Adding and subtracting fractions – Year 4 maths worksheet answers to download as PDF

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1. Answer to Question 1

   1. ²⁄₅ is shaded and ³⁄₅ is not.
   2. ⁵⁄₈ is shaded and ³⁄₈ is not.
   3. ⁷⁄₁₀ is shaded and ³⁄₁₀ is not.
   4. ³⁄₄ is shaded and ¹⁄₄ is not.

2. Answer to Question 2

   1. The denominator goes from 2 to 8, which is × 4. So ¹⁄₂ = ⁴⁄₈.
   2. The denominator goes from 4 to 8, which is × 2. So ³⁄₄ = ⁶⁄₈.
   3. The denominator goes from 3 to 12, which is × 4. So ²⁄₃ = ⁸⁄₁₂.
   4. The denominator goes from 10 to 2, which is ÷ 5. So ⁵⁄₁₀ = ¹⁄₂.

3. Answer to Question 3

   1. Add the numerators and keep the denominator: 2 + 3 = 5, so ²⁄₉ + ³⁄₉ = ⁵⁄₉.
   2. Add the numerators and keep the denominator: 4 + 5 = 9, so ⁴⁄₁₀ + ⁵⁄₁₀ = ⁹⁄₁₀.
   3. Add the numerators and keep the denominator: 5 + 4 = 9, so ⁵⁄₆ + ⁴⁄₆ = ⁹⁄₆, which is 1 ³⁄₆ as a mixed number.
   4. Add the numerators and keep the denominator: 3 + 5 = 8, so ³⁄₈ + ⁵⁄₈ = ⁸⁄₈, which is 1 whole.

4. Answer to Question 4

   1. Subtract the numerators and keep the denominator: 5 − 2 = 3, so ⁵⁄₇ − ²⁄₇ = ³⁄₇. It cannot be simplified.
   2. Subtract the numerators and keep the denominator: 9 − 4 = 5, so ⁹⁄₁₀ − ⁴⁄₁₀ = ⁵⁄₁₀. This can be simplified to ¹⁄₂.
   3. Subtract the numerators and keep the denominator: 11 − 5 = 6, so ¹¹⁄₁₂ − ⁵⁄₁₂ = ⁶⁄₁₂. This can be simplified to ¹⁄₂.
   4. Subtract the numerators and keep the denominator: 6 − 3 = 3, so ⁶⁄₆ − ³⁄₆ = ³⁄₆. This can be simplified to ¹⁄₂.

5. Answer to Question 5

   1. 7 ÷ 4 = 1 remainder 3, so ⁷⁄₄ = 1 ³⁄₄.
   2. 11 ÷ 5 = 2 remainder 1, so ¹¹⁄₅ = 2 ¹⁄₅.
   3. 2 wholes = 6 thirds, so 2 ¹⁄₃ = 6 thirds + 1 third = ⁷⁄₃.
   4. 1 whole = 8 eighths, so 1 ³⁄₈ = 8 + 3 = ¹¹⁄₈.

6. Answer to Question 6

   1. ³⁄₄ of 20: 20 ÷ 4 = 5, then 3 × 5 = 15.
   2. ²⁄₅ of 30: 30 ÷ 5 = 6, then 2 × 6 = 12.
   3. ⁵⁄₆ of 24: 24 ÷ 6 = 4, then 5 × 4 = 20.
   4. ⁷⁄₁₀ of 50: 50 ÷ 10 = 5, then 7 × 5 = 35.

7. Answer to Question 7

   1. Anna: ²⁄₈; Ben: ³⁄₈; Cara: ¹⁄₈.
   2. 2 + 3 = 5, so ⁵⁄₈.
   3. 2 + 3 + 1 = 6 slices are eaten, so 2 slices are left: ²⁄₈ = ¹⁄₄. Check: ⁸⁄₈ − ⁶⁄₈ = ²⁄₈.
   4. Yes, he is right. 2 slices out of 8 is ²⁄₈, which is the same as ¹⁄₄ of the pizza.

8. Answer to Question 8

   1. Add the numerators and keep the denominator: 3 + 4 = 7, so ³⁄₁₀ + ⁴⁄₁₀ = ⁷⁄₁₀. So ⁷⁄₁₀.
   2. 3 + 4 + 2 = 9, so they drink ⁹⁄₁₀ in total.
   3. ¹⁄₁₀ is not drunk: ¹⁰⁄₁₀ − ⁹⁄₁₀ = ¹⁄₁₀.
   4. 50 ÷ 10 = 5, so 5 bottles were not drunk.

9. Answer to Question 9

   1. ⁵⁄₁₂ of the garden.
   2. 3 + 2 = 5, so ⁵⁄₁₂ has carrots and beans. This cannot be simplified because 5 and 12 have no common factor.
   3. 5 + 3 + 2 = 10 beds are used, so 2 beds are empty: ²⁄₁₂ = ¹⁄₆.
   4. Half of 12 = 6 beds. Only 2 beds are empty, so there is not enough space.

10. Answer to Question 10

    1. 36 ÷ 4 = 9 marbles.
    2. 36 ÷ 3 = 12 marbles.
    3. 36 − 9 − 12 = 15 marbles.
    4. He got 9 marbles. 9 ÷ 3 = 3 and 2 × 3 = 6 marbles.

11. Answer to Question 11

    1. 120 ÷ 5 = 24, so 24 pages.
    2. 2 × 24 = 48 pages.
    3. 1 + 2 = 3, so she has read ³⁄₅ of the book (72 pages).
    4. 120 − 72 = 48 pages (or ²⁄₅ of 120 = 48).

12. Answer to Question 12

    1. 3 + 2 = 5, so ⁵⁄₈.
    2. ⁸⁄₈ − ⁵⁄₈ = ³⁄₈.
    3. 40 ÷ 8 = 5, and 3 × 5 = 15 m.
    4. 3 × 5 = 15 m. (Same as Monday, because the fraction is also ³⁄₈.)

13. Answer to Question 13

    1. 30 ÷ 3 = 10 children.
    2. 30 ÷ 5 = 6 children chose swimming and 30 ÷ 6 = 5 children chose tennis.
    3. ¹⁄₃ = ¹⁰⁄₃₀, ¹⁄₅ = ⁶⁄₃₀ and ¹⁄₆ = ⁵⁄₃₀. Add: 10 + 6 + 5 = 21, so ²¹⁄₃₀ = ⁷⁄₁₀.
    4. 30 − 21 = 9 children chose gymnastics, which is ⁹⁄₃₀ = ³⁄₁₀ of the club.

14. Answer to Question 14

    1. Add the numerators and keep the denominator: 3 + 2 = 5, so ³⁄₄ + ²⁄₄ = ⁵⁄₄, which is 1 ¹⁄₄ as a mixed number. So one batch uses 1 ¹⁄₄ cups altogether.
    2. 2 × ³⁄₄ = ⁶⁄₄ = 1 ²⁄₄ cups (1 ¹⁄₂ cups).
    3. 2 × ²⁄₄ = ⁴⁄₄ = 1 cup.
    4. 2 cups = ⁸⁄₄. ⁸⁄₄ − ⁶⁄₄ = ²⁄₄ = ¹⁄₂ cup left.

15. Answer to Question 15

    1. 60 ÷ 2 = 30 children.
    2. 60 ÷ 5 = 12 by minibus and 60 ÷ 4 = 15 by train.
    3. ¹⁄₂ = ¹⁰⁄₂₀, ¹⁄₅ = ⁴⁄₂₀ and ¹⁄₄ = ⁵⁄₂₀. Add: 10 + 4 + 5 = 19, so ¹⁹⁄₂₀ travel by vehicle and ¹⁄₂₀ walk.
    4. 60 ÷ 20 = 3, so 3 children walk. Check: 60 − 30 − 12 − 15 = 3.
    5. ¹⁹⁄₂₀ is more than ¹⁵⁄₂₀ (which is ³⁄₄), so she is right.

16. Answer to Question 16

    1. 60 ÷ 4 = £15.
    2. 60 ÷ 3 = £20 on the game and 60 ÷ 6 = £10 on sweets and drinks.
    3. 15 + 20 + 10 = £45.
    4. ¹⁄₄ = ³⁄₁₂, ¹⁄₃ = ⁴⁄₁₂ and ¹⁄₆ = ²⁄₁₂. Add: 3 + 4 + 2 = 9, so ⁹⁄₁₂ is spent and ³⁄₁₂ (¹⁄₄) is saved.
    5. 60 − 45 = £15, which is ¹⁄₄ of £60.

17. Answer to Question 17

    1. 240 ÷ 8 = 30, and 3 × 30 = 90 km.
    2. 240 ÷ 4 = 60 km.
    3. ¹⁄₄ = ²⁄₈. Add: ³⁄₈ + ²⁄₈ = ⁵⁄₈.
    4. ⁸⁄₈ − ⁵⁄₈ = ³⁄₈ is left. 3 × 30 = 90 km. Check: 240 − 90 − 60 = 90.
    5. 90 ÷ 60 = 1 remainder 30, so it takes 1 hour 30 minutes (1 ¹⁄₂ hours).

18. Answer to Question 18

    1. 3 + 4 = 7, so ⁷⁄₁₂.
    2. 3 + 4 + 2 = 9 sections are done, so 12 − 9 = 3 sections on Thursday.
    3. ³⁄₁₂ = ¹⁄₄ (divide the top and bottom by 3).
    4. 24 ÷ 3 = 8 children are away, so 24 − 8 = 16 children are at school.
    5. Wednesday: ²⁄₁₂ = ¹⁄₆. She is right.

19. Answer to Question 19

    1. 48 ÷ 6 = 8 jars.
    2. 48 ÷ 4 = 12 jars of jellies and 48 ÷ 3 = 16 jars of toffees.
    3. ¹⁄₆ = ²⁄₁₂, ¹⁄₄ = ³⁄₁₂ and ¹⁄₃ = ⁴⁄₁₂. Add: 2 + 3 + 4 = 9, so ⁹⁄₁₂ = ³⁄₄.
    4. Mints: ³⁄₁₂ of 48 = 12 jars. Check: 48 − 8 − 12 − 16 = 12 jars.
    5. 16 ÷ 4 = 4 and 3 × 4 = 12 jars sold, so 16 − 12 = 4 jars are left.

20. Answer to Question 20

    1. Three numerators must add to 16 (because 2 wholes = ¹⁶⁄₈). The only possibilities are: ³⁄₈ + ⁶⁄₈ + ⁷⁄₈, ⁴⁄₈ + ⁵⁄₈ + ⁷⁄₈. There are 2 answers.
    2. The numerators must differ by 3. Two possible pairs are ⁴⁄₈ and ¹⁄₈ (⁴⁄₈ − ¹⁄₈ = ³⁄₈), and ⁷⁄₈ and ⁴⁄₈ (⁷⁄₈ − ⁴⁄₈ = ³⁄₈). Others: ⁵⁄₈ and ²⁄₈, ⁶⁄₈ and ³⁄₈.
    3. The three fractions must be different, and ¹⁄₈ three times uses the same fraction three times. Also, ¹⁄₈ + ¹⁄₈ + ¹⁄₈ = ³⁄₈, which is much less than 2.