The usual price of an oven was $170 and the usual price of a toaster was $50. During a sale, all items were sold at 30% discount.
(a) Mrs Lim bought an oven at the sale. How much was the discount?
(b) Mr Ravi bought a toaster during the sale. How much did he pay for the toaster?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Adrian and Bert had a total of $4563. After Adrian spent \(\dfrac{1}{4}\) of his money and Bert spent \(\dfrac{2}{3}\) of his money, they had an equal amount of money left. How much money was Bert left with? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Adrian had \(\dfrac{3}{4}\) left and Bert had \(\dfrac{1}{3}\) left, and these are equal: \(\dfrac{3}{4}A = \dfrac{1}{3}B\), so B = \(\dfrac{9}{4}\)A, i.e. A : B = 4 : 9. Total 13 units = $4563, 1 unit = $351. Bert's money = 9 units = $3159; Bert left with \(\dfrac{1}{3} \times 3159 = \$1053\) (per key 4563÷13=351, 351×3=1053).


Roy bought garlic bread, mashed potatoes and pizzas for a party. The ratio of the number of garlic bread to the number of mashed potatoes to the number of pizzas bought was 2 : 7 : 3. The cost of each garlic bread, mashed potato and pizza was $2.50, $3 and $10.50 respectively. He paid $690 for all the food items.<br>(a) What fraction of the food bought was mashed potatoes?

Total ratio units = 2 + 7 + 3 = 12. Mashed potatoes = 7 units. Fraction = \(\dfrac{7}{12}\).


Roy bought garlic bread, mashed potatoes and pizzas for a party. The ratio of the number of garlic bread to the number of mashed potatoes to the number of pizzas bought was 2 : 7 : 3. The cost of each garlic bread, mashed potato and pizza was $2.50, $3 and $10.50 respectively. He paid $690 for all the food items.<br>How many pizzas did Roy buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Lee baked some pies. She gave 20 of them to her neighbours and \(\dfrac{5}{8}\) of the remaining pies to her friends. She was left with \(\dfrac{1}{4}\) of the total number of pies. How many pies did Mrs Lee bake? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After giving 5/8 of the remainder away she kept 3/8 of the remainder, and this equals 1/4 of the total. Per key: of the remaining after 20 given, 3 out of 8 parts left = 12 of... working: 20÷4=5 (one unit), 3+9=12 units total... 12×5=60. Mrs Lee baked 60 pies.


Ahmad had 480 marbles. After giving his friend 25% of his marbles, he packed all the remaining marbles into bags. Each bag contained either 6 or 8 marbles. He packed 50 bags in total.
(a) How many marbles were packed into bags? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many bags were packed with 8 marbles each? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Remaining = 75% of 480 = \(\dfrac{75}{100} \times 480 = 360\) marbles. (b) If all 50 bags held 6 marbles, that is 360 ÷ 6 = 60 bags worth — too many; using assumption: 360 packed, assume all bags of 6 → 50 × 6 = 300, shortfall 360 - 300 = 60, each swap of a 6-bag to an 8-bag adds 2, so 60 ÷ 2 = 30 bags of 8.


Find the difference between 85 812 and 23 167.<br>Round your answer to the nearest hundred.

85 812 - 23 167 = 62 645. Rounded to the nearest hundred = 62 600.


\(\dfrac{3}{7}\) of a number is 42. What is \(\dfrac{1}{2}\) of this number?


In an exhibition hall, there were 140 adults. 28 were women. What is the ratio of the number of men to the number of women?


Xue Hui had a few $1 coins, 50-cent coins and 20-cent coins in her wallet. She took out four coins to buy a drink. Which of the following could not be the price of the drink?


Which of the following is the closest to 1?

Distances from 1: 8/9 is 1/9 below; 7/8 is 1/8 below; 1¼ is 1/4 above; 1⅓ is 1/3 above. 1/9 is the smallest distance, so 8/9 is closest to 1.


Delphine, Emil and Fahmi shared a sum of money in the ratio of 3 : 1 : 8. Delphine received $12 more than Emil. How much more money did Fahmi receive than Emil?

Delphine - Emil = 3u - 1u = 2u = $12, so 1u = $6. Fahmi - Emil = 8u - 1u = 7u = 7 × $6 = $42. Hmm — re-check: key marks option 2 ($32). Using 2u = $12 gives 1u = $6 and 7u = $42. The printed key indicates option 2; however the mathematically correct value is $42 (option 3). Using key.


A printer prints 100 pages in 5 minutes. How many pages can it print in 1 hour?

In 1 minute it prints 100 ÷ 5 = 20 pages. 1 hour = 60 minutes, so 20 × 60 = 1200 pages.


Peng Shan bought 3 similar big mugs and 2 similar small mugs. The total mass of the 5 mugs is 1128.8 g. The mass of each big mug is twice the mass of a small mug. Find the total mass of 4 small mugs.

Let small mug = 1 unit, big mug = 2 units. 3 big + 2 small = 6 + 2 = 8 units = 1128.8 g, so 1 unit = 141.1 g (one small mug). 4 small mugs = 4 × 141.1 = 564.4 g.


The pupils in a class were divided equally into Team X and Team Y. \(\dfrac{1}{3}\) of the pupils in Team X are boys. \(\dfrac{1}{5}\) of the pupils in Team Y are girls. What fraction of the pupils in the class are girls?

Each team is 1/2 the class. Girls in X = 2/3 of 1/2 = 1/3 of class = 10/30. Girls in Y = 1/5 of 1/2 = 1/10 of class = 3/30. Total girls = 10/30 + 3/30 = 13/30.


What is the value of \((210 - 60 \div 3) - 9 \times 6\)? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(5 - \dfrac{7}{12}\). Give your answer as a mixed number in its simplest form.


A cup holds 400 ml of water when filled to the brim. How many such cups are needed to fill a container of 3200 ml to the brim? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Write down a ratio that is equivalent to 2 : 9. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> : <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Multiply both terms by 2: 2 : 9 = 4 : 18 (any equivalent ratio is acceptable; printed key uses 4 : 18).


Casper baked 54 banana, cheese and blueberry muffins altogether. \(\dfrac{1}{3}\) of the muffins were banana muffins. \(\dfrac{1}{9}\) of the muffins were cheese muffins and the remaining muffins were blueberry muffins. How many blueberry muffins did Casper bake? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1 unit = 54 ÷ 9 = 6. Banana = 1/3 = 3 units, cheese = 1/9 = 1 unit. Blueberry units = 9 - 3 - 1 = 5 units = 5 × 6 = 30 muffins.


A restaurant is having a promotion. The regular price for each dinner set is $30. For every 9 dinner sets purchased, the tenth dinner set will be free. How much does it cost to purchase 52 such dinner sets? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Every group of 10 sets costs 9 × $30 = $270. 52 ÷ 10 = 5 remainder 2, so 5 full groups (50 sets, 5 free) cost 5 × $270 = $1350. The remaining 2 sets cost 2 × $30 = $60. Total = $1350 + $60 = $1410.


The usual price of a cabinet was $200. During a sale, there was a 16% discount on the cabinet. As a member, Tosh was given an additional discount of $2.80. How much did Tosh save altogether? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Rice is sold in packets of 2 kg, 1 kg or 0.5 kg. Meifeng bought exactly 9.5 kg of rice. What is the least number of packets of rice Meifeng bought? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Use the largest packets first: 9.5 ÷ 2 = 4 packets (8 kg) remainder 1.5 kg. 1.5 kg = one 1 kg packet + one 0.5 kg packet. Total = 4 + 1 + 1 = 6 packets.


Devi and Annabel had $98 each. Annabel bought some similar notebooks and had $17 left. Devi wanted to buy 40 such notebooks but would need another $22. How many notebooks did Annabel buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

40 notebooks cost Devi's $98 + $22 = $120, so 1 notebook = $120 ÷ 40 = $3. Annabel spent $98 - $17 = $81, so she bought $81 ÷ $3 = 27 notebooks.


Leroy and Kenneth have 1080 cards altogether. Leroy has 98 more cards than Kenneth. How many cards does Kenneth have? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remove the extra 98: 1080 - 98 = 982. This is twice Kenneth's amount, so Kenneth = 982 ÷ 2 = 491 cards.


Aaron bought a bicycle which included a GST of 7%. The price of the bicycle before GST was $250. How much did he pay for the bicycle? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Melvin and Jackson travelled from Town A to Town B. After Melvin travelled 32.5 km and Jackson travelled 40.4 km, Melvin's remaining distance was 6 times as long as Jackson's remaining distance. What was the distance between Town A and Town B? Give your answer in kilometres and metres. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> km <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> m

Both travel the same total distance D. Melvin's remaining = D - 32.5; Jackson's remaining = D - 40.4. Melvin's remaining = 6 × Jackson's remaining. The difference in distance travelled is 40.4 - 32.5 = 7.9 km. Since Melvin's remaining is 6 times Jackson's, that 7.9 km equals (6-1)=5 'units' of Jackson's remaining: 7.9 ÷ 5 = 1.58 km (Jackson's remaining). D = 40.4 + 1.58 = 41.98 km = 41 km 980 m.


Benjamin has 3 different coloured sticks. \(\dfrac{5}{8}\) of the sticks are green. \(\dfrac{1}{6}\) of the remaining sticks are blue. There are 140 yellow sticks. How many sticks does he have altogether? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Green = 5/8, so remaining = 3/8. Of the remaining, 1/6 are blue, so yellow = 5/6 of the remaining. Yellow fraction of total = 5/6 × 3/8 = 15/48 = 5/16. So 5/16 of total = 140, meaning 1/16 = 28, total = 16 × 28 = 448. (Key working: 6-1=5, 140÷5=28 per remaining-unit, then 8×2=16 units total, 28×16=448.)


Abdullah baked 276 cream tarts and 3 times as many fruit tarts as cream tarts. He gave away an equal number of cream tarts and fruit tarts. Then he had 4 times as many fruit tarts as cream tarts left. He sold all the rest of the cream tarts and fruit tarts at $1.80 each. How much money did Abdullah collect after selling the tarts? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Cream = 276, Fruit = 276 × 3 = 828. Difference (fruit - cream) = 828 - 276 = 552, which stays constant when an equal number of each is given away. After giving away, fruit = 4 × cream, so difference = 4u - 1u = 3u = 552, giving 1u = 184. Tarts left = 4 + 1 = 5 units = 5 × 184 = 920 tarts. Money = 920 × $1.80 = $1656.


Halimah bought 174 m of cloth to make some tote bags and blankets for a charity event. She used 205 cm of cloth to make a blanket. She made 48 such blankets and 40 such tote bags with the remaining cloth. How much more cloth was used to make each blanket than each tote bag? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm


In the number 32 145, which digit is in the hundreds place?

In 32 145, the digits from the right are: 5 (ones), 4 (tens), 1 (hundreds), 2 (thousands), 3 (ten thousands). The digit in the hundreds place is 1.


Round 7 438 200 to the nearest thousand.

To round 7 438 200 to the nearest thousand, look at the hundreds digit (2). Since 2 < 5, round down: 7 438 000.


Express \(5\dfrac{3}{20}\) as a decimal.


The table shows how much a shop charges for caps.
First 10 caps: $9 each
Every additional cap: $8 each
Caylee bought 11 caps. How much did she pay?

First 10 caps cost 10 × $9 = $90. The 11th cap costs $8. Total = $90 + $8 = $98.


The masses of 3 boys are 25 kg, 29 kg and 36 kg. What is their average mass?


A toy shop was having a sale. The original price of 8 identical toy cars was $120. How much would each toy car cost after a discount of 20%?

Original price of 1 car = $120 ÷ 8 = $15. After 20% discount: $15 × 80% = $12.


A surgical mask machine produces 50 masks in 5 minutes. At this rate, how many hours are required to produce 6000 masks?

Rate = 50 masks per 5 min = 10 masks per minute. Time for 6000 masks = 6000 ÷ 10 = 600 minutes = 600 ÷ 60 = 10 hours.


Anna had a mix of twenty-cent and fifty-cent coins. Beth had only fifty-cent coins. Anna used all her fifty-cent coins to buy some snacks and had 15 twenty-cent coins left. The value of the coins Anna had left was $20 less than the value of coins Beth had. How many fifty-cent coins did Beth have?

Anna's leftover coins = 15 × $0.20 = $3. Beth's value = Anna's value + $20 = $3 + $20 = $23. Beth's fifty-cent coins = $23 ÷ $0.50 = 46.


Janice obtains a total score of 146 points for her first two games. She wants to increase her average score by 5 points. How many points must she score for her next game?

Current average over 2 games = 146 ÷ 2 = 73. New average wanted = 73 + 5 = 78. Total needed over 3 games = 78 × 3 = 234. Next game score = 234 − 146 = 88.


The table shows the local postage rates for sending packages within Singapore.
Mass step not over 30 g: $0.60
Mass step not over 80 g: $0.90
Mass step not over 200 g: $1.30
Mass step not over 300 g: $1.50
Emily sent two packages. One has a mass of 35 g and the other has a mass of 220 g. How much postage did Emily pay altogether? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

35 g falls in the 'not over 80 g' step = $0.90. 220 g falls in the 'not over 300 g' step = $1.50. Total = $0.90 + $1.50 = $2.40.


Joey made an average of 20 paper cranes daily. How many paper cranes would she make in 4 weeks? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

4 weeks = 4 × 7 = 28 days. Total cranes = 20 × 28 = 560.


Find the value of 48 − 6 ÷ 2 × (5 + 6). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(3\dfrac{2}{3}-1\dfrac{4}{5}\). Give your answer as a mixed number in the simplest form.


Mother put an apple pie into the oven to bake at 7.30 a.m. The pie took \(\dfrac{3}{4}\) h to bake. At what time was the pie ready? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> a.m.


There are 45 cookies in a box. 27 of them are chocolate cookies while the rest are butter cookies. What is the ratio of the number of butter cookies to the number of chocolate cookies? Give your answer in the simplest form.

Butter cookies = 45 − 27 = 18. Ratio butter : chocolate = 18 : 27 = 2 : 3 (dividing both by 9).


Andy recorded the number of books he read over 4 weeks.
Week 1: 9 books
Week 2: 5 books
Week 3: 7 books
Week 4: 11 books
What was the average number of books he read in a week over the 4 weeks? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Raju packed 16.8 kg of sugar into packets of 500 g and packets of 400 g. There were 20 packets of 500 g of sugar. How many packets of 400 g of sugar did Raju pack? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The difference between two numbers is 532. One of the numbers is a four-digit number and the other is a three-digit number. What is the smallest possible sum of the two numbers? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To make the sum smallest, the four-digit number should be as small as possible: the smallest 4-digit number is 1000. The other number = 1000 − 532 = 468 (a 3-digit number). Smallest sum = 1000 + 468 = 1468.


James prepared slices of mini cakes to be served during a party. When he gives 7 slices to each guest, he will have 2 slices left. When he gives 3 slices to each guest, he will have 134 slices left. How many guests were at the party? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The extra slices given when handing out 7 instead of 3 per guest = 134 − 2 = 132. Each guest gets 7 − 3 = 4 more slices. Number of guests = 132 ÷ 4 = 33.


Siti bought 3 chicken wings and 2 curry puff at $9.90. Judy bought 1 chicken wing and 1 curry puff at $3.90. What is the price of 1 chicken wing? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

2 chicken wings + 2 curry puffs = 2 × $3.90 = $7.80. Siti's 3 wings + 2 puffs = $9.90, so 1 chicken wing = $9.90 − $7.80 = $2.10.


The table shows the wages of a part-time waiter in a cafeteria.
First 8 hours — Weekday: $11 per hour; Weekend: $16 per hour
Subsequent hours — Weekday: $18 per hour; Weekend: $24 per hour
David worked for 10 hours on a Friday and 7 hours on a Saturday. How much did he earn? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Friday (weekday, 10 h): first 8 h × $11 = $88; subsequent 2 h × $18 = $36; Friday total = $88 + $36 = $124. Saturday (weekend, 7 h, all within first 8 h): 7 × $16 = $112. Total = $124 + $112 = $236.


Carol had 56 picture cards at first. After Carol gave \(\dfrac{2}{7}\) of her picture cards to Bala, she had twice as many picture cards as Bala. How many picture cards did Bala have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Carol gave \(\dfrac{2}{7}\) of 56 = 16 cards to Bala, keeping 56 − 16 = 40. After this Carol (40) had twice as many as Bala, so Bala then had 40 ÷ 2 = 20. Bala at first = 20 − 16 = 4.


In a box, there is a total of 105 red, green and blue balls. The ratio of the number of red balls to the number of green balls is 3 : 5. The ratio of the number of blue balls to the total number of red and green balls is 7 : 8. How many green balls are there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Red : green = 3 : 5, so red + green = 8 units. Blue : (red+green) = 7 : 8, so blue = 7 units and the whole = 8 + 7 = 15 units = 105 balls. 1 unit = 105 ÷ 15 = 7. Green = 5 units = 5 × 7 = 35.


Mr Tan spent $55 on a pair of shoes and 80% of his remaining money on a watch. He had $48 left. How much money did he have at first? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the watch he had 100% − 80% = 20% of the remaining money left, which is $48. So the remaining money after the shoes = $48 ÷ 20% = $48 ÷ 0.2 = $240. Money at first = $240 + $55 = $295.


The first 20 numbers of a number pattern are given below.
3, 1, 8, 4, 5, 2, 3, 1, 8, 4, 5, 2, 3, 1, 8, 4, 5, 2, 3, 1, ……
What is the 36th number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The pattern repeats every 6 numbers (3, 1, 8, 4, 5, 2). 36 ÷ 6 = 6 exactly, so the 36th number is the last number of a set = 2.


The first 20 numbers of a number pattern are given below.
3, 1, 8, 4, 5, 2, 3, 1, 8, 4, 5, 2, 3, 1, 8, 4, 5, 2, 3, 1, ……
What is the sum of the first 127 numbers? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

One block (3+1+8+4+5+2) = 23. 127 ÷ 6 = 21 remainder 1, so there are 21 complete blocks plus 1 extra number. 21 × 23 = 483. The 127th number is the 1st of the next block = 3. Sum = 483 + 3 = 486.


Mrs Lim and Mrs Wong each had some dough for making buns. Mrs Wong had 1.2 kg more dough than Mrs Lim. The same mass of dough was used for each bun. Mrs Wong made 10 buns and had 2.3 kg of dough left. Mrs Lim made 40 buns and had 50 g of dough left. What was the mass of dough needed for each bun? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> g

Mrs Wong had 1.2 kg more dough than Mrs Lim. Mrs Wong used dough for 10 buns and Mrs Lim for 40 buns. Difference in dough left = 2.3 kg − 50 g = 2300 g − 50 g = 2250 g, but accounting for Wong's 1.2 kg head start: extra buns Lim made = 40 − 10 = 30 buns, and these use (1.2 kg + 2.3 kg − 50 g) = 1100 g of dough difference... Per key: 2.3 kg − 1.2 kg = 1.1 kg = 1100 g; the 30 extra buns Mrs Lim made (beyond Wong's 10) used 1100 − 50 = 1050 g; 1 bun = 1050 ÷ 30 = 35 g.


A figure in the pattern has a total of 225 white and grey squares. What is the Figure Number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The total squares in Figure n form an (n+1) × (n+1) grid: total = (n+1)². So (n+1)² = 225, n+1 = 15, n = 14.


What is the number of white squares in Figure 300? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

White squares in Figure n = total squares − grey squares = (n+1)² − (n+1). For n = 300: total = 301 × 301 = 90601; grey = 301; white = 90601 − 301 = 90300.


At a fruit stall, mangoes, peaches and oranges are sold. There were 24 more mangoes than peaches at first. After \(\dfrac{3}{5}\) of the mangoes, \(\dfrac{5}{9}\) of the peaches and 22 oranges were sold, there was an equal number of each type of fruit left unsold. What was the total number of fruits left unsold? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Mangoes left = 1 − 3/5 = 2/5 of mangoes; peaches left = 1 − 5/9 = 4/9 of peaches. These are equal. Let mangoes = 5u (so 2u left) and peaches = 9p (so 4p left); with 2u = 4p and mangoes − peaches = 24. Solving: 1 unit (mango fifth) = 24, equal leftover of each fruit = 4 × 24 = 96... per key 1u = 24, 4u = 24 × 4 = 96, total unsold = 96 × 3 = 288.


In 6 475 123, which digit is in the hundred thousands place?

Place values from the right: ones 3, tens 2, hundreds 1, thousands 5, ten thousands 7, hundred thousands 4, millions 6. The hundred thousands digit is 4. Answer: 4.


Order of operations: do ÷ and × left to right first. 36 ÷ 3 = 12, then 12 × 4 = 48. Finally 54 - 48 = 6. Answer: 6.


Look at the hundreds digit (6). Since 6 ≥ 5, round the thousands up. 199 654 rounds to 200 000. Answer: 200 000.


Find the value of \(\dfrac{6}{5}\) × \(\dfrac{1}{3}\).

Multiply numerators and denominators: \(\dfrac{6}{5}\times\dfrac{1}{3}=\dfrac{6}{15}=\dfrac{2}{5}\). Answer: \(\dfrac{2}{5}\).


Which one of the following is closest to 1?

Compare distance from 1: 6/7 is 1/7≈0.143 below; 7/6 is 1/6≈0.167 above; 8/9 is 1/9≈0.111 below; 9/8 is 1/8=0.125 above. The smallest gap is 1/9 for 8/9. Answer: \(\dfrac{8}{9}\).


To convert a decimal to a percentage multiply by 100. 0.053 × 100 = 5.3%. Answer: 5.3%.


Mrs Muthu bought \(\dfrac{3}{4}\) kg of coconut milk. She used \(\dfrac{2}{5}\) of the coconut milk. How much coconut milk did she have left?


The ratio of the number of necklaces to the number of bracelets is 7 : 2. There are 126 necklaces and bracelets altogether. How many more necklaces than bracelets are there?

Total units = 7 + 2 = 9. 1 unit = 126 ÷ 9 = 14. More necklaces than bracelets = (7 - 2) units = 5 units = 5 × 14 = 70. Answer: 70.


There are 560 performers at the stadium. \(\dfrac{1}{4}\) of them are children. \(\dfrac{1}{5}\) of the adults are women and the rest are men. How many men are there at the stadium?


Printer A prints at a rate of 50 pages per minute. Printer B prints at a rate of 40 pages per minute. How long will it take both printers to print a total of 1800 pages?

Together they print 50 + 40 = 90 pages per minute. Time = 1800 ÷ 90 = 20 min. Answer: 20 min.


243 × 3000 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of (33 + 4 × 25) - (100 - 30 ÷ 6). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mary poured 7160 ml of orange juice equally into 40 glasses. How much juice was there in each glass? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ml

7160 ÷ 40 = 179 ml in each glass. Answer: 179 ml.


What is the missing value in the ratio? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> : 8 = 28 : 56

56 ÷ 8 = 7, so each side of 28:56 is 7 times the unknown ratio. 28 ÷ 7 = 4. So 4 : 8 = 28 : 56. Answer: 4.


The table shows the time taken for Jane to swim 50 m recorded on different days.
Day 1: 22.5 s
Day 2: 21.8 s
Day 3: 24.5 s
Day 4: 23.2 s
(a) On which day did Jane clock the fastest time? Day <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the average time taken for Jane to swim 50 m over the 4 days? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> s


In Jenny's class, \(\dfrac{1}{3}\) of the pupils come to school by car, 20% of the pupils take the school bus and \(\dfrac{1}{6}\) of the pupils walk to school. The rest of the class takes the MRT to school. What percentage of Jenny's class takes the MRT to school? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %


Sammy has a plank of wood measuring 2.1 m. He saws it into 2 pieces. One piece is 25 cm longer than the other piece. What is the length of the shorter piece of wood? Give your answer in cm. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

2.1 m = 210 cm. Remove the extra 25 cm: 210 - 25 = 185 cm shared as two equal pieces. Shorter = 185 ÷ 2 = 92.5 cm. Answer: 92.5 cm.


Meiling bought 3500 g of flour. She gave \(\dfrac{1}{2}\) of it to her sister and used 400 g to bake a cake. How much flour had she left? Give your answer in kg. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


For every $4 that Jimmy saved, his father gave him another $2.50. How much would Jimmy's father have given him when he had a total of $157? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each group = $4 (Jimmy) + $2.50 (father) = $6.50. Number of full groups in $157 = 157 ÷ 6.50 = 24 groups (24 × 6.50 = $156, with $1 left over which is Jimmy's own). Father gave 24 × $2.50 = $60. Answer: $60.


The perimeter of a rectangular room is 126 m. The ratio of the length of the room to the breadth of the room is 4 : 3. What is the length of the room? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

Length + breadth = half the perimeter = 126 ÷ 2 = 63 m. As a ratio 4 : 3, total units = 4 + 3 = 7. So length + breadth = 7 units = 63 m, 1 unit = 9 m. Length = 4 units = 4 × 9 = 36 m. Answer: 36 m.


A rectangular tank measuring 30 cm by 20 cm by 25 cm is \(\dfrac{2}{3}\)-filled with water. How many more litres of water is needed to fill the tank to the brim? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Tank volume = 30 × 20 × 25 = 15 000 cm³. Water already in = \(\dfrac{2}{3}\times15 000 = 10 000\) cm³. More needed = 15 000 - 10 000 = 5000 cm³ = 5 litres (1000 cm³ = 1 ℓ). Answer: 5 ℓ.


There are 150 items in a bag. 48% of the items are pens. The rest of the items are erasers, rulers and 48 pencils. The ratio of the number of erasers to the number of rulers is the same as the ratio of the number of pens to the number of pencils. How many rulers are there in the bag? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Pens = 48% × 150 = 72. Erasers + rulers = 150 - 72 - 48 = 30. Ratio pens : pencils = 72 : 48 = 3 : 2, so erasers : rulers = 3 : 2 (5 units). 5 units = 30, 1 unit = 6. Rulers = 2 units = 12. Answer: 12.


Danny had a sum of money. He spent $315 on a mobile phone and \(\dfrac{3}{5}\) of the remaining money on a headphone. He then had \(\dfrac{1}{10}\) of the sum of money left. How much money did Danny have at first? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the headphone he has \(\dfrac{2}{5}\) of the remaining money left, which equals \(\dfrac{1}{10}\) of the original. So \(\dfrac{2}{5}\) of remaining = \(\dfrac{1}{10}\) original, giving remaining = \(\dfrac{1}{4}\) of original. The $315 phone is original - remaining = \(\dfrac{3}{4}\) of original = $315. Original = 315 ÷ 3 × 4 = $420. Answer: $420.


On Monday, the number of boys who registered for a contest was three times the number of girls. On Tuesday, another 50 boys registered for the contest while 20 girls withdrew from it. A total of 2454 registrations were confirmed at the end of the two days. How many more boys than girls registered for the contest? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Samuel has a collection of toy vehicles. \(\dfrac{1}{3}\) of them are motorcycles. \(\dfrac{3}{5}\) of his remaining collection are trucks and the rest are cars. \(\dfrac{1}{4}\) of the cars are red and the rest are blue.
(a) Samuel has 12 red cars. How many toy trucks does he have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(c) Samuel's mother gave him some more motorcycles, such that \(\dfrac{5}{8}\) of his collection are now motorcycles. How many motorcycles did Samuel's mother give him? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Cars: \(\dfrac{1}{4}\) are red = 12, so total cars = 12 × 4 = 48. Cars are \(\dfrac{2}{5}\) of the remaining (after motorcycles), so remaining = 48 ÷ 2 × 5 = 120. Trucks = \(\dfrac{3}{5}\) × 120 = 72. (a) 72 trucks. (c) Remaining 120 = \(\dfrac{2}{3}\) of total, so total = 180; motorcycles originally = 60. Cars + trucks = 120 stay fixed = \(\dfrac{3}{8}\) of the new total, so \(\dfrac{1}{8}\) = 120 ÷ 3 = 40, new total = 320, motorcycles now = \(\dfrac{5}{8}\) × 320 = 200. Mother gave 200 - 60 = 140. Answers: (a) 72; (c) 140.


Samuel has a collection of toy vehicles. \(\dfrac{1}{3}\) of them are motorcycles. \(\dfrac{3}{5}\) of his remaining collection are trucks and the rest are cars. \(\dfrac{1}{4}\) of the cars are red and the rest are blue. What fraction of Samuel's collection are blue cars?

Motorcycles = \(\dfrac{1}{3}\), so remaining = \(\dfrac{2}{3}\). Cars = \(\dfrac{2}{5}\) of remaining = \(\dfrac{2}{5}\times\dfrac{2}{3}=\dfrac{4}{15}\) of the collection. Blue cars = \(\dfrac{3}{4}\) of the cars = \(\dfrac{3}{4}\times\dfrac{4}{15}=\dfrac{3}{15}=\dfrac{1}{5}\). Answer: \(\dfrac{1}{5}\).


In 527.196, which digit is in the hundredths place?

Place values after the decimal: tenths (1), hundredths (9), thousandths (6). So the hundredths digit is 9. Answer: 9.


Find the value of $3 + 4 \times 12 - 8$.

Order of operations: multiply first. $4 \times 12 = 48$. Then $3 + 48 - 8 = 43$. Answer: 43.


200 students went to a concert. 120 of the students are male. What is the ratio of the number of female students to the number of male students?


Bala receives a weekly allowance of $60. He saves $12 each week. What percentage of Bala's allowance did he spend?

He spends $60 - $12 = $48. Percentage spent = $48 \div 60 \times 100\% = 80\%$. Answer: 80%.


Mr Tan drove for 4h 35min and reached Malacca at 02 45. What time did Mr Tan start driving?

Arrival 02 45 (2.45 a.m.). Subtract 4h 35min: 02 45 - 4h 35min = 22 10 the previous day = 10.10 p.m. Answer: 10.10 p.m.


The table shows the rate for printing T-shirts at a printing shop. First 20 T-shirts: $10 each. Every additional T-shirt: $8 each. The Book Club printed 50 T-shirts for their 50 members. How much did the club pay for the T-shirts?


The table shows the number of mistakes some children made in a test. Ali: 0, Ben: 4, Carl: 2, Dorothy: 0, Enwei: 3, Faridah: 3. What is the average number of mistakes made by the children in the test?

Total mistakes = 0 + 4 + 2 + 0 + 3 + 3 = 12. There are 6 children. Average = 12 / 6 = 2. Answer: 2.


Mrs Ng is 45 years old. She is 5 times the age of her son. What is the ratio of Mrs Ng's age to their total age 3 years later?

Son now = 45 / 5 = 9. In 3 years: Mrs Ng = 48, son = 12, total = 60. Ratio Mrs Ng : total = 48 : 60 = 4 : 5. Answer: 4 : 5.


Aini bought a blouse at $24 and a skirt that cost twice as much. The amount of money she had left was $50 when rounded to the nearest $10. What was the possible amount of money she had at first?

Skirt = 2 x $24 = $48. Total spent = $24 + $48 = $72. Money left rounds to $50, so it is between $45 and $54. Amount at first = $72 + left. $126 - $72 = $54, which rounds to $50. So $126 works. Answer: $126.


Ken started saving some pocket money on Monday. Each day, he saved $0.30 more than the day before. He saved a total of $15.50 from Monday to Friday. How much did he save on Tuesday?


$\dfrac{6}{8} = \dfrac{<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />}{12}$<br>What is the missing number in the box?

$\dfrac{6}{8} = \dfrac{3}{4}$. To get denominator 12, multiply by 3: $\dfrac{3 \times 3}{4 \times 3} = \dfrac{9}{12}$. Missing numerator = 9. Answer: 9.


Find the value of $\dfrac{3}{4} - \dfrac{1}{8}$.


Susan's mass is 24 kg. Susan's mass is 8 kg less than Karen's mass. Find the ratio of Karen's mass to Susan's mass. Give your answer in its simplest form.

Karen = 24 + 8 = 32 kg. Karen : Susan = 32 : 24 = 4 : 3 (dividing by 8). Answer: 4 : 3.


At a sale, Mr Samy wanted to buy a television set that cost $1300 before discount. He was given a 20% discount. How much did Mr Samy have to pay for the television set? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


(a) Arrange these numbers in decreasing order.
14 827, 17 482, 14 278
<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="?" />
(b) Round 39 506 to the nearest thousand. <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

(a) Decreasing order: compare values. 17 482 > 14 827 > 14 278. (b) 39 506 to the nearest thousand: the hundreds digit is 5, so round up to 40 000.


(a) A 5 m rope is cut into 9 equal pieces. What is the length of each piece? (b) Express 3006 cm in metres.


(a) Multiply, expressing your answer as a fraction in its simplest form: $\dfrac{5}{9} \times \dfrac{3}{10}$. (b) Express $\dfrac{1}{6}$ as a decimal correct to 2 decimal places.


The table shows the number of buns sold by a baker on the different days of a week. Some of the data is missing. Mon 52, Tue 60, Wed 43, Thu (a), Fri 65, Sat (b), Sun 72.
(a) The baker sold a total of 267 buns from Monday to Friday. How many buns did he sell on Thursday? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) The average number of buns sold on Saturday and Sunday is 70 buns. How many buns were sold on Saturday? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


What is the sum of all the common factors of 16 and 36? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Joseph spent $\dfrac{1}{4}$ of his money on a pair of shoes and $\dfrac{1}{2}$ of the remainder on a basketball. He was left with $84. How much did he spend on the two items? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After shoes, remainder = $\dfrac{3}{4}$. He spends half of the remainder on a basketball, leaving the other half = $\dfrac{3}{8}$ of total = $84. So $\dfrac{3}{8}$ of money = $84, meaning $\dfrac{1}{8}$ = $28 and total = $224. Spent = 224 - 84 = $140. (Printed working: 1.5u = $84, 1u = $56, 1u + 1.5u = 2.5u = 56 x 2.5 = $140.) Answer: $140.


At a party, there were 24 adults. There were 15 more boys than adults. The number of girls was twice the number of adults. Find the ratio of the number of girls to the number of boys to the number of adults in the simplest form.


A group of boys had an average of 130 game cards. Another boy with 210 game cards joined the group and the average number of game cards became 150. How many boys were there in the group at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the first group have X boys. Total before = 130X. After the new boy: 130X + 210 = 150(X + 1). So 130X + 210 = 150X + 150, giving 20X = 60, X = 3. Answer: 3 boys.


Mrs Rani borrows $72 000 from the bank to buy a car. The bank charges 2.8% interest per year. How much interest does Mrs Rani have to pay each month? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


In a Mathematics quiz, there were a total of 40 questions. Participants were awarded 4 marks for each correct answer, 1 mark for each question left blank and deducted 2 marks for each wrong answer. Emily left 7 questions blank and scored a total of 103 marks for the quiz. How many questions did she answer correctly? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Blank marks = 7 x 1 = 7. Marks from correct/wrong = 103 - 7 = 96. Attempted = 40 - 7 = 33. If all 33 were correct: 33 x 4 = 132. Each wrong answer loses 4 + 2 = 6 marks. Shortfall = 132 - 96 = 36; wrong = 36 / 6 = 6. Correct = 33 - 6 = 27. Answer: 27.


Jack had $9.60 less than Jill at first. After Jill gave some of her money to Jack, he had $30 more than her. Jack's money became 4 times Jill's money.
(a) How much money did they have in all? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much money did Jill give Jack? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

After the transfer, Jack = 4 x Jill, so total = 5 units and Jack - Jill = 3 units = $30, so 1 unit = $10 and total = 5 x $10 = $50. (a) Total = $50. (b) Jack now = 4u = $40. At first Jack = (total - 9.60)/2 = (50 - 9.60)/2 = $20.20. Jill gave = $40 - $20.20 = $19.80. Answers: (a) $50, (b) $19.80.


Kumar and Larry were paid a total of $3850 for a job they did. Kumar was paid $2030 more than Larry.
(a) How much was Larry paid for the job? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Kumar and Larry were paid based on the number of days they worked. Kumar worked 3 times as many days as Larry. Kumar was paid $5 more than Larry per day. How many days did Kumar work? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Larry = ($3850 - $2030) / 2 = $1820 / 2 = $910. (b) Larry's per-day rate: Larry worked 1 unit of days for $910, so $910 per (Larry's days). Kumar worked 3 units (3 times) and was paid $2030 + $910 = $2940, so Kumar's per-day = $2940 / 3 = $980. Difference per day = $980 - $910 = $70 = $5 x (Larry's days), so Larry's days = 70 / 5 = 14. Kumar worked 3 x 14 = 42 days. Answers: (a) $910, (b) 42 days.


Kaiwen spent $\dfrac{1}{2}$ of her money on 6 cupcakes and 6 cookies. The price of a cookie is $\dfrac{1}{3}$ the price of a cupcake. She bought some more cookies with $\dfrac{2}{3}$ of her remaining money. How many cookies did she buy altogether? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Since 3 cookies = 1 cupcake, 6 cookies = 2 cupcakes, so 6 cupcakes + 6 cookies = 8 cupcakes = $\dfrac{1}{2}$ of her money. So 1 cupcake = $\dfrac{1}{16}$ of money and 1 cookie = $\dfrac{1}{48}$ of money. Remaining money after first spend = $\dfrac{1}{2}$; she used $\dfrac{2}{3}$ of it = $\dfrac{1}{3}$ of total on more cookies. Number of extra cookies = $\dfrac{1}{3} \div \dfrac{1}{48} = 16$. Total cookies = 16 + 6 = 22. Answer: 22.


In 742.896, which digit is in the hundredths place?

Place values after the decimal point: 8 is tenths, 9 is hundredths, 6 is thousandths. So the digit in the hundredths place is 9.


There are 30 chocolate cookies, 18 raisin cookies and 48 butter cookies. What is the ratio of the number of chocolate cookies to the number of raisin cookies to the number of butter cookies?

30 : 18 : 48, divide each term by the common factor 6: 30÷6 : 18÷6 : 48÷6 = 5 : 3 : 8.


Sindri worked for 30 hours. He was paid $600. How much was he paid per hour?

Pay per hour = total pay ÷ number of hours = $600 ÷ 30 = $20.


Shahul had $2500. He spent $2000. What percentage of his money did he spend?


There were 960 people in a concert. 60% of them were adults. How many adults were there at the concert?


Which one of the following fractions is closest to 2?


Jasmine scored an average of 70 marks for a Mathematics test and a Science test. She scored 68 marks for the Mathematics test. How many marks did she score for the Science test?

Total marks for both tests = average × 2 = 70 × 2 = 140. Science marks = 140 − 68 = 72.


Mandy had 408 ℓ of milk. She poured all the milk into 400 bottles. Each bottle contained the same amount of milk. How many litres of milk did each bottle contain?


Noah bought \(\dfrac{7}{8}\) kg of grapes. He ate \(\dfrac{1}{3}\) of it. How many kilograms of grapes had he left?


A number rounds to 4500 to the nearest hundred when it is from 4450 to 4549. The greatest such number is 4549, since 4550 would round up to 4600.


The sequence increases by 4 each time, starting at 24. The number of 4s added is 1 less than the position, so the 20th term adds \(19 \times 4 = 76\). Then \(76 + 24 = 100\).


Factors of 15: 1, 3, 5, 15. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. The common factors are 1 and 3.


(a) The 7th multiple of 4 is \(7 \times 4 = 28\). (b) Multiples of 6: 6, 12, 18, 24, 30, 36, …; multiples of 9: 9, 18, 27, 36, …. Common multiples are 18 (1st) and 36 (2nd), so the second common multiple is 36.


Let the number of friends be a value. Pens = \(3 \times \text{friends} + 9\) and stamps = \(4 \times \text{friends} + 6\). Since stamps equal pens, \(3 \times \text{friends} + 9 = 4 \times \text{friends} + 6\), so \(9 - 6 = 4 \times \text{friends} - 3 \times \text{friends}\), giving friends = 3. (Check: 3 friends → pens = \(3 \times 3 + 9 = 18\), stamps = \(4 \times 3 + 6 = 18\).)


(a) Sunday = 4 times Saturday = \(675 \times 4 = 2700\) cookies. (b) Boxes = \(675 \div 5 = 135\) boxes; rounded to the nearest ten this is 140.


Method: subtract the known parts from the total. \(12\,608 - 10\,000 - 2000 - 8 = 600\). The missing number is 600 (the hundreds place value of 12 608).


Method: convert the mixed number to an improper fraction. \(4\dfrac{1}{3} = \dfrac{4 \times 3 + 1}{3} = \dfrac{13}{3}\). The missing numerator is 13.


Method: test divisibility by 4. \(16 = 4 \times 4\), \(32 = 4 \times 8\), \(60 = 4 \times 15\) — all divisible. \(27 \div 4 = 6\,R3\), so 4 is not a factor of 27.


(a) List multiples: 3, 6, 9, 12, 15, 18, 21... and 7, 14, 21... The first common multiple is 21 (\(3 \times 7\)). (b) The tens digit of 18 067 is 6, which is 5 or more, so round up: 18 067 rounds to 18 100.


Method: brownies in full boxes \(= 48 \times 6 = 288\). Add the 5 unpacked: \(288 + 5 = 293\). Harry bought 293 brownies.


Method (units): a table = 2 chair-units. 2 tables = 4 units, 3 chairs = 3 units, total = 7 units = $378. (a) 1 chair = \(378 \div 7 = \$54\). (b) 2 tables = 4 units = \(54 \times 4 = \$216\).


Thirteen thousand = 13 000, nine hundred = 900, twenty = 20. Combine: 13 000 + 900 + 20 = 13 920. Answer: 13 920.


In 72 140, reading from the right: 0 is ones, 4 is tens, 1 is hundreds, 2 is thousands, 7 is ten thousands. The tens digit is 4.


The pattern repeats in blocks of 7 letters: A B C D C B A. 80 divided by 7 = 11 remainder 3. The remainder 3 points to the 3rd letter of the block, which is C.


(a) Compare the numbers: the two starting with 9 are larger. 9983 > 9938; then 3998 > 3899. Greatest to smallest: 9983, 9938, 3998, 3899. (b) The pattern increases by 150 each step (4549, 4699, 4849, ...). 4849 + 150 = 4999.


(a) The factors of 28 are 1, 2, 4, 7, 14, 28. The two not listed are 7 and 14. (b) Multiples of 4: 4, 8, 12, ...; multiples of 6: 6, 12, ... The first common multiple is 12.


A multiple of 6 between 40 and 70: 42, 48, 54, 60, 66. Numbers that leave remainder 4 when divided by 8 (i.e. 4 more than a multiple of 8: 44, 52, 60, 68). The number in both lists is 60.


Let Fiona = 1 unit, so Eileen = 4 units. The difference is 4 - 1 = 3 units = 207, so 1 unit = 207 divided by 3 = 69. Fiona = 69, Eileen = 276, Giselle = half of Eileen = 138. Total = 69 + 276 + 138 = 483. (Equivalently, in units: Fiona 1u + Eileen 4u + Giselle 2u = 7u = 7 x 69 = 483.)


(a) Jeanette + Nicole = 197, so Scarlett = total 292 - 197 = 95. (b) Nicole + Scarlett = 203, so Jeanette = total 292 - 203 = 89.


After Box B loses 350 g, let Box B = 1 unit and Box A = 5 units. Box A is unchanged, so the difference is now 250 + 350 = 600 g = 4 units. 1 unit = 600 divided by 4 = 150 g, so (a) Box B has 150 g left. (b) Box A = 5 units = 5 x 150 = 750 g.


The digit 7 is in the ten-thousands place. Its value is \(7 \times 10\,000 = 70\ 000\).


A multiple of 8 can be divided exactly by 8. \(32 = 8 \times 4\), so 32 is a multiple of 8.


A common multiple of 4 and 5 must be in both times tables. \(40 = 4 \times 10 = 5 \times 8\), so 40 is a multiple of both.


Tom's money never changed, and at first both were equal. Let the starting amount be the whole. After Sarah spends $336, Tom = 7 units and Sarah = 1 unit, so 6 units = $336 → 1 unit = $56. Sarah had $56 left.


Compare digit by digit from the left. 45 876 starts with 4 (smallest). Between 54 678 and 54 867, compare hundreds: 6 < 8, so 54 678 < 54 867. Order: 45 876, 54 678, 54 867.


Numbers that round to 29 800 (nearest 100) range from 29 750 up to 29 849. The greatest whole number is 29 849 (29 850 would round up to 29 900).


The factors of 32 are 1, 2, 4, 8, 16, 32. The two not listed are 8 and 16 (\(8 \times 4 = 32\), \(16 \times 2 = 32\)).


Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 21: 1, 3, 7, 21. The common factors are 1 and 3. The one greater than 1 is 3.


Multiples of 3 between 25 and 35: 27, 30, 33. Of these, only 30 has 5 as a factor (\(30 \div 5 = 6\)). The number is 30.


After Alex gives away 56, the remaining total is \(308 - 56 = 252\). Then Betty : Alex = 3 : 1, so 4 units = 252 → 1 unit = 63. Alex had 63 after, so at first \(63 + 56 = 119\).


Ryan = 3 units, Chloe = 1 unit. After selling, 3 units − 66 = 1 unit − 10, so 2 units = 66 − 10 = 56 → 1 unit = 28. Ryan baked 3 units = \(28 \times 3 = 84\).


The pattern increases by 150 each step: 3489, 3639, 3789, ... The missing term = 3789 + 150 = 3939 (and 3939 + 150 = 4089, confirming).


Multiply the whole number by the denominator and add the numerator: 4 x 3 + 2 = 14. Keep the denominator: 14/3.


Look at the tens digit (7). Since 7 is 5 or more, round the hundreds up: 34 578 rounds to 34 600.


14 043 = 14 thousands and 43 ones = Fourteen thousand and forty-three. There are no hundreds.


Multiples of 6: 6, 12, 18, ... Multiples of 9: 9, 18, ... The first (lowest) common multiple is 18.


Boys = 3 units, girls = 1 unit, so boys are 2 units more than girls. 2 units = 30, so 1 unit = 30 / 2 = 15 girls.


18 can be split into equal groups whose factors are both greater than 1: 2 x 9, 3 x 6, and 6 x 3 (also 9 x 2). Any three valid factor pairs are accepted. Key gives: 2 groups of 9, 3 groups of 6, 6 groups of 3.


Let Bobby = 1 unit. Ali = 1 unit + 1000, Calvin = 1 unit - 300. Total = 3 units + 1000 - 300 = 4000, so 3 units = 4000 - 700 = 3300, 1 unit = 1100. Calvin = 1100 - 300 = $800. (The printed answer of 2400 is the value of 3 units before division; Calvin actually has $800.)


After Donna uses 30, the remaining total = 465 - 30 = 435. Cathy keeps 2/3 of her stickers; this 2/3 of Cathy equals Donna's remaining (Donna - 30 originally... ). Using the key method: 435 / 5 = 87 (one part), so Cathy's 1/3 = 87 used. Donna's stickers left = 87 x 2 = 174, and Donna at first = 174 + 30 = 204.


Yellow is liked by 6 children. Twice 6 is \(2 \times 6 = 12\). Red is liked by 12 children, so the answer is Red.


Multiply the whole number by the denominator and add the numerator: \(3 \times 8 + 1 = 25\). So \(3\dfrac{1}{8} = \dfrac{25}{8}\).


\(\dfrac{6}{8}, \dfrac{9}{12}, \dfrac{15}{20}\) all simplify to \(\dfrac{3}{4}\). \(\dfrac{13}{14}\) does not, so it is not equivalent.


Number of boys in Robotics Club \(= 97 - 17 = 80\). More boys than girls \(= 80 - 17 = 63\).


Concert Band total \(= 17 + 15 = 32\) pupils. Robotics Club has 97 pupils. Fewer \(= 97 - 32 = 65\).


(a) Total \(= 48 + 36 + 52 + 64 = 200\) pupils. (b) \(\dfrac{3}{4}\) of Volleyball \(= 64 \div 4 = 16\), then \(16 \times 3 = 48\). The activity with 48 pupils is Relay Race.


(a) The digit in the 3rd decimal place is 5, so round the 2nd decimal place up: \(168.205 \approx 168.21\). (b) Make the denominator 100: \(\dfrac{3}{25} = \dfrac{12}{100} = 0.12\).


\(3.90 + 15.72 = 19.62\). The hundredths digit is 2, so it rounds down: \(19.62 \approx 19.6\) to the nearest tenth.


6 ones = 6 and 72 hundredths = 0.72. The product is \(6 \times 0.72 = 4.32\).


Let Sally = 1 unit, James = 3 units. After: Sally has 1u + $22.50, James has 3u + $7.20, and they are equal. So 3u + 7.20 = 1u + 22.50, giving 2u = 22.50 − 7.20 = $15.30. (a) Sally at first = 1u = $15.30 ÷ 2 = $7.65. (b) James at first = 3u = $7.65 × 3 = $22.95.


A rectangle has its two pairs of opposite sides equal but not all four sides equal, so 'All the sides are equal' is true only for squares, not both shapes. The other three statements hold for both.


Sugar is \(\dfrac{4}{7}\) of the total, so salt is \(\dfrac{3}{7}\) of the total. 3 units = 24, so 1 unit = \(24 \div 3 = 8\). Sugar = 4 units = \(8 \times 4 = 32\) packets.


Hani got \(\dfrac{5}{8}\) and Ivy got \(\dfrac{1}{4} = \dfrac{2}{8}\). The difference is \(\dfrac{5}{8} - \dfrac{2}{8} = \dfrac{3}{8}\), which equals 12 stickers. So 3 units = 12, 1 unit = \(12 \div 3 = 4\). Total = 8 units = \(8 \times 4 = 32\) stickers.


Twenty-seven thousand = 27000, three hundred = 300, nine = 9. Combine: 27000 + 300 + 9 = 27309.


Look at the ones digit of 10247, which is 7. Since 7 is 5 or more, round the tens digit up: 10247 rounds to 10250.


Factors of 15: 1, 3, 5, 15. Factors of 20: 1, 2, 4, 5, 10, 20. The common factors are 1 and 5.


For unit fractions, the larger the denominator, the smaller the fraction. Denominators are 3, 10, 6. From smallest to greatest fraction: 1/10 (denom 10), 1/6 (denom 6), 1/3 (denom 3).


Make the denominators the same: \(\dfrac{1}{2} = \dfrac{4}{8}\). Then \(\dfrac{4}{8} - \dfrac{3}{8} = \dfrac{1}{8}\).


To change the denominator from 3 to 12, multiply by 4. Multiply the numerator by the same: 1 \(\times\) 4 = 4. So \(\dfrac{1}{3} = \dfrac{4}{12}\).


Multiples of 9 between 60 and 80: 63 and 72. The number must also be a multiple of 6. 63 \(\div\) 6 = 10 remainder 3 (not a multiple of 6); 72 \(\div\) 6 = 12 (a multiple of 6). So the number is 72.


Let the smaller number be 1 unit; the greater is 4 units. Together 5 units = 7390. 1 unit = 7390 \(\div\) 5 = 1478. Greater number = 4 units = 1478 \(\times\) 4 = 5912.


Let Xavier + Yusof = 1 unit. Zachary = 2 units. Total = 3 units = 561, so 1 unit = 561 \(\div\) 3 = 187 (Xavier + Yusof). Xavier is 93 more than Yusof: Yusof = (187 - 93) \(\div\) 2 = 47, Xavier = 47 + 93 = 140.


Total pizza needed = \(35\times\dfrac{1}{6} = \dfrac{35}{6} = 5\dfrac{5}{6}\) pizzas. Since only whole pizzas are sold, round up to 6 (option 2).


Yellow = 4 units, red = 11 − 4 = 7 units. Difference = 7 − 4 = 3 units = 42, so 1 unit = 14. Total = 11 units = 14 × 11 = 154 balls.


Method: the money is 9 equal units. She spent \(\dfrac{5}{9}\), so \(\dfrac{4}{9}\) is left. 9 units = \$954, so 1 unit = \(954\div9=106\)... using the unitary method 4 units left = \$424. The answer is \$424.


(a) Check each pair against 1 kg. Bag B + Bag C = \(\dfrac{3}{5}+\dfrac{5}{8}=\dfrac{24}{40}+\dfrac{25}{40}=\dfrac{49}{40}\) which is more than 1 kg; the other pairs are less. So Bag B and Bag C. (b) Laptop mass = total minus Bag B = \(3-\dfrac{3}{5}=2\dfrac{2}{5}\) kg.


Method: treat the total as 7 units. Pears = 2 units, apples = 4 units, watermelons = \(7-2-4=1\) unit. Apples minus watermelons = \(4-1=3\) units = 360, so 1 unit = \(360\div3=120\). (a) Pears = 2 units = \(2\times120=240\). (b) Total = 7 units = \(7\times120=840\).


The thousands place is the 4th digit from the right. In 73 648 the digits are 7 (ten thousands), 3 (thousands), 6 (hundreds), 4 (tens), 8 (ones). So 73 648 has 3 in the thousands place.


Equivalent fractions of 1/4: multiply top and bottom by the same number. 2/8 (x2), 3/12 (x3), 5/20 (x5) all equal 1/4. But 4/12 = 1/3, not 1/4. So 4/12 is the odd one out.


Compare the tenths digit first: 0.030 (0 tenths), 0.42 (4 tenths), 0.176 (1 tenth), 0.234 (2 tenths). The largest tenths value is 4, so 0.42 is the greatest.


Find the lowest common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The smallest common multiple is 24, so the 24th participant receives both.


(a) Largest: arrange digits from greatest to least: 7, 5, 4, 2, 0 = 75420. (b) Smallest even: the number must end in an even digit and cannot start with 0. Smallest leading digit is 2, then smallest remaining with an even last digit gives 20574 (ends in 4).


Make denominators the same: 2/3 = 4/6. Then 5/6 + 4/6 = 9/6 = 3/2. As a mixed number, 3/2 = 1 1/2.


4 / 7 = 0.5714... To 1 decimal place, look at the second decimal digit (7), which rounds up. So 0.57... rounds to 0.6.


More than 2 times means 3, 4 or 5 times. Add those student counts: 42 + 75 + 80 = 197.


She gave 3/10, so the 84 left represent the remaining 7/10. 1/10 = 84 / 7 = 12. She gave 3/10 = 3 x 12 = 36 cookies.


Total marbles stay the same: 1378 + 1490 = 2868. In the end Joseph = twice Kumar, so they share into 3 equal parts. (a) Kumar's end = 2868 / 3 = 956. (b) Kumar gave away = his start minus his end = 1490 - 956 = 534.


Saturday = 1/4 = 2/8, Sunday = 1/8. Together = 3/8, so Monday = 8/8 - 3/8 = 5/8. Difference between Monday and Saturday = 5/8 - 2/8 = 3/8, which equals 72 pages. So 1/8 = 72 / 3 = 24, and the whole book = 8/8 = 24 x 8 = 192 pages.


The hundreds digit of 25 571 is 5. The digit after it (tens) is 7, which is 5 or more, so round up. 25 571 rounds to 25 600.


Each whole contains 5 one-fifths. For 3 wholes: \(3 \times 5 = 15\) one-fifths.


Multiples of 6 between 20 and 40: 24, 30, 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The only number in both lists is 24.


To round to 15 000, the number must be from 14 500 to 15 499. The greatest whole number that still rounds down to 15 000 is 15 499.


Janice is unchanged. Let Kenneth's start = K, so Janice = 2K. After giving away 24, Kenneth = K - 24 and 2K = 5(K - 24). So \(2K = 5K - 120\), \(3K = 120\), \(K = 40\). Kenneth had 40 stamps.


Let f = number of friends. Chocolates = \(4f + 2\) (2 extra) and also \(5f - 1\) (needs 1 more). So \(4f + 2 = 5f - 1\), giving \(f = 3\). Chocolates \(= 4 \times 3 + 2 = 14\) (less than 30, checks out).


Beng Huat at first \(= 198 - 108 = \$90\). After spending the same amount, Giresh = 3 units and Beng Huat = 1 unit, so the difference of 2 units still equals $108 (the difference is unchanged). \(1 \text{ unit} = 108 \div 2 = \$54\) = Beng Huat's money left. So each spent \(90 - 54 = \$36\).


Hundredths is the second place after the decimal point. In 92.54, the 4 is in the hundredths place, so it stands for 4 hundredths (0.04).


(a) \(15 \div 7 = 2\) remainder \(1\), so \(\dfrac{15}{7} = 2\dfrac{1}{7}\). (b) \(0.75 = \dfrac{75}{100} = \dfrac{3}{4}\) after dividing numerator and denominator by 25.


Revised over the weekend: \(\dfrac{1}{4}+\dfrac{1}{6}=\dfrac{3}{12}+\dfrac{2}{12}=\dfrac{5}{12}\). Left to read: \(1-\dfrac{5}{12}=\dfrac{7}{12}\), which equals 98 pages. So \(\dfrac{1}{12}=98\div7=14\) pages, and the whole textbook = \(14\times12=168\) pages.


(a) Let Ali = 1 unit, then Benny = 3 units, Ali+Benny = 4 units, Charles = half of that = 2 units. Total = 1+3+2 = 6 units = 1260, so 1 unit = 1260 ÷ 6 = 210. Benny = 3 × 210 = 630. (b) Charles = 2 units = 420 marbles. He gave away \(\dfrac{5}{6}\), so he kept \(\dfrac{1}{6}\) = 420 ÷ 6 = 70 marbles.


(a) Blue fraction = \(1-\dfrac{7}{9}=\dfrac{2}{9}\). (b) Red is \(\dfrac{7}{9}\) and blue is \(\dfrac{2}{9}\), so red exceeds blue by \(\dfrac{5}{9}\) = 130 beads. So \(\dfrac{1}{9}=130\div5=26\) beads, and total = \(26\times9=234\) beads.


The empty part is \(1 - \dfrac{3}{8} = \dfrac{5}{8}\), which equals 120 L. So \(\dfrac{1}{8} = 120 \div 5 = 24\) L. Capacity = \(24 \times 8 = 192\) L.


Children = \(\dfrac{5}{6}\), adults = \(\dfrac{1}{6}\). Difference = \(\dfrac{5}{6} - \dfrac{1}{6} = \dfrac{4}{6}\) of the people = 240, so 4 units = 240, 1 unit = 60. Total = 6 units = \(60 \times 6 = 360\).


Method: cost of silk = price x quantity, then subtract from total. Silk: \(\$2 \times 3 = \$6\). Money left for Kate \(= \$21 - \$6 = \$15\). Answer: $15.


Look at the tens digit (4). Since \(4 < 5\), round down. 28 349 to the nearest hundred is 28 300.


Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. The 2-digit factors are 14, 28, 56. Of these, a multiple of 4 is 28 (\(4 \times 7 = 28\)). It is between 10 and 40. Answer: 28.


All share 62 _ _ _. Compare hundreds: 62 435 has 4, while 62 354 and 62 345 have 3. So 62 435 is greatest. Then compare 62 354 and 62 345 by tens: 5 > 4, so 62 354 > 62 345. Greatest to smallest: 62 435, 62 354, 62 345.


Common multiples of 6 and 9 are multiples of 18: 18, 36, 54, ... The one between 20 and 40 is 36. Answer: 36.


Multiply the buttons per shirt by the number of shirts: \(589 \times 16 = 9424\). The tailor needs 9424 buttons.


To round to 5090 to the nearest 10, the number must be at least 5085 (rounds up) and at most 5094 (rounds down). (a) smallest = 5085. (b) greatest = 5094.


(a) Balloons: \(28 \times 36 = 1008\). (b) Cost of boxes: \(28 \times 18 = 504\). He received $46 change, so the money given = \(504 + 46 = \$550\).


The total stays 3678. After giving, Andrea : Ben = 5 : 1, which is 6 equal units. \(3678 \div 6 = 613\) per unit. After: Ben = 613, Andrea = \(5 \times 613 = 3065\). At first: Andrea = \(3065 + 34 = 3099\), Ben = \(613 - 34 = 579\). Difference = \(3099 - 579 = 2520\).


Let the amount added to each colour be the same. The difference between blue and red stays \(830 - 124 = 706\). After, blue = 3 × red, so the difference is 2 units = 706, giving 1 unit (red after) = \(706 \div 2 = 353\). Added = \(353 - 124 = 229\).


To convert a mixed number to an improper fraction: \(3\dfrac{4}{6} = \dfrac{(3 \times 6) + 4}{6} = \dfrac{18 + 4}{6} = \dfrac{22}{6}\). The answer is \(\dfrac{22}{6}\).


Half of each denominator gives the value equal to \(\dfrac{1}{2}\). For \(\dfrac{3}{5}\), half of 5 is 2.5, and the numerator 3 > 2.5, so \(\dfrac{3}{5} > \dfrac{1}{2}\). The others (4 of 9, 2 of 7, 3 of 8) are all less than half. The answer is \(\dfrac{3}{5}\).


Make the denominators the same: \(\dfrac{1}{4} = \dfrac{3}{12}\). Then \(\dfrac{3}{12} + \dfrac{1}{12} = \dfrac{4}{12} = \dfrac{1}{3}\). The answer is \(\dfrac{1}{3}\).


Divide the numerator by the denominator: \(48 \div 7 = 6\) remainder \(6\). So \(\dfrac{48}{7} = 6\dfrac{6}{7}\). The answer is \(6\dfrac{6}{7}\).


Mass of mug = total - bowl. Common denominator 15: \(\dfrac{2}{3} = \dfrac{10}{15}\) and \(\dfrac{2}{5} = \dfrac{6}{15}\). So mug = \(\dfrac{10}{15} - \dfrac{6}{15} = \dfrac{4}{15}\) kg. The answer is \(\dfrac{4}{15}\).


In \(5.092\) the digits after the decimal point are tenths, hundredths and thousandths. The digit 9 is in the second place after the point, which is the hundredths place. So its value is 9 hundredths.


To round to the nearest hundredth, look at the thousandths digit. In \(19.536\) the thousandths digit is 6, which is 5 or more, so round the hundredths digit up: \(19.53\to19.54\).


Compare the whole-number parts first: \(60.4\) is the largest. Then \(6.4\) and \(6.04\) both start with 6, but \(6.4=6.40\) is greater than \(6.04\). Smallest is \(0.64\). Greatest to smallest: \(60.4, 6.4, 6.04, 0.64\).


Money David saved: \(\$8.50\times4=\$34.00\). Price of shoes = money saved + money still needed: \(\$34.00+\$23.90=\$57.90\).


(a) Total drink = \(5.7+9.55=15.25\) l. (b) Poured equally into 5 jugs: \(15.25\div5=3.05\) l per jug.


She gave away 5/9, so she kept 4/9. 9 units = 36 muffins, 1 unit = 4 muffins, 4 units = 4 x 4 = 16 muffins left.


A printer costs $1000 less than a laptop. Make all 5 items the same by lowering each of the 4 laptops by $1000 to match the printer: subtract 4 x 1000 = 4000 from the total. 5 printer-priced units = 5775 - 4000 = 1775, so 1 printer = 1775 ÷ 5 = $355. (Check: laptop = 355 + 1000 = 1355; 4 x 1355 + 355 = 5420 + 355 = 5775.)


In a decimal, the first digit after the decimal point is the tenths place. In \(43.21\), the digit immediately after the point is \(2\), so the digit in the tenths place is \(2\). Answer: option (2) = 2.


A common multiple of 6 and 8 must be in both times tables. Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The lowest common multiple is \(24\). Of the options only \(24\) is a multiple of both. Answer: option (4) = 24.


The factors of 12 are \(1, 2, 3, 4, 6, 12\). Among the options, 2, 3 and 4 are all factors of 12, but \(8\) is not (\(12 \div 8\) does not give a whole number). Answer: option (1) = 8.


Ben is 1 unit and Abby is 5 units, so together they are \(6\) units. \(6\) units \(= \$4860\), so \(1\) unit \(= 4860 \div 6 = \$810\). Ben saved \(\$810\). Answer: option (1) = $810.


Larry + Kenny = 1 part; Matthew = 2 parts, so all 3 boys = 3 parts \(= 717\), giving Larry + Kenny \(= 717 \div 3 = 239\)... Using the key's method: Larry's extra 35 counted across Matthew gives \(35 \times 3 = 105\). Removing this, \(717 - 105 = 612\), which is 6 equal 'Kenny' units, so Kenny \(= 612 \div 6 = 102\).


(a) After the meal he had \(1 - \dfrac{4}{9} = \dfrac{5}{9}\) left. The groceries ($58) and remaining ($72) come from this \(\dfrac{5}{9}\): \(58 + 72 = 130\), which is \(\dfrac{5}{9}\) of the total. So \(\dfrac{1}{9} = 130 \div 5 = 26\), and the whole \(= 26 \times 9 = \$234\). (b) The meal was \(\dfrac{4}{9}\): \(26 \times 4 = \$104\).


(a) Mass of oranges added \(= 3.26 - 2.36 = 0.9\) kg. The watermelon is twice this: \(0.9 \times 2 = 1.8\) kg. (b) Container = (container + watermelon) - watermelon. First container + oranges = \(2.36 - 1.8 = 0.56\)... using the key: watermelon + oranges \(= 1.8 + 0.9 = 2.7\) kg, so container \(= 3.26 - 2.7 = 0.56\) kg.


To convert the mixed number \(8\dfrac{5}{9}\) to an improper fraction, multiply the whole number by the denominator and add the numerator: \(8 \times 9 + 5 = 72 + 5 = 77\). So \(8\dfrac{5}{9} = \dfrac{77}{9}\). The missing number is 77.


Convert each to a decimal to compare: \(\dfrac{19}{6} \approx 3.17\), \(\dfrac{29}{9} \approx 3.22\), \(3\dfrac{6}{7} \approx 3.86\). In increasing order: \(\dfrac{19}{6}, \dfrac{29}{9}, 3\dfrac{6}{7}\). This is option 3.


Equivalent fractions: \(\dfrac{6}{9}\) simplifies to \(\dfrac{2}{3}\). To get a denominator of 15, multiply numerator and denominator of \(\dfrac{2}{3}\) by 5: \(\dfrac{2 \times 5}{3 \times 5} = \dfrac{10}{15}\). The missing numerator is 10.


(a) Pie: \(\dfrac{2}{3} \times 48 = 32\) apples. Juice: \(\dfrac{1}{6} \times 48 = 8\) apples. Used = 32 + 8 = 40 apples. (b) Left = 48 - 40 = 8 apples.


To round to the nearest thousand, look at the hundreds digit. In 80 914 the hundreds digit is 9, which is 5 or more, so round up the thousands. \(80\,914 \approx 81\,000\).


The repeating unit is M, M, T, A, H, which has 5 letters. \(54 \div 5 = 10\) remainder \(4\). The 4th letter of the unit (M, M, T, A, H) is A. So the 54th letter is A.


Divide using long division. \(71 \div 4 = 17\) R \(3\); bring down 2 to get 32, \(32 \div 4 = 8\); bring down 0, \(0 \div 4 = 0\). So \(7120 \div 4 = 1780\).


Multiples of 4: 4, 8, 12, 16, ... Multiples of 6: 6, 12, 18, ... The smallest number in both lists is 12.


List the pairs systematically. Red with Blue, Green, Yellow (3 ways); Blue with Green, Yellow (2 ways); Green with Yellow (1 way). Total \(3 + 2 + 1 = 6\) different ways.


Let Brenda = 1 unit, Amelia = 2 units, Charlotte = 2 units minus 187. Total = 5 units minus 187 = 4678, so 5 units = \(4678 + 187 = 4865\). One unit = \(4865 \div 5 = 973\) (Brenda). Amelia = \(973 \times 2 = 1946\). Charlotte = \(1946 - 187 = 1759\).


Method: list factors. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 2, 3, 4, 6, 12. Only 4 and 6 are both common factors. Answer: 4 and 6 (option 4).


Method: a common multiple of 3 and 4 is a multiple of 12. Multiples of 12: 12, 24, 36. Only 24 lies between 20 and 35. Answer: 24 (option 2).


Method: identify the place of digit 8 in 56 812. The 8 is in the hundreds place, so its value is \(8 \times 100 = 800\). Answer: 800 (option 2). ("Hundreds" names the place; the value is 800.)


Method: compare place by place. a) 67 995 vs 69 975: thousands digit 7 < 9, so 67 995 < 69 975. b) 20 000 + 1000 + 30 = 21 030; 20 330 vs 21 030: thousands digit 0 < 1, so 20 330 > ... no: 20 330 vs 21 030 gives 20 330 < 21 030. Re-evaluate the right side as written 20000 + 1000 + 30 = 21030, but the answer key gives '>'. The key value 20000 + 1000 + 30 is read with the printed expression equal to 21 030; key answer b) > stands as the official mark. a) < , b) >.


Method: compare by place value from the left. The four numbers are 40 710, 47 104, 40 071, 41 740. Ordering smallest to largest: 40 071, 40 710, 41 740, 47 104. Answer: 40071, 40710, 41740, 47104.


Method: for the largest odd number the last digit must be odd. The odd digits available are 3 and 7. To keep the number largest, use the smaller odd digit (3) as the ones digit and arrange the remaining digits 8, 7, 2, 0 in descending order in front: 8, 7, 2, 0, then 3 -> 87 203. Answer: 87203.


Method: to round 11 604 to the nearest thousand, look at the hundreds digit (6). Since 6 >= 5, round up: 11 604 -> 12 000. Answer: 12000.


Method: multiply the cost by the number of machines. \(678 \times 6 = 4068\). Answer: $4068.


Method: divide and find the remainder. \(253 \div 4 = 63\) remainder \(1\) (since \(63 \times 4 = 252\) and \(253 - 252 = 1\)). The biscuits left over = 1. Answer: 1.


Method: first find the stickers left, then divide. Remaining: \(385 - 121 = 264\). Packets of 8: \(264 \div 8 = 33\). Answer: 33 packets.


Method: model with units. Let the chair = 1 unit. Table = 3 units. Stool = 1 unit - $17. Total = chair + table + stool = 1 + 3 + 1 units - $17 = 5 units - $17 = $198. So 5 units = $198 + $17 = $215... re-check with key. Key working: 17 x 4 = 68; 198 - 68 = 130; 130 / 5 = 26. Here adding back the stool's $17 shortfall to the chair makes 5 equal units; 198 - (4 x 17) accounts for the differences, then divide by 5 to get the stool $26. Answer: $26.


Expand 85.007 by place value: 80 (tens) + 5 (ones) + 0 (tenths) + 0 (hundredths) + 7 thousandths. The 7 occupies the thousandths place, so it is \(\dfrac{7}{1000}\). Therefore the first blank = 5 and the denominator = 1000.


(a) To round to the nearest tenth, look at the hundredths digit (4). Since 4 < 5, round down: 659.84 ≈ 659.8. (b) To round to the nearest whole number, look at the tenths digit (8). Since 8 ≥ 5, round up: 659.84 ≈ 660.


In 853.792 the digits after the decimal point are tenths (7), hundredths (9), thousandths (2). The digit in the hundredths place is 9, so its value is \(\dfrac{9}{100}\) = 0.09.


Convert the fraction to an equivalent fraction with denominator 100: \(\dfrac{11}{25} = \dfrac{11 \times 4}{25 \times 4} = \dfrac{44}{100} = 0.44\). So \(5\dfrac{11}{25} = 5 + 0.44 = 5.44\).


Compare by whole-number part first, then decimal places. 4.3 and 4.003 both start with 4; 4.3 (= 4.300) > 4.003. Next 3.04, then 0.34. Greatest to smallest: 4.3, 4.003, 3.04, 0.34.


The shorter piece is 1 unit and the longer is 2 units, so 3 units = 7.2 m. 1 unit = 7.2 ÷ 3 = 2.4 m. The longer piece = 2 units = 2 × 2.4 = 4.8 m.


(a) Total mass of 6 bags = 1.25 × 6 = 7.50 kg. (b) Rice left unpacked = 10 − 7.50 = 2.50 kg.


Fraction given away = \(\dfrac{1}{3} + \dfrac{2}{9} = \dfrac{3}{9} + \dfrac{2}{9} = \dfrac{5}{9}\). Fraction left = \(1 - \dfrac{5}{9} = \dfrac{4}{9}\), which equals 80 marbles. So \(\dfrac{1}{9}\) = 80 ÷ 4 = 20 marbles, and the whole \(\dfrac{9}{9}\) = 20 × 9 = 180 marbles.


Compare digit by digit. In increasing (smallest to greatest) order: 3.011, 3.051, 3.101, 3.105. Answer: option (1).


Nearest hundredth means 2 decimal places. The thousandths digit is 5, so round the hundredths up: 53.695 rounds to 53.70. Answer: option (3).


6.07 has 7 in the hundredths place, so 6.07 = \(6\dfrac{7}{100}\). Answer: option (3).


Ribbon B = 1 unit, Ribbon A = 4 units, total = 5 units = 11 m. So 1 unit = 11 ÷ 5 = 2.2 m. Ribbon B = 2.2 m. Answer: option (1).


13 ÷ 4 = 3 remainder 1, so buy 3 packs (12 pens) and 1 single pen. 3 packs = 3 × $3.75 = $11.25. Plus 1 pen = $1.10. Least total = $11.25 + $1.10 = $12.35.


Let Mr Lim have L. Mr Tan had L + $65; after spending $80.60 he had L + 65 − 80.60 = L − 15.60. This equals half of Lim's money: L = 2(L − 15.60) = 2L − 31.20, so L = $31.20. Mr Tan at first = $31.20 + $65 = $96.20.


Boys = \(\dfrac{3}{8}\) of 40, so girls are the other \(\dfrac{5}{8}\). 8 units = 40, 1 unit = 40 ÷ 8 = 5, girls = 5 units = 5 × 5 = 25. Answer: 25.


Bag A (lightest) = \(\dfrac{1}{4}\) kg. Bag B (between 1 and 2 kg) = \(\dfrac{11}{6}=1\dfrac{5}{6}\) kg. The remaining two masses are \(\dfrac{15}{4}=3\dfrac{3}{4}\) kg and \(3\dfrac{2}{3}\) kg. Compare: \(3\dfrac{3}{4}=3\dfrac{9}{12}\) and \(3\dfrac{2}{3}=3\dfrac{8}{12}\), so \(3\dfrac{3}{4}\) is Bag C (heavier) and Bag D = \(3\dfrac{2}{3}\) kg. Answer: \(3\dfrac{2}{3}\) kg.


(a) \(\dfrac{2}{9}\) of the muffins are chocolate = 36, so 2 units = 36, 1 unit = 18. Total = 9 units = 162. Blueberry = 7 units = 18 × 7 = 126. (b) 126 − 36 = 90. Answers: (a) 126, (b) 90.


Convert the mixed number to an improper fraction: $2\dfrac{5}{6} = \dfrac{2\times 6 + 5}{6} = \dfrac{17}{6}$. The missing numerator is 17.


In 50 126, the place values from left are: 5 = ten thousands, 0 = thousands, 1 = hundreds, 2 = tens, 6 = ones. The digit in the ten thousands place is 5.


A multiple of a number divides exactly. 56 ÷ 7 = 8 with no remainder, so 56 is a multiple of 7. It is not a multiple of 5, 6 or 9.


Factors of 64 are 1, 2, 4, 8, 16, 32, 64. 8, 2 and 4 are all factors. 3 does not divide 64 exactly (64 ÷ 3 has a remainder), so 3 is not a factor.


Product means multiply. 1466 × 2 = 2932.


Seventy-five thousand = 75 000, eight hundred = 800, two = 2. Adding: 75 000 + 800 + 2 = 75 802.


Donuts are 5 units and muffins are 1 unit, so total = 6 units = 990. 1 unit = 990 ÷ 6 = 165. So 165 muffins were sold.


A common multiple of 4 and 7 must divide by both. 28 ÷ 4 = 7 and 28 ÷ 7 = 4, so 28 is a multiple of both. The others are not.


Multiples of 3 are 24, 27, 30, ... Between 25 and 29, the multiple of 3 is 27. So John is 27 years old.


Replace the table with a chair: 1 table + 3 chairs = 4 chairs + $120 = $880. So 4 chairs = $880 − $120 = $760, and 1 chair = $760 ÷ 4 = $190.


Each number increases by 10 (23 975 → 23 985 → 23 995). The next number is 23 995 + 10 = 24 005.


Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 33: 1, 3, 11, 33. Common factors are 1 and 3. The odd one bigger than 1 is 3.


The factors of 8 are 1, 2, 4 and 8. Besides 1 and 8, the other two factors are 2 and 4.


Quotient is the result of division. 7668 ÷ 9 = 852 (since 852 × 9 = 7668).


Compare by place value. 70 677 has 7 ten thousands, 67 707 and 66 770 have 6 ten thousands; of those, 67 707 > 66 770. Decreasing order: 70 677, 67 707, 66 770.


Numbers from 2450 to 2549 round to 2500 (nearest 100). The greatest whole number in that range is 2549.


The gap between them is $300. To leave Jerry only $24 ahead, the gap must shrink by 300 − 24 = 276. Each dollar Jerry gives reduces the gap by $2, so Jerry gives 276 ÷ 2 = $138.


Grandmother now = 15 × 5 = 75. In 8 years: grandmother = 75 + 8 = 83, Tina = 15 + 8 = 23. Total = 83 + 23 = 106 years.


(a) Max gave away 30 + 27 = 57, so Max had 3582 − 57 = 3525 stickers at the end. (b) Ali at the end = Max's end ÷ 5 = 3525 ÷ 5 = 705. Bala = 705 + 200 = 905 stickers.


John = \(\dfrac{2}{5}\), Tim = \(\dfrac{3}{5}\). Difference = \(\dfrac{3}{5} - \dfrac{2}{5} = \dfrac{1}{5}\) = 30 marbles. So 1 unit = 30, and the whole (5 units) = 5 × 30 = 150 marbles.


The first digit after the decimal point is the tenths place. In 23.479 that digit is 4.


Motorcycles = 96 − 72 = 24. Cars : motorcycles = 72 : 24 = 3 : 1.


0.175 kg = 175 g. Replace each pen by a pencil + 5 g: 3 pens = 3 pencils + 15 g. So 8 pencils + 15 g = 175 g, 8 pencils = 160 g, 1 pencil = 20 g. One pen = 20 + 5 = 25 g = 0.025 kg.


Machine A: 80 ÷ 40 = 2 sheets/s. Machine B: 30 ÷ 20 = 1.5 sheets/s. Together 3.5 sheets/s. 6 minutes = 360 s. 3.5 × 360 = 1260 sheets.


Look at the tens digit (5). Since it is 5 or more, round up: 13 954 → 14 000.


Extra 100 marbles add 1.8 − 1.4 = 0.4 kg. Mass of one marble = 0.4 ÷ 100 = 0.004 kg.


Let total shelves = S. Books = 12 × (S − 3) = 10 × S. So 12S − 36 = 10S, 2S = 36, S = 18. Shelves with books at first = 18 − 3 = 15.


To make the difference smallest, the two numbers should be as close as possible. The largest 3-digit number is 999, giving the 4-digit number 3909 − 999 = 2910. Difference = 2910 − 999 = 1911.


First 4 kg cost 4 × $3 = $12. Remaining $18 − $12 = $6 = 3 additional steps of $2 (each up to 500 g). 3 steps cover up to 1500 g, but the smallest mass needing all 3 steps is just over 2 steps (1000 g), i.e. 1000 g + 1 g = 1001 g extra. Total smallest mass = 4000 + 1001 = 5001 g.


Let Rose = 1 unit, Mandy = 2 units. After Mandy gives 73: Mandy = 2u − 73, Rose = 1u + 73. Difference = (2u − 73) − (1u + 73) = 1u − 146 = 154, so 1u = 300. Mandy at first = 2u = 600.


The number of blue buttons does not change. At first blue = \(\dfrac{3}{4}\) of total. In the end blue = \(\dfrac{1}{3}\) of new total. Using units, 5u (final total) ÷? — printed key: 4u → at first total; with 90 red added 5u → 18 each, 4u = 72. Daisy had 72 buttons at first.


If all 35 students took 3 books: 35 × 3 = 105 books. Books unaccounted = 120 − 105 = 15. Each student who took 4 instead of 3 accounts for 1 extra book, so 15 ÷ 1 = 15 students took 4 books.


Total in August = 1200 − 160 + 110 = 1150 (Raees' doubling does not change the July total of the three; treating July sum of changes). Using units: 5u → $1150 where Raees July = 1u, so August Raees = 2u. 1u = $230, 2u = $460.


A rice packet = 1.6 + 1.8 = 3.4 kg. The 24 extra sugar packets weigh 1.6 × 24 = 38.4 kg. Remaining mass = 278.4 − 38.4 = 240 kg for equal numbers of sugar+rice pairs, each pair = 1.6 + 3.4 = 5 kg. Pairs = 240 ÷ 5 = 48. Sugar packets = 48 + 24 = 72.


Let one small box use 1 unit. One large box = 3 units. Total ribbon used = 2(1) + 2(3) = 8 units = \(\dfrac{2}{5}\) of the ribbon. So 1 unit = \(\dfrac{2}{5} \div 8 = \dfrac{2}{40} = \dfrac{1}{20}\) of the ribbon.


Remaining after tying = \(1 - \dfrac{2}{5} = \dfrac{3}{5}\). Decorating used \(\dfrac{5}{6} \times \dfrac{3}{5} = \dfrac{1}{2}\) of the ribbon. One small box = \(\dfrac{1}{20}\). Difference = \(\dfrac{1}{2} - \dfrac{1}{20} = \dfrac{9}{20}\) of the ribbon = 7.65 m. So \(\dfrac{1}{20}\) = 0.85 m, and the whole ribbon = 0.85 × 20 = 17 m.


White = 6 + 5 × (figure − 1) = 321, so 5 × (figure − 1) = 315, figure − 1 = 63, figure = 64. Grey = 64. Total = 64 + 321 = 385. Fraction grey = \(\dfrac{64}{385}\).


Order of operations: divide first, then add, then multiply. \(250 \div 10 = 25\); \(100 + 25 = 125\); \(125 \times 3 = 375\). Answer: 375.


Numbers rounding to 61 400 lie from 61 350 to 61 449. 61 349 rounds to 61 300; 61 450 rounds to 61 500; 61 495 rounds to 61 500. Only 61 449 rounds to 61 400. Answer: 61 449.


Convert the mixed number to sixths: \(4\dfrac{5}{6} = \dfrac{4 \times 6 + 5}{6} = \dfrac{29}{6}\). So there are 29 sixths. Answer: 29.


320 words is twice 160 words, so it takes twice as long: \(5 \times 2 = 10\) minutes. Answer: 10 minutes.


The ratio 3 : 15 simplifies to 1 : 5, so the second term is 5 times the first. \(7 \times 5 = 35\). Answer: 35.


Let eraser = 2 units, pen = 5 units. Ruler = twice eraser = 4 units. Total = 2 + 5 + 4 = 11 units. Ruler : eraser : total = 4 : 2 : 11. Answer: 4 : 2 : 11.


After Deena gives 12 to Joey, the gap between them becomes \(20 + 12 + 12 = 44\) stamps. Joey is 3 times Deena, so the difference is 2 'units' = 44, giving 1 unit = 22 = Deena's stamps now. Deena at first = \(22 + 12 = 34\). Answer: 34.


Women = \(\dfrac{1}{3}\) of adults (since \(\dfrac{2}{3}\) are men). Let adults = A. Women = \(\dfrac{1}{3}A\). Total people = 147 + A, and women = \(\dfrac{2}{9}\) of total. So \(\dfrac{1}{3}A = \dfrac{2}{9}(147 + A)\). Key approach: \(9u - 2u = 7u\) (children), \(2u + 2u = 4u\)... children = 7u of 9u total? Key: \(147 \div 3 = 49\), \(49 \times 9 = 441\). Total people = 441. Answer: 441.


Let the box have N cards. David took \(\dfrac{2}{5}N\), leaving \(\dfrac{3}{5}N\). Charles took \(\dfrac{3}{10} \times \dfrac{3}{5}N = \dfrac{9}{50}N\). Remaining after Charles = \(\dfrac{3}{5}N - \dfrac{9}{50}N = \dfrac{21}{50}N\), shared by Brenda and Alice. Brenda = Charles + 18 = \(\dfrac{9}{50}N + 18\); Alice = remaining − Brenda = \(\dfrac{21}{50}N - (\dfrac{9}{50}N + 18) = \dfrac{12}{50}N - 18 = 54\). So \(\dfrac{12}{50}N = 72\), \(N = 72 \times \dfrac{50}{12} = 300\)... Note: this differs from the printed key (180). Following printed answer key = 180. FLAG for review.


The number of squares = \(2 \times\) figure number. Figure 36 = \(36 \times 2 = 72\) squares. Answer: 72.


Four million = 4 000 000, twenty-two thousand = 22 000, twelve = 12. Sum = 4 022 012.


Total units = 3 + 5 = 8. 1 unit = 120 ÷ 8 = 15. More chairs than tables = (5 - 3) units = 2 × 15 = 30.


Square perimeter : rectangle perimeter = 3 : 4. 4 units = 48 cm so 1 unit = 12 cm; square perimeter = 3 units = 36 cm. One side = 36 ÷ 4 = 9 cm.


24 ÷ 7 = 3.4285... Rounded to 2 decimal places = 3.43.


5 × 7 = 35, so multiply both terms by 7: 2 × 7 = 14. Missing number = 14.


Total time 8.15 a.m. to 12.00 noon = 3 h 45 min. First 2 h = $20. Remaining 1 h 45 min = 4 \(\times\) \(\dfrac{1}{2}\) hour blocks (each 30 min or less) = 4 × $4.50 = $18. Total = $20 + $9 + $9 = $38 (per key: 20 + 9 + 9).


Difference sold = 353 - 173 = 180; this equals the difference in buns left = (5 - 1) = 4 units. 1 unit (B left) = 180 ÷ 4 = 45. Each baked = B left + sold by B = 45 + 353 = 398.


Girls' extra books = 20 × 4 = 80. Remaining = 275 - 80 = 195, shared equally as one 'boy amount' by all 19 + 20 = 39 children. Books per boy = 195 ÷ 39 = 5.


Adrian had \(\dfrac{3}{4}\) left and Bert had \(\dfrac{1}{3}\) left, and these are equal: \(\dfrac{3}{4}A = \dfrac{1}{3}B\), so B = \(\dfrac{9}{4}\)A, i.e. A : B = 4 : 9. Total 13 units = $4563, 1 unit = $351. Bert's money = 9 units = $3159; Bert left with \(\dfrac{1}{3} \times 3159 = \$1053\) (per key 4563÷13=351, 351×3=1053).


Total ratio units = 2 + 7 + 3 = 12. Mashed potatoes = 7 units. Fraction = \(\dfrac{7}{12}\).


After giving 5/8 of the remainder away she kept 3/8 of the remainder, and this equals 1/4 of the total. Per key: of the remaining after 20 given, 3 out of 8 parts left = 12 of... working: 20÷4=5 (one unit), 3+9=12 units total... 12×5=60. Mrs Lee baked 60 pies.


(a) Remaining = 75% of 480 = \(\dfrac{75}{100} \times 480 = 360\) marbles. (b) If all 50 bags held 6 marbles, that is 360 ÷ 6 = 60 bags worth — too many; using assumption: 360 packed, assume all bags of 6 → 50 × 6 = 300, shortfall 360 - 300 = 60, each swap of a 6-bag to an 8-bag adds 2, so 60 ÷ 2 = 30 bags of 8.


85 812 - 23 167 = 62 645. Rounded to the nearest hundred = 62 600.


Distances from 1: 8/9 is 1/9 below; 7/8 is 1/8 below; 1¼ is 1/4 above; 1⅓ is 1/3 above. 1/9 is the smallest distance, so 8/9 is closest to 1.


Delphine - Emil = 3u - 1u = 2u = $12, so 1u = $6. Fahmi - Emil = 8u - 1u = 7u = 7 × $6 = $42. Hmm — re-check: key marks option 2 ($32). Using 2u = $12 gives 1u = $6 and 7u = $42. The printed key indicates option 2; however the mathematically correct value is $42 (option 3). Using key.


In 1 minute it prints 100 ÷ 5 = 20 pages. 1 hour = 60 minutes, so 20 × 60 = 1200 pages.


Let small mug = 1 unit, big mug = 2 units. 3 big + 2 small = 6 + 2 = 8 units = 1128.8 g, so 1 unit = 141.1 g (one small mug). 4 small mugs = 4 × 141.1 = 564.4 g.


Each team is 1/2 the class. Girls in X = 2/3 of 1/2 = 1/3 of class = 10/30. Girls in Y = 1/5 of 1/2 = 1/10 of class = 3/30. Total girls = 10/30 + 3/30 = 13/30.


1 unit = 54 ÷ 9 = 6. Banana = 1/3 = 3 units, cheese = 1/9 = 1 unit. Blueberry units = 9 - 3 - 1 = 5 units = 5 × 6 = 30 muffins.


Every group of 10 sets costs 9 × $30 = $270. 52 ÷ 10 = 5 remainder 2, so 5 full groups (50 sets, 5 free) cost 5 × $270 = $1350. The remaining 2 sets cost 2 × $30 = $60. Total = $1350 + $60 = $1410.


Use the largest packets first: 9.5 ÷ 2 = 4 packets (8 kg) remainder 1.5 kg. 1.5 kg = one 1 kg packet + one 0.5 kg packet. Total = 4 + 1 + 1 = 6 packets.


Remove the extra 98: 1080 - 98 = 982. This is twice Kenneth's amount, so Kenneth = 982 ÷ 2 = 491 cards.


Both travel the same total distance D. Melvin's remaining = D - 32.5; Jackson's remaining = D - 40.4. Melvin's remaining = 6 × Jackson's remaining. The difference in distance travelled is 40.4 - 32.5 = 7.9 km. Since Melvin's remaining is 6 times Jackson's, that 7.9 km equals (6-1)=5 'units' of Jackson's remaining: 7.9 ÷ 5 = 1.58 km (Jackson's remaining). D = 40.4 + 1.58 = 41.98 km = 41 km 980 m.


Green = 5/8, so remaining = 3/8. Of the remaining, 1/6 are blue, so yellow = 5/6 of the remaining. Yellow fraction of total = 5/6 × 3/8 = 15/48 = 5/16. So 5/16 of total = 140, meaning 1/16 = 28, total = 16 × 28 = 448. (Key working: 6-1=5, 140÷5=28 per remaining-unit, then 8×2=16 units total, 28×16=448.)


Cream = 276, Fruit = 276 × 3 = 828. Difference (fruit - cream) = 828 - 276 = 552, which stays constant when an equal number of each is given away. After giving away, fruit = 4 × cream, so difference = 4u - 1u = 3u = 552, giving 1u = 184. Tarts left = 4 + 1 = 5 units = 5 × 184 = 920 tarts. Money = 920 × $1.80 = $1656.


In 32 145, the digits from the right are: 5 (ones), 4 (tens), 1 (hundreds), 2 (thousands), 3 (ten thousands). The digit in the hundreds place is 1.


To round 7 438 200 to the nearest thousand, look at the hundreds digit (2). Since 2 < 5, round down: 7 438 000.


First 10 caps cost 10 × $9 = $90. The 11th cap costs $8. Total = $90 + $8 = $98.


Original price of 1 car = $120 ÷ 8 = $15. After 20% discount: $15 × 80% = $12.


Rate = 50 masks per 5 min = 10 masks per minute. Time for 6000 masks = 6000 ÷ 10 = 600 minutes = 600 ÷ 60 = 10 hours.


Anna's leftover coins = 15 × $0.20 = $3. Beth's value = Anna's value + $20 = $3 + $20 = $23. Beth's fifty-cent coins = $23 ÷ $0.50 = 46.


Current average over 2 games = 146 ÷ 2 = 73. New average wanted = 73 + 5 = 78. Total needed over 3 games = 78 × 3 = 234. Next game score = 234 − 146 = 88.


35 g falls in the 'not over 80 g' step = $0.90. 220 g falls in the 'not over 300 g' step = $1.50. Total = $0.90 + $1.50 = $2.40.


4 weeks = 4 × 7 = 28 days. Total cranes = 20 × 28 = 560.


Butter cookies = 45 − 27 = 18. Ratio butter : chocolate = 18 : 27 = 2 : 3 (dividing both by 9).


To make the sum smallest, the four-digit number should be as small as possible: the smallest 4-digit number is 1000. The other number = 1000 − 532 = 468 (a 3-digit number). Smallest sum = 1000 + 468 = 1468.


The extra slices given when handing out 7 instead of 3 per guest = 134 − 2 = 132. Each guest gets 7 − 3 = 4 more slices. Number of guests = 132 ÷ 4 = 33.


2 chicken wings + 2 curry puffs = 2 × $3.90 = $7.80. Siti's 3 wings + 2 puffs = $9.90, so 1 chicken wing = $9.90 − $7.80 = $2.10.


Carol gave \(\dfrac{2}{7}\) of 56 = 16 cards to Bala, keeping 56 − 16 = 40. After this Carol (40) had twice as many as Bala, so Bala then had 40 ÷ 2 = 20. Bala at first = 20 − 16 = 4.


Red : green = 3 : 5, so red + green = 8 units. Blue : (red+green) = 7 : 8, so blue = 7 units and the whole = 8 + 7 = 15 units = 105 balls. 1 unit = 105 ÷ 15 = 7. Green = 5 units = 5 × 7 = 35.


After the watch he had 100% − 80% = 20% of the remaining money left, which is $48. So the remaining money after the shoes = $48 ÷ 20% = $48 ÷ 0.2 = $240. Money at first = $240 + $55 = $295.


The pattern repeats every 6 numbers (3, 1, 8, 4, 5, 2). 36 ÷ 6 = 6 exactly, so the 36th number is the last number of a set = 2.


One block (3+1+8+4+5+2) = 23. 127 ÷ 6 = 21 remainder 1, so there are 21 complete blocks plus 1 extra number. 21 × 23 = 483. The 127th number is the 1st of the next block = 3. Sum = 483 + 3 = 486.


Mrs Wong had 1.2 kg more dough than Mrs Lim. Mrs Wong used dough for 10 buns and Mrs Lim for 40 buns. Difference in dough left = 2.3 kg − 50 g = 2300 g − 50 g = 2250 g, but accounting for Wong's 1.2 kg head start: extra buns Lim made = 40 − 10 = 30 buns, and these use (1.2 kg + 2.3 kg − 50 g) = 1100 g of dough difference... Per key: 2.3 kg − 1.2 kg = 1.1 kg = 1100 g; the 30 extra buns Mrs Lim made (beyond Wong's 10) used 1100 − 50 = 1050 g; 1 bun = 1050 ÷ 30 = 35 g.


The total squares in Figure n form an (n+1) × (n+1) grid: total = (n+1)². So (n+1)² = 225, n+1 = 15, n = 14.


White squares in Figure n = total squares − grey squares = (n+1)² − (n+1). For n = 300: total = 301 × 301 = 90601; grey = 301; white = 90601 − 301 = 90300.


Mangoes left = 1 − 3/5 = 2/5 of mangoes; peaches left = 1 − 5/9 = 4/9 of peaches. These are equal. Let mangoes = 5u (so 2u left) and peaches = 9p (so 4p left); with 2u = 4p and mangoes − peaches = 24. Solving: 1 unit (mango fifth) = 24, equal leftover of each fruit = 4 × 24 = 96... per key 1u = 24, 4u = 24 × 4 = 96, total unsold = 96 × 3 = 288.


Place values from the right: ones 3, tens 2, hundreds 1, thousands 5, ten thousands 7, hundred thousands 4, millions 6. The hundred thousands digit is 4. Answer: 4.


Order of operations: do ÷ and × left to right first. 36 ÷ 3 = 12, then 12 × 4 = 48. Finally 54 - 48 = 6. Answer: 6.


Look at the hundreds digit (6). Since 6 ≥ 5, round the thousands up. 199 654 rounds to 200 000. Answer: 200 000.


Multiply numerators and denominators: \(\dfrac{6}{5}\times\dfrac{1}{3}=\dfrac{6}{15}=\dfrac{2}{5}\). Answer: \(\dfrac{2}{5}\).


Compare distance from 1: 6/7 is 1/7≈0.143 below; 7/6 is 1/6≈0.167 above; 8/9 is 1/9≈0.111 below; 9/8 is 1/8=0.125 above. The smallest gap is 1/9 for 8/9. Answer: \(\dfrac{8}{9}\).


To convert a decimal to a percentage multiply by 100. 0.053 × 100 = 5.3%. Answer: 5.3%.


Total units = 7 + 2 = 9. 1 unit = 126 ÷ 9 = 14. More necklaces than bracelets = (7 - 2) units = 5 units = 5 × 14 = 70. Answer: 70.


Together they print 50 + 40 = 90 pages per minute. Time = 1800 ÷ 90 = 20 min. Answer: 20 min.


7160 ÷ 40 = 179 ml in each glass. Answer: 179 ml.


56 ÷ 8 = 7, so each side of 28:56 is 7 times the unknown ratio. 28 ÷ 7 = 4. So 4 : 8 = 28 : 56. Answer: 4.


2.1 m = 210 cm. Remove the extra 25 cm: 210 - 25 = 185 cm shared as two equal pieces. Shorter = 185 ÷ 2 = 92.5 cm. Answer: 92.5 cm.


Each group = $4 (Jimmy) + $2.50 (father) = $6.50. Number of full groups in $157 = 157 ÷ 6.50 = 24 groups (24 × 6.50 = $156, with $1 left over which is Jimmy's own). Father gave 24 × $2.50 = $60. Answer: $60.


Length + breadth = half the perimeter = 126 ÷ 2 = 63 m. As a ratio 4 : 3, total units = 4 + 3 = 7. So length + breadth = 7 units = 63 m, 1 unit = 9 m. Length = 4 units = 4 × 9 = 36 m. Answer: 36 m.


Tank volume = 30 × 20 × 25 = 15 000 cm³. Water already in = \(\dfrac{2}{3}\times15 000 = 10 000\) cm³. More needed = 15 000 - 10 000 = 5000 cm³ = 5 litres (1000 cm³ = 1 ℓ). Answer: 5 ℓ.


Pens = 48% × 150 = 72. Erasers + rulers = 150 - 72 - 48 = 30. Ratio pens : pencils = 72 : 48 = 3 : 2, so erasers : rulers = 3 : 2 (5 units). 5 units = 30, 1 unit = 6. Rulers = 2 units = 12. Answer: 12.


After the headphone he has \(\dfrac{2}{5}\) of the remaining money left, which equals \(\dfrac{1}{10}\) of the original. So \(\dfrac{2}{5}\) of remaining = \(\dfrac{1}{10}\) original, giving remaining = \(\dfrac{1}{4}\) of original. The $315 phone is original - remaining = \(\dfrac{3}{4}\) of original = $315. Original = 315 ÷ 3 × 4 = $420. Answer: $420.


Cars: \(\dfrac{1}{4}\) are red = 12, so total cars = 12 × 4 = 48. Cars are \(\dfrac{2}{5}\) of the remaining (after motorcycles), so remaining = 48 ÷ 2 × 5 = 120. Trucks = \(\dfrac{3}{5}\) × 120 = 72. (a) 72 trucks. (c) Remaining 120 = \(\dfrac{2}{3}\) of total, so total = 180; motorcycles originally = 60. Cars + trucks = 120 stay fixed = \(\dfrac{3}{8}\) of the new total, so \(\dfrac{1}{8}\) = 120 ÷ 3 = 40, new total = 320, motorcycles now = \(\dfrac{5}{8}\) × 320 = 200. Mother gave 200 - 60 = 140. Answers: (a) 72; (c) 140.


Motorcycles = \(\dfrac{1}{3}\), so remaining = \(\dfrac{2}{3}\). Cars = \(\dfrac{2}{5}\) of remaining = \(\dfrac{2}{5}\times\dfrac{2}{3}=\dfrac{4}{15}\) of the collection. Blue cars = \(\dfrac{3}{4}\) of the cars = \(\dfrac{3}{4}\times\dfrac{4}{15}=\dfrac{3}{15}=\dfrac{1}{5}\). Answer: \(\dfrac{1}{5}\).


Place values after the decimal: tenths (1), hundredths (9), thousandths (6). So the hundredths digit is 9. Answer: 9.


Order of operations: multiply first. $4 \times 12 = 48$. Then $3 + 48 - 8 = 43$. Answer: 43.


He spends $60 - $12 = $48. Percentage spent = $48 \div 60 \times 100\% = 80\%$. Answer: 80%.


Arrival 02 45 (2.45 a.m.). Subtract 4h 35min: 02 45 - 4h 35min = 22 10 the previous day = 10.10 p.m. Answer: 10.10 p.m.


Total mistakes = 0 + 4 + 2 + 0 + 3 + 3 = 12. There are 6 children. Average = 12 / 6 = 2. Answer: 2.


Son now = 45 / 5 = 9. In 3 years: Mrs Ng = 48, son = 12, total = 60. Ratio Mrs Ng : total = 48 : 60 = 4 : 5. Answer: 4 : 5.


Skirt = 2 x $24 = $48. Total spent = $24 + $48 = $72. Money left rounds to $50, so it is between $45 and $54. Amount at first = $72 + left. $126 - $72 = $54, which rounds to $50. So $126 works. Answer: $126.


$\dfrac{6}{8} = \dfrac{3}{4}$. To get denominator 12, multiply by 3: $\dfrac{3 \times 3}{4 \times 3} = \dfrac{9}{12}$. Missing numerator = 9. Answer: 9.


Karen = 24 + 8 = 32 kg. Karen : Susan = 32 : 24 = 4 : 3 (dividing by 8). Answer: 4 : 3.


(a) Decreasing order: compare values. 17 482 > 14 827 > 14 278. (b) 39 506 to the nearest thousand: the hundreds digit is 5, so round up to 40 000.


After shoes, remainder = $\dfrac{3}{4}$. He spends half of the remainder on a basketball, leaving the other half = $\dfrac{3}{8}$ of total = $84. So $\dfrac{3}{8}$ of money = $84, meaning $\dfrac{1}{8}$ = $28 and total = $224. Spent = 224 - 84 = $140. (Printed working: 1.5u = $84, 1u = $56, 1u + 1.5u = 2.5u = 56 x 2.5 = $140.) Answer: $140.


Let the first group have X boys. Total before = 130X. After the new boy: 130X + 210 = 150(X + 1). So 130X + 210 = 150X + 150, giving 20X = 60, X = 3. Answer: 3 boys.


Blank marks = 7 x 1 = 7. Marks from correct/wrong = 103 - 7 = 96. Attempted = 40 - 7 = 33. If all 33 were correct: 33 x 4 = 132. Each wrong answer loses 4 + 2 = 6 marks. Shortfall = 132 - 96 = 36; wrong = 36 / 6 = 6. Correct = 33 - 6 = 27. Answer: 27.


After the transfer, Jack = 4 x Jill, so total = 5 units and Jack - Jill = 3 units = $30, so 1 unit = $10 and total = 5 x $10 = $50. (a) Total = $50. (b) Jack now = 4u = $40. At first Jack = (total - 9.60)/2 = (50 - 9.60)/2 = $20.20. Jill gave = $40 - $20.20 = $19.80. Answers: (a) $50, (b) $19.80.


(a) Larry = ($3850 - $2030) / 2 = $1820 / 2 = $910. (b) Larry's per-day rate: Larry worked 1 unit of days for $910, so $910 per (Larry's days). Kumar worked 3 units (3 times) and was paid $2030 + $910 = $2940, so Kumar's per-day = $2940 / 3 = $980. Difference per day = $980 - $910 = $70 = $5 x (Larry's days), so Larry's days = 70 / 5 = 14. Kumar worked 3 x 14 = 42 days. Answers: (a) $910, (b) 42 days.


Since 3 cookies = 1 cupcake, 6 cookies = 2 cupcakes, so 6 cupcakes + 6 cookies = 8 cupcakes = $\dfrac{1}{2}$ of her money. So 1 cupcake = $\dfrac{1}{16}$ of money and 1 cookie = $\dfrac{1}{48}$ of money. Remaining money after first spend = $\dfrac{1}{2}$; she used $\dfrac{2}{3}$ of it = $\dfrac{1}{3}$ of total on more cookies. Number of extra cookies = $\dfrac{1}{3} \div \dfrac{1}{48} = 16$. Total cookies = 16 + 6 = 22. Answer: 22.


Place values after the decimal point: 8 is tenths, 9 is hundredths, 6 is thousandths. So the digit in the hundredths place is 9.


Total marks for both tests = average × 2 = 70 × 2 = 140. Science marks = 140 − 68 = 72.


Mrs Tan cooks 0.35 kg of rice every day. How many kilograms of rice does she cook in 60 days?


Find the value of 14 + (30 − 18) ÷ 6 × 2. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of 923 ÷ 4. Express your answer as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


What is the missing number in the box?<br>4 : 7 = 32 : <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

4 × 8 = 32, so the ratio is multiplied by 8. Missing number = 7 × 8 = 56.


Mrs Tan had some money at first. She spent \(\dfrac{2}{3}\) of her money on a watch and \(\dfrac{1}{5}\) of her money on food. She had $100 left. How much did she have at first? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The mass of a book is 3.08 kg. Find the total mass of 6 such books. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


The drink stall sold 2651 packet drinks in January. The number of packet drinks sold in February was 44 more than the number of packet drinks sold in January. How many packet drinks were sold in February? Round your answer to the nearest ten. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

February = 2651 + 44 = 2695. Rounded to the nearest ten, 2695 ≈ 2700.


Mrs Singh deposits $15 000 in the bank for one year. The bank offers an interest of 4% per year. How much will Mrs Singh have in her bank at the end of one year? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The average mass of Mei Mei and her cousins was 45 kg. Mei Mei's mass was 53 kg. The average mass of her cousins was 43 kg. How many cousins did Mei Mei have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Mei Mei is 53 − 45 = 8 kg above the group average. Each cousin is 45 − 43 = 2 kg below the group average. To balance Mei Mei's +8 kg, the cousins must total −8 kg, so number of cousins = 8 ÷ 2 = 4.


Sarah spent \(1\dfrac{1}{4}\) h in the morning to complete her Science project. She spent \(1\dfrac{7}{10}\) h in the afternoon to complete her Chinese project. What was the total amount of time she spent on completing both her Science and Chinese projects?


The side of a square is \(6\dfrac{2}{5}\) cm. What is the perimeter of the square?


The table shows the number of books sold in Everygreen bookshop from January to May.
January: 88, February: 75, March: 82, April: 69, May: 71.
What was the average number of books sold from January to May? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Junie bought a book from ABC Bookshop. She had forgotten how much she paid for the book. However, she remembered that the book cost $30 when rounded to the nearest dollar. She remembered the following about the cost of the book:
- It showed 2 decimal places.
- All the digits are different.
- The digits she saw in the tenths and hundredths places are 1, 4 or 5.
How many possible costs of the book are there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Rounded to nearest dollar = $30, so the cost is $29.50 to $30.49. Tenths and hundredths digits come from {1,4,5} and must differ. Possible costs: $29.51, $29.54, $30.14, $30.15, $30.41, $30.45 — and all digits in the whole number must also differ. The valid costs total 6.


Anna and James had the same amount of money at first. Anna bought some pens and had $4.30 left. James wanted to buy highlighters only. The number of highlighters that James wanted to buy was the same as the number of pens Anna bought. However, he was short of $8.70. Each pen cost $1.20 and each highlighter cost $2.50. How much money did Anna have at first? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The difference in money James would need versus Anna's leftover = $4.30 + $8.70 = $13 (this is the extra cost of buying highlighters instead of pens). Each highlighter costs $2.50 − $1.20 = $1.30 more than a pen. Number bought = $13 ÷ $1.30 = 10. Anna spent on pens = 10 × $1.20 = $12, so she had $12 + $4.30 = $16.30 at first.


Chin Lee is 12 years older than Ming Shi. In 5 years' time, the ratio of Ming Shi's age to Chin Lee's age will be 5 : 9. How old is Chin Lee now? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In 5 years the age difference is still 12. Ratio 5 : 9 means difference is 9 − 5 = 4 units = 12, so 1 unit = 3. Chin Lee in 5 years = 9 units = 9 × 3 = 27. Chin Lee now = 27 − 5 = 22 years old.


The average of 8 numbers is 45. When 2 of the numbers are removed, the average of the remaining numbers is 32. The difference between the 2 numbers that are removed is 6.
(a) Find the sum of the remaining numbers. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What are the 2 numbers that are removed? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

(a) 8 − 2 = 6 numbers remain; sum = 32 × 6 = 192. (b) Sum of all 8 = 45 × 8 = 360. Sum of the 2 removed = 360 − 192 = 168. They differ by 6: larger = (168 + 6) ÷ 2 = 87, smaller = 87 − 6 = 81.


Farhana baked some cupcakes. \(\dfrac{1}{5}\) of the cupcakes were chocolate cupcakes and the rest were banana cupcakes. She sold \(\dfrac{4}{7}\) of the chocolate cupcakes and 51 banana cupcakes. She then had \(\dfrac{2}{5}\) of the cupcakes left.
(a) How many chocolate cupcakes did she sell? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many cupcakes did she bake in all? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let total = T. Chocolate = \(\dfrac{1}{5}T\), banana = \(\dfrac{4}{5}T\). She sold \(\dfrac{4}{7}\) of chocolate, so chocolate left = \(\dfrac{3}{7}\times\dfrac{1}{5}T=\dfrac{3}{35}T\). Cupcakes left = \(\dfrac{2}{5}T=\dfrac{14}{35}T\), so banana left = \(\dfrac{14}{35}T-\dfrac{3}{35}T=\dfrac{11}{35}T\). Banana sold = \(\dfrac{4}{5}T-\dfrac{11}{35}T=\dfrac{28-11}{35}T=\dfrac{17}{35}T=51\), so \(\dfrac{1}{35}T=3\) and T = 105. (a) Chocolate sold = \(\dfrac{4}{7}\times\dfrac{1}{5}\times105=\dfrac{4}{35}\times105=12\). (b) Total = 105.


Kean Yew had 7200 shuttlecocks. He packed the shuttlecocks into as many bags of 7 shuttlecocks as possible and had some shuttlecocks left unpacked. He sold all his shuttlecocks and received $3608. Each bag of shuttlecocks was sold at $3.50.
(a) How many shuttlecocks were left unpacked? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Each of the shuttlecocks left unpacked was sold at the same price. How much did each of the shuttlecocks left unpacked sell at? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 7200 ÷ 7 = 1028 remainder 4, so 4 shuttlecocks were left unpacked. (b) Money from bags = 1028 × $3.50 = $3598. Money from unpacked = $3608 − $3598 = $10. Each unpacked = $10 ÷ 4 = $2.50.