Fractions: unit and non-unit – Year 3 maths worksheet answers to download as PDF

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1. Answer to Question 1

   1. \(\frac{1}{6}\) is a unit fraction: the numerator is 1.
   2. \(\frac{3}{5}\) is a non-unit fraction: the numerator is 3.
   3. \(\frac{1}{10}\) is a unit fraction: the numerator is 1.
   4. \(\frac{7}{8}\) is a non-unit fraction: the numerator is 7.
   5. \(\frac{2}{3}\) is a non-unit fraction: the numerator is 2.

2. Answer to Question 2

   1. 1 of 4 equal parts is shaded: \(\frac{1}{4}\). The numerator is 1, so it is a unit fraction.
   2. 5 of 6 equal parts are shaded: \(\frac{5}{6}\). The numerator is more than 1, so it is a non-unit fraction.
   3. 3 of 10 equal parts are shaded: \(\frac{3}{10}\), a non-unit fraction because the numerator is 3.
   4. 1 of 8 equal parts is shaded: \(\frac{1}{8}\), a unit fraction.

3. Answer to Question 3

   1. Counting in tenths adds one tenth each time: \(\frac{1}{10}, \frac{2}{10}\), then \(\frac{3}{10}\), then \(\frac{4}{10}\).
   2. After \(\frac{7}{10}\) come \(\frac{8}{10}\) and \(\frac{9}{10}\).
   3. Ten tenths fill the whole line, so \(\frac{10}{10}\) = 1 whole.
   4. 5 tenths is half of the 10 tenths, so \(\frac{5}{10} = \frac{1}{2}\). The missing number is 1.

4. Answer to Question 4

   1. Divide 18 by 2: 18 ÷ 2 = 9. So \(\frac{1}{2}\) of 18 is 9. Check: 9 × 2 = 18.
   2. Divide 21 by 3: 21 ÷ 3 = 7. So \(\frac{1}{3}\) of 21 is 7. Check: 7 × 3 = 21.
   3. Divide 32 by 4: 32 ÷ 4 = 8. So \(\frac{1}{4}\) of 32 is 8. Check: 8 × 4 = 32.
   4. Divide 45 by 5: 45 ÷ 5 = 9. So \(\frac{1}{5}\) of 45 is 9. Check: 9 × 5 = 45.
   5. Divide 60 by 10: 60 ÷ 10 = 6. So \(\frac{1}{10}\) of 60 is 6. Check: 6 × 10 = 60.

5. Answer to Question 5

   1. Divide 12 by 3: 12 ÷ 3 = 4. Multiply by 2: 4 × 2 = 8.
   2. Divide 20 by 4: 20 ÷ 4 = 5. Multiply by 3: 5 × 3 = 15.
   3. Divide 30 by 5: 30 ÷ 5 = 6. Multiply by 4: 6 × 4 = 24.
   4. Divide 50 by 10: 50 ÷ 10 = 5. Multiply by 3: 5 × 3 = 15.
   5. Divide 24 by 8: 24 ÷ 8 = 3. Multiply by 5: 3 × 5 = 15.

6. Answer to Question 6

   1. Same denominator, so add the numerators: 3 + 4 = 7. \(\frac{3}{10} + \frac{4}{10} = \frac{7}{10}\).
   2. 5 + 2 = 7, so \(\frac{5}{8} + \frac{2}{8} = \frac{7}{8}\). The denominator stays 8 because the size of each part does not change.
   3. Subtract the numerators: 9 − 4 = 5. \(\frac{9}{10} - \frac{4}{10} = \frac{5}{10}\), which is also a half.
   4. 6 − 5 = 1, so \(\frac{6}{7} - \frac{5}{7} = \frac{1}{7}\).
   5. 1 + 2 = 3, so \(\frac{1}{5} + \frac{2}{5} = \frac{3}{5}\).

7. Answer to Question 7

   1. Ella eats 2 of the 8 slices: \(\frac{2}{8}\). The numerator is 2, so it is a non-unit fraction (it equals \(\frac{1}{4}\)).
   2. Her dad eats 1 slice: \(\frac{1}{8}\), a unit fraction.
   3. Add the slices: 2 + 3 + 1 = 6. \(\frac{2}{8} + \frac{3}{8} + \frac{1}{8} = \frac{6}{8}\).
   4. The whole pizza is \(\frac{8}{8}\): \(\frac{8}{8} - \frac{6}{8} = \frac{2}{8}\). That is 2 slices for her mum.

8. Answer to Question 8

   1. \(\frac{1}{4}\) of 24 means 24 ÷ 4. Half of 24 is 12, half of 12 is 6, so the winning team gets 6 sweets.
   2. \(\frac{1}{3}\) of 24 means 24 ÷ 3 = 8 sweets, because 3 × 8 = 24.
   3. Add the two teams: 6 + 8 = 14 sweets given out.
   4. Mr Hill keeps the rest: 24 − 14 = 10 sweets.

9. Answer to Question 9

   1. £20 ÷ 5 = £4, then 2 × £4 = £8.
   2. £20 ÷ 5 = £4.
   3. £20 ÷ 10 = £2.
   4. Total used: 8 + 4 + 2 = £14. £20 − £14 = £6.

10. Answer to Question 10

    1. 30 ÷ 5 = 6, 3 × 6 = 18.
    2. 30 ÷ 10 = 3.
    3. 30 − 18 − 3 = 9.
    4. \(\frac{9}{30}\) = \(\frac{3}{10}\).

11. Answer to Question 11

    1. 1000 ÷ 10 = 100 ml, then 3 × 100 = 300 ml.
    2. 4 × 100 = 400 ml.
    3. \(\frac{10}{10}\) − \(\frac{3}{10}\) − \(\frac{4}{10}\) = \(\frac{3}{10}\).
    4. 1000 − 300 − 400 = 300 ml. This matches \(\frac{3}{10}\) of 1000.

12. Answer to Question 12

    1. \(\frac{1}{2}\) of 40 is 40 ÷ 2 = 20 bulbs in the flower bed.
    2. \(\frac{1}{4}\) of 40 is 40 ÷ 4 = 10 bulbs in pots (half of 20).
    3. Take both amounts away from 40: 40 − 20 − 10 = 10 bulbs by the gate.
    4. 10 out of 40 is \(\frac{10}{40}\). Divide the numerator and the denominator by 10 to get \(\frac{1}{4}\). Also \(1 - \frac{1}{2} - \frac{1}{4} = \frac{1}{4}\).

13. Answer to Question 13

    1. 36 ÷ 3 = 12, then 2 × 12 = 24.
    2. 36 ÷ 6 = 6.
    3. 36 − 24 − 6 = 6.
    4. \(\frac{6}{36}\) = \(\frac{1}{6}\).

14. Answer to Question 14

    1. 60 ÷ 2 = 30 minutes.
    2. 60 ÷ 4 = 15 minutes.
    3. 3 × 15 = 45 minutes.
    4. 60 ÷ 10 = 6 and 60 ÷ 5 = 12. 6 + 12 = 18 minutes.

15. Answer to Question 15

    1. 24 ÷ 2 = 12 slices of pizza.
    2. 24 ÷ 3 = 8 slices of cake.
    3. 1 − \(\frac{1}{2}\) − \(\frac{1}{3}\) = \(\frac{6}{6}\) − \(\frac{3}{6}\) − \(\frac{2}{6}\) = \(\frac{1}{6}\).
    4. 24 ÷ 6 = 4. Check: 12 + 8 + 4 = 24.

16. Answer to Question 16

    1. 60 ÷ 5 = 12, then 2 × 12 = 24.
    2. 60 ÷ 10 = 6, then 3 × 6 = 18.
    3. 60 − 24 − 18 = 18.
    4. \(\frac{18}{60}\) = \(\frac{3}{10}\). Both groups are 18 books, so the fractions are equal.

17. Answer to Question 17

    1. 100 ÷ 10 = 10, so 3 × 10 = 30.
    2. 4 × 10 = 40.
    3. \(\frac{3}{10}\) + \(\frac{4}{10}\) = \(\frac{7}{10}\).
    4. \(\frac{7}{10}\) = 70 pieces, which is more than 50. Yes. Left: 100 − 70 = 30 pieces.

18. Answer to Question 18

    1. Tom multiplied by 4. You must divide: 20 ÷ 4 = 5. Wrong.
    2. 20 ÷ 5 = 4, 3 × 4 = 12. Right.
    3. The denominator stays the same: \(\frac{5}{7}\). Wrong.
    4. 7 − 2 = 5 and the denominator stays 9. Right.

19. Answer to Question 19

    1. 400 ÷ 4 = 100, 3 × 100 = 300 m.
    2. 400 ÷ 10 = 40, 7 × 40 = 280 m.
    3. 300 − 280 = 20 m. Amy is further.
    4. Half of 400 = 200 m run. 400 − 200 = 200 m to go.

20. Answer to Question 20

    1. 36 ÷ 4 = 9.
    2. 36 − 9 = 27.
    3. 27 ÷ 3 = 9.
    4. 27 − 9 = 18 left. \(\frac{18}{36}\) = \(\frac{1}{2}\) of the counters.