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Fractions Revision – Solutions

Section A

For each question, four options are given. One of them is the correct answer. Make your choice (1, 2, 3 or 4) and write your answer in the brackets.

1. 3 boys shared half a pizza equally. What fraction of the original pizza did each boy receive?

(1) (2) (3) (4)

Fraction each boy received = ÷ 3

=

=

Ans: (4)

2. 900 + + = __________

(1) 900.99 (2) 901.89 (3) 909.99 (4) 990.89

900 + + = 900 + 0.9 + 0.99

= 901.89

Ans: (2)

3. What is the value of – ?

(1) (2) (3) (4) 1

– = –

=

Ans: (3)

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4. After Mei Mei gave away of her stamps and Wan Xi gave away of her stamps,

they had the same number of stamps left. They had 312 stamps left. How many stamps they have altogether at first?

(1) 600 (2) 624 (3) 676 (4) 728

Number of stamps each girl had left = 312 ÷ 2

= 156

of Mei Mei’s stamps = 156

of Mei Mei’s stamps = 156 ÷ 3

= 52

of Mei Mei’s stamps = 7 52

= 364

Number of stamps Mei Mei had at first = 364

of Wan Xi’s stamps = 156

of Wan Xi’s stamps = 2 156

= 312

Number of stamps Wan Xi had at first = 312

Number of stamps they had altogether at first = 364 + 312

= 676

Ans: (4)

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5. Arrange the following fractions in descending order.

, , 1

(1) , 1 , (2) , 1 , (3) 1 , , (4) , , 1

= 1

Smallest fraction =

Compare 1 and 1 .

=

=

Largest fraction = 1

In descending order: 1 , ,

Ans: (3)

6. How many tenths are there in 1 ?

(1) 14 (2) 12 (3) 7 (4) 4

1 =

=

= 14

Number of tenths = 14

Ans: (1)

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7. of a number is 27. What is of the number?

(1) 243 (2) 54 (3) 3 (4) 6

of the number = 27

of the number = 2 27

= 54

of the number = 54

= 6

Ans: (4)

8. How many are there in the number statement below so that the statement is true?

÷ ÷ ÷ … … ÷ = 16

(1) 7 (2) 6 (3) 5 (4) 4

÷ = 2 = 1

1 ÷ = 1 2 = 2

2 ÷ = 2 2 = 4

4 ÷ = 4 2 = 8

8 ÷ = 8 2 = 16

Number of = 6

Ans: (2)

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9. Which of the following fractions is closest to ?

(1) (2) (3) (4)

Tip: Change all the fractions to decimals.

= = 0.6

= 0.666… (Difference = 0.066…)

= 0.7 (Difference = 0.1)

= = 0.55 (Difference = 0.05)

= = 0.68 (Difference = 0.08)

Ans: (3)

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10. The figure is made up of three equilateral triangles ADC, ABD and BED.

What fraction of the Figure ABEC is shaded?

(1) (2) (3) (4)

Notice that in Triangle ACD, of the triangle is shaded.

Similarly in Triangle ABD, of the triangle is shaded.

Therefore 2 out of 6 parts of Figure ABEC is shaded.

Fraction of Figure ABEC shaded =

=

Ans: (2)

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Section B

Questions 11 to 15 carry 1 mark each. Questions 16 to 20 carry 2 marks each. Show your working clearly and write your answers in the spaces provided. For questions which require units, give your answers in the units provided.

11. Write down the fraction exactly between and .

Method 1: Calculation

Difference between the two fractions = –

= –

=

Divide the difference into 2 = ÷ 2

=

=

Fraction exactly in between = –

= –

=

= (Ans)

Method 2: Observation

=

Find the fraction between and .

Continue using equivalent fractions:

=

=

Fraction exactly in between = = (Ans)

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12. How many minutes are there in 4 h?

Number of minutes = 4 60

= 60

= 260 (Ans)

13. of a number is 81. What is of the number?

of the number = 81

of the number = 81 ÷ 3

= 27

of the number = 7 27

= 189

of the number = 189

= 42 (Ans)

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14. In the number line below, BC is of AB. What is the fraction represented by B?

Difference between and = –

= –

=

3 units =

1 unit =

B = –

=

= (Ans)

15. Express as a decimal, correct to 2 decimal places.

= 6 ÷ 7

= 0.857…

= 0.86 (2 decimal places) (Ans)

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16. Peter has as many books as Kate. Cindy has as many books as Peter. Cindy has

96 books, how many books does Kate have?

Peter : Kate : Cindy

2 5 : 3 5

5 2 : 4 2

10 : 15 : 8

8 units = 96

1 unit = 96 ÷ 8

= 12

15 units = 15 12

= 180

Number of books Kate has = 180 (Ans)

17. Joe had as much money as Hope at first. After both of them received $27 each,

Joe had as much money as Hope. How much money did both of them have at first?

Joe : Hope Difference

Before 3 : 5 2

After 3 2 : 4 2 1 2

6 : 8 2

(6 – 3 =) 3 units = $27

1 unit = $27 ÷ 3

= $9

(3 + 5 =) 8 units = 8 $9

= $72

Amount of money both of them had at first = $72 (Ans)

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18. The mass of a bottle completely filled with sand was 3 kg. After of the sand was

poured away, the mass of the bottle containing the remaining sand was 900 g. What

was the mass of the bottle, in grams, when it was empty?

Mass of of the sand = 3000 – 900

= 2100 g

Mass of of the sand = 2100 ÷ 3

= 700 g

Mass of the empty bottle = 900 – 700

= 200 g (Ans)

19. In the figure, ABCD is a rectangle. X and Y are midpoints of BC and DC. What fraction of the figure is the shaded triangle?

Area ADY = of ABCD

Area ABX = of ABCD

Area XCY = of ABCD

Fraction of the figure that is the shaded triangle = 1 – – –

= – – –

= (Ans)

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20. Julianna had a sum of money. After spending of it on a dress and of the

remainder on a book, she had $8 left. How much money did Julianna have at first?

of the remainder = $8

of the remainder = 6 $8

= $48

Remaining amount of money = $48

of the original sum of money = $48

of the original sum of money = $48 ÷ 3

= $16

of the original sum of money = 5 $16

= $80

Amount of money Julianna had at first = $80 (Ans)

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Section C

Show your working clearly and write your answers in the spaces provided. The number of marks is shown in brackets [ ] at the end of each question or part-question.

21. William had $108 more than Samuel. After William spent of his money and Samuel

spent half of his, both boys had a total of $102 left. How much money did each of

them have at first?

3 units + $27 = $102

3 units = $102 – $27

= $75

1 unit = $75 ÷ 3

= $25

4 units = 4 $25

= $100

Amount of money William had at first = $100 + $108

= $208 (Ans)

Amount of money Samuel had at first = $100 (Ans)

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22. There are 64 more boys than girls in an auditorium. of the girls and of the boys

wore spectacles. A same number of boys and girls wore spectacles. How many boys

and girls wore spectacles altogether?

Fraction of girls who wore spectacles =

Fraction of boys who wore spectacles = =

Girls ⟶ 3 units

Boys ⟶ 4 units

(4 – 3 =) 1 unit = 64

4 units = 4 64

= 256

Number of boys and girls who wore spectacles altogether = 256 (Ans)

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23. In a bookstore, the cost of a magazine is of the cost of a book. Peter used of his

money to buy 8 magazines and 13 books. How many books could he buy with of

his money?

Cost of 1 magazine = 5 units

Cost of 1 book = 8 units

Cost of 8 magazines and 13 books = 8 5 + 13 8

= 40 + 104

= 144 units

of his money = 144 units

of his money = 144 ÷ 2

= 72 units

of his money = 5 72

= 360 units

Number of books he could buy = 360 ÷ 8

= 45 (Ans)

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24. Dylan has 340 square and round stickers altogether. of his square stickers is 28

more than of his round stickers. How many square stickers and how many round

stickers does Dylan have?

9 units = 340 – 26 – 26

= 288

1 unit = 288 ÷ 9

= 32

4 units = 4 32

= 128

5 units = 5 32

= 160

Number of square stickers = 128 + 26 + 26

= 180 (Ans)

Number of round stickers = 160 (Ans)

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25. There were some pupils in a school canteen. The number of girls was of the

number of boys. After of the girls and of the boys left, there were 124 pupils

remaining in the canteen.

(a) What fraction of pupils left the canteen?

(b) How many pupils were there in the canteen at first?

(a) Girls : Boys

2 : 3

10 : 15 ⟵ Make the number of units for girls divisible by 5. However, the number of units for boys is not divisible by 2.

20 : 30 ⟵ Now, the number of units for girls is divisible by 5, and the number of units for boys is divisible by 2.

Number of girls who left the canteen = 20

= 4 units

Number of boys who left the canteen = 30

= 15 units

Fraction of pupils who left the canteen =

= (Ans)

(b) Number of girls remaining = 20 – 4

= 16 units

Number of boys remaining = 30 – 15

= 15 units

(16 + 15 =) 31 units = 124

1 unit = 124 ÷ 31

= 4

(20 + 30 =) 50 units = 50 4

= 200

Number of pupils in the canteen at first = 200 (Ans)

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26. Daisy had as much money as Leslie. Daisy received $220 from her mother and

Leslie spent $50. In the end, Daisy had twice as much money as Leslie. How much

money did Daisy have at first?

Daisy Leslie

Before 3 units 4 units

+ $220 – $50

After 2 parts 1 part

3 units + $220 = 2 parts

4 units – $50 = 1 part ⇒ 8 units – $100 = 2 parts

(8 – 3 =) 5 units = $220 + $100

= $320

1 unit = $320 ÷ 5

= $64

3 units = 3 $64

= $192

Amount of money Daisy had at first = $192 (Ans)

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27. Nicole, Pamela and Timmy shared a sack of rice. Nicole took of the rice and an

extra kg of the rice. Pamela took of the remaining rice and an extra kg of rice.

Timmy took the rest of the 13 kg of rice. What was the original mass of the sack of

rice the three of them shared?

Timmy’s share = 13 kg

Timmy and Pamela’s share = 2

= 27 kg

Nicole, Timmy and Pamela’s share = 2

= 55 kg

Original mass of the sack of rice = 55 kg (Ans)

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28. Ben had a sum of money. He spent of his money on a shirt, and of his money on

a bag. He then spent of the remainder on a pair of trousers and another $26 on a

belt. He had of his money left. How much did the shirt cost?

Fraction of money spent on the shirt and bag = +

= +

=

Remaining amount of money = 1 –

= –

=

Fraction of money spent on the pair of trousers =

=

Fraction of money spent on belt = 1 – – –

= – – –

=

=

of his money = $26

of his money = 4 $26

= $104

Cost of the shirt = $104 (Ans)

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29. There were 112 fewer Singapore stamps than Malaysia stamps in an album. Janet

gave away of the Singapore stamps and of the Malaysia stamps. The number of

Malaysia stamps left was twice as many as the number of Singapore stamps left.

How many stamps were there in the album at first?

Fraction of Singapore stamps left = 1 –

=

=

Fraction of Malaysia stamps left = 1 –

=

=

Singapore stamps ⟶ 20 units

Malaysia stamps ⟶ 48 stamps

(48 – 20 =) 28 units = 112

1 unit = 112 ÷ 28

= 4

(20 + 48 =) 68 units = 68 4

= 272

Number of stamps in the album at first = 272 (Ans)

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30. An MRT train departed from Jurong station. At Clementi station, of the passengers

alighted and 100 passengers boarded the train. At Woodlands station, of the

passengers alighted and 80 passengers boarded the train. There were 350

passengers on the train when it left Woodlands station. How many passengers were

there when the train departed from Jurong station?

On the train Alighted Boarded

Jurong station - - -

↓ ?

Clementi station 100

↓ ?

Woodlands station 80

350

Woodlands station

Number of passengers on the train after alighting and before boarding

= 350 – 80

= 270

of the passengers = 270

of the passengers = 270 ÷ 9

= 30

of the passengers = 10 30

= 300

Number of passengers on the train after leaving Clementi station = 300

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Clementi station

Number of passengers on the train after alighting and before boarding

= 300 – 100

= 200

of the passengers = 200

of the passengers = 200 ÷ 2

= 100

of the passengers = 5 100

= 500

Number of passengers on the train after leaving Jurong station = 500 (Ans)

END