Equivalent Fractions Worksheet - Free Printable

Let's solve each of the equivalent fractions problems step by step, using the rule: Multiply or divide both the numerator and denominator by the same number to get an equivalent fraction.

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1) $ \frac{2}{3} = \frac{?}{9} $

We want the denominator to go from 3 → 9.
$ 3 \times 3 = 9 $, so multiply numerator by 3:
$ 2 \times 3 = 6 $

✔ Answer: $ \frac{6}{9} $

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2) $ \frac{2}{5} = \frac{?}{15} $

5 → 15: $ 5 \times 3 = 15 $, so multiply numerator by 3:
$ 2 \times 3 = 6 $

✔ Answer: $ \frac{6}{15} $

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3) $ \frac{1}{7} = \frac{?}{14} $

7 → 14: $ 7 \times 2 = 14 $, so multiply numerator by 2:
$ 1 \times 2 = 2 $

✔ Answer: $ \frac{2}{14} $

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4) $ \frac{3}{3} = \frac{?}{9} $

$ \frac{3}{3} = 1 $, so we want $ \frac{?}{9} = 1 $ → $ ? = 9 $

Alternatively: 3 → 9 is ×3, so $ 3 \times 3 = 9 $

✔ Answer: $ \frac{9}{9} $

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5) $ \frac{3}{4} = \frac{9}{?} $

Numerator goes from 3 → 9: $ 3 \times 3 = 9 $, so multiply denominator by 3:
$ 4 \times 3 = 12 $

✔ Answer: $ \frac{9}{12} $

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6) $ \frac{1}{2} = \frac{6}{?} $

Numerator: 1 → 6: $ 1 \times 6 = 6 $, so denominator: $ 2 \times 6 = 12 $

✔ Answer: $ \frac{6}{12} $

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7) $ \frac{5}{6} = \frac{?}{18} $

6 → 18: $ 6 \times 3 = 18 $, so $ 5 \times 3 = 15 $

✔ Answer: $ \frac{15}{18} $

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8) $ \frac{1}{5} = \frac{3}{?} $

Numerator: 1 → 3: $ 1 \times 3 = 3 $, so denominator: $ 5 \times 3 = 15 $

✔ Answer: $ \frac{3}{15} $

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9) $ \frac{2}{9} = \frac{?}{18} $

9 → 18: ×2 → $ 2 \times 2 = 4 $

✔ Answer: $ \frac{4}{18} $

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10) $ \frac{3}{5} = \frac{?}{20} $

5 → 20: ×4 → $ 3 \times 4 = 12 $

✔ Answer: $ \frac{12}{20} $

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11) $ \frac{2}{6} = \frac{6}{?} $

Numerator: 2 → 6: ×3 → denominator: $ 6 \times 3 = 18 $

✔ Answer: $ \frac{6}{18} $

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12) $ \frac{3}{7} = \frac{9}{?} $

3 → 9: ×3 → denominator: $ 7 \times 3 = 21 $

✔ Answer: $ \frac{9}{21} $

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13) $ \frac{4}{12} = \frac{?}{3} $

Simplify: $ \frac{4}{12} = \frac{1}{3} $, so numerator must be 1

Or: 12 → 3: ÷4 → $ 4 \div 4 = 1 $

✔ Answer: $ \frac{1}{3} $

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14) $ \frac{4}{6} = \frac{?}{3} $

6 → 3: ÷2 → $ 4 \div 2 = 2 $

✔ Answer: $ \frac{2}{3} $

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15) $ \frac{3}{6} = \frac{1}{?} $

3 → 1: ÷3 → denominator: $ 6 \div 3 = 2 $

✔ Answer: $ \frac{1}{2} $

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16) $ \frac{9}{12} = \frac{?}{4} $

12 → 4: ÷3 → $ 9 \div 3 = 3 $

✔ Answer: $ \frac{3}{4} $

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17) $ \frac{4}{10} = \frac{?}{5} $

10 → 5: ÷2 → $ 4 \div 2 = 2 $

✔ Answer: $ \frac{2}{5} $

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18) $ \frac{5}{10} = \frac{?}{2} $

10 → 2: ÷5 → $ 5 \div 5 = 1 $

✔ Answer: $ \frac{1}{2} $

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19) $ \frac{4}{16} = \frac{1}{?} $

4 → 1: ÷4 → denominator: $ 16 \div 4 = 4 $

✔ Answer: $ \frac{1}{4} $

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20) $ \frac{8}{8} = \frac{?}{2} $

$ \frac{8}{8} = 1 $, so need $ \frac{?}{2} = 1 $ → ? = 2

Or: 8 → 2: ÷4 → $ 8 \div 4 = 2 $

✔ Answer: $ \frac{2}{2} $

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21) $ \frac{8}{10} = \frac{4}{?} $

8 → 4: ÷2 → denominator: $ 10 \div 2 = 5 $

✔ Answer: $ \frac{4}{5} $

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22) $ \frac{2}{?} = \frac{8}{12} $

Simplify $ \frac{8}{12} = \frac{2}{3} $ → so denominator is 3

Or: 8 → 2: ÷4 → denominator: $ 12 \div 4 = 3 $

✔ Answer: $ \frac{2}{3} $

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23) $ \frac{1}{?} = \frac{5}{15} $

Simplify $ \frac{5}{15} = \frac{1}{3} $ → denominator is 3

✔ Answer: $ \frac{1}{3} $

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24) $ \frac{1}{?} = \frac{3}{21} $

$ \frac{3}{21} = \frac{1}{7} $ → denominator is 7

✔ Answer: $ \frac{1}{7} $

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25) $ \frac{2}{?} = \frac{4}{18} $

Simplify $ \frac{4}{18} = \frac{2}{9} $ → denominator is 9

✔ Answer: $ \frac{2}{9} $

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26) $ \frac{3}{?} = \frac{9}{15} $

Simplify $ \frac{9}{15} = \frac{3}{5} $ → denominator is 5

✔ Answer: $ \frac{3}{5} $

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27) $ \frac{5}{9} = \frac{15}{?} $

5 → 15: ×3 → denominator: $ 9 \times 3 = 27 $

✔ Answer: $ \frac{15}{27} $

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28) $ \frac{4}{?} = \frac{16}{20} $

Simplify $ \frac{16}{20} = \frac{4}{5} $ → denominator is 5

✔ Answer: $ \frac{4}{5} $

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29) $ \frac{3}{10} = \frac{12}{?} $

3 → 12: ×4 → denominator: $ 10 \times 4 = 40 $

✔ Answer: $ \frac{12}{40} $

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30) $ \frac{?}{9} = \frac{8}{36} $

Simplify $ \frac{8}{36} = \frac{2}{9} $ → numerator is 2

✔ Answer: $ \frac{2}{9} $

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31) $ \frac{5}{7} = \frac{?}{35} $

7 → 35: ×5 → $ 5 \times 5 = 25 $

✔ Answer: $ \frac{25}{35} $

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32) $ \frac{6}{11} = \frac{18}{?} $

6 → 18: ×3 → denominator: $ 11 \times 3 = 33 $

✔ Answer: $ \frac{18}{33} $

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## ✔ Final Answers:

1) $ \frac{6}{9} $
2) $ \frac{6}{15} $
3) $ \frac{2}{14} $
4) $ \frac{9}{9} $
5) $ \frac{9}{12} $
6) $ \frac{6}{12} $
7) $ \frac{15}{18} $
8) $ \frac{3}{15} $
9) $ \frac{4}{18} $
10) $ \frac{12}{20} $
11) $ \frac{6}{18} $
12) $ \frac{9}{21} $
13) $ \frac{1}{3} $
14) $ \frac{2}{3} $
15) $ \frac{1}{2} $
16) $ \frac{3}{4} $
17) $ \frac{2}{5} $
18) $ \frac{1}{2} $
19) $ \frac{1}{4} $
20) $ \frac{2}{2} $
21) $ \frac{4}{5} $
22) $ \frac{2}{3} $
23) $ \frac{1}{3} $
24) $ \frac{1}{7} $
25) $ \frac{2}{9} $
26) $ \frac{3}{5} $
27) $ \frac{15}{27} $
28) $ \frac{4}{5} $
29) $ \frac{12}{40} $
30) $ \frac{2}{9} $
31) $ \frac{25}{35} $
32) $ \frac{18}{33} $

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🔍 Summary Tips:

- To find missing numbers, look at what you multiplied or divided the known part by.
- Always check that the ratio stays the same.
- Simplify fractions when needed to help spot patterns.

Let me know if you'd like this printed in a table format!