Fractions, Decimals and Percentages: Mathematics questions

Section A: objective questions

8 marks

Choose the correct answer.

Write 7 3/8 as an improper fraction.

73/8
59/8
56/8
10/8

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7 × 8 = 56, and 56 + 3 = 59. Keep the denominator: 59/8.

For the teacher: Remembering, low difficulty, standard 2.1.1

Textbook p. 68

Diagram 1 shows 3 bars, each cut into 5 equal parts. Which improper fraction shows the shaded parts?

Three bars each cut into 5 parts: the first two fully shaded, the third with 3 parts shaded — Diagram 1

5/13
23/5
6/5
13/5

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Two full bars are 2 × 5 = 10 fifths. Add 3 more fifths: 13/5. This is the same as 2 3/5.

For the teacher: Understanding, low difficulty, standard 2.1.1

Textbook p. 68

3/10 + 4/5 = ______

1 1/10
7/15
7/10
1 7/10

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4/5 = 8/10. 3/10 + 8/10 = 11/10 = 1 1/10. Never add the denominators (that gives 7/15).

For the teacher: Applying, low difficulty, standard 2.1.2

Textbook p. 72

5 1/3 − 2 2/3 = ______

3 1/3
2 1/3
2 2/3
3 2/3

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Regroup: 5 1/3 = 4 4/3. Then 4 4/3 − 2 2/3 = 2 2/3. (Check: 16/3 − 8/3 = 8/3 = 2 2/3.)

For the teacher: Applying, medium difficulty, standard 2.1.3

Textbook p. 76

5/6 of 48 pupils took part in a march. How many pupils took part?

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48 ÷ 6 = 8 pupils in each part. 5 × 8 = 40.

For the teacher: Applying, low difficulty, standard 2.1.5

Textbook p. 84

6.4 + 0.58 + 12 = ______

18.62
19.8
12.74
18.98

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Line up the decimal points: 6.40 + 0.58 + 12.00 = 18.98.

For the teacher: Applying, low difficulty, standard 2.2.1

Textbook p. 86

Diagram 2 shows a number line divided into eighths. What is the value of P?

Number line from 0 to 2 divided into eighths with P at the 13th mark — Diagram 2

1 5/8
1 3/8
13/16
2 5/8

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Each part is 1/8. P is the 13th mark, so P = 13/8 = 1 5/8.

For the teacher: Understanding, medium difficulty, standard 2.1.1

Textbook p. 69

18 out of 25 pupils in a class wear spectacles. What is the percentage?

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18/25 = (18 × 4)/(25 × 4) = 72/100 = 72%.

For the teacher: Applying, low difficulty, standard 2.3.2

Textbook p. 96

Section B: structured questions

36 marks

Answer all questions. Show your working.

Change the fractions.

[1 mark] (a)Write 4 7/9 as an improper fraction.

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4 × 9 + 7 = 43, so 43/9 [1]1

Tick each point you got.

[1 mark] (b)Write 38/5 as a mixed number.

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38 ÷ 5 = 7 remainder 3, so 7 3/5 [1]1

Tick each point you got.

For the teacher: Remembering, low difficulty, standard 2.1.1

Textbook p. 68

Convert.

[1 mark] (a)Write 7/25 as a percentage.

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7/25 = 28/100 = 28% [1]1

Tick each point you got.

[1 mark] (b)Write 35% as a fraction in the simplest form.

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35/100 = 7/20 [1]1

Tick each point you got.

[1 mark] (c)Which is larger, 3/5 or 65%?

3/565%

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65%

3/5 = 60/100 = 60%, and 65% is more than 60%.

For the teacher: Understanding, low difficulty, standard 2.3.1

Textbook p. 95

Puan Ros has 3 1/2 kg of flour. She uses 1 3/4 kg to bake bread.

[2 marks] (a)How much flour is left?

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3 1/2 = 3 2/4 = 2 6/4, so 2 6/4 − 1 3/4 = 1 3/4 [1]1
Answer: 1 3/4 kg [1]1

Tick each point you got.

[1 mark] (b)She buys another 2 1/4 kg of flour. What is the mass of flour now?

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1 3/4 + 2 1/4 = 4 kg [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 2.1.3

Textbook p. 77

There are 120 pupils in Year 4. 3/8 of them walk to school and 1/4 ride bicycles.

[1 mark] (a)How many pupils walk to school?

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120 ÷ 8 = 15, 3 × 15 = 45 [1]1

Tick each point you got.

[1 mark] (b)How many pupils ride bicycles?

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120 ÷ 4 = 30 [1]1

Tick each point you got.

[2 marks] (c)How many pupils neither walk nor ride bicycles?

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45 + 30 = 75 [1]1
120 − 75 = 45 [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 2.1.5

Textbook p. 84

Diagram 3 shows a grid of 100 equal squares. Some squares are shaded blue.

A 10 by 10 grid with 24 squares shaded blue — Diagram 3

[1 mark] (a)What is the percentage of the squares that are shaded?

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24% [1]1

Tick each point you got.

[2 marks] (b)Write the fraction of squares that are not shaded in the simplest form.

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76/100 [1]1
76/100 = 19/25 [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 2.3.2

Textbook p. 96

Calculate.

[2 marks] (a)8.46 + 0.739 + 15 =

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8.460 + 0.739 = 9.199 [1]1
9.199 + 15 = 24.199 [1]1

Tick each point you got.

[2 marks] (b)20 − 7.085 =

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20.000 − 7.085 [1]1
12.915 [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 2.2.2

Textbook p. 88

Solve these problems.

[2 marks] (a)A packet of sugar has a mass of 0.345 kg. What is the mass of 5 packets?

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5 × 0.345 [1]1
1.725 kg [1]1

Tick each point you got.

[2 marks] (b)A jug has 3.6 ℓ of juice. It is poured equally into 8 cups. How much juice is in each cup?

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3.6 ÷ 8 [1]1
0.45 ℓ [1]1

Tick each point you got.

[1 mark] (c)1 000 × 4.07 =

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4 070 [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 2.2.3

Textbook p. 91

Encik Fong has a rope that is 10 m long. He uses 2.85 m to tie books and 3.12 m to tie used goods, as in Diagram 4.

A rope of 10 m split into 2.85 m for books, 3.12 m for used goods and a part marked ? — Diagram 4

[2 marks] (a)What is the length of rope left?

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2.85 + 3.12 = 5.97 [1]1
10 − 5.97 = 4.03 m [1]1

Tick each point you got.

[1 mark] (b)What is the difference between the length used for books and the length used for used goods?

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3.12 − 2.85 = 0.27 m [1]1

Tick each point you got.

For the teacher: Analysing, high difficulty, standard 2.4.1

Textbook p. 99

Hana got 36 out of 40 marks in a Science quiz. Ravi got 21 out of 25 marks in a Mathematics quiz. Lim got 17 out of 20 marks in a Bahasa Malaysia quiz.

[2 marks] (a)Write each pupil's marks as a percentage.

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Hana: 36/40 = 90/100 = 90% [1]1
Ravi: 21/25 = 84%; Lim: 17/20 = 85% [1]1

Tick each point you got.

[1 mark] (b)Who did best in the quizzes? Give a reason.

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Hana, because 90% is the highest percentage [1]1

Tick each point you got.

For the teacher: Evaluating, medium difficulty, standard 2.4.1

Textbook p. 101

Faiz says: "2/5 + 3/5 = 5/10, because 2 + 3 = 5 and 5 + 5 = 10."

[1 mark] (a)Is Faiz correct?

YesNo

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The denominator stays the same when the denominators are equal.

[2 marks] (b)Explain the mistake and give the correct answer.

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We add the numerators only and keep the denominator; the size of the parts does not change [1]1
2/5 + 3/5 = 5/5 = 1 [1]1

Tick each point you got.

For the teacher: Evaluating, medium difficulty, standard 2.1.2

Textbook p. 71

Write two different proper fractions that have different denominators and add up to exactly 1. Show that your fractions add up to 1.

[3 marks] (a)Your two fractions and your working.

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Two proper fractions with different denominators, for example 1/2 and 3/6, or 6/10 and 2/5 [1]1
Change to the same denominator [1]1
Sum shown as 1 (for example 3/6 + 3/6 = 6/6 = 1) [1]1

Tick each point you got.

For the teacher: Creating, high difficulty, standard 2.1.4

Textbook p. 81

Section A: objective questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Section B: structured questions

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19