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Primary 4 Mathematics · Chapter 6 · Answers and explanations

Lesson 6.1: Recall: Adding and Subtracting Fractions (answers)

Section A · Multiple choice 4 marks

1. Find the value of 38 + 28.1 mark

382858
(A) 58(B) 516(C) 18(D) 68
Answer: (A) 58The denominators are the same, so add the numerators: 3 + 2 = 5. The answer is 58. (Do not add the denominators!)

2. Find the value of 12 + 14.1 mark

1214
(A) 26(B) 34(C) 12(D) 16
Answer: (B) 34Change 12 to quarters: 12 = 24. Then 24 + 14 = 34.

3. Find the value of 710 − 25.1 mark

(A) 12(B) 55(C) 310(D) 35
Answer: (C) 310Change 25 to tenths: 25 = 410. Then 710 − 410 = 310.

4. Find the value of 56 − 13.1 mark

(A) 43(B) 46(C) 13(D) 12
Answer: (D) 1213 = 26. 56 − 26 = 36. Simplify: 36 = 12.

Section B · Write your answer 11 marks

5. Find the value of 29 + 49. Give your answer in the simplest form.1 mark

Answer: 2329 + 49 = 69. Divide the top and bottom by 3: 69 = 23.

6. Find the value of 34 + 18.1 mark

Answer: 7834 = 68. 68 + 18 = 78.

7. Find the value of 910 − 35.1 mark

Answer: 31035 = 610. 910 − 610 = 310.

8. Find the value of 16 + 23.1 mark

Answer: 5623 = 46. 16 + 46 = 56.

9. Find the value of 78 − 12.1 mark

3878
Answer: 3812 = 48. 78 − 48 = 38.

10. Find the sum of 12, 14 and 18.2 marks

Answer: 78Change all to eighths: 12 = 48, 14 = 28.
48 + 28 + 18 = 78.

11. 35 + ? = 910. Find the missing number.2 marks

Answer: 310Subtract: 910 − 35.
35 = 610, so 910 − 610 = 310.
Check: 610 + 310 = 910.

12. Mei ate 14 of a pizza and Raj ate 38 of the pizza. What fraction of the pizza did they eat? What fraction of the pizza was left?2 marks

Pizza381438
Answer: 58 eaten; 38 leftEaten: 14 = 28, so 28 + 38 = 58.
Left: 1 − 58 = 88 − 58 = 38.
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Primary 4 Mathematics · Chapter 6 · Answers and explanations

Lesson 6.2: Addition and Subtraction of Fractions (answers)

Section A · Multiple choice 4 marks

1. Find the value of 34 + 58.1 mark

3458
(A) 812(B) 1 38(C) 78(D) 1 18
Answer: (B) 1 3834 = 68. 68 + 58 = 118. Change to a mixed number: 118 = 1 38.

2. Find the value of 1 − 38.1 mark

58381
(A) 78(B) 38(C) 58(D) 28
Answer: (C) 581 = 88. 88 − 38 = 58.

3. Find the value of 3 − 1 25.1 mark

(A) 2 35(B) 1 25(C) 2 25(D) 1 35
Answer: (D) 1 353 − 1 = 2, then 2 − 25: take 1 whole and write it as 55.
1 + (55 − 25) = 1 + 35 = 1 35.

4. Find the value of 2 12 + 1 34.1 mark

(A) 4 14(B) 3 14(C) 3 46(D) 4 34
Answer: (A) 4 14Add the wholes: 2 + 1 = 3. Add the fractions: 12 + 34 = 24 + 34 = 54 = 1 14.
3 + 1 14 = 4 14.

Section B · Write your answer 11 marks

5. Find the value of 56 + 13. Give your answer as a mixed number.1 mark

Answer: 1 1613 = 26. 56 + 26 = 76 = 1 16.

6. Find the value of 710 + 45. Give your answer in the simplest form.1 mark

Answer: 1 1245 = 810. 710 + 810 = 1510 = 1 510 = 1 12.

7. Find the value of 1 − 512.1 mark

5127121
Answer: 7121 = 1212. 1212 − 512 = 712.

8. Find the value of 4 − 2 34.1 mark

Answer: 1 144 − 2 = 2, then 2 − 34: 2 = 1 + 44, so 1 + (44 − 34) = 1 + 14 = 1 14.

9. Find the value of 1 38 + 2 12.1 mark

Answer: 3 78Wholes: 1 + 2 = 3. Fractions: 38 + 12 = 38 + 48 = 78.
3 + 78 = 3 78.

10. Find the value of 2 78 + 1 34.2 marks

Answer: 4 58Wholes: 2 + 1 = 3. Fractions: 78 + 34 = 78 + 68 = 138 = 1 58.
3 + 1 58 = 4 58.

11. Find the value of 3 78 − 1 12.2 marks

Answer: 2 38Wholes: 3 − 1 = 2. Fractions: 78 − 12 = 78 − 48 = 38.
2 + 38 = 2 38.

12. Ali ran 1 12 km on Monday and 2 34 km on Tuesday. How far did he run in all?2 marks

112234? km
Answer: 4 14 km1 12 + 2 34: wholes 1 + 2 = 3. Fractions: 12 + 34 = 24 + 34 = 54 = 1 14.
3 + 1 14 = 4 14. He ran 4 14 km.
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Primary 4 Mathematics · Chapter 6 · Answers and explanations

Lesson 6.3: Word Problems: Adding and Subtracting Fractions (answers)

Section A · Multiple choice 4 marks

1. Mei used 38 m of ribbon for a bow and 14 m of ribbon for a card. How many metres of ribbon did she use in all?1 mark

382858
(A) 412(B) 18(C) 58(D) 34
Answer: (C) 5814 = 28. 38 + 28 = 58. She used 58 m.

2. A jug had 710 L of milk. 25 L was poured out. How many litres of milk were left?1 mark

41031071025?
(A) 55(B) 12(C) 910(D) 310
Answer: (D) 31025 = 410. 710 − 410 = 310. 310 L was left.

3. Ben ate 13 of a cake. Cara ate 16 of the cake. What fraction of the cake was left?1 mark

Cake1316?1
(A) 12(B) 23(C) 56(D) 16
Answer: (A) 1213 = 26. Eaten: 26 + 16 = 36.
Left: 66 − 36 = 36 = 12.

4. A rope is 2 m long. 34 m of it is cut off. How many metres of rope are left?1 mark

34? m2 m
(A) 14(B) 1 14(C) 1 34(D) 2 34
Answer: (B) 1 142 = 1 + 44. 44 − 34 = 14. So 1 + 14 = 1 14. The rope left is 1 14 m.

Section B · Write your answer 11 marks

5. Jun walked 25 km to the shop. Then he walked another 310 km to the park. How far did he walk in all?1 mark

25310710
Answer: 710 km25 = 410. 410 + 310 = 710. He walked 710 km.

6. Tom poured 12 L of juice into a jug. He then poured 34 L more. How much juice was in the jug?1 mark

1234? L
Answer: 1 14 L12 = 24. 24 + 34 = 54 = 1 14. There was 1 14 L of juice.

7. A ribbon is 1 m long. 38 m is cut off. How long is the ribbon that is left?1 mark

38? m1 m
Answer: 58 m1 = 88. 88 − 38 = 58. The ribbon left is 58 m.

8. A plank is 3 m long. A carpenter saws off 1 35 m. How long is the plank that is left?1 mark

135? m3 m
Answer: 1 25 m3 − 1 = 2. 2 − 35 = 1 + (55 − 35) = 1 + 25 = 1 25.
The plank left is 1 25 m.

9. Sara spent 14 of her money on a book and 38 of her money on a pen. What fraction of her money was left?1 mark

Money1438?1
Answer: 3814 = 28. Spent: 28 + 38 = 58.
Left: 88 − 58 = 38.

10. Jar A has 34 kg of flour. Jar B has 18 kg less flour than Jar A. How much flour is there in the two jars altogether?2 marks

Jar A34Jar B5818
Answer: 1 38 kgJar B: 34 = 68, so 68 − 18 = 58 kg.
Both jars: 68 + 58 = 118 = 1 38. There is 1 38 kg of flour.

11. Mrs Lim bought 2 12 kg of rice. She used 34 kg on Monday and 1 14 kg on Tuesday. How much rice was left?2 marks

34114? kg212
Answer: 12 kgUsed: 34 + 1 14 = 1 44 = 2 kg.
Left: 2 12 − 2 = 12 kg.

12. Dev cycled 34 km on Monday. On Tuesday he cycled 12 km farther than on Monday. How far did he cycle in the two days altogether?2 marks

Mon34Tue341254
Answer: 2 kmTuesday: 34 + 12 = 34 + 24 = 54 km.
Total: 34 + 54 = 84 = 2 km.
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Primary 4 Mathematics · Chapter 6 · Answers and explanations

Lesson 6.4: Fraction of a Set (answers)

Section A · Multiple choice 4 marks

1. What fraction of the counters is shaded?1 mark

3 of the 4 equal groups are shaded: three-quarters
(A) 912(B) 14(C) 312(D) 34
Answer: (D) 34There are 12 counters and 9 are shaded: 912. Divide the top and bottom by 3: 912 = 34.

2. Find 15 of 35.1 mark

(A) 7(B) 5(C) 30(D) 175
Answer: (A) 7Share 35 into 5 equal groups: 35 ÷ 5 = 7. So 15 of 35 is 7.

3. Find 34 of 48.1 mark

(A) 12(B) 36(C) 45(D) 16
Answer: (B) 361 quarter of 48 = 48 ÷ 4 = 12. 3 quarters = 3 × 12 = 36.

4. There are 40 sweets in a bag. 38 of them are red. How many red sweets are there?1 mark

(A) 5(B) 25(C) 15(D) 24
Answer: (C) 151 eighth of 40 = 40 ÷ 8 = 5. 3 eighths = 3 × 5 = 15 red sweets.

Section B · Write your answer 11 marks

5. Find 16 of 54.1 mark

Answer: 954 ÷ 6 = 9.

6. Find 58 of 24 counters.1 mark

1 group = 3 counters, 5 groups = 15 counters
Answer: 1524 ÷ 8 = 3 in each group. 5 × 3 = 15.

7. Find 710 of 60.1 mark

Answer: 4260 ÷ 10 = 6. 7 × 6 = 42.

8. What fraction of the counters is shaded? Give your answer in the simplest form.1 mark

2 of the 5 equal groups are shaded
Answer: 25There are 20 counters and 8 are shaded: 820. Divide the top and bottom by 4: 820 = 25.

9. Out of 40 pupils in a class, 15 walk to school. What fraction of the pupils walk to school?1 mark

Answer: 381540: divide the top and bottom by 5 to get 38.

10. How many more is 56 of 48 than 34 of 48?2 marks

Answer: 456 of 48: 48 ÷ 6 = 8, 5 × 8 = 40.
34 of 48: 48 ÷ 4 = 12, 3 × 12 = 36.
40 − 36 = 4.

11. A box has 60 beads. 25 of the beads are red and 13 of the beads are blue. The rest are green. How many green beads are there?2 marks

Answer: 16Red: 60 ÷ 5 = 12, 2 × 12 = 24.
Blue: 60 ÷ 3 = 20.
Green: 60 − 24 − 20 = 16.

12. In a club of 40 pupils, 35 are girls. How many more girls than boys are there in the club?2 marks

Answer: 8Girls: 40 ÷ 5 = 8, 3 × 8 = 24.
Boys: 40 − 24 = 16.
24 − 16 = 8 more girls.
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Primary 4 Mathematics · Chapter 6 · Answers and explanations

Lesson 6.5: Word Problems: Fraction of a Set (answers)

Section A · Multiple choice 4 marks

1. Tom had 48 marbles. He gave 14 of them to his friend. How many marbles did he have left?1 mark

12? left48
(A) 36(B) 12(C) 60(D) 44
Answer: (A) 36He gave away 48 ÷ 4 = 12 marbles. Left: 48 − 12 = 36. (Or 3 units of 12 = 36.)

2. 35 of the pupils in a class are girls. There are 24 girls. How many pupils are there in the class?1 mark

Girls24? pupils
(A) 72(B) 40(C) 16(D) 60
Answer: (B) 403 units = 24, so 1 unit = 24 ÷ 3 = 8. 5 units = 5 × 8 = 40 pupils.

3. 27 of the ribbons in a box are red. There are 10 red ribbons. How many ribbons are there in the box?1 mark

Red10? ribbons
(A) 25(B) 70(C) 35(D) 14
Answer: (C) 352 units = 10, so 1 unit = 10 ÷ 2 = 5. 7 units = 7 × 5 = 35 ribbons.

4. Ali had $60. He spent 25 of his money on a book. How much money did he have left?1 mark

$24? left$60
(A) $24(B) $12(C) $40(D) $36
Answer: (D) $36Spent: 60 ÷ 5 = 12, 2 × 12 = $24. Left: 60 − 24 = $36.

Section B · Write your answer 11 marks

5. There are 72 pupils in a choir group. 58 of them are girls. How many boys are there?1 mark

45? boys72
Answer: 27Girls: 72 ÷ 8 = 9, 5 × 9 = 45.
Boys: 72 − 45 = 27. (Or 3 units × 9 = 27.)

6. Jia read 13 of her storybook. She read 14 pages. How many pages are there in the book?1 mark

14? pages
Answer: 421 unit = 14 pages. 3 units = 3 × 14 = 42 pages.

7. Raj had 45 cards. He gave 29 of them to Sam. How many cards did Raj have left?1 mark

10? left45
Answer: 351 unit = 45 ÷ 9 = 5. Gave away: 2 × 5 = 10. Left: 45 − 10 = 35.

8. 34 of the passengers on a bus are adults. The other 9 passengers are children. How many passengers are on the bus?1 mark

Adults9? passengers
Answer: 36Children are 1 unit = 9. The whole is 4 units: 4 × 9 = 36 passengers.

9. Sam has 56 coins. 38 of them are $1 coins. How many of his coins are not $1 coins?1 mark

$1 coins? other56
Answer: 351 unit = 56 ÷ 8 = 7. Not $1 coins: 5 units = 5 × 7 = 35.

10. Mrs Tan baked 64 muffins. She sold 38 of them in the morning and 14 of them in the afternoon. How many muffins were left?2 marks

2416? left64
Answer: 241 unit = 64 ÷ 8 = 8. Morning: 3 × 8 = 24. Afternoon: 14 = 28, so 2 × 8 = 16.
Left: 64 − 24 − 16 = 24 muffins.

11. Ben spent 25 of his money on a book and 15 of his money on lunch. He had $18 left. How much money did he have at first?2 marks

booklunch$18$452 units = $18
Answer: $45Spent: 25 + 15 = 35, so left = 25.
2 units = $18, so 1 unit = $9. 5 units = 5 × $9 = $45.

12. Lina has some beads. 38 of them are red, 14 of them are blue and the other 15 beads are green. How many beads does she have in all? How many of them are blue?2 marks

redblue15403 units = 15
Answer: 40; 10Blue: 14 = 28. Red and blue = 3 + 2 = 5 units, so green = 8 − 5 = 3 units.
3 units = 15, so 1 unit = 5. All the beads: 8 × 5 = 40.
Blue: 2 × 5 = 10.
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Primary 4 Mathematics · Chapter 6 · Answers and explanations

Chapter 6 Revision Paper: Fractions (II) (answers)

Section A · Multiple choice 10 marks

1. Find the value of 512 + 14.1 mark

(A) 38(B) 12(C) 712(D) 23
Answer: (D) 2314 = 312. 512 + 312 = 812 = 23. (Do not add the denominators.)

2. Find the value of 1112 − 23.1 mark

(A) 14(B) 34(C) 13(D) 112
Answer: (A) 1423 = 812. 1112 − 812 = 312 = 14.

3. Find the value of 35 + 710.1 mark

(A) 23(B) 1 310(C) 1 110(D) 1315
Answer: (B) 1 31035 = 610. 610 + 710 = 1310 = 1 310.

4. Find the value of 5 − 2 38.1 mark

(A) 3 38(B) 3 58(C) 2 58(D) 2 38
Answer: (C) 2 585 = 4 + 88, so 5 − 2 38 = (4 − 2) + (88 − 38) = 2 + 58 = 2 58.

5. Find the value of 56 + 34.1 mark

(A) 45(B) 1 112(C) 1 512(D) 1 712
Answer: (D) 1 712Change both to twelfths: 56 = 1012 and 34 = 912. 1012 + 912 = 1912 = 1 712.

6. What is 38 of 40?1 mark

(A) 15(B) 25(C) 5(D) 120
Answer: (A) 1540 ÷ 8 = 5, so 1 eighth of 40 is 5. 3 eighths = 3 × 5 = 15.

7. There are 18 counters. 12 of them are shaded. What fraction of the counters are shaded? Give your answer in its simplest form.1 mark

(A) 13(B) 23(C) 1 12(D) 29
Answer: (B) 2312 out of 18 counters are shaded: 1218. Divide the top and bottom by 6: 23. (13 is the fraction not shaded.)

8. 37 of a number is 21. What is the number?1 mark

Number21?21
(A) 9(B) 63(C) 49(D) 28
Answer: (C) 493 units = 21, so 1 unit = 21 ÷ 3 = 7. The number is 7 units = 7 × 7 = 49.

9. Hao had 32 marbles. He gave 38 of them to his friend. How many marbles did Hao have left?1 mark

Hao122032
(A) 12(B) 24(C) 29(D) 20
Answer: (D) 201 eighth of 32 = 32 ÷ 8 = 4. 3 eighths = 12 marbles given away. Marbles left: 32 − 12 = 20.

10. 35 of the pupils in a class are boys. There are 12 girls. How many pupils are in the class?1 mark

Classboys1230 pupils2 units = 12
(A) 30(B) 18(C) 20(D) 60
Answer: (A) 30Girls are 1 − 35 = 25 of the class. 2 units = 12, so 1 unit = 6. The class has 5 units = 5 × 6 = 30 pupils.

Section B · Short answers 4 marks

11. Find the value of 710 + 25.1 mark

Answer: 1 11025 = 410. 710 + 410 = 1110 = 1 110.

12. Find the value of 3 − 1 512.1 mark

Answer: 1 7123 = 2 + 1212. 3 − 1 512: 2 − 1 = 1 and 1212 − 512 = 712. The answer is 1 712.

13. Find 56 of 48.1 mark

Answer: 4048 ÷ 6 = 8, so 1 sixth of 48 is 8. 5 sixths = 5 × 8 = 40.

14. Find the value of 1 − 512 − 14. Give your answer in its simplest form.1 mark

Answer: 1314 = 312. 1 = 1212. 1212 − 512 − 312 = 412 = 13.

Section C · Show your working 16 marks

15. Tom ran 34 km in the morning and 58 km in the evening. How many kilometres did he run altogether?2 marks

Total3458138
Answer: 1 38 km34 = 68. Total: 68 + 58 = 118 = 1 38 km.

16. A tank had 4 litres of water. 2 310 litres were used. How much water was left in the tank?2 marks

Tank231017104 litres
Answer: 1 710 litres4 = 3 + 1010. 4 − 2 310: 3 − 2 = 1 and 1010 − 310 = 710. Left: 1 710 litres.

17. Mrs Lee used 12 of her flour to bake bread and 16 of her flour to bake a cake. What fraction of her flour was left? Give your answer in its simplest form.2 marks

Flourbreadcake26113
Answer: 1312 = 36. Flour used: 36 + 16 = 46. Flour left: 1 − 46 = 26 = 13.

18. Rope A is 56 m long. Rope B is 13 m shorter than Rope A. What is the total length of the two ropes?2 marks

A56B3613
Answer: 1 13 m13 = 26. Rope B: 56 − 26 = 36 = 12 m. Total: 56 + 36 = 86 = 1 13 m.

19. A florist had 72 flowers. 58 of them were roses. How many of the flowers were not roses?2 marks

Flowersroses?72 flowers3 × 9 = 27
Answer: 2772 ÷ 8 = 9, so 1 unit = 9. Not roses: 3 units = 3 × 9 = 27.

20. There are 48 pupils in a class. 512 of them walk to school and 14 of them take the bus. The rest are driven to school. How many pupils are driven to school?2 marks

Classwalkbus1648 pupils2012
Answer: 1648 ÷ 12 = 4, so 1 unit = 4 pupils. 14 = 312. Walk and bus: 5 + 3 = 8 units. Driven: 12 − 8 = 4 units = 4 × 4 = 16 pupils.

21. Ravi gave 29 of his stickers to his sister and 13 of his stickers to his brother. He had 20 stickers left. How many stickers did Ravi have at first?2 marks

Ravisisterbrother2045 stickers4 units = 20
Answer: 4513 = 39. Given away: 2 + 3 = 5 units out of 9. Left: 9 − 5 = 4 units = 20, so 1 unit = 5. At first: 9 units = 9 × 5 = 45 stickers.

22. Jun spent 14 of his money on a toy. He then spent 25 of the remainder on a book. He had $27 left. How much money did Jun have at first?2 marks

Moneytoybook$27$6015 units
Answer: $60Draw 4 units for his money; the toy is 1 unit. The remainder is 3 units. Cut every unit into 5 small units, so the whole bar has 20 small units. Toy: 5 small units. Remainder: 15 small units; book = 25 of 15 = 6 small units; left = 9 small units. 9 small units = $27, so 1 small unit = $3. At first: 20 × $3 = $60.
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