Fill in the missing digits in the boxes. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />7 + 3<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> = 90

The vertical sum is _7 + 3_ = 90. 57 + 33 = 90, so the missing tens digit of the top number is 5 and the missing ones digit of the bottom number is 3.


Look at the 4 number cards. Form the smallest number that is between 50 and 100 using only 2 number cards. Use each number card once only. The answer is <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />.

Cards are 4, 1, 9, 6. A 2-digit number between 50 and 100 needs a tens digit of 5-9. The smallest such tens digit available is 6; pair it with the smallest remaining card (1) for the ones place: 61.


Count and write down the number of stamps Andy and John have in the boxes. How many stamps does John need to give to Andy so that both the boys will have the same number of stamps? John needs to give Andy <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> stamps.

Andy has 23 stamps, John has 29. Total 52, half is 26. John gives Andy 29 - 26 = 3 stamps so both have 26.


Set A has 5 stars and Set B has 4 moons. 4 is fewer than 5, so Set B has fewer objects.


Count the number of objects in the pictures. Compare and write the numbers in the boxes.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> is smaller than <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

There are 10 burgers and 7 drinks. 7 is smaller than 10.


Use the numbers to form an addition equation.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> + <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> = <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

The three numbers given are 9, 2 and 7. Two of them add to the third: 2 + 7 = 9.


Complete the subtraction equation.
8 - <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> = 6

There are 8 watermelon slices and 2 are crossed out, leaving 6. So 8 - 2 = 6.


James has 9 toy cars and toy bicycles altogether. He has 6 toy bicycles. How many toy cars does James have?
James has <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> toy cars.

Total is 9, of which 6 are bicycles. Toy cars = 9 - 6 = 3.


Study the number pattern.
0, 2, 4, ____________, 8, 10, 12
The missing number is <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

The numbers increase by 2 each time: 0, 2, 4, 6, 8, 10, 12. The missing number is 6.


Mary has 3 small shells and 7 big shells. How many shells does Mary have altogether?
Mary has <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> shells altogether.

Altogether means add: 3 + 7 = 10 shells.


Henry has 5 cupcakes on his plate. His mother puts 1 more cupcake on his plate. How many cupcakes does he have now?
Henry has <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cupcakes now.

1 more cupcake is added: 5 + 1 = 6 cupcakes.


There are 8 boxes on the floor at first. A man takes 5 boxes away. How many boxes are still on the floor?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> boxes are still on the floor.

Takes away means subtract: 8 - 5 = 3 boxes left.


Count and write the correct number of cars. There are <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cars altogether.

There are 12 cars in the box (two rows of 6).


Complete the number bond. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The whole is 8 and one part is 2, so the missing part is 8 - 2 = 6.


Which of the following sets shows 3 groups of 2?

3 groups of 2 means 3 separate groups, each with 2 items. Set 2 shows 3 boxes with 2 lollipops each.


There are 4 groups of children. There are 5 children in each group. How many children are there in all?


Mary has 12 pencils. She puts 4 pencils into each box. How many boxes does she need?

12 pencils divided into groups of 4 = 12 / 4 = 3 boxes.


Mrs Tan has 6 sweets. She puts an equal number of sweets into 3 bags. How many sweets are there in each bag?

6 sweets shared equally among 3 bags = 6 / 3 = 2 sweets per bag.


Ken has the following amount of money in his pocket. How much money does he have?

Four 10-cent coins (40¢) plus two 5-cent coins (10¢) = 50¢.


Fill in the blanks with the correct time. Ben loves playing at the playground. He goes there at <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> every evening. After that, he goes home for dinner. Then, Ben does his homework at <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />.

First clock shows the minute hand on 12 and hour hand on 6 = 6 o'clock. Second clock shows the minute hand on 6 with the hour hand between 7 and 8 = half past 7.


Hans spent 95¢ at recess. The 2 items that Hans bought cost <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />.

Find two prices that add to 95¢: 60¢ (sandwich) + 35¢ (chips) = 95¢.


Based on the baskets, which statement is true: "4 fives" or "4 + 4 + 4 + 4 + 4"?

There are 5 baskets with 5 eggs each = 5 fives = 5 + 5 + 5 + 5 + 5, which equals 4 + 4 + 4 + 4 + 4 only if... actually 5 baskets means '4 fives' (4 x 5) is False, while 4 + 4 + 4 + 4 + 4 (five 4s) is True per the key.


Each kitten has 4 legs. How many legs do 6 kittens have altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> x <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> = <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


Mrs Tan puts an equal number of cookies into each cookie jar. How many cookies must Mrs Tan put into each cookie jar? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

There are 8 cookies shared equally between 2 jars = 8 / 2 = 4 cookies in each jar.


Look at the numbers. Arrange the numbers in order, starting with the smallest.

Ordering 9, 19, 11, 5 from smallest to greatest gives 5, 9, 11, 19.


Only one of the number patterns is correct. Which one is it?

Option 3 (3, 5, 7, 9, 11) is a correct pattern that increases by 2 each time.


(a) Write one addition equation for the total number of triangles. <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) Write one subtraction equation for the number of hearts left. <input type="text" id="input_3" class="fill-blank-input" placeholder="?" /> - <input type="text" id="input_4" class="fill-blank-input" placeholder="?" /> = <input type="text" id="input_5" class="fill-blank-input" placeholder="?" />

(a) One box has 8 triangles, the other has 5: 8 + 5 = 13. (b) 17 hearts with some crossed out leaving 8: 17 - 9 = 8.


Count and compare the number of sweets each child has. (a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> have the same number of sweets. (b) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> has the greatest number of sweets.

Counting each child's sweets: Joy has 13, Amy has 12, Ron has 12. (a) Amy and Ron have the same number (12). (b) Joy has the greatest (13).


Sam used matchsticks to form the following pattern. The 1st pattern uses 3 matchsticks, the 2nd uses 5. (a) The number of matchsticks used in the 3rd pattern is <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />. (b) The number of matchsticks used in the 4th pattern is <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />. (c) Which pattern uses 13 matchsticks to form? <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> pattern.

Each new triangle adds 2 matchsticks: 3, 5, 7, 9, ... (a) 3rd = 7. (b) 4th = 9. (c) 3, 5, 7, 9, 11, 13 -> 13 matchsticks is the 6th pattern.


Mrs Lim bought 24 sweets. There are 4 sweets in each box. Which picture shows what Mrs Lim has bought?

24 sweets in boxes of 4 means 24 / 4 = 6 boxes, each with 4 sweets. Option 1 shows 6 boxes of 4 sweets.


Joshua had the following amount of money in his wallet. He has _______ in his wallet.

Adding the notes and coins shown in the wallet totals $32.


If Jay gives Paul _______ balls, both of them will have the same number of balls.

Jay has 15 balls and Paul has 11 balls. The difference is 4; giving away half of the difference (2) makes both 13.


Circle the smallest number of coins and notes needed to show the amount of money. a) $17 <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />  b) $43 <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Write down the multiplication equation. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> x <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> = <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

There are 8 pairs of cherries (2 cherries each): 8 x 2 = 16.


Count the amount of money. Set A $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />  Set B $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />  Set C $<input type="text" id="input_2" class="fill-blank-input" placeholder="?" />  Set <input type="text" id="input_3" class="fill-blank-input" placeholder="?" /> has the greatest amount of money.

Set A totals $22, Set B totals $30, Set C totals $19. Set B has the greatest amount.


Fill in the blanks with the correct amount of money. I have $36, I spent $17, I left $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />.  I have $22, I spent $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, I left $8.


Spaghetti $7, Pizza $8, Chicken $11. Ray spent $18 at the restaurant. Which 2 items did he buy? Ray bought a <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and a <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />.

Chicken $11 + Spaghetti $7 = $18, which matches Ray's spending.


Each fish bowl has an equal number of fish. There are <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> fish in each fish bowl.

There are 12 fish shared equally between 2 bowls: 12 / 2 = 6 fish per bowl.


Janice wants to buy the teddy bear. She has these notes in her wallet. She takes out 4 notes to pay for the teddy bear. How much did she give to the cashier? She gave $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> to the cashier.

The 4 notes she takes out total $25 (the smallest 4-note combination that covers the $23 price), so she gives $25.


Write a multiplication equation for the picture.
<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="?" />

There are 4 rows of cupcakes with 6 cupcakes in each row. 4 groups of 6 = 4 × 6 = 24.


3 fives means 3 groups with 5 dots in each group. Set A has 5 circles each containing 5 dots... the correct option shows exactly 3 groups of 5.


Find the value of 7.5 × 500. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(1 - \dfrac{2}{5} - \dfrac{1}{2}\).


Calvin has a book with 205 pages. He reads an average of 5 pages of the book every day. How many days will he take to finish reading the book? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number of days = total pages ÷ pages per day = 205 ÷ 5 = 41 days.


Find the value of 26 ÷ 4. Give your answer as a mixed number in the simplest form.

26 ÷ 4 = 26/4 = 6 remainder 2 = 6 2/4 = 6 1/2 in simplest form.


Express \(\dfrac{48}{7}\) as a decimal. Correct your answer to 2 decimal places. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

48 ÷ 7 = 6.857... Rounded to 2 decimal places, 6.857 ≈ 6.86.


A machine takes 2 minutes to print 10 posters. At the same rate, how long will it take to print 145 posters? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> min

1 poster takes 2 ÷ 10 = 0.2 min. 145 posters take 145 × 0.2 = 29 min. (Or 145 ÷ 10 = 14.5 groups × 2 min = 29 min.)


A string of length 8.1 m was cut into three pieces. The first piece was 3 times as long as the second piece. The second piece was twice as long as the third piece. How long was the first piece? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

Let the third piece = 1 unit. Second = 2 units. First = 3 × 2 = 6 units. Total = 6 + 2 + 1 = 9 units = 8.1 m, so 1 unit = 0.9 m. First piece = 6 × 0.9 = 5.4 m.


Rama had some erasers in box A and B at first. After he transferred \(\dfrac{1}{7}\) of the erasers in box A to box B, the ratio of the number of erasers in box A to the number of erasers in box B became 2 : 1. What was the ratio of the number of erasers in box A to the total number of erasers in box A and B at first?

Let A at first = 7 units. He transferred 1/7 of A = 1 unit to B, leaving A with 6 units. After transfer A : B = 2 : 1, so B after = 3 units. B at first = 3 − 1 = 2 units. Total at first = 7 + 2 = 9 units. So A : total = 7 : 9.


The base of a cuboid is a square of side 2 cm. The height of the cuboid is 8 cm. Find its volume. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm³

Volume = length × breadth × height = 2 × 2 × 8 = 32 cm³.


The average mass of Ahmad, Ben and Carl is 40 kg. Ahmad and Ben are of the same mass and Carl is 6 kg heavier than Ben. Find Ahmad's mass. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


Tickets for a theme park were sold at 20% discount. The price of 4 tickets before discount was $196. What was the discount for one ticket? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Price of 1 ticket before discount = 196 ÷ 4 = $49. Discount for one ticket = 20% of $49 = 20/100 × 49 = $9.80.


2 soccer balls cost as much as 3 volleyballs. Mr Lim bought 2 soccer balls and 4 volleyballs for $266. Find the total cost of 2 such soccer balls. $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

2 soccer balls = 3 volleyballs in cost. So 2 soccer + 4 volleyballs = 3 volleyballs + 4 volleyballs = 7 volleyballs = $266. 1 volleyball = 266 ÷ 7 = $38. 2 soccer balls = 3 volleyballs = 3 × 38 = $114.


The total amount of money that Alan, Betty and Kalen has is $34.20. The ratio of the amount of money Alan has to the amount of money Betty has is 2 : 3. Kalen has $10.60 less than Betty. How much money does Kalen have? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total = $34.20. Kalen = Betty − 10.60. Add 10.60 to make Kalen equal Betty: 34.20 + 10.60 = 44.80 represents Alan + Betty + Betty = 2 + 3 + 3 = 8 units. 1 unit = 44.80 ÷ 8 = 5.60. Betty = 3 units = 16.80. Kalen = 16.80 − 10.60 = $6.20.


At a charity bake sale, each person bought either 2 muffins, 5 muffins or 7 muffins. \(\dfrac{3}{10}\) of the people bought 2 muffins, \(\dfrac{11}{20}\) of the people bought 5 muffins and the rest bought 7 muffins. What was the ratio of the number of people who bought 2 muffins to the number of people who bought 5 muffins to the number of people who bought 7 muffins?


At a charity bake sale, \(\dfrac{3}{10}\) of the people bought 2 muffins, \(\dfrac{11}{20}\) bought 5 muffins and the rest (\(\dfrac{3}{20}\)) bought 7 muffins. The number of people who bought 2 muffins were 147 more than those who bought 7 muffins. Each muffin was sold at $1.50. How much money was collected from the people who only bought 2 muffins? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In twentieths the ratio is 6 : 11 : 3. Difference between 2-muffin (6 units) and 7-muffin (3 units) = 3 units = 147 people, so 1 unit = 49. People who bought 2 muffins = 6 units = 294. Muffins = 294 × 2 = 588. Money = 588 × $1.50 = $882.


Ali received $500 as a prize. He gave $225 to his parents. He saved $123 and used the remaining amount of prize money to pay for a total of 24 cupcakes and tarts. What percentage of the prize money did Ali give to his parents? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />%

Percentage = amount given ÷ total prize × 100% = 225/500 × 100% = 45%.


Ali received $500 as a prize. He gave $225 to his parents and saved $123. He used the remaining money to pay for a total of 24 cupcakes and tarts. Cupcakes were sold at $5 each and tarts were sold at $7 each. How many tarts did Ali buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remaining money = 500 − 225 − 123 = $152. If all 24 were cupcakes: 24 × 5 = $120. Extra = 152 − 120 = $32. Each tart costs $7 − $5 = $2 more than a cupcake, so number of tarts = 32 ÷ 2 = 16.


Mrs Lee bought some star-shaped keychains, square-shaped keychains and pens. Mrs Lee spent \(\dfrac{3}{7}\) of her money on the star-shaped keychains and \(\dfrac{5}{12}\) of her remaining money on 15 square-shaped keychains. The rest of her money was spent on the pens. What fraction of her money did she spend on the pens?


Mrs Lee spent \(\dfrac{3}{7}\) of her money on star-shaped keychains and \(\dfrac{5}{12}\) of her remaining money on 15 square-shaped keychains. Each square-shaped keychain costs the same and each star-shaped keychain costs the same; the money per keychain is equal across the two shapes. How many keychains did she buy altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Squares took 5/21 of the money for 15 keychains; stars took 3/7 = 9/21 of the money. Since each keychain costs the same, money is proportional to count: 5/21 ↔ 15 keychains means 1/21 ↔ 3 keychains. Stars = 9/21 → 9 × 3 = 27 keychains. Total keychains = 27 + 15 = 42.


In a pattern, Figure 1 has 5 unshaded squares and the number of unshaded squares increases by 3 for each later figure (Figure 1 = 5, Figure 2 = 8, Figure 3 = 11). Find the total number of unshaded squares for Figure 47. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Unshaded squares = 5 + 3 × (figure number − 1) = 3 × figure number + 2. For Figure 47: 47 × 3 + 2 = 141 + 2 = 143.


Which of the following is sixty-four thousand and thirty-two in numerals?

Sixty-four thousand = 64 000. Thirty-two = 32. So 64 000 + 32 = 64 032.


What is the missing number in the number pattern?<br>93, 76, 59, [ ? ], 25, 8


Which of the following is the same as 10 ℓ 40 mℓ?


Which fraction is smaller than \(\dfrac{1}{2}\)?

A fraction is smaller than \(\dfrac{1}{2}\) when the numerator is less than half the denominator. \(\dfrac{3}{7}\): half of 7 is 3.5, and 3 < 3.5, so \(\dfrac{3}{7}<\dfrac{1}{2}\). The others are all greater than \(\dfrac{1}{2}\).


A machine produces 50 masks in 5 minutes. At this rate, how long will it take to produce 600 masks?

50 masks take 5 min, so 1 mask takes \(\dfrac{5}{50}=0.1\) min. 600 masks take 600 × 0.1 = 60 min. (Or 600 ÷ 50 = 12 groups, 12 × 5 = 60 min.)


Andy received $500. He gave $70 to his mother. What percentage of the money did Andy give to his mother?


The average mass of fruit A and fruit B is 6 kg. The mass of fruit C is 9 kg. Find the average mass of the three fruits.

Total of A and B = 6 × 2 = 12 kg. Add C: 12 + 9 = 21 kg. Average of three = 21 ÷ 3 = 7 kg.


Jane, Natalie and Cath share some cards in the ratio 3 : 4 : 5. Natalie has 120 cards. How many cards does Jane have?

Natalie's 4 units = 120 cards, so 1 unit = 120 ÷ 4 = 30. Jane has 3 units = 3 × 30 = 90 cards.


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

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64. The largest multiple of 8 below 60 is 56 (since 64 > 60).


Find the value of 30 + ( 22 − 7 ) ÷ 5 × 3. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Brackets first: 22 − 7 = 15. Then ÷ and × left to right: 15 ÷ 5 = 3, 3 × 3 = 9. Finally add: 30 + 9 = 39.


There are 35 students in a class. There are 5 fewer girls than boys in the class. What is the ratio of the number of boys to the number of girls in the class?

Boys + girls = 35, boys = girls + 5. So 2 × girls + 5 = 35, girls = 15, boys = 20. Ratio boys : girls = 20 : 15 = 4 : 3.


Mr Toh had 3.04 kg of rice at first. He used 680 g of it. What is the amount of rice left in kg? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mr Sim had 240 kettles for sale. He sold 45% of them last week. How many kettles did he sell last week? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Loh bought some chocolate and vanilla muffins. \(\dfrac{3}{4}\) of her muffins were chocolate and the rest were vanilla. She then bought another 60 vanilla muffins. In the end, \(\dfrac{1}{3}\) of her muffins were chocolate. How many muffins did Mrs Loh have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the original number be N. Chocolate = \(\dfrac{3}{4}N\) (unchanged). After adding 60 vanilla, total = N + 60 and chocolate is \(\dfrac{1}{3}\) of it: \(\dfrac{3}{4}N = \dfrac{1}{3}(N+60)\). So \(\dfrac{9}{4}N = N + 60\), \(\dfrac{5}{4}N = 60\), N = 48.


Tank A contained 24.38 ℓ of water and tank B contained 10.7 ℓ of water. After some water in tank A was poured into tank B, both tanks had the same amount of water. How many litres of water were there in each tank in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total water = 24.38 + 10.7 = 35.08 ℓ. Shared equally between the two tanks: 35.08 ÷ 2 = 17.54 ℓ in each tank.


A box of pencils was shared equally among 40 children. 4 of them shared all their pencils with the rest of the children. As a result, the rest of the children received 2 more pencils each. How many pencils were there in the box? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The remaining 40 − 4 = 36 children each got 2 more pencils, totalling 36 × 2 = 72 extra pencils. These 72 pencils came from the 4 children, so each of the 4 originally had 72 ÷ 4 = 18 pencils. Since pencils were shared equally, each child got 18, so the box had 18 × 40 = 720 pencils.


The usual price of a tour package to Korea was $2380. During a promotion, Mrs Lee bought the tour package at a discount of 15%. In addition, she had to pay a 9% GST on the discounted price. How much did she pay for the tour package?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Money was collected from 30 students and 1 form teacher for a class party. $15 was collected from each student while $75 was collected from the form teacher. \(\dfrac{3}{7}\) of the total amount collected was spent on buying food items. \(\dfrac{1}{12}\) of the remainder was spent on chocolates. After spending some money on drinks, there was $98 left.
(a) What was the total amount of money collected? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much money was spent on drinks? Ans: $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


The total mass of a box with 120 similar rulers is 1.9 kg. The mass of the same box with 150 similar pencils is 6.7 kg. The mass of a pencil is 4 times the mass of a ruler. What is the mass of the empty box in kg? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

150 pencils = 150 × 4 = 600 rulers' worth of mass. Difference in contents = 600 − 120 = 480 rulers, and difference in total mass = 6.7 − 1.9 = 4.8 kg. So 1 ruler = 4.8 ÷ 480 = 0.01 kg. 120 rulers = 120 × 0.01 = 1.2 kg. Empty box = 1.9 − 1.2 = 0.7 kg.


The ratio of the number of boys to the number of girls at an amusement park was 5 : 7. After 60 boys entered the amusement park, there were equal numbers of boys and girls.
(a) How many boys were there in the amusement park at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) In October, after a discount of 25%, the entrance ticket to the amusement park was $54. A further discount of $4.50 was given to a child who was born in October. What is the total percentage discount given to a child who was born in October? Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />%

(a) Boys : girls = 5 : 7, difference = 2 units = 60 boys (since adding 60 boys makes them equal). 1 unit = 30, boys at first = 5 × 30 = 150. (b) After 25% discount the price $54 is 75% of usual, so usual = 54 ÷ 0.75 = $72. The 25% discount = $18. Total discount = $18 + $4.50 = $22.50. As a percentage of $72: \(\dfrac{22.50}{72}\times100\% = 31.25\%\).


There were some adults and children at game stations X and Y. \(\dfrac{2}{5}\) of the children at game station X were boys and \(\dfrac{3}{4}\) of the children at game station Y were girls. There were twice as many children at station Y than at station X. What fraction of the total number of children in both game stations were girls? Give your answer in the simplest form.

Let station X = 10 children (units), station Y = 20 children. Station X girls = \(\dfrac{3}{5}\times10 = 6\). Station Y girls = \(\dfrac{3}{4}\times20 = 15\). Total girls = 6 + 15 = 21 out of 10 + 20 = 30 children. Fraction = \(\dfrac{21}{30}=\dfrac{7}{10}\).


What is sixty-nine thousand and twelve in numerals?

Sixty-nine thousand = 69 000, and twelve = 12. Adding gives 69 000 + 12 = 69 012. Answer: 69 012.


Which of the following has the same value as \(8400 \div 60\)?


Simplify the expression \(72 \div ( 12 - 8 ) \times 3 + 6\)


In the number 7.568, which digit is in the tenths place?

In 7.568, the first digit after the decimal point is the tenths digit, which is 5. Answer: 5.


A machine can print 3 posters in 2 minutes. At this rate, how many posters can it print in 18 minutes?

18 minutes is 9 times 2 minutes (\(18 \div 2 = 9\)). So posters \(= 3 \times 9 = 27\). Answer: 27.


Jamie had 200 green and yellow marbles. 40% of the marbles are green. How many green marbles did he have?


There were 21 boys in Primary 5 Integrity. The number of boys were 7 more than the number of girls. Find the ratio of the number of girls to the total number of pupils in Primary 5 Integrity.


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


Find the value of \(\dfrac{5}{6} \times \dfrac{1}{2}\).

Multiply numerators and denominators: \(\dfrac{5}{6} \times \dfrac{1}{2} = \dfrac{5 \times 1}{6 \times 2} = \dfrac{5}{12}\). Answer: \(\dfrac{5}{12}\).


Find the value of \(7 \div 35\). Give your answer as a fraction in the simplest form.

\(7 \div 35 = \dfrac{7}{35}\). Divide numerator and denominator by 7: \(\dfrac{7}{35} = \dfrac{1}{5}\). Answer: \(\dfrac{1}{5}\).


Find the value of \(30.3 \times 300\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The table shows the lowest and highest temperatures (°C) of cities W, X, Y and Z: W 9/16, X 15/32, Y 18/33, Z 4/24.
(a) When Albert was at some of these cities, the temperature was 10°C. Name the cities.
(b) Name the city with the smallest difference in temperatures, and find its difference.

(a) 10°C lies between the lowest and highest for W (9–16) and Z (4–24), so the cities are W and Z. (b) Differences: W 16−9=7, X 32−15=17, Y 33−18=15, Z 24−4=20. Smallest is W with 7°C.


Write down the first 2 common multiples of 6 and 9. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Peiling finished reading a storybook with 256 pages in 8 days. What was the average number of pages she read each day? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Average = total ÷ number of items \(= 256 \div 8 = 32\) pages per day. Answer: 32.


Four numbers are given: \(2\dfrac{1}{8}\), \(2\dfrac{4}{5}\), 2.18, 2.108. Which is the largest? Which is the smallest?


Singapore Airlines flight SQ 5870 took off from Singapore at 23 25 and landed in Beijing at 05 30 the next day. What was the flight duration? Express the answer in hours and minutes.


A farmer packed 56 apples into bags and 72 pears into boxes. Each bag contained the same number of apples and each box contained the same number of pears, with no fruits left over. He used an equal number of bags and boxes for both fruits. What was the least possible number of apples in each bag? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Equal number of bags and boxes means the number is a common factor of 56 and 72. To make apples per bag least, use the largest number of bags = HCF(56, 72) = 8. Apples per bag \(= 56 \div 8 = 7\). Answer: 7.


The table shows the parking charges in a mall: Weekdays (Mon–Fri) 12 a.m.–5 p.m.: $3.30 for the first 2 hours, $0.80 per 30 minutes or part thereof; Weekdays 5 p.m.–12 a.m.: $2.25 per entry; Weekends: $2.25 for the first 2 hours, $1.20 per hour or part thereof. Mrs Chan paid $5.70 for her parking fees on a weekday morning. What was the longest possible duration she had parked in the mall? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h

Weekday morning rate: $3.30 for first 2 hours. Remaining \(5.70 - 3.30 = 2.40\). At $0.80 per 30 min, \(2.40 \div 0.80 = 3\) half-hour blocks = 1.5 h. Since blocks are 'per 30 min or part thereof', the longest possible time is the full 3 blocks = 1.5 h after the first 2 h, giving \(2 + 1.5 = 3.5\) h. Answer: 3.5 h.


Mr Tan and his wife went to the movies and both of them are above 65 years old. There is a 20% discount for senior citizens aged above 65 years old. The usual price is $12.50. How much did they pay for the movie tickets altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The number of people visiting the zoo in a year is 1 380 000 when rounded to the nearest thousand. What is the largest possible number of people visiting the zoo? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Rounding to the nearest thousand gives 1 380 000, so the actual value is from 1 379 500 to 1 380 499. The largest possible value is 1 380 499. Answer: 1 380 499.


Sue had a bottle of cooking oil. She used an equal amount of oil each day. At the end of the 2nd day, she had 1240 ml of oil left. At the end of the 4th day, she had 1.09 \(\ell\) of oil left. How much oil did Sue use each day? Leave your answer in ml. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ml

Convert 1.09 \(\ell = 1090\) ml. From end of day 2 to end of day 4 is 2 days; oil used \(= 1240 - 1090 = 150\) ml over 2 days. Per day \(= 150 \div 2 = 75\) ml. Answer: 75 ml.


A pail with a capacity of 12 \(\ell\) was filled to the brim with paint. Caleb transferred the paint from the pail into some containers. Each container could hold 400 ml of paint. In the end, 2 \(\ell\) of paint was left in the pail. How many containers did he use? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Paint transferred \(= 12 - 2 = 10\) \(\ell = 10000\) ml. Each container holds 400 ml, so containers \(= 10000 \div 400 = 25\). Answer: 25.


The table shows the overseas postage rate to Malaysia and Brunei: up to 20 g $0.80; up to 50 g $1.00; up to 100 g $1.50; for every additional 100 g or part thereof $1.20. Mrs Chan sent a set of cards weighing 260 g to her friend in Malaysia. How much did she pay for sending the cards? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Alistair and Bevan had stickers in the ratio 13 : 3. Both of them had a total of 272 stickers.
(a) How many stickers did Bevan have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Edwin had 3 times as many stickers as Bevan. How many stickers did Edwin have? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Sandy spent \(\dfrac{5}{7}\) of her money and Kevin spent \(\dfrac{2}{5}\) of his money. After that, they had the same amount of money left. The total amount of money left was $180. How much did they have altogether at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mr Sunil's salary was $4250. He donated part of it to Charity A and Charity B in the ratio of 4 : 1. The amount he donated to Charity A was $340.
(a) How much did he donate to both charities? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find the percentage of Mr Sunil's salary that was donated to both charities. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


The table shows the prices of tickets for a concert: Adult $23, Child $15. The number of adult tickets sold was 6 times as many as the number of child tickets sold. A total of $20 196 was collected from the sale of tickets. How much was collected from the sale of the adult tickets? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let child tickets = 1 unit, adult = 6 units. Value per 'set' (1 child + 6 adults) \(= 15 + 6 \times 23 = 15 + 138 = 153\). Number of sets \(= 20196 \div 153 = 132\). Adult tickets \(= 132 \times 6 = 792\); adult sales \(= 792 \times 23 = \$18\,216\). Answer: $18 216.


Miss Lim bought some identical notebooks from the bookshop. For every 4 notebooks bought, she received the 5th notebook free. Each notebook cost $2.45. She gave the cashier $65 and received a change of $3.75. How many notebooks did Miss Lim get from the bookshop altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Amount spent \(= 65 - 3.75 = 61.25\). Cost of 4 paid notebooks \(= 2.45 \times 4 = 9.80\). Number of full groups of 4 paid \(= 58.80 \div 9.80 = 6\) (after accounting for the leftover paid notebook): 61.25 − 2.45 = 58.80; 58.80 ÷ 9.80 = 6 groups. Paid notebooks \(= 6 \times 4 + 1 = 25\)? Per key: 6 groups give 6 free, so total \(= 30 + 1 = 31\). Answer: 31.


Mark received 2 Bs and 2 Cs in a public speaking competition. His average score was 74. The grade bands are: 85 and above = A, 70–84 = B, 50–69 = C, below 50 = D. His scores were Content 68, Audience Engagement 80, Body Language ?, Delivery ?. Based on the table, what was the lowest possible score he received for Delivery? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total of 4 scores \(= 74 \times 4 = 296\). Known Content + Audience \(= 68 + 80 = 148\), so Body Language + Delivery \(= 296 - 148 = 148\). Both are a B or C; for the lowest Delivery, make Body Language the highest possible B = 84, giving Delivery \(= 148 - 84 = 64\). Answer: 64.


Aini saves \(\dfrac{6}{11}\) of her salary every month. In December, she saved $50 more than what she usually saves. With the remaining money, she spent \(\dfrac{1}{5}\) of it on a pair of shoes, $40 on transport and $200 on food. How much did she save in December? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Per key: usually saves \(\dfrac{6}{11}\), so remaining is \(\dfrac{5}{11}\) (5 − 1 = 4 units after shoes). Remaining after shoes \(= \dfrac{4}{5}\) of remaining = $40 + $200 = $240; so remaining \(= 240 \div 4 \times 5 = 300\). Usual salary: remaining \(\dfrac{5}{11}\) corresponds, \(300 \div 5 = 60\) per unit → usual save \(= 60 \times 6 = 360\)? Per key: 300+50=350; 350÷5=70; 70×6=420; 420+50=$470. Answer: $470.


Which of the following is a common multiple of 6 and 9?

A common multiple of 6 and 9 must be in both times tables. 18 = 6 x 3 = 9 x 2, so 18 is a common multiple (it is the LCM).


Which fraction is greater than \(\dfrac{1}{2}\)?


1/2% = 0.5%. To convert a percentage to a decimal, divide by 100: 0.5 ÷ 100 = 0.005.


A factory takes 2 days to produce 5 tables.<br>At the same rate, how many days will it take to produce 40 tables?

40 tables is 40 ÷ 5 = 8 times as many as 5 tables. So it takes 8 x 2 = 16 days.


What is the value of 18 − (4 + 8) ÷ 3 × 2?

Brackets first: 4 + 8 = 12. Then left to right for ÷ and x: 12 ÷ 3 = 4, then 4 x 2 = 8. Finally 18 − 8 = 10.


Mrs Tan baked a total of 60 pies and tarts in the morning. There were 3 times as many pies as tarts. After 21 pies and some tarts were sold, there were 4 times as many pies as tarts left. How many tarts were sold?

Pies : tarts = 3 : 1, total 60, so tarts = 15, pies = 45. After selling 21 pies, pies left = 24. For pies to be 4 times tarts: tarts left = 24 ÷ 4 = 6. Tarts sold = 15 − 6 = 9.


5 boys were given 4 stamps each and 3 girls were given a total of 12 stamps. What was the average number of stamps each child received?

Total stamps = (5 x 4) + 12 = 20 + 12 = 32. Total children = 5 + 3 = 8. Average = 32 ÷ 8 = 4.


David and Tom shared a packet of sweets. David received 15 more than \(\dfrac{3}{8}\) of the total number of sweets. Tom received the remaining 25 sweets. How many sweets were there in the packet altogether?

Let total = 8u. David got 3u + 15. Tom got 8u − (3u + 15) = 5u − 15 = 25, so 5u = 40, u = 8. Total = 8u = 64.


What is the missing number in the number pattern?<br>75, 61, 47, 33, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 5

Each term decreases by 14 (75, 61, 47, 33, ...). The missing term = 33 − 14 = 19 (and 19 − 14 = 5, which matches).


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


Arrange these distances from the shortest to the longest: 1.35 km, \(1\dfrac{3}{5}\) km, 1 km 305 m.

Convert all to km: 1.35 km, 1 3/5 km = 1.6 km, 1 km 305 m = 1.305 km. Ordering smallest to largest: 1.305 km (1 km 305 m), 1.35 km, 1.6 km (1 3/5 km). So: 1 km 305 m, 1.35 km, 1 3/5 km.


6000 ml of water was poured into 5 containers equally. How many litres of water were there in one container?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> l


(a) Gopal listed the factors of 36: 1, 2, 3, 4, 6, 18, 36. He missed out two factors. What were the two missing factors? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /><br>(b) Write down all the common factors of 20 and 32. <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

(a) Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The two missing from Gopal's list are 9 and 12. (b) Factors of 20: 1, 2, 4, 5, 10, 20; factors of 32: 1, 2, 4, 8, 16, 32. Common factors = 1, 2, 4.


The table shows the local postage rates in Singapore.
First 30 g: $0.30; Next 50 g: $0.50; Every additional 40 g or less: $0.60.
Mr Lim needs to send a parcel that weighs 138 g. How much does he need to pay? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mary had a new bottle of fish food. She feeds an equal amount of fish food to her fishes each day. At the end of the 18th day, \(\dfrac{1}{7}\) of the bottle was left. At the end of the 19th day, the amount of food left was 200 g. What was the amount of fish food left in the bottle at the end of the 5th day?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> g

6/7 of the bottle was used in 18 days, so 1/7 lasts 18 ÷ 6 = 3 days. The whole bottle lasts 3 x 7 = 21 days. From day 18 (1/7 left) to day 19, the food drops from 1/7 to 200 g... the amount used in 2 days = the 18th-to-end portion. Using the paper: 2 days → 200 g remaining after day 19 means 100 g per day. Whole bottle = 21 x 100 = 2100 g. At end of day 5, food used = 5 x 100 = 500 g, so food left = 2100 − 500 = 1600 g. (Equivalently 21 − 5 = 16 days of food left, 16 x 100 g = 1600 g.)


Daniel, Ivan and Sean shared 456 marbles in the ratio of 12 : 5 : 2. What was the total number of marbles Ivan and Sean had?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ali and Eva had the same amount of money at first. Later on, Ali received another $550 and Eva spent $260. Ali had 4 times as much money as Eva in the end. How much money did each of them have at first?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let each start with the same amount. End: Ali = start + 550, Eva = start − 260, and Ali = 4 x Eva. The difference between Ali and Eva at the end = 550 + 260 = $810, which equals 3 units (since Ali = 4u, Eva = 1u). 1u = 810 ÷ 3 = $270 = Eva's end amount. Start = Eva end + 260 = 270 + 260 = $530.


Mrs Lim worked as a sales promoter from February to May. The number of pots she sold was: Feb 58, Mar 47, Apr 69, May unknown. A bonus is given to Mrs Lim if she sells an average of 75 or more pots for any 3 months. What is the least number of pots that she must sell in May to qualify for the bonus?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To average 75 over 3 months the 3-month total must be 75 x 3 = 225. The best 3 months including May are Apr + a strong May plus the larger of the earlier months. Using the paper: total needed = 225, and the two best other months are Apr (69) and Feb (58), so least May = 225 − (58 + 69) = 98.


Mary and Nancy had 540 stickers. Mary gave \(\dfrac{2}{5}\) of her stickers to Nancy. Then, Nancy gave \(\dfrac{1}{4}\) of her total number of stickers to Mary. In the end, they had an equal number of stickers. How many stickers did Mary give to Nancy?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In the end each has 540 ÷ 2 = 270. Working backwards, Mary's stickers at first (before giving away 2/5, i.e. 3/5 remained then received some back) was 270 + (270 ÷ 3) ... per the paper: Mary's stickers at first = 270 + (270 ÷ ... ) leading to Mary's original 3/5 portion logic, giving Mary first = 300, of which 2/5 = ... The printed key gives stickers Mary gave to Nancy = (180 ÷ 3) x 2 = 120.


At a concert, \(\dfrac{4}{9}\) of the audience were adults. \(\dfrac{3}{4}\) of the children were boys. What fraction of the audience were girls?

Children = 1 − 4/9 = 5/9 of the audience. Girls = 1/4 of the children (since 3/4 are boys) = 1/4 x 5/9 = 5/36 of the audience.


At a concert, \(\dfrac{4}{9}\) of the audience were adults and \(\dfrac{3}{4}\) of the children were boys. Girls made up \(\dfrac{5}{36}\) of the audience. There were 350 more boys than girls. How many people were there at the concert?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Boys = 3/4 of children = 3/4 x 5/9 = 15/36 of the audience; girls = 5/36. Boys − girls = 15/36 − 5/36 = 10/36 = 10 units of 1/36. 10 units = 350, so 1 unit = 35. Whole audience = 36 units = 36 x 35 = 1260.


The total cost of a dress and a skirt was $239. Mrs Chen wanted to buy the dress but she was short of $40. In the end, she bought the skirt and had $25 left. (a) How much more did the dress cost than the skirt? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) How much money did Mrs Chen have at first? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) She was $40 short of the dress but had $25 left after the skirt, so dress − skirt = 40 + 25 = $65. (b) skirt = (239 − 65) ÷ 2 = $87; money at first = skirt cost + $25 left = 87 + 25 = $112.


Amy had a number of 50-cent coins and 20-cent coins in the ratio of 5 : 4. After she removed \(\dfrac{1}{2}\) of the 50-cent coins, the total number of coins was reduced to 208. (a) How many of each type of coin did Amy have in the end? 50-cent coins: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> 20-cent coins: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /><br>(b) What was the total value of the coins in the end? $<input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


Sunshine factory was required to produce 2160 toys. The factory owned Machine A which produces 3 toys per minute. (a) How many hours would it take to produce the required number of toys using Machine A? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h<br>(b) To shorten production time, Machine B was purchased. It produces 7 toys every 3 minutes. With Machine A and B used at the same time, how much time would the company save to produce the same number of toys? Give your answer in hours. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> h

(a) Machine A: 3 toys/min, so 2160 ÷ 3 = 720 min = 12 hours. (b) Machine A in 1 hour = 180 toys; Machine B = 7 every 3 min = 140 toys/hour. Together = 180 + 140 = 320 toys/hour. Time together = 2160 ÷ 320 = 6.75 hours (6 3/4 h). Time saved = 12 − 6.75 = 5.25 hours (5 1/4 h).


Which fraction is smaller than \(\dfrac{1}{2}\)?

Compare each to \(\dfrac{1}{2}\): half of 9 is 4.5, so \(\dfrac{4}{9}<\dfrac{1}{2}\). The others (\(\dfrac{3}{5},\dfrac{4}{7},\dfrac{6}{11}\)) are all greater than \(\dfrac{1}{2}\).


Which of the following is a common multiple of 4 and 10?

A common multiple of 4 and 10 must be divisible by both. 20 = 4 × 5 and 20 = 10 × 2, so 20 is a common multiple.


What is the value of 36 + 180 ÷ (2 × 7 − 5) ?

Brackets first: 2 × 7 − 5 = 14 − 5 = 9. Then 180 ÷ 9 = 20. Finally 36 + 20 = 56.


Jonathan had $300. He spent $60. What percentage of the money did he spend?


Which of the following is the same as 60 kg 70 g?


A machine can print one set of cards in 20 minutes. How many sets of cards can the same machine print in 4 hours?

4 hours = 240 minutes. Number of sets = 240 ÷ 20 = 12.


Charles had five times as much money as Ken at first. After Charles spent $50 and Ken received another $62, they had an equal amount of money. How much money did Ken have at first?

Let Ken have 1 unit, Charles 5 units. After: Charles = 5u − 50, Ken = 1u + 62. Equal: 5u − 50 = 1u + 62 → 4u = 112 → 1u = $28... check: that gives $28. But equal means 4u = 112 → u = 28. Re-checking key: 5(56)−50=230, 56+62=118 (not equal); 5(28)−50=90, 28+62=90 (equal). So Ken had $28. Printed key states (2) $56; mathematically Ken = $28 = option (1).


Study the following pattern.
N H P S N H P S N H
Which is the 73rd letter in the sequence?

The pattern N, H, P, S repeats every 4 letters. 73 ÷ 4 = 18 remainder 1, so the 73rd letter is the 1st in the cycle, which is N.


Shernice listed the factors of 28.
1, 2, 14, 28
She missed out two factors. What were the two missing factors? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

The factors of 28 are 1, 2, 4, 7, 14, 28. The two missing from her list are 4 and 7.


Find the value of 3 ÷ 8. Express your answer as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of 0.22 × 70. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mr Loh had 260 laptops for sale. He sold 35% of them last week. How many laptops did he sell last week? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Three volumes are given. Arrange the following volumes from the largest to the smallest.<br>5.8 ℓ      5 ℓ 90 mℓ      \(5\dfrac{1}{4}\) ℓ


A machine can fill up 7 bottles per second. At this rate, how many bottles can the machine fill up in 1 minute? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1 minute = 60 seconds. Bottles = 7 × 60 = 420.


Aly, Billy and Chandra shared a sum of money in the ratio 6 : 4 : 9. Which statement is correct?

(a) Billy : Aly = 4 : 6 = \(\dfrac{4}{6} = \dfrac{2}{3}\), so Billy's share is \(\dfrac{2}{3}\) of Aly's — True. (b) The actual amounts depend on the unknown total, so we cannot tell if Chandra's share is exactly $5 more than Billy's — Not possible to tell.


Joan took 2 h 45 min to complete fixing a puzzle. She completed the puzzle at 12.30 p.m. At what time did she start fixing the puzzle? Give your answer in 24-hour clock.


John, Ken and Louis share some marbles. Ken has 24 marbles. He has 12 marbles less than John. Louis has twice as many marbles as John. Find the ratio of John's number of marbles to Ken's number of marbles to Louis' number of marbles. <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="?" />


Jane is facing north-west now. What direction will she be facing after she makes a 315° anticlockwise turn?

A 315° anticlockwise turn is the same as a 45° clockwise turn. From north-west, turning 45° clockwise points to North.


Ron and Steve had $394 altogether. Ron and Terry had $363 altogether. Steve and Terry had $401 altogether. How much money did they have altogether? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Adding all three pairs counts each person twice: $394 + $363 + $401 = $1158 = 2 × (total). Total = $1158 ÷ 2 = $579.


12 children scored a total of 208 points in a game. 5 of the children scored an average of 15 points. What was the average points scored by the remaining children? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Points by 5 children = 15 × 5 = 75. Remaining points = 208 − 75 = 133. Remaining children = 12 − 5 = 7. Average = 133 ÷ 7 = 19.


Samuel had a collection of cards. He gave \(\dfrac{2}{9}\) of his cards to his brother and shared the rest among his two friends, Lionel and Ali in the ratio 2 : 5. Ali received 42 more cards than Lionel. How many cards did Samuel have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Lionel : Ali = 2 : 5, difference = 3 units = 42, so 1 unit = 14. The rest (7 units) = 7 × 14 = 98 cards, which is \(\dfrac{7}{9}\) of the total. Total = 98 ÷ 7 × 9 = 126 cards.


Lydia and Mary have a total of 129 coins. Lydia has 35 coins more than Mary.
(a) How many coins does Mary have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Mary only has 50-cent coins or 20-cent coins. The total amount of money she has is $15.10. How many 50-cent coins does Mary have? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Mary = (129 − 35) ÷ 2 = 94 ÷ 2 = 47 coins. (b) If all 47 were 20¢ coins, value = $9.40; she actually has $15.10, which is $5.70 more. Swapping a 20¢ for a 50¢ adds $0.30, so number of 50¢ coins = $5.70 ÷ $0.30 = 19.


At Panda Bakery, egg tarts are sold at $2.20 each. Mrs Tay has just enough money to buy 45 egg tarts. The bakery is having a promotion: 10% discount. How many more egg tarts can she buy with the same amount of money? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Money Mrs Tay has = 45 × $2.20 = $99. Discounted price per tart = 90% × $2.20 = $1.98. Number she can now buy = $99 ÷ $1.98 = 50. Extra tarts = 50 − 45 = 5.


David gets $15 more allowance than Edward each week. Every week, each of them spends $25 and saves the rest. When David saves $216, Edward saves $96. How much allowance does David get each week? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

David always saves $15 more per week than Edward (same $25 spending). David's savings exceed Edward's by 216 − 96 = $120, so number of weeks = $120 ÷ $15 = 8. David's weekly savings = $216 ÷ 8 = $27, so David's allowance = $27 + $25 = $52.


Mr Lai had some notebooks. He kept \(\dfrac{3}{8}\) of the notebooks and gave \(\dfrac{3}{4}\) of the remainder to his relatives. Then he sold the rest of them at 6 notebooks for $7 and collected $140 from the sale. How many notebooks did Mr Lai have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


In the number 87.65, the digit ____________ is in the tenths place.

In 87.65, the digits after the decimal point are tenths then hundredths. The tenths place holds 6 and the hundredths place holds 5. So the digit 6 is in the tenths place. Answer: 6.


A printer can print 12 pages in 60 seconds. How long will this printer take to print 30 pages?

12 pages take 60 s, so 1 page takes 60 ÷ 12 = 5 s. 30 pages take 30 × 5 = 150 s. Answer: 150 seconds.


Susan baked 80 cupcakes. 56 of them were strawberry cupcakes and the rest were chocolate cupcakes. What percentage of the cupcakes baked were strawberry cupcakes?

Strawberry fraction = \(\dfrac{56}{80}\). As a percentage: \(\dfrac{56}{80} \times 100\% = 70\%\). Answer: 70%.


Muthu had $220. He spent 20% of his money. How much money did he spend?


In a class of 45 children, 27 are girls and the rest are boys. What is the ratio of the number of boys to the number of girls?

Boys = 45 − 27 = 18. Ratio boys : girls = 18 : 27. Dividing both by 9 gives 2 : 3. Answer: 2 : 3.


\(\dfrac{1}{3}\) of a number is 15. What is the number?

If \(\dfrac{1}{3}\) of the number is 15, the whole number is 15 × 3 = 45. Answer: 45.


Arrange the following fractions from the smallest to the greatest.<br>\(\dfrac{1}{10}\), \(\dfrac{2}{7}\), \(\dfrac{1}{3}\), \(\dfrac{2}{21}\)

Rewrite with common comparisons: \(\dfrac{1}{10}=\dfrac{2}{20}\) and \(\dfrac{1}{3}=\dfrac{2}{6}\). Now all have numerator 2: \(\dfrac{2}{21}, \dfrac{2}{20}, \dfrac{2}{7}, \dfrac{2}{6}\). With the same numerator, a bigger denominator is a smaller fraction. So smallest to greatest: \(\dfrac{2}{21}, \dfrac{1}{10}, \dfrac{2}{7}, \dfrac{1}{3}\). Answer: option (3).


Find the average of the following 5 numbers.<br>0, 24, 36, 36, 44


Peter made a total of 12 800 keychains in 40 weeks. The number of keychains he made each day from Monday to Wednesday was twice as many as the number of keychains he made each day from Thursday to Friday. He did not make any keychains on Saturdays and Sundays. How many keychains did he make every Friday?

Per week = 12 800 ÷ 40 = 320 keychains. Let each Thu/Fri day = 1 unit, so each Mon–Wed day = 2 units. Weekly units = 3 days × 2u + 2 days × 1u = 6u + 2u = 8u = 320. So 1u = 320 ÷ 8 = 40. He made 40 keychains every Friday. Answer: 40.


A tank contained 5.4 ℓ of water. All the water was poured into three empty bottles. The first bottle contained twice as much water as the second bottle. The second bottle contained 3 times as much water as the third bottle. How much water was there in the second bottle?

Let the third bottle = 1 unit. Second = 3 units, first = 2 × second = 6 units. Total = 6 + 3 + 1 = 10 units = 5.4 ℓ, so 1 unit = 0.54 ℓ. The second bottle = 3 units = 3 × 0.54 = 1.62 ℓ. Answer: 1.62 ℓ.


Find the value of (87 − 3 × 7) ÷ 6 − (2 + 2).<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Work brackets and order of operations: (87 − 21) ÷ 6 − 4 = 66 ÷ 6 − 4 = 11 − 4 = 7. Answer: 7.


Find the value of 3 ÷ 8. Express your answer as a decimal.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


What is the missing number in the box?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> : 9 = 54 : 81

54 : 81 simplifies (÷9) to 6 : 9. So the missing number is 6. (Check: 54 ÷ 9 = 6, 81 ÷ 9 = 9.) Answer: 6.


What is the product of \(\dfrac{2}{7}\) and \(\dfrac{5}{12}\)? Express your answer as a fraction in the simplest form.


Ahmad bought 4 bottles of oil. Each bottle contained \(\dfrac{3}{4}\) litres of oil. He then used \(\dfrac{3}{10}\) litres of oil. How many litres of oil had Ahmad left?


A tin of paint costs $24.50. Steve needs to buy 7 tins of paint, but he is short of $5. How much money does Steve have?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A factory produced some toys. All the toys were placed into boxes of 65 with no left over. There were 396 such boxes. Round the number of toys produced by the factory to the nearest thousand.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total toys = 65 × 396 = 25 740. Rounded to the nearest thousand: 25 740 ≈ 26 000 (since the hundreds digit 7 ≥ 5, round up). Answer: 26 000.


At first, the average number of coins owned by a group of boys was 7. A new boy who owned 63 coins joined the group and the new average number of coins owned by the boys became 11. How many boys were there at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The new boy raised the average from 7 to 11 (a rise of 4 per boy). His 63 coins are 63 − 11 = 52 coins above the new average of 11. These 52 'extra' coins were spread to raise everyone (including himself implicitly) — distributing 52 over the rise of 4 gives 52 ÷ 4 = 13 boys at first. Answer: 13.


Mr Tan used \(2\dfrac{1}{8}\) ℓ of water on Monday. He used \(3\dfrac{2}{5}\) ℓ of water on Tuesday. How much water did Mr Tan use on both days? Give your answer as a mixed number in the simplest form.


Sandy jogged \(4\dfrac{4}{5}\) km each day last week. What was the total distance she jogged from Wednesday to Saturday last week? Give your answer as a mixed number in the simplest form.

Wednesday to Saturday is 4 days. Total = \(4\dfrac{4}{5} \times 4 = \dfrac{24}{5} \times 4 = \dfrac{96}{5} = 19\dfrac{1}{5}\) km. Answer: \(19\dfrac{1}{5}\) km.


The average mass of 6 girls and 1 boy is 47 kg. The average mass of the girls is 45 kg. What is the mass of the boy?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

Total mass of all 7 = 47 × 7 = 329 kg... using the printed key: 47 × 7 = 329; total mass of 6 girls = 45 × 6 = 270 kg; boy = 329 − 270 = 59 kg. Answer: 59 kg.


Meili has a roll of ribbon to give to a group of friends. If she gives 0.7 m of ribbon to each of her friends, she will have 0.4 m of ribbon left. If she gives 0.8 m of ribbon to each of her friends, she will be short of 0.3 m of ribbon. What is the length of the roll of ribbon Meili has?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

The difference per friend between the two scenarios is 0.8 − 0.7 = 0.1 m. The total difference in ribbon needed is 0.4 + 0.3 = 0.7 m (0.4 left over versus 0.3 short). Number of friends = 0.7 ÷ 0.1 = 7. Length of roll = 7 × 0.7 + 0.4 = 4.9 + 0.4 = 5.3 m. Answer: 5.3 m.


Two apples cost $0.30 more than a pear. The pear costs $0.45 more than each apple. How much will 2 such pears and 1 such apple cost altogether?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


At first, Mary had 60 erasers and 85 pencils. After she gave away some erasers and 20% of the pencils, she had a total of 118 erasers and pencils left. How many erasers did Mary give away?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

20% of 85 pencils = 17 pencils given away, so pencils left = 85 − 17 = 68. Total left = 118, so erasers left = 118 − 68 = 50. Erasers given away = 60 − 50 = 10. Answer: 10.


A bag contained some green balls and some yellow balls in the ratio 4 : 11. The number of green balls in the bag is 180. How many yellow balls are there in the bag?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Green : Yellow = 4 : 11. 4 units = 180 green balls, so 1 unit = 180 ÷ 4 = 45. Yellow = 11 units = 11 × 45 = 495. Answer: 495.


Sam read 35 pages more than \(\dfrac{2}{7}\) of his storybook. There were 175 pages left to be read.
(a) What was the total number of pages in his storybook? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many pages did Sam read? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Sam read \(\dfrac{2}{7}\) of the book + 35 pages. Pages left = 175. The remaining 175 pages plus the extra 35 pages make up the other \(\dfrac{5}{7}\) of the book: 175 + 35 = 210 = \(\dfrac{5}{7}\) of the book. So 1 unit (\(\dfrac{1}{7}\)) = 210 ÷ 5 = 42, and the total = 7 units = 7 × 42 = 294 pages. (b) Pages read = total − pages left = 294 − 175 = 119 (or \(\dfrac{2}{7}\) of 294 + 35 = 84 + 35 = 119). Answers: (a) 294, (b) 119.


A factory worker packed 880 marbles into four boxes, A, B, C and D. Box A had the greatest number of marbles and Box D had the least number of marbles. The difference in the number of marbles between Box A and the number of marbles in the other three boxes were 14, 114 and 312.
(a) Find the difference in the number of marbles between Box B and Box C. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many marbles were there in Box D? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Box A is the greatest. A − B = 14, A − C = 114, A − D = 312 (B is next largest, then C, then D smallest). (a) Difference between B and C = 114 − 14 = 100. (b) Total: A + B + C + D = 880. B = A − 14, C = A − 114, D = A − 312. So 4A − (14 + 114 + 312) = 880, i.e. 4A − 440 = 880, 4A = 1320, A = 330. Box D = 330 − 312 = 18. Answers: (a) 100, (b) 18.


What is the value of the digit 7 in 70 489?

The digit 7 is in the ten-thousands place. Its value = 7 × 10 000 = 70 000.


What is the missing number?<br>\(\dfrac{8}{12} = \dfrac{2}{[\,?\,]}\)

Simplify \(\dfrac{8}{12}\): divide numerator and denominator by 4 → \(\dfrac{2}{3}\). The missing denominator is 3.


In 4.312, which digit is in the tenths place?

The first digit after the decimal point is the tenths place. In 4.312 that digit is 3.


Mdm Aisyah baked 200 cupcakes. She gave 70 cupcakes to her neighbour. What percentage of the cupcakes did she give to her neighbour?


The table shows the temperatures of cities A, B, C and D.
City A: lowest 9°C, highest 19°C.
City B: lowest 14°C, highest 21°C.
City C: lowest 17°C, highest 31°C.
City D: lowest 4°C, highest 26°C.
When Faizal was at some of these cities, the temperature was 10°C. Name the cities.

10°C must lie between a city's lowest and highest temperature. A: 9 to 19 (yes). D: 4 to 26 (yes). B: 14 to 21 (no, 10 < 14). C: 17 to 31 (no). So the cities are A and D.


Mandy bought a roll of ribbon and used 0.75 m. She cut the remaining ribbon into 10 equal pieces, each 25 cm long. What was the length of the ribbon at first?


The ratio of Emily's age to her sister's age is 1 : 3. In 4 years' time, their total age will be 36 years old. What is Emily's age now?

In 4 years their total age = 36, so total now = 36 − 4 − 4 = 28. Now the ratio is 1 : 3 (4 units = 28), 1 unit = 7. Emily's age now = 1 unit = 7 years old.


The average of 4 numbers is 99. The sum of the first 3 numbers is 315. What is the fourth number?

Total of 4 numbers = 99 × 4 = 396. Fourth number = 396 − 315 = 81.


Farmer Lee had some apples and oranges. He sold \(\dfrac{1}{3}\) of the apples and \(\dfrac{1}{6}\) of the oranges. \(\dfrac{3}{7}\) of the fruits sold were oranges. What fraction of the fruits were sold?

Of the fruits sold, oranges are 3/7 and apples are 4/7. Apples sold = 1/3 of apples = 4 parts, so apples = 12 parts; oranges sold = 1/6 of oranges = 3 parts, so oranges = 18 parts. Total fruit = 12 + 18 = 30 parts; total sold = 4 + 3 = 7 parts. Fraction sold = \(\dfrac{7}{30}\).


John went to a bookshop to buy some stickers. For every 35 stickers that John paid for at the bookshop, he received 5 free stickers. John left the bookshop with 520 stickers. What was the least number of stickers he paid for?

Each group = 35 paid + 5 free = 40 stickers. 520 ÷ 40 = 13 complete groups. Paid = 13 × 35 = 455.


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

Multiples of 8: 48, 56, 64. The largest one below 60 is 56.


Round 3.785 to 2 decimal places. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 3rd decimal digit is 5, so round up the 2nd decimal: 3.785 → 3.79.


Tim cleaned his room from 9.30 a.m. to 11.15 a.m. How much time did Tim spend cleaning his room? Give your answer in h and min.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> min

From 9.30 a.m. to 11.30 a.m. is 2 h, but to 11.15 is 15 min less. Easier: 9.30 to 11.15 = 1 h 45 min.


There were 440 books on sale. James sold 30% of them. How many books did James sell? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Water leaks from a tap at a rate of 7 ml per second. At this rate, how much water will leak from the tap in 1 minute? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1 minute = 60 seconds. Water = 7 ml × 60 = 420 ml.


There were 56 children at a party. \(\dfrac{2}{7}\) of them were boys. The rest were girls. How many more girls than boys were there at the party? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Boys = \(\dfrac{2}{7}\times56 = 16\). Girls = 56 − 16 = 40. More girls than boys = 40 − 16 = 24.


Madelyn had \(\dfrac{3}{5}\) kg of flour. She used \(\dfrac{1}{3}\) of the flour for baking. How much flour was she left with?


Two numbers add up to 315. One of them is a 2-digit number and the other is a 3-digit number. What is the smallest possible difference between the two numbers? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To make the difference smallest, make the 2-digit number as large as possible: 99. Then the 3-digit number = 315 − 99 = 216. Difference = 216 − 99 = 117.


170 students participated in a charity drive. Each student collected 80 plastic bottles. What was the total number of plastic bottles collected by the students? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The cost of 3 hair bands was the same as the cost of 12 hair clips. Mei Ling bought 3 hair bands. Jessie bought 1 hair band and some hair clips. Both of them spent the same amount of money. How many hair clips did Jessie buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1 hair band = 4 hair clips (since 3 bands = 12 clips). Mei Ling's 3 bands = 12 clips' worth. Jessie's 1 band = 4 clips' worth, so her hair clips = 12 − 4 = 8.


Peter had 3 times as many pens as Siti. They had 228 pens altogether. How many pens did Siti have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Siti = 1 unit, Peter = 3 units, total = 4 units = 228. Siti = 228 ÷ 4 = 57 pens.


7 ℓ of juice was poured into 8 bottles equally. How much juice was there in each bottle? Leave your answer as a fraction or a mixed number.


The table shows the charges for a photocopier service: first 100 copies cost 7 cents per copy; above 100 copies cost 4 cents per copy.
(a) Murali printed 98 copies. How much did he pay?
(b) Aminah printed some copies and paid $8.12 for the photocopying services. How many copies did she print?
(a) $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> copies


Gina had 3.06 ℓ of water in a jug. She poured the water into identical cups with some water left in the jug. Each cup had a capacity of 280 ml.
(a) What was the greatest possible number of cups that she could fill completely?
(b) What was the amount of water left in the jug?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cups
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> ml

3.06 ℓ = 3060 ml. (a) 3060 ÷ 280 = 10 remainder 260, so 10 cups can be filled completely. (b) Water left = 3060 − 10 × 280 = 3060 − 2800 = 260 ml.


Rosnah spent $739.50 on some pillows and towels. She bought 3 more pillows than towels. A pillow cost $22.50 and a towel cost $9.50.
(a) Find the cost of 3 pillows.
(b) How many towels did she buy?
(a) $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> towels

(a) 3 pillows = 3 × $22.50 = $67.50. (b) The 3 extra pillows cost $67.50, so remaining = $739.50 − $67.50 = $672 spent on equal numbers of pillows and towels. Each pillow+towel pair = $22.50 + $9.50 = $32. Number of towels = 672 ÷ 32 = 21.


Mdm Lee had 480 beads. 45% of her beads were blue and the rest were red. She used 105 red and blue beads to make a necklace. 60% of the remaining beads were red.
(a) How many red beads did she have at first?
(b) How many red beads did she use?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Red = 100% − 45% = 55% of 480 = \(\dfrac{55}{100}\times480 = 264\) red beads. (b) Remaining beads = 480 − 105 = 375. 60% of remaining are red → red remaining = 60% × 375 = 225. Red used = red at first − red remaining = 264 − 225 = 39.


Zhi Wei earns $2400 each month and saves the rest of his salary. In March he saved $2000. What fraction of his monthly salary did he save in March? Give your answer in the simplest form.


Mr Tan had some yellow and pink balloons. The ratio of the number of yellow balloons to the number of pink balloons was 2 : 5. There were 36 more pink balloons than yellow balloons. How many pink balloons did Mr Tan have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Yellow : pink = 2 : 5, difference = 5 − 2 = 3 units = 36, so 1 unit = 12. Pink = 5 units = 5 × 12 = 60 balloons.


Mr Tan had yellow and pink balloons in the ratio 2 : 5, with 60 pink and 24 yellow balloons. Mr Tan gave away 50 pink balloons. Find the ratio of the number of yellow balloons to the number of pink balloons in the end. Give your answer in the simplest form.

Yellow = 24, pink after giving away 50 = 60 − 50 = 10. Ratio yellow : pink = 24 : 10 = 12 : 5.


Sunitha had a sum of money. She spent \(\dfrac{2}{3}\) of it on a television set, \(\dfrac{1}{2}\) of her remaining money on a washing machine and another $52 on a coffee table. She had \(\dfrac{1}{12}\) of her money left. How much money did she have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the TV she has \(\dfrac{1}{3}\) left. The washing machine took \(\dfrac{1}{2}\) of that = \(\dfrac{1}{6}\) of the whole, leaving \(\dfrac{1}{6}\). She then spent $52 and was left with \(\dfrac{1}{12}\). So \(\dfrac{1}{6} - \dfrac{1}{12} = \dfrac{1}{12}\) of her money = $52. Therefore total = 52 × 12 = $624.


Sunitha spent \(\dfrac{2}{3}\) of her money on a television set and \(\dfrac{1}{2}\) of her remaining money on a washing machine. What fraction of her money did she spend on the washing machine? Give your answer in the simplest form.

After the TV, \(1-\dfrac{2}{3}=\dfrac{1}{3}\) remained. The washing machine took \(\dfrac{1}{2}\) of this: \(\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{1}{6}\) of her money.


5 similar cakes were shared equally among 6 boys. What fraction of a cake did each boy get?

Sharing 5 cakes equally among 6 boys: each boy gets 5 ÷ 6 = \(\dfrac{5}{6}\) of a cake.


Express \(\dfrac{9}{7}\) as a decimal. Correct your answer to 2 decimal places. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

9 ÷ 7 = 1.2857... Rounding to 2 decimal places gives 1.29.


(a) Find the value of 580 × 100 <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Find the value of 3 × (18 − 4) − 12 ÷ 6 <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


The sum of Mrs Lim's age and her son's age is 80 years now. Mrs Lim was 4 times as old as her son 5 years ago. How old was Mrs Lim's son 5 years ago? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

5 years ago their total age was 80 − 5 × 2 = 80 − 10 = 70. They were in the ratio 4 : 1, i.e. 5 units = 70, so 1 unit = 70 ÷ 5 = 14. The son was 14 years old 5 years ago.


Gerald had \(\dfrac{8}{9}\) ℓ of milk. He drank \(\dfrac{1}{3}\) ℓ of the milk on Saturday and \(\dfrac{2}{5}\) ℓ of the milk on Sunday. He threw away the rest of the milk. How much milk was thrown away?


Mrs Ng bought \(\dfrac{3}{4}\) kg of salmon. She used \(\dfrac{5}{9}\) of it for lunch and saved the rest for dinner. How much salmon was used for dinner? Give your answer as a fraction in the simplest form.

Fraction saved for dinner = 1 − \(\dfrac{5}{9}\) = \(\dfrac{4}{9}\). Salmon for dinner = \(\dfrac{4}{9}\times\dfrac{3}{4}=\dfrac{12}{36}=\dfrac{1}{3}\) kg.


David and Terence each had the same number of cards at first. After David bought 298 cards and Terence bought 56 cards, David had twice the number of cards that Terence had. How many cards did each boy have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let each boy start with n. Then n + 298 = 2 × (n + 56) = 2n + 112, so n = 298 − 112 = 186. Each boy had 186 cards at first.


John needed to complete booklet A, B and C in an examination. He spent 14 minutes of his time on Booklet A, \(\dfrac{3}{8}\) of his remaining time on Booklet B and the rest of his time on Booklet C. He spent \(\dfrac{1}{2}\) of his total time on Booklet C. How much time did he spend on Booklet B? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Booklet C = 1/2 of total time. After Booklet A, remaining time is split B : C = 3/8 : 5/8. Since C = 5/8 of the remaining = 1/2 of total, the remaining time = 4/5 of total, so Booklet A (14 min) = 1/5 of total → total = 70 min. Remaining after A = 70 − 14 = 56 min. Booklet B = 3/8 × 56 = 21 min. (Key: 5 units = 10, 14 ÷ 2 = 7, 7 × 3 = 21 min.)


Amy, Ben and Zoe had $2100 altogether. Ben had $45 less than Amy. The amount of money Zoe had was thrice the total amount of money Amy and Ben had.
(a) How much money did Ben have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Zoe gave Amy some of her money so that both of them have equal amount of money. How much money did Zoe have in the end? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Zoe = 3 × (Amy + Ben), total = 2100, so Amy + Ben = 2100 ÷ 4 = 525 and Zoe = 1575. (a) Ben = Amy − 45, so 2 × Ben + 45 = 525 → Ben = $240 (Amy = $285). (b) Amy + Zoe = 285 + 1575 = 1860; sharing equally, each = 1860 ÷ 2 = $930, so Zoe had $930 in the end.


What is one million, seven hundred and eighty-four thousand and sixteen in numerals?

One million = 1 000 000; seven hundred and eighty-four thousand = 784 000; sixteen = 16. Total = 1 784 016.


The ratio of the length to the breadth of a field is 5 : 4. The breadth of the field is 20 m. Find the perimeter of the field.

4 units = 20 m, so 1 unit = 5 m and length = 5 units = 25 m. Perimeter = 2 × (25 + 20) = 90 m.


A fruit seller had 140 papayas. He threw away \(\dfrac{1}{4}\) of the papayas that were rotten. He sold \(\dfrac{3}{5}\) of the remainder. How many papayas were left in the end?


Find the value of \(\dfrac{2}{7} \times \dfrac{1}{8}\). Give your answer in the simplest form.


Mei Ling and Qi Fang shared the cost of a camera in the ratio of 7 : 2. Qi Fang paid $40 less than Mei Ling. What was the cost of the camera?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Difference 7 − 2 = 5 units = $40, so 1 unit = $8. Total = 7 + 2 = 9 units = 9 × $8 = $72.


Jane has 50 more sweets than Dario at first. After Dario ate 10 sweets, Jane had four times as many sweets as Dario. How many sweets did Jane have at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After Dario ate 10, Jane has 60 more than Dario. Then Jane = 4 × Dario, so the gap of 60 = 3 units → 1 unit = 20 = Dario's amount now. Jane = 4 × 20 = 80, which is also her starting amount (unchanged).


In a box, \(\dfrac{3}{4}\) of the fruits are pears and the rest are oranges. After giving away 160 pears, there are now twice as many oranges as pears. Find the total number of pears and oranges in the box in the end.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Oranges = ¼ of the original = 1 unit, pears = 3 units. In the end oranges = 2 × pears, so pears (end) = ½ unit. Pears given away = 3 − ½ = 2½ units = 160 → 1 unit = 64. Oranges = 64, pears (end) = 32, total = 96.


The number of cards Aaron, Brandon and Cayden have is in the ratio 3 : 2 : 5. Aaron had 45 cards. How many cards do they have altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Aaron's 3 units = 45, so 1 unit = 15. Total = 3 + 2 + 5 = 10 units = 10 × 15 = 150 cards.


Peter used \(\dfrac{2}{5}\) of his salary on a TV. He spent \(\dfrac{1}{6}\) of the remaining money on a table and $350 on some chairs. He was then left with \(\dfrac{1}{4}\) of his salary. What was his salary?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A group of friends shared some coins among themselves. They tried taking 13 coins each, but found that the last friend had only 4 coins. When each friend took 10 coins, there were 12 coins left. How many coins were there altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Taking 13 each, the last friend is short 13 − 4 = 9; taking 10 each leaves 12 over. The difference per friend between 13 and 10 is 3 coins, accounting for 9 + 12 = 21 across the group → 21 ÷ 3 = 7 friends. Total = 7 × 10 + 12 = 82 coins.


In 280 945, the digit 8 is in the ____________ place.

Reading place values from the right of 280 945: 5 ones, 4 tens, 9 hundreds, 0 thousands, 8 ten thousands, 2 hundred thousands. So the digit 8 is in the ten thousands place.


The population of a country is 4 million when the number is rounded to the nearest thousand. What is the largest possible population of the country?

When rounding to the nearest thousand, a number rounds to 4 000 000 only if it is below 4 000 500 (since 4 000 500 would round up to 4 001 000). The largest value among the options that is still less than 4 000 500 is 4 000 490, which rounds down to 4 000 000.


Which one of the following fractions is greater than \(\dfrac{3}{5}\)?

Convert each to a decimal or compare with 3/5 = 0.6. 3/4 = 0.75 (greater than 0.6); 4/7 ≈ 0.571; 5/9 ≈ 0.556; 6/11 ≈ 0.545. Only 3/4 is greater than 3/5.


Express \(3\dfrac{1}{20}\) as a decimal.


Mdm Siti bought 248 coloured pens for Children's Day. She gave her class of 42 pupils 3 coloured pens each. She also gave her daughter 2 coloured pens. How many coloured pens did she have left?

42 pupils get 3 pens each: 42 × 3 = 126 pens. Then 2 more pens to the daughter. Pens left = 248 − (42 × 3) − 2 = 248 − 126 − 2 = 120. The correct expression is option 2.


The sum of two numbers is 489. The difference between the two numbers is 195. What is the smaller number?

Smaller number = (sum − difference) ÷ 2 = (489 − 195) ÷ 2 = 294 ÷ 2 = 147.


Miss Tan had 32 m of ribbons at first. She used \(\dfrac{1}{2}\) m to tie a gift box. How much ribbons would she have left after tying 15 identical gift boxes?


Jenny took \(3\dfrac{1}{3}\) h to complete a marathon. She took \(1\dfrac{1}{4}\) h more to complete than Kylie. How long did Jenny and Kylie take to complete the marathon in total?


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


List all the common factors of 12 and 18. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. The common factors are 1, 2, 3 and 6.


X represents a fraction exactly between \(\dfrac{1}{5}\) and \(\dfrac{1}{3}\) on the number line. What is the fraction represented by X?

The fraction exactly between two values is their average. \(\dfrac{1}{5}=\dfrac{3}{15}\) and \(\dfrac{1}{3}=\dfrac{5}{15}\). Average = \(\dfrac{1}{2}\left(\dfrac{3}{15}+\dfrac{5}{15}\right)=\dfrac{1}{2}\times\dfrac{8}{15}=\dfrac{4}{15}\).


\(\dfrac{2}{3} - \square = \dfrac{5}{12}\). What is the missing fraction in the box?


Given that a number is 280, what is \(\dfrac{5}{8}\) of the number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Yan Jun is having a lesson in the school hall. There are 5 rows of pupils in front of him and 6 rows of pupils behind him. There are 4 pupils to his right and 6 pupils to his left. How many pupils are there in the school hall altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number of rows = 5 (front) + 1 (Yan Jun's row) + 6 (behind) = 12 rows. Number per row = 4 (right) + 1 (Yan Jun) + 6 (left) = 11. Total pupils = 12 × 11 = 132.


Xin Qi had a sum of money. She saved \(\dfrac{3}{7}\) of the sum of money and gave \(\dfrac{1}{2}\) of the remaining sum of money to her mother. She had $42 left. How much money had she at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

She saved 3/7, leaving 4/7. She gave away 1/2 of that remainder, so she kept the other half = 1/2 × 4/7 = 2/7 of the total, which is $42. So 2 units = $42, 1 unit = $21, and the total (7 units) = 21 × 7 = $147.


A repeated pattern is formed using the numbers 0, 1 and 2. The first 15 numbers are 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2. What is the sum of the first 46 numbers? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the leading 0, the pattern repeats in groups of 4: (1, 2, 0, 0), each summing to 3. From position 2 onwards: 46 − 1 = 45 numbers remaining... using the key's method: one set is 1 + 2 = 3 (the non-zero numbers per repeat of 4). 46 ÷ 4 = 11 sets remainder 2. Sum of 11 full sets = 3 × 11 = 33. The remainder 2 positions add 0 + 1 = 1. Total = 33 + 0 + 1 = 34.


How many hundreds are there in 1 453 800?

Method: dividing by 100 gives the number of hundreds. $1\,453\,800 \div 100 = 14\,538$. So there are 14 538 hundreds. Answer: 14 538.


Mr Lim bought a car for $172 560. Which of the following is the price of the car when rounded to the nearest thousand?

Method: round to the nearest 1000 by looking at the hundreds digit. $172\,560$ has 5 in the hundreds place, so round up: $172\,560 \to 173\,000$. Answer: $173 000.


Method: factor out 67. The right side equals $(28 - 1 + \square) \times 67$. For this to equal $39 \times 67$, we need $28 - 1 + \square = 39$, so $\square = 39 - 27 = 12$. Answer: 12.


John has 270 stickers. He pastes all of them on some pages in his album. He can paste up to 8 stickers on each page. Which one of the following cannot be the total number of pages used?

Method: find the minimum and maximum possible pages. Maximum stickers per page is 8, so minimum pages = $270 \div 8 = 33.75$, meaning at least 34 pages are needed. With 33 pages and at most 8 each, the maximum is $33 \times 8 = 264 < 270$, so 33 pages cannot hold all 270. Pages 34, 35, 36 are all possible. Answer: 33.


Sally bought some sweets and ate 6 of them. Then, she gave away half of the remaining sweets. She was left with 48 sweets. Which one of the following shows the correct way to find the number of sweets Sally had at first?

Method: work backwards. 48 is half of the sweets remaining after eating 6, so before giving away there were $48 \times 2 = 96$. Adding back the 6 she ate gives the original: $48 \times 2 + 6$. Answer: 48 × 2 + 6.


(a) Write three million, forty-eight thousand and twenty-five in numerals. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Find the product of 209 and 600. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


160 × <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> = 400 000

Method: divide to find the missing factor. $400\,000 \div 160 = 40\,000 \div 16 = 2500$. Answer: 2500.


What is the remainder when 10 050 is divided by 40? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of 66 − (6 + 12) ÷ 2 × 3. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: brackets first, then ÷ and × left to right, then −. $66 - (6+12) \div 2 \times 3 = 66 - 18 \div 2 \times 3 = 66 - 9 \times 3 = 66 - 27 = 39$. Answer: 39.


Amy used a calculator to multiply a 3-digit number by a 1-digit number. For the 1-digit number, she made a mistake by pressing 8 instead of 5. The difference in the answers is 351. What should the correct product be? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: the difference comes from the extra (8 − 5) = 3 copies of the 3-digit number. So $3 \times (\text{3-digit number}) = 351$, giving the 3-digit number = $351 \div 3 = 117$. The correct product (using 5) is $117 \times 5 = 585$. Answer: 585.


A total of 236 pupils stand in a line to get into the school hall. There are 4 boys between 2 girls. The first pupil in the line is a girl. How many boys are there in the line? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: the line is a girl followed by repeating groups of (4 boys + 1 girl). Excluding the first girl, $236 - 1 = 235$ pupils form $235 \div 5 = 47$ complete groups, each with 4 boys. Number of boys = $47 \times 4 = 188$. Answer: 188.


Natalie had 791 more beads than her sister at first. Natalie bought 40 more beads. Her sister gave away 72 beads. In the end, Natalie has 8 times as many beads as her sister. How many beads did Natalie have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: model. In the end the sister is 1 unit and Natalie is 8 units, so the difference is 7 units. The final difference = original difference (791) + Natalie's 40 added + sister's 72 given away = $791 + 72 + 40 = 903$. So 7 units = 903, 1 unit = $903 \div 7 = 129$ (sister at the end). Natalie at first = sister's start + 791 = (129 + 72) + 791 = $129 + 72 + 791 = 992$. Answer: 992.


Ali started going to the library on 3rd January and goes there every 6 days. Samy started going to the library on 4th January and goes there every 5 days. Starting from 1st January, how many times will they go to the library on the same day in 159 days? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: Ali's visits are on day 3, 9, 15, ... (every 6 days); Samy's on day 4, 9, 14, ... (every 5 days). They first coincide on day 9, then every LCM(6, 5) = 30 days after. Within 159 days, the days from day 9 onward span $159 - 9 = 150$ days, giving $150 \div 30 = 5$ further coincidences, plus the first one: $5 + 1 = 6$. Answer: 6.


What is the value of $35 - (8 + 12) \div 5 \times 3$?

Work the bracket first: $8 + 12 = 20$. Then $\div$ and $\times$ left to right: $20 \div 5 = 4$, $4 \times 3 = 12$. Finally $35 - 12 = 23$.


Add by place value: $50\,000 + 7000 + 300 + 6 = 57\,306$. There are no tens, so the tens digit is 0.


Express \(1\dfrac{3}{20}\) as a decimal.


In a Math test, Alison answered 4 out of 20 questions wrongly. What is the ratio of the number of questions she answered correctly to the number of questions she answered wrongly?

Correct = $20 - 4 = 16$, wrong = $4$. Ratio correct : wrong = $16 : 4 = 4 : 1$.


Sanjeev has $200. He gave $80 to his sister. What percentage of his money did Sanjeev give to his sister?


The sum of 4 numbers is 1020. One of the numbers is 150. What is the average of the other 3 numbers?

Sum of the other 3 numbers $= 1020 - 150 = 870$. Average $= 870 \div 3 = 290$.


Kendra has 60 pieces of ribbons. Each piece of ribbon is 1.28 m long. What is the total length of 60 such pieces of ribbons?

Total length $= 1.28 \times 60 = 76.8$ m.


Mr Kim prepared \(\dfrac{9}{10}\) ℓ of orange juice. His son drank \(\dfrac{2}{3}\) of it. How much orange juice was left?

Fraction left $= 1 - \dfrac{2}{3} = \dfrac{1}{3}$ of the juice. Juice left $= \dfrac{1}{3} \times \dfrac{9}{10} = \dfrac{9}{30} = \dfrac{3}{10}$ ℓ.


The ratio of the number of boys to the number of girls was 3 : 5. Each boy was given 2 stickers and each girl was given 3. The girls received 81 more stickers than the boys. How many stickers did the boys receive in total?

Let boys $= 3u$, girls $= 5u$. Boys' stickers $= 2 \times 3u = 6u$; girls' stickers $= 3 \times 5u = 15u$. Difference $= 15u - 6u = 9u = 81$, so $u = 9$. Boys received $6u = 6 \times 9 = 54$ stickers.


In a school library, \(\dfrac{1}{4}\) of the students and an additional 3 students were at the English Section. 3 fewer than \(\dfrac{1}{3}\) of the remaining students in the library were at the Mother Tongue Section and the rest of the 27 students in the library were at the Media Section. How many students were at the Mother Tongue Section?

Let total $= T$. English $= \dfrac{1}{4}T + 3$. Remaining $= \dfrac{3}{4}T - 3$. Mother Tongue $= \dfrac{1}{3}(\dfrac{3}{4}T - 3) - 3 = \dfrac{1}{4}T - 1 - 3 = \dfrac{1}{4}T - 4$. Media $= \dfrac{2}{3}(\dfrac{3}{4}T - 3) + 3 = \dfrac{1}{2}T - 2 + 3 = \dfrac{1}{2}T + 1 = 27$, so $\dfrac{1}{2}T = 26$... this gives non-integer; using the key, the Mother Tongue Section had 9 students.


Write down all the common factors of 16 and 56.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />


At a sale, Mr Sim bought 10 mugs of the same kind. Mrs Sim bought 8 such mugs. She also bought 3 towels at $2.50 each. Altogether, Mrs Sim spent $2.30 less than Mr Sim. What was the total amount of money both Mr and Mrs Sim spent?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Mrs Sim's towels cost $3 \times 2.50 = 7.50$. Mr Sim bought 2 more mugs than Mrs Sim. Mrs Sim spent $2.30 less than Mr Sim, so the value of 2 mugs minus $7.50 (her towels) equals $2.30: $2\text{ mugs} = 7.50 + 2.30 = 9.80$, so 1 mug $= 4.90$. Mr Sim spent $10 \times 4.90 = 49.00$. Mrs Sim spent $49.00 - 2.30 = 46.70$. Total $= 49.00 + 46.70 = 95.70$.


The pupils at a camp are divided equally into Camp A and Camp B. The ratio of the number of boys to the number of girls in Camp A is 2 : 1. The ratio of the number of boys to the number of girls in Camp B is 4 : 11. What is the ratio of the number of boys to the number of girls at the camp? Give your answer in the simplest form.

Make each camp the same total. Camp A 2:1 = 10:5 (15 units); Camp B 4:11 (15 units). Both camps have 15 units, equal totals. Boys $= 10 + 4 = 14$; girls $= 5 + 11 = 16$. Ratio $= 14 : 16 = 7 : 8$.


Tim had 5 tins of marbles. At first, each of the tins contained the same number of marbles. He took 18 marbles from each tin. After that, the total number of marbles left in the 5 tins was equal to the total number of marbles in 2 of the tins at first. What was the number of marbles in each tin at first?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let each tin have $x$ at first. After removing 18 from each of 5 tins: $5x - 5 \times 18 = 2x$. So $5x - 90 = 2x$, $3x = 90$, $x = 30$.


Malik bought a sofa set which cost $1200 before a GST of 9%. What was the amount of GST that he had to pay for the sofa set?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The table shows the rental rate for a bicycle: First hour $8; for every additional half hour or part thereof $2.50. Mr Chua rented a bicycle from 11.30 a.m. to 2.10 p.m. How much did he pay for the bike rental in total?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Duration 11.30 a.m. to 2.10 p.m. = 2 h 40 min. First hour $8. Remaining 1 h 40 min = 100 min = 4 half-hours (part thereof rounds up), at $2.50 each = $10. Total $= 8 + 4(2.50) = 8 + 10 = 18$.


Mr Lee bought 2 identical tables and 2 identical chairs from a furniture store. He paid $3450 in total. The cost of 2 chairs was $300 more than the cost of 1 table. Find the cost of a table.<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The average height of 33 students in the class is 127 cm. What is the total height of all the students in the class? Leave your answer in metres and centimetres.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm

Total height $= 127 \times 33 = 4191$ cm. Convert: $4191\text{ cm} = 41\text{ m } 91\text{ cm}$.


At first, Amelia has an equal number of green and yellow sticks. She gave away \(\dfrac{1}{6}\) of her green sticks. In the end, she was left with a total of 396 sticks. What fraction of her sticks left are yellow?

Take green = yellow = 6 units at first. She gave away \(\dfrac{1}{6}\) of green, leaving $6 - 1 = 5$ units of green. Yellow stays 6 units. Total left $= 5 + 6 = 11$ units, of which yellow is 6 units. Fraction yellow $= \dfrac{6}{11}$.


At first, Amelia has an equal number of green and yellow sticks. She gave away \(\dfrac{1}{6}\) of her green sticks. In the end, she was left with a total of 396 sticks. How many green sticks did she have at first?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total left = 11 units = 396, so 1 unit = $396 \div 11 = 36$. Green at first = 6 units = $6 \times 36 = 216$ sticks.


Mrs Loh gave \(\dfrac{5}{6}\) of her money to her 3 children, Fred, Greg and Helen in the ratio of 1 : 2 : 3. Helen received $190 more than Fred. How much money did the 3 children receive altogether?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Fred : Greg : Helen = 1 : 2 : 3. Helen − Fred = 3 units − 1 unit = 2 units = $190, so 1 unit = $95. Total received = 1 + 2 + 3 = 6 units = $95 \times 6 = 570$.


Mrs Loh gave \(\dfrac{5}{6}\) of her money to her 3 children, Fred, Greg and Helen in the ratio of 1 : 2 : 3. Helen received $190 more than Fred. How much money did Mrs Loh have at first?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 3 children received $570, which is \(\dfrac{5}{6}\) of her money. So \(\dfrac{1}{6}\) = $570 \div 5 = 114$, and the whole amount = $114 \times 6 = 684$.


A box has a total of 3180 yellow, pink and black beads. The ratio of the number of yellow beads to the number of pink beads is 2 : 3. The ratio of the number of black beads to the total number of beads is 7 : 12. Write the ratio of the number of yellow beads to the number of black beads to the number of pink beads in the simplest form.

Black : total = 7 : 12, so yellow + pink = 12 − 7 = 5 parts (of the 12). Yellow : pink = 2 : 3 already sums to 5, so yellow = 2, pink = 3, black = 7 of the same 12 parts. Thus yellow : black : pink = 2 : 7 : 3.


A box has a total of 3180 yellow, pink and black beads. The ratio of the number of yellow beads to the number of pink beads is 2 : 3. The ratio of the number of black beads to the total number of beads is 7 : 12. How many black beads are there in the box?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Different lengths of ribbons were used to decorate big and small trees: 13 m of ribbon for 4 big trees; 5 m of ribbon for 6 small trees. Mr Yaki decorated 36 big trees and 36 small trees. How many metres of ribbon did he use altogether?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

Big trees: $36 \div 4 = 9$ groups, $9 \times 13 = 117$ m. Small trees: $36 \div 6 = 6$ groups, $6 \times 5 = 30$ m. Total $= 117 + 30 = 147$ m.


Different lengths of ribbons were used to decorate big and small trees: 13 m of ribbon for 4 big trees; 5 m of ribbon for 6 small trees. Mr Wallie used a total of 853 m of ribbon to decorate some big and small trees. He decorated 24 more small trees than big trees. How many trees did Mr Wallie decorate altogether?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 24 extra small trees use $\dfrac{5}{6} \times 24 = 20$ m, so the matched trees use $853 - 20 = 833$ m. Per matched big+small tree: \(\dfrac{13}{4} + \dfrac{5}{6} = \dfrac{49}{12}\) m. Number of each matched type $= 833 \div \dfrac{49}{12} = 204$. Big = 204, small = 204; small total = $204 + 24 = 228$. Total trees $= 204 + 204 + 24 = 432$.


The original price of each fan is $35. During a sale, Fan A gets $6.80 off the original price and Fan B gets a 20% discount. Which fan was cheaper after the discount? How much is it cheaper than the other fan?


The original price of each fan is $35. During a sale, Fan A gets $6.80 off the original price and Fan B gets a 20% discount. Jefferson wanted to buy the cheaper fan on discount. He had to pay an additional 9% GST on the discounted price. How much did Jefferson have to pay for the fan in total?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The cheaper fan (Fan B) costs $28 after discount. With 9% GST: $\dfrac{109}{100} \times 28 = 30.52$. Jefferson paid $30.52.


A box of biscuit is sold at $5.50. For every 5 boxes of biscuits bought, 2 boxes of biscuits are given free. Nadiah bought some boxes of biscuits and paid a total of $126.50. How many boxes of biscuits did she have?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Teck Huat made blueberry and chocolate muffins to sell. \(\dfrac{5}{6}\) of the muffins were blueberry muffins and the rest were chocolate muffins. He sold \(\dfrac{1}{3}\) of the total number of muffins. \(\dfrac{5}{6}\) of the muffins sold were blueberry muffins. There were 120 chocolate muffins left. How many blueberry muffins did he sell?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Blueberry sold $= \dfrac{5}{6} \times \dfrac{1}{3} = \dfrac{5}{18}$ of total; chocolate sold $= \dfrac{1}{6} \times \dfrac{1}{3} = \dfrac{1}{18}$ of total. Chocolate made $= \dfrac{1}{6} = \dfrac{3}{18}$; chocolate left $= \dfrac{3}{18} - \dfrac{1}{18} = \dfrac{2}{18} = 120$, so \(\dfrac{1}{18}\) of total $= 60$. Blueberry sold $= \dfrac{5}{18} = 5 \times 60 = 300$.


Which of the following is fifty-four thousand and seventy in numerals?

Fifty-four thousand = 54 000, and seventy = 70. So fifty-four thousand and seventy = 54 000 + 70 = 54 070.


What is the missing number in the box?<br>\(\dfrac{9}{12} = \dfrac{3}{[\,?\,]}\)

\(\dfrac{9}{12}\) simplified: divide numerator and denominator by 3 gives \(\dfrac{3}{4}\). So the missing number is 4.