\dfrac{1}{5}\), \(\dfrac{2}{1000}\)


Last year, Bertrand completed a race in 51.98 seconds. This year, he completed the same race and was faster by 1.31 seconds. What was Bertrand's timing this year? Round your answer to 1 decimal place. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> s

51.98 − 1.31 = 50.67 s. Rounded to 1 decimal place = 50.7 s. Answer: 50.7 s.


The height of a cuboid is 20 m. Its height is twice its length. Its breadth is 6 m shorter than its length. Find the volume of the cuboid. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m³

Height = 20 m. Length = 20 ÷ 2 = 10 m. Breadth = 10 − 6 = 4 m. Volume = 20 × 10 × 4 = 800 m³. Answer: 800 m³.


At first, a pot contained \(\dfrac{2}{5}\) ℓ of water. Keisha added another \(\dfrac{1}{2}\) ℓ of water into the pot. Then she used \(\dfrac{2}{9}\) of all the water in the pot. How much water did Keisha use? Express your answer as a fraction in its simplest form.


The ratio of Jim's age to Frank's age is 1 : 6. In 5 years' time, they would be 73 years old altogether. What is Jim's age now? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In 5 years they add 5 + 5 = 10 years total, so their combined age now = 73 − 10 = 63. Ratio 1 : 6 means 7 equal units = 63, so 1 unit = 63 ÷ 7 = 9. Jim's age now = 1 unit = 9 years old. Answer: 9.


Two different whole numbers add up to 140. One of them is a 2-digit number and the other is a 3-digit number. What are the two numbers that will give the greatest possible difference? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

For the greatest difference, make the 3-digit number as large as possible and the 2-digit number as small as possible. The smallest 3-digit number that keeps the other a 2-digit number: smallest 2-digit number is 10, giving 140 − 10 = 130 (a 3-digit number). Difference = 130 − 10 = 120, the greatest possible. Answer: 10 and 130.


When a number is divided by 3, the answer is 6041. What is the answer obtained when the same number is divided by 7? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


There were 1780 people at a carnival. 45% of them were adults and the rest were children. How many children were at the carnival? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Cecily and Nadine shared the total cost of a handbag. Cecily paid $39 more than \(\dfrac{4}{9}\) of the total cost of the handbag. Nadine paid $186. How much did the handbag cost? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Cecily paid \(\dfrac{4}{9}\) of the cost + $39, so Nadine paid the rest: total − (\(\dfrac{4}{9}\) + $39) = \(\dfrac{5}{9}\) of the cost − $39. So \(\dfrac{5}{9}\) of the cost − $39 = $186, giving \(\dfrac{5}{9}\) of the cost = $225. \(\dfrac{1}{9}\) = 225 ÷ 5 = $45, so total = 45 × 9 = $405. Answer: $405.


Winsy had some purple beads and an equal number of red beads and yellow beads. The ratio of the number of purple beads to the number of red beads was 5 : 7. Winsy had 210 more red beads than purple beads. How many red beads and yellow beads did she have altogether? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Purple : red = 5 : 7. The difference = 7 − 5 = 2 units = 210, so 1 unit = 105. Red = 7 units = 735, and yellow = red = 735 (equal number). Red + yellow = 735 + 735 = 1470. Answer: 1470 beads.


At Doughnut Empire, each doughnut is sold at $1.10 or in a box of 11 for $8.90. Mrs Kor wants to buy exactly 208 doughnuts. What is the least amount of money that she needs to pay for the doughnuts? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Boxes are cheaper per doughnut ($8.90 ÷ 11 ≈ $0.81 vs $1.10). 208 ÷ 11 = 18 boxes (198 doughnuts) remainder 10. Buy 18 boxes: 18 × $8.90 = $160.20, covering 198 doughnuts; buy the remaining 10 singly: 10 × $1.10 = $11. Total = $160.20 + $11 = $171.20. Answer: $171.20.


Vinette had some white and black face masks. \(\dfrac{1}{6}\) of them were white. She gave away \(\dfrac{1}{3}\) of the white face masks and \(\dfrac{1}{3}\) of the black face masks. In the end, she had 156 white and black face masks altogether. How many black face masks did Vinette have at first? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

She gave away 1/3 of every mask, so she kept 2/3 of the total. 2/3 of total = 156, so total = 156 × 3 ÷ 2 = 234 masks at first. White = 1/6 × 234 = 39, so black = 234 − 39 = 195. (Printed working: total at first 18 units, 1 + 5 = 6 ... 156 ÷ 12 = 13, 13 × 15 = 195.) Answer: 195 black face masks.


Singapore's population was 6 014 723 last year. Express this number to the nearest thousand.

Method: round to the nearest thousand by looking at the hundreds digit. 6 014 723 has 7 in the hundreds place, so round up: 6 014 723 → 6 015 000. Final answer: 6 015 000.


In 13.02, which digit is in the tenths place?

Method: identify decimal place values. In 13.02 the first digit after the decimal point is the tenths place, which is 0. Final answer: 0.


Rina makes a necklace using 12 pink pearls and 18 white pearls. What fraction of the pearls are white?

Method: white ÷ total. Total pearls = 12 + 18 = 30. White = 18. Fraction = \(\dfrac{18}{30}=\dfrac{3}{5}\). Final answer: \(\dfrac{3}{5}\).


What is the value of (63 + 27) ÷ 3 – 12 × 2?

Method: order of operations (brackets, then × and ÷, then –). (63 + 27) = 90; 90 ÷ 3 = 30; 12 × 2 = 24; 30 – 24 = 6. Final answer: 6.


The average of 3 numbers is 34. One of the numbers is 28. Which of the following are the other two numbers?

Method: total = average × number of items. Total = 34 × 3 = 102. The other two = 102 – 28 = 74. 36 + 38 = 74. Final answer: 36, 38.


The table shows the rates for renting a bicycle at a shop.
First hour: $8
Every additional 30 min or part thereof: ?
Daisy rented two bicycles from 3.00 pm to 5.50 pm. She paid a total of $32 for renting the bicycles. How much did Daisy have to pay for every additional 30 min or part thereof for renting a bicycle?

Method: work out the charge per bicycle, then the additional-period rate. 3.00 pm to 5.50 pm = 2 h 50 min. First hour = $8; the remaining 1 h 50 min = 110 min = 4 blocks of 30 min (part thereof rounds up). Total for two bicycles = $32, so each bicycle = $16. Additional charge per bicycle = $16 – $8 = $8 over 4 blocks = $2 per 30 min. Final answer: $2.


At first, Mrs Ang had twice as many red beads as yellow beads. She used \(\dfrac{2}{3}\) of her yellow beads and some of her red beads to make some necklaces. In the end, \(\dfrac{3}{5}\) of the beads left were red beads. What fraction of her red beads did Mrs Ang use?

Method: use units. Let yellow = 3u, so red = 6u. Yellow used = \(\dfrac{2}{3}\times3u = 2u\), so yellow left = 1u. In the end red is \(\dfrac{3}{5}\) of beads left, so yellow (1u) is \(\dfrac{2}{5}\) of the remainder → remainder = \(\dfrac{5}{2}u\), giving red left = \(\dfrac{3}{2}u\). Red used = 6u – \(\dfrac{3}{2}u\) = \(\dfrac{9}{2}u\). Fraction of red used = \(\dfrac{9/2\,u}{6u}=\dfrac{3}{4}\). Final answer: \(\dfrac{3}{4}\).


Mrs Samy baked chocolate and strawberry cupcakes at a children's party. The number of chocolate cupcakes was \(\dfrac{5}{7}\) the number of strawberry cupcakes. Mrs Samy then baked some blueberry cupcakes. In the end, 25% of the cupcakes were chocolate cupcakes. What percentage of cupcakes were blueberry cupcakes?

Method: chocolate : strawberry = 5 : 7, so chocolate = 5 parts, strawberry = 7 parts. After adding blueberry, chocolate (5 parts) = 25% of total, so total = 20 parts. Strawberry = 7 parts. Blueberry = 20 – 5 – 7 = 8 parts = \(\dfrac{8}{20}\times100\% = 40\%\). Final answer: 40%.


Find the value of 20.1 – 0.68. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: subtract decimals lining up the points. 20.10 – 0.68 = 19.42. Final answer: 19.42.


Find the value of \(\dfrac{5}{7}\times\dfrac{8}{15}\). Give your answer in its simplest form.

Method: multiply numerators and denominators, then simplify. \(\dfrac{5}{7}\times\dfrac{8}{15}=\dfrac{40}{105}\). Divide top and bottom by 5: \(\dfrac{8}{21}\). Final answer: \(\dfrac{8}{21}\).


(a) Find the value of \(\dfrac{2}{5}+\dfrac{3}{8}\).<br>(b) Express 2.68 as a mixed number in the simplest form.


The timetable shows the time of 4 different trains from City X to City Y.
Train A: leaves 8.15 a.m., arrives 10.05 a.m.
Train B: leaves 8.25 a.m., arrives 10.40 a.m.
Train C: leaves 8.40 a.m., arrives 11.00 a.m.
Train D: leaves 9.05 a.m., arrives 11.20 a.m.
(a) Find the time taken for Train D to travel from City X to City Y. Give your answer in h and min. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> min
(b) Sue wants to take a train to City Y. Her watch shows 8.20 a.m. when she arrives at the station in City X. She realises that her watch is 10 min slower. What is the earliest time she can reach City Y? <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> a.m.

Method: (a) Train D: 9.05 a.m. to 11.20 a.m. = 2 h 15 min. (b) Watch shows 8.20 a.m. but is 10 min slow, so the real time is 8.30 a.m. The earliest train she can still catch leaves at 8.40 a.m. (Train C), which arrives 11.00 a.m. Final answers: (a) 2 h 15 min; (b) 11.00 a.m.


Zhi Xiang went to a shop to buy a bag. The shop gave a discount of $5 for every $25 spent. Zhi Xiang paid $96 for a bag. What was the price of the bag before the discount? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: for every $25 of original price the customer pays $20 (after $5 discount). $96 paid ÷ $20 = 4.8 groups → but using whole $25 groups: 4 full groups cost $80 (original $100), remaining $16 paid corresponds to $16 original (no further $25 reached). Original = $100 + $16 = $116. Check: total discount = $20, $116 – $20 = $96. Final answer: $116.


Christopher has $63.
Box of 9 cupcakes – $25
1 cupcake – $3
What is the greatest number of cupcakes he can buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: maximise cupcakes per dollar. A box of 9 for $25 is best value. 2 boxes = $50 for 18 cupcakes, leaving $63 – $50 = $13. With $13 at $3 each, buy 4 single cupcakes ($12). Total = 18 + 4 = 22 cupcakes. Final answer: 22.


The table shows the times taken by five robots to complete a maze.
Robot A: 4.5 s, Robot B: 6.81 s, Robot C: 3.92 s, Robot D: 4.12 s, Robot E: 5.1 s.
(a) Which robot was the fastest to complete the maze? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Robot F completed the same maze. The average time taken for all 6 robots was 4.73 s. What was the time taken by Robot F to complete the maze? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> s

Method: (a) the fastest robot has the smallest time: Robot C at 3.92 s. (b) total time for 6 robots = 4.73 × 6 = 28.38 s. Robot F = 28.38 – (4.5 + 6.81 + 3.92 + 4.12 + 5.1) = 28.38 – 24.45 = 3.93 s. Final answers: (a) Robot C; (b) 3.93 s.


Corinne saved 20% of her monthly income. In August, her income decreased by 15%. As a result, her savings in August was decreased by $120 compared to her savings in July. What was her income in July? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: July savings = 20% of income. After a 15% income drop, savings = 20% × 85% = 17% of July income. The fall in savings = 20% – 17% = 3% of July income = $120. So 1% = $40, and 100% = $4000. Final answer: $4000.


Vinesh drove from Singapore to Malacca at an average speed of 90 km/h. On the return journey, he took the same route and covered \(\dfrac{1}{3}\) of the distance in 1 hour. Then he reduced his speed to 70 km/h for the rest of the journey. Vinesh took 4 hours for the return journey. How long did he take to drive from Singapore to Malacca? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h

Method: on the return, \(\dfrac{2}{3}\) of the distance was covered in the remaining 3 h at 70 km/h, so \(\dfrac{2}{3}\)distance = 70 × 3 = 210 km. Total distance = 210 ÷ \(\dfrac{2}{3}\) = 315 km. The outward trip at 90 km/h took 315 ÷ 90 = 3.5 h. Final answer: 3.5 h.


A shop sold electronic devices was having a sale. 1st item at 15% discount, 2nd item at 20% discount. Price of 2nd item must be equal or lower than the price of 1st item. Mr Poh bought a tablet at $230 and a laptop at $550. How much did he pay for the two items? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: the 1st item (15% off) must be the higher-priced one, so the laptop ($550) gets 15% off and the tablet ($230) gets 20% off. Laptop = 85% × $550 = $467.50. Tablet = 80% × $230 = $184. Total = $467.50 + $184 = $651.50. Final answer: $651.50.


A shop sale gives the 1st item 15% discount and the 2nd item 20% discount (2nd item priced equal or lower than the 1st). Mr Chian bought two identical smart watches. He received a total discount of $147. What was the price of one smart watch before the discount? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: identical watches, so one gets 15% off and the other 20% off. Total discount = 15% + 20% = 35% of one watch's price = $147. So 1% = $147 ÷ 35 = $4.20, and 100% = $420. Final answer: $420.


Ray uses lines and dots to form figures that follow a pattern. The table shows the number of lines and dots for the first four figures:
Figure 1: 6 dots, 6 lines; Figure 2: 9 dots, 10 lines; Figure 3: 12 dots, 14 lines; Figure 4: 15 dots, 18 lines.
(a) Complete the table for Figure 5: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> dots and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> lines.
(b) A figure in the pattern has 108 dots. What is the Figure number? <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />
(c) Find the total number of dots and lines in Figure 72. <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

Method: dots increase by 3 each figure (dots = 3 × figure number + 3); lines increase by 4 each figure (lines = 4 × figure number + 2). (a) Figure 5: dots = 15 + 3 = 18; lines = 18 + 4 = 22. (b) 108 dots: 108 ÷ 3 = 36, then 36 – 1 = 35 → Figure 35. (c) Figure 72: dots = 73 × 3 = 219; lines = 219 + 72 – 1 = 290; total = 219 + 290 = 509. Final answers: (a) 18 dots, 22 lines; (b) Figure 35; (c) 509.


Tina had a total of 754 pearl necklaces and bead necklaces for sale. After selling twice as many pearl necklaces as bead necklaces, she had \(\dfrac{1}{3}\) of the pearl necklaces and \(\dfrac{1}{4}\) of the bead necklaces left. What was the total number of pearl and bead necklaces left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: pearls left = \(\dfrac{1}{3}\) pearls (so \(\dfrac{2}{3}\) sold); beads left = \(\dfrac{1}{4}\) beads (so \(\dfrac{3}{4}\) sold). Pearls sold = 2 × beads sold: \(\dfrac{2}{3}P = 2\times\dfrac{3}{4}B\) → \(\dfrac{2}{3}P=\dfrac{3}{2}B\). Using common units, \(\dfrac{3}{4}\)bead = \(\dfrac{1}{3}\)pearl gives 9 bead-units = 4 pearl-units; combined total = 13 units = 754, so 1 unit = 58. Necklaces left = 4 units = 4 × 58 = 232. Final answer: 232.


At a school bookshop, erasers are only sold in packs of 4 and pencils are only sold in packs of 5. Erasers: 4 for $1.99. Pencils: 5 for $2.99. Mr Lim spent $139.45 buying some erasers and pencils for Children's Day. He put all the erasers and pencils into bags. The ratio of the number of erasers to the number of pencils in each bag was 2 : 3. How many pencils did he buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: erasers : pencils = 2 : 3, but they are bought in packs of 4 and 5, so a whole-pack ratio is (4×5) : (5×6) = 20 erasers : 30 pencils per set, i.e. 5 eraser-packs and 6 pencil-packs. Cost of one set = ($1.99 × 5) + ($2.99 × 6) = $9.95 + $17.94 = $27.89. Number of sets = $139.45 ÷ $27.89 = 5 sets. Pencils = (5 × 6) × 5 = 150 pencils. Final answer: 150.


Gary spent \(\dfrac{5}{8}\) of his money on 10 identical notebooks and 10 identical files. Then, he spent \(\dfrac{5}{6}\) of his remaining money on a bag. What fraction of Gary's money was spent on the bag?

Method: remaining after books/files = 1 – \(\dfrac{5}{8} = \dfrac{3}{8}\). Bag = \(\dfrac{5}{6}\) of remaining = \(\dfrac{5}{6}\times\dfrac{3}{8} = \dfrac{15}{48} = \dfrac{5}{16}\). Final answer: \(\dfrac{5}{16}\).


Gary spent \(\dfrac{5}{8}\) of his money on 10 identical notebooks and 10 identical files, then \(\dfrac{5}{6}\) of his remaining money on a bag. Each file cost $4 more than each notebook and the bag cost $38 more than each notebook. How much money had Gary left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Which of the following is seven hundred and three thousand and twelve in numerals?

Seven hundred and three thousand = 703 000; and twelve = 12. So the number is 703 012.


The average of three numbers is 40. The sum of another two numbers is 50. What is the average of the 5 numbers?

Sum of the three numbers = 3 × 40 = 120. Total of all five = 120 + 50 = 170. Average = 170 ÷ 5 = 34.


In a marathon relay race, four runners ran one after another without any stop in between. The second runner started running at the same time the first runner completed running and so on. The chart shows the time each runner started running. The last runner completed the race at 1.30 p.m.
Start times: First 10.30 a.m., Second 11.20 a.m., Third 12.15 p.m., Last 12.55 p.m.
How much more time did the slowest runner take than the fastest runner?

Each runner's time = next start minus own start (last finishes 1.30 p.m.). First = 10.30→11.20 = 50 min; Second = 11.20→12.15 = 55 min; Third = 12.15→12.55 = 40 min; Last = 12.55→1.30 = 35 min. Slowest = 55 min, fastest = 35 min. Difference = 55 − 35 = 20 min.


Aaron had $55 more than Shanti at first. After Aaron used \(\dfrac{2}{5}\) of his money and Shanti used \(\dfrac{1}{3}\) of her money, Aaron had $27 more than Shanti. How much did Shanti have left at the end?


A sum of money was shared between John and Ken in the ratio 3 : 4. John used all his money to buy 8 identical toy cars that cost $1.50 each. Ken used some of his money to buy 3 such toy cars. How much money had Ken left?

John spent 8 × $1.50 = $12 (all his share, 3 units). So 1 unit = $4, Ken's share = 4 units = $16. Ken bought 3 cars = 3 × $1.50 = $4.50. Ken left = $16 − $4.50 = $11.50.


Find the value of \(20 - (4 + 8 \div 4) + 5\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(68.2 \div 4\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


May's clock at home slows down 1 minute after every 6 hours since the battery runs low from 12 midnight. It is now showing 6.00 p.m. What should be the correct time now? Leave your answer in 24-hour clock. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From midnight, the clock shows 6.00 p.m. = 18 hours elapsed on the clock. It loses 1 min per 6 hours, so in 18 hours it has lost 3 minutes. The correct time is 3 minutes ahead: 18:00 + 3 min = 18:03, i.e. 1803.


A baker had three boxes of flour weighing 2.7 kg, 3.4 kg and 5.02 kg. He repacked them equally into four bags. What is the mass of each bag? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The table shows the prices of pens and erasers sold at a bookshop: an Eraser costs \(b\) cents and a Pen costs \(2b\) cents. Mark spent $4.20 on 5 erasers and 1 pen. Find the value of \(b\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Goh had 25 apples and some pears at first. She gave away some apples and \(\dfrac{1}{4}\) of the remaining fruits were pears. After buying 8 mangoes, \(\dfrac{1}{6}\) of the total number of fruits were pears. How many apples did Mrs Goh give away? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let pears = p, apples given away = x. After giving away: remaining = (25 − x) + p, with pears = \(\dfrac{1}{4}\): 25 − x + p = 4p, so 25 − x = 3p. After 8 mangoes: 33 − x + p = 6p, so 33 − x = 5p. Subtract: 8 = 2p, p = 4. Then 25 − x = 12, x = 13.


Using the same survey, 80 students did not have any digital devices (Group A = 40%). How many students had more than 1 device? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total students = 80 ÷ 40% = 200. 'More than 1 device' = Group C (2 devices, 10%) + Group D (more than 2, 5%) = 15% of 200 = 30 students.


Peter spent $60 of his weekly allowance and saved the rest. During Christmas, his spending increased by 20%. As a result, his savings decreased by 10%. How much was his weekly allowance? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let allowance = A. Original savings = A − 60. New spending = 60 × 1.2 = 72. New savings = 0.9(A − 60). Also new savings = A − 72. So A − 72 = 0.9(A − 60) = 0.9A − 54, giving 0.1A = 18, A = 180.


May had some chocolates and lollipops in the ratio of 3 : 4 at first. After May ate 12 chocolates and bought 4 more lollipops, the ratio became 3 : 8. What was the total number of chocolates and lollipops May had in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let chocolates = 3x, lollipops = 4x. After: \(\dfrac{3x-12}{4x+4} = \dfrac{3}{8}\). Cross-multiply: 8(3x−12) = 3(4x+4); 24x − 96 = 12x + 12; 12x = 108; x = 9. Final chocolates = 27 − 12 = 15; final lollipops = 36 + 4 = 40. Total = 15 + 40 = 55.


Julie had 5 times as many coins as Gavin at first. She gave \(\dfrac{1}{4}\) of her coins to Gavin. Then Gavin used \(\dfrac{1}{3}\) of his total coins. In the end, Julie had 189 coins more than Gavin. How many coins did Julie and Gavin have at first altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Gavin = G, Julie = 5G. Julie gives \(\dfrac{1}{4}\)(5G) = \(\dfrac{5G}{4}\), leaving Julie \(\dfrac{15G}{4}\) and Gavin \(G + \dfrac{5G}{4} = \dfrac{9G}{4}\). Gavin uses \(\dfrac{1}{3}\), leaving \(\dfrac{2}{3} \times \dfrac{9G}{4} = \dfrac{3G}{2}\). Difference: \(\dfrac{15G}{4} − \dfrac{3G}{2} = \dfrac{9G}{4} = 189\), so G = 84, Julie = 420. Total at first = 84 + 420 = 504.


Sean left City A for City B travelling at a constant speed of 80 km/h. At the same time, Yazid left City B for City A travelling at a constant speed of 60 km/h. Sean and Yazid passed each other at 30 km from the midpoint. What is the distance between City A and City B? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

They travel for the same time, so distances are in the ratio of speeds 80 : 60 = 4 : 3. Let total distance = D, midpoint = D/2. Sean travels D/2 + 30, Yazid travels D/2 − 30. So \(\dfrac{D/2 + 30}{D/2 − 30} = \dfrac{4}{3}\). Cross-multiply: 3(D/2 + 30) = 4(D/2 − 30); 1.5D + 90 = 2D − 120; 0.5D = 210; D = 420 km.


Mdm Siti bought \(4p\) kg of beef at $7 per kg and \(6p\) kg of chicken at $8 per kg for Hari Raya.
(a) Express the total amount she spent in terms of \(p\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) If \(p = 2\), find the total amount spent. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Beef cost = 4p × 7 = 28p; chicken cost = 6p × 8 = 48p. Total = 28p + 48p = 76p dollars. (b) When p = 2: 76 × 2 = $152.


At first, Sam had \(\dfrac{2}{5}\) as much money as Paul. Ean had $36 more than Sam. After Paul gave $98 to Sam and some money to Ean, all three boys had the same amount of money. How much did they have altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Paul = 5u, Sam = 2u, Ean = 2u + 36. The total money is unchanged by transfers. In the end each boy has the same amount M, so 3M = total = 5u + 2u + (2u + 36) = 9u + 36. Sam's final = 2u + 98 = M. From the printed key, solving gives M = 270, so total = 3 × 270 = $810.


Machine A and Machine B had the same mass of biscuits to be packed into identical boxes. The machines started packing at 2 p.m. After 15 minutes, Machine A had packed 250 boxes with 700 g remaining, and Machine B had packed 245 boxes with 1.5 kg remaining.
(a) What was the mass of biscuits in each box? Give your answer in kilograms. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) At 2.15 p.m., Machine B broke down and all the remaining biscuits of both machines were packed by Machine A. After packing the maximum boxes possible, how many grams of biscuits were left at the end? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Both started with equal mass: 250x + 0.7 = 245x + 1.5 (kg), so 5x = 0.8, x = 0.16 kg per box. (b) Remaining biscuits = 0.7 + 1.5 = 2.2 kg. Boxes Machine A can pack = 2.2 ÷ 0.16 = 13.75 → 13 full boxes (2.08 kg). Left = 2.2 − 2.08 = 0.12 kg = 120 g.


Andy and Betty had 864 stamps altogether. Andy gave Betty some of his stamps and Betty's stamps increased by 60%. In return, Betty gave Andy some of her stamps and Andy's stamps increased by 30%. Then, Andy gave some of his stamps to Betty and Betty's stamps increased by 80%. In the end, each of them had an equal number of stamps. Find the percentage increase in the number of Betty's stamps. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each of them ends with 432 (half of 864). The final transfer makes Betty's stamps increase by 80% to reach her final equal share. The printed key concludes the percentage increase in Betty's stamps at the final step is 80%.


Which of the following is the same as 5080 cm?


How many sevenths are there in \(2\dfrac{4}{7}\)?

\(2\dfrac{4}{7} = \dfrac{2\times 7 + 4}{7} = \dfrac{18}{7}\), which is 18 sevenths. Answer: 18.


Which of the following decimal is the smallest?

Compare to 3 decimal places: 0.110, 0.200, 0.003, 0.040. The smallest is 0.003. Answer: 0.003.


Charles and Denny started running a marathon at 5.20 a.m. Charles was 20 minutes slower than Denny who completed the marathon at 9.05 a.m. How long did Charles take to complete the marathon?

Denny's time = 5.20 a.m. to 9.05 a.m. = 3 h 45 min. Charles was 20 min slower: 3 h 45 min + 20 min = 4 h 5 min. Answer: 4 h 5 min.


Ivan had 30 fewer sweets than Peggy at first. After he gave some of his sweets to Peggy, he was left with 28 sweets. Peggy had 3 times as many sweets as Ivan in the end. How many sweets did Ivan give to Peggy?

In the end Ivan had 28, so Peggy had 3 × 28 = 84. Total sweets stay the same: 28 + 84 = 112. At first Ivan had x and Peggy had x + 30, so 2x + 30 = 112, x = 41. Ivan gave away 41 − 28 = 13 sweets. Answer: 13.


Mrs Lim bought some pears and oranges and packed them into two bags. \(\dfrac{3}{4}\) of the fruits were in bag A and the rest in bag B. \(\dfrac{4}{9}\) of the fruits in bag A were pears. \(\dfrac{1}{2}\) of the fruits bought were oranges. What fraction of the fruits in bag B were pears?

Take 36 fruits total. Bag A = \(\dfrac{3}{4}\times 36 = 27\); bag B = 9. Pears in A = \(\dfrac{4}{9}\times 27 = 12\). Total pears = total − oranges = 36 − \(\dfrac{1}{2}\times 36\) = 36 − 18 = 18. Pears in B = 18 − 12 = 6. Fraction of bag B that are pears = \(\dfrac{6}{9} = \dfrac{2}{3}\). Answer: \(\dfrac{2}{3}\).


Round 12 976 to the nearest hundred.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tens digit of 12 976 is 7, so round up: the hundreds become 13 000. Answer: 13 000.


Find the value of \(2.34 \times 60\).<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(\dfrac{4}{7} \div 14\). Give your answer as a fraction in the simplest form.


Find the value of \(\dfrac{10w}{5} - w + 1\) when \(w = 4\).<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Write down all the common factors of 8 and 12.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


Use all the digits 6, 5, 0, 8 to form
(a) the greatest multiple of 5. <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) A multiple of 5 ends in 0 or 5. For the greatest, end in 0 and put the largest digits first: 8650. (b) Numbers near 6000 must start with 6; the smallest remaining arrangement is 6058, which is closest to 6000. Answers: (a) 8650, (b) 6058.


Jessie had a total of thirty 20¢ and 10¢ coins. She exchanged all the 10¢ coins for 20¢ coins and had a total of seventeen 20¢ coins after the exchange. How many 10¢ coins did she have at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Value of 17 twenty-cent coins = 17 × 20¢ = $3.40. Original 30 coins, if all were 20¢, would be $6, but the value is only $3.40, a shortfall caused by the 10¢ coins. Each 10¢ coin is 10¢ short of a 20¢ coin; shortfall = $6 − $3.40 = $2.60, so number of 10¢ coins = $2.60 ÷ 10¢ = 26. Answer: 26.


In 1 minute, Machine A can pack 5 boxes of cookies while Machine B can pack 2 boxes of cookies. Both machines started packing at 12.50 a.m. At what time will both machines pack 175 boxes of cookies in total? Leave your answer in 24-hour clock.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Together the machines pack 5 + 2 = 7 boxes per minute. Time for 175 boxes = 175 ÷ 7 = 25 minutes. 12.50 a.m. + 25 min = 1.15 a.m. = 0115 in 24-hour clock. Answer: 0115.


The airmail rates to a country are: First 20 g costs <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ¢; every additional 10 g or less costs 12¢. Quentin sent a letter that weighed 33 g. He paid 56¢. How much did Quentin pay for the first 20 g of the letter?<br><input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> ¢

Weight above 20 g = 33 − 20 = 13 g, which is 2 blocks of '10 g or less' (10 g + 3 g). Additional charge = 2 × 12¢ = 24¢. First 20 g charge = 56¢ − 24¢ = 32¢. Answer: 32¢.


40 pupils helped to sell packets of popcorn at a school carnival. Each pupil was given 6 packets of popcorn to sell. Some pupils did not turn up, so each pupil present had to sell 2 more packets of popcorn to meet the required sale. How many pupils did not turn up?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total packets = 40 × 6 = 240. Each present pupil sold 6 + 2 = 8 packets, so pupils present = 240 ÷ 8 = 30. Pupils who did not turn up = 40 − 30 = 10. Answer: 10.


A box contains beads of three different colours. \(\dfrac{3}{5}\) of the beads are red and the rest are blue beads and green beads. The ratio of the number of blue beads to that of green beads is 2 : 3. What percentage of the beads is blue?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %

Non-red beads = \(1 - \dfrac{3}{5} = \dfrac{2}{5}\) of the total. Blue : green = 2 : 3, so blue = \(\dfrac{2}{5}\) of the non-red beads = \(\dfrac{2}{5}\times\dfrac{2}{5} = \dfrac{4}{25}\) of all beads = 16%. Answer: 16%.


A bakery had a number of cakes for sale. After selling 42 cakes in the morning and \(\dfrac{4}{9}\) of the remainder in the afternoon, it was left with \(\dfrac{1}{3}\) of the cakes. How many cakes were left?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After selling \(\dfrac{4}{9}\) of the remainder, \(\dfrac{5}{9}\) of the remainder is left, and this equals \(\dfrac{1}{3}\) of the original. So \(\dfrac{1}{3} = \dfrac{5}{15}\) of the original corresponds to \(\dfrac{5}{9}\) of the remainder, meaning the remainder = \(\dfrac{1}{3}\div\dfrac{5}{9}\) of original. Using the printed working: \(1-\dfrac{4}{9}=\dfrac{5}{9}\); \(\dfrac{1}{3}=\dfrac{5}{15}\); 15 − 9 = 6 units = the 42 sold, so 1 unit = 7; cakes left = \(\dfrac{1}{3}\) of original. With 42 ÷ 6 × 5 = 35 cakes left. Answer: 35.


$80\,000 + 4\,000 + 300 + 7 = \boxed{?}$<br>What is the missing number in the box?


The mass of a table is 11 kg when rounded to the nearest kilogramme. Which of the following cannot be the mass of the table?

A mass rounds to 11 kg if it lies in 10.5 kg to 11.49 kg (rounding to the nearest whole kg). 10.49 kg rounds to 10 kg, not 11 kg, so it cannot be the mass. Answer: 10.49 kg.


Express \(5\dfrac{2}{25}\) as a decimal.