Equivalent fractions and comparing fractions – Year 3 maths worksheet answers to download as PDF

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1. Answer to Question 1

   1. The bar has 4 equal parts and 1 is shaded. The denominator counts the equal parts and the numerator counts the shaded ones: \(\frac{1}{4}\).
   2. The bar has 8 equal parts and 3 are shaded, so the fraction is \(\frac{3}{8}\) (three eighths).
   3. The bar has 5 equal parts and 2 are shaded, so the fraction is \(\frac{2}{5}\) (two fifths).
   4. The bar has 10 equal parts and 7 are shaded, so the fraction is \(\frac{7}{10}\) (seven tenths).

2. Answer to Question 2

   1. Each half of the top bar covers 2 quarters of the bottom bar. So \(\frac{1}{2} = \frac{2}{4}\) and the missing number is 2. Both the numerator and the denominator were doubled.
   2. One third of the bar lines up with 2 sixths. So \(\frac{1}{3} = \frac{2}{6}\): the missing number is 2 (1 × 2 = 2 and 3 × 2 = 6).
   3. Each quarter splits into 2 eighths, so 3 quarters make 3 × 2 = 6 eighths. \(\frac{3}{4} = \frac{6}{8}\): the missing number is 6.

3. Answer to Question 3

   1. \(\frac{1}{2}\) = \(\frac{3}{6}\): 1 × 3 = 3 and 2 × 3 = 6.
   2. \(\frac{1}{3}\) = \(\frac{4}{12}\): 1 × 4 = 4 and 3 × 4 = 12.
   3. \(\frac{2}{5}\) = \(\frac{4}{10}\): 2 × 2 = 4 and 5 × 2 = 10.
   4. \(\frac{3}{4}\) = \(\frac{6}{8}\): 3 × 2 = 6 and 4 × 2 = 8.
   5. \(\frac{1}{5}\) = \(\frac{2}{10}\): 1 × 2 = 2 and 5 × 2 = 10.

4. Answer to Question 4

   1. 2 × 5 = 10, so 1 × 5 = 5.
   2. 3 × 3 = 9, so 2 × 3 = 6.
   3. 4 ÷ 2 = 2, so 8 ÷ 2 = 4.
   4. 6 ÷ 2 = 3, so 10 ÷ 2 = 5.

5. Answer to Question 5

   1. \(\frac{3}{8}\) < \(\frac{5}{8}\) (same denominator: compare numerators)
   2. \(\frac{2}{9}\) < \(\frac{7}{9}\) (same denominator: compare numerators)
   3. \(\frac{1}{4}\) > \(\frac{1}{6}\) (same numerator: the bigger denominator is the smaller fraction)
   4. \(\frac{1}{3}\) > \(\frac{1}{10}\) (same numerator: the bigger denominator is the smaller fraction)
   5. \(\frac{4}{5}\) > \(\frac{2}{5}\) (same denominator: compare numerators)

6. Answer to Question 6

   1. \(\frac{2}{7}\) + \(\frac{3}{7}\) = \(\frac{5}{7}\). The denominator stays 7.
   2. \(\frac{4}{9}\) + \(\frac{2}{9}\) = \(\frac{6}{9}\). The denominator stays 9.
   3. \(\frac{6}{7}\) − \(\frac{2}{7}\) = \(\frac{4}{7}\). The denominator stays 7.
   4. \(\frac{5}{10}\) − \(\frac{4}{10}\) = \(\frac{1}{10}\). The denominator stays 10.

7. Answer to Question 7

   1. \(\frac{4}{8}\) = \(\frac{1}{2}\).
   2. \(\frac{2}{4}\) = \(\frac{1}{2}\).
   3. They eat the same amount: \(\frac{4}{8}\) = \(\frac{2}{4}\) = half a pizza.
   4. \(\frac{3}{8}\) and \(\frac{2}{4}\) = \(\frac{4}{8}\). 4 eighths is more than 3 eighths, so Zack ate more.

8. Answer to Question 8

   1. \(\frac{3}{10}\).
   2. \(\frac{5}{10}\) = \(\frac{1}{2}\).
   3. \(\frac{3}{10}\) + \(\frac{5}{10}\) = \(\frac{8}{10}\).
   4. 3 + 5 + 1 = 9 eaten, so \(\frac{1}{10}\) is left. Check: 10 − 9 = 1 square, \(\frac{1}{10}\).

9. Answer to Question 9

   1. 5 of the 12 equal slices are eaten before tea, so the fraction is \(\frac{5}{12}\).
   2. 4 of the 12 slices are eaten at tea time: \(\frac{4}{12}\), which is the same as \(\frac{1}{3}\).
   3. The denominators are the same, so add the numerators: \(\frac{5}{12} + \frac{4}{12} = \frac{9}{12}\) of the cake has been eaten.
   4. 12 − 9 = 3 slices are left, which is \(\frac{3}{12}\). 3 slices is a quarter of 12, so \(\frac{3}{12} = \frac{1}{4}\): a quarter of the cake is left.

10. Answer to Question 10

    1. \(\frac{1}{2}\).
    2. 2 quarters = 1 half, so 2 pieces.
    3. 4 eighths = 1 half, so 4 pieces.
    4. \(\frac{1}{4}\) = \(\frac{2}{8}\). 3 eighths is more than 2 eighths, so yes, she is right.

11. Answer to Question 11

    1. 6 out of 12 apples is \(\frac{6}{12}\). Divide the numerator and denominator by 6: \(\frac{6}{12} = \frac{1}{2}\).
    2. 4 out of 12 is \(\frac{4}{12}\). Divide both numbers by 4: \(\frac{4}{12} = \frac{1}{3}\).
    3. 2 out of 12 is \(\frac{2}{12}\). Divide both numbers by 2: \(\frac{2}{12} = \frac{1}{6}\).
    4. For unit fractions, the bigger the denominator, the smaller the fraction. So the order is \(\frac{1}{6}, \frac{1}{3}, \frac{1}{2}\), and the first pack has the biggest share (6 apples).

12. Answer to Question 12

    1. Change to eighths: Dan has \(\frac{3}{4}\) = \(\frac{6}{8}\), Ben has \(\frac{1}{2}\) = \(\frac{4}{8}\). The numerators are 7, 4, 5 and 6, so Aisha ran the furthest.
    2. \(\frac{1}{2}\) = \(\frac{4}{8}\), which is the smallest. Ben.
    3. \(\frac{7}{8}\) − \(\frac{6}{8}\) = \(\frac{1}{8}\).
    4. \(\frac{4}{8}\), \(\frac{5}{8}\), \(\frac{6}{8}\), \(\frac{7}{8}\). Order: Ben, Cara, Dan, Aisha.

13. Answer to Question 13

    1. 8 of the 10 equal parts are full in the morning: \(\frac{8}{10}\) of the tank.
    2. 5 of 10 parts are full at lunchtime: \(\frac{5}{10}\). Five is half of ten, so another name is \(\frac{1}{2}\).
    3. The tank went from 8 tenths to 5 tenths: \(\frac{8}{10} - \frac{5}{10} = \frac{3}{10}\) was used.
    4. Yes, he is right. Half the tank is \(\frac{5}{10}\), and \(\frac{3}{10} \lt \frac{5}{10}\), so he used less than half.

14. Answer to Question 14

    1. English takes 2 of the 8 sessions: \(\frac{2}{8}\). Divide both numbers by 2 to get \(\frac{1}{4}\), a quarter of the day.
    2. Maths and science together use 2 + 1 = 3 sessions: \(\frac{2}{8} + \frac{1}{8} = \frac{3}{8}\).
    3. The whole day is \(\frac{8}{8}\). Break and lunch take \(\frac{1}{8}\), so \(\frac{8}{8} - \frac{1}{8} = \frac{7}{8}\) is left for lessons.
    4. Half of 8 sessions is 4 sessions. 4 is more than 3, so half the day is more than 3 sessions.

15. Answer to Question 15

    1. Lily \(\frac{3}{4}\), Omar \(\frac{4}{6}\), Ravi \(\frac{5}{8}\), Sara \(\frac{6}{10}\).
    2. \(\frac{3}{4}\) = \(\frac{6}{8}\), and \(\frac{6}{8}\) > \(\frac{5}{8}\), so Lily eats more.
    3. No. The slices are different sizes. \(\frac{5}{8}\) < \(\frac{6}{8}\) = \(\frac{3}{4}\). Eighths are smaller than quarters. So Ravi is wrong.
    4. 6 − 4 = 2 slices left. \(\frac{2}{6}\) = \(\frac{1}{3}\).

16. Answer to Question 16

    1. \(\frac{4}{8}\) = \(\frac{1}{2}\). The answer is \(\frac{4}{8}\).
    2. \(\frac{2}{8}\) = \(\frac{1}{4}\) and \(\frac{6}{8}\) = \(\frac{3}{4}\).
    3. Eighths: \(\frac{4}{8}\), \(\frac{3}{8}\), \(\frac{6}{8}\), \(\frac{2}{8}\). Order: \(\frac{1}{4}\), \(\frac{3}{8}\), \(\frac{1}{2}\), \(\frac{3}{4}\).
    4. \(\frac{1}{2}\) = \(\frac{4}{8}\) and \(\frac{3}{4}\) = \(\frac{6}{8}\). 5 is between 4 and 6, so yes.

17. Answer to Question 17

    1. Lanes 1, 2 and 3 are for beginners: 3 of the 10 lanes, which is \(\frac{3}{10}\).
    2. Lanes 4, 5 and 6 are for improvers: 3 lanes, so \(\frac{3}{10}\) again.
    3. Lanes 7, 8, 9 and 10 are 4 lanes: \(\frac{4}{10}\). A third of 10 lanes would be 3 and a bit lanes, and 4 is more than that, so \(\frac{4}{10}\) is more than a third.
    4. Beginners and improvers use \(\frac{3}{10} + \frac{3}{10} = \frac{6}{10}\). Divide the numerator and denominator by 2: \(\frac{6}{10} = \frac{3}{5}\).

18. Answer to Question 18

    1. The numerator was doubled (1 to 2) but the denominator went from 3 to 5, not 6. Wrong: \(\frac{1}{3}\) = \(\frac{2}{6}\).
    2. \(\frac{3}{4}\) = \(\frac{6}{8}\) and 6 > 5. Right.
    3. Add numerators only: 2 + 3 = 5. The denominator stays 9. Wrong: \(\frac{5}{9}\).
    4. The bigger denominator gives the smaller fraction. Wrong: \(\frac{1}{6}\) < \(\frac{1}{4}\).

19. Answer to Question 19

    1. Roses \(\frac{3}{12}\), tulips \(\frac{4}{12}\), herbs \(\frac{2}{12}\).
    2. \(\frac{3}{12}\) = \(\frac{1}{4}\), \(\frac{4}{12}\) = \(\frac{1}{3}\), \(\frac{2}{12}\) = \(\frac{1}{6}\).
    3. 12 − (3 + 4 + 2) = 3 beds. \(\frac{3}{12}\) = \(\frac{1}{4}\).
    4. Both are \(\frac{3}{12}\), so they are equal.

20. Answer to Question 20

    1. \(\frac{1}{2}\) = \(\frac{2}{4}\) = \(\frac{3}{6}\) = \(\frac{5}{10}\).
    2. \(\frac{1}{2}\) = \(\frac{4}{8}\) and \(\frac{3}{4}\) = \(\frac{6}{8}\). Between 4 and 6 comes 5, so \(\frac{5}{8}\) is between them.
    3. No. The only whole number between 4 and 6 is 5, so \(\frac{5}{8}\) is the only eighth between \(\frac{1}{2}\) and \(\frac{3}{4}\).