Equivalent fractions practice worksheet for students to complete.

Let's solve each problem step by step to find the equivalent fractions. Equivalent fractions are fractions that represent the same value, even though they may look different.

We'll use multiplication or division to find missing numerators or denominators so that the fractions remain equal.

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1. $ \frac{1}{2} = \frac{\square}{6} = \frac{\square}{8} $

- To go from 2 to 6: Multiply denominator by 3 → So numerator must also be multiplied by 3:
$ 1 \times 3 = 3 $ → $ \frac{3}{6} $
- To go from 2 to 8: Multiply denominator by 4 → So numerator: $ 1 \times 4 = 4 $ → $ \frac{4}{8} $

✔ Answer: $ \frac{1}{2} = \frac{3}{6} = \frac{4}{8} $

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2. $ \frac{1}{4} = \frac{\square}{12} = \frac{\square}{20} $

- 4 to 12: multiply by 3 → $ 1 \times 3 = 3 $ → $ \frac{3}{12} $
- 4 to 20: multiply by 5 → $ 1 \times 5 = 5 $ → $ \frac{5}{20} $

✔ Answer: $ \frac{1}{4} = \frac{3}{12} = \frac{5}{20} $

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3. $ \frac{1}{8} = \frac{\square}{16} = \frac{\square}{32} $

- 8 to 16: ×2 → $ 1 \times 2 = 2 $ → $ \frac{2}{16} $
- 8 to 32: ×4 → $ 1 \times 4 = 4 $ → $ \frac{4}{32} $

✔ Answer: $ \frac{1}{8} = \frac{2}{16} = \frac{4}{32} $

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4. $ \frac{3}{4} = \frac{\square}{8} = \frac{\square}{16} $

- 4 to 8: ×2 → $ 3 \times 2 = 6 $ → $ \frac{6}{8} $
- 4 to 16: ×4 → $ 3 \times 4 = 12 $ → $ \frac{12}{16} $

✔ Answer: $ \frac{3}{4} = \frac{6}{8} = \frac{12}{16} $

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5. $ \frac{5}{6} = \frac{\square}{12} = \frac{\square}{24} $

- 6 to 12: ×2 → $ 5 \times 2 = 10 $ → $ \frac{10}{12} $
- 6 to 24: ×4 → $ 5 \times 4 = 20 $ → $ \frac{20}{24} $

✔ Answer: $ \frac{5}{6} = \frac{10}{12} = \frac{20}{24} $

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6. $ \frac{3}{5} = \frac{\square}{10} = \frac{\square}{15} $

- 5 to 10: ×2 → $ 3 \times 2 = 6 $ → $ \frac{6}{10} $
- 5 to 15: ×3 → $ 3 \times 3 = 9 $ → $ \frac{9}{15} $

✔ Answer: $ \frac{3}{5} = \frac{6}{10} = \frac{9}{15} $

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7. $ \frac{4}{5} = \frac{\square}{25} = \frac{\square}{30} $

- 5 to 25: ×5 → $ 4 \times 5 = 20 $ → $ \frac{20}{25} $
- 5 to 30: ×6 → $ 4 \times 6 = 24 $ → $ \frac{24}{30} $

✔ Answer: $ \frac{4}{5} = \frac{20}{25} = \frac{24}{30} $

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8. $ \frac{1}{9} = \frac{\square}{18} = \frac{\square}{45} $

- 9 to 18: ×2 → $ 1 \times 2 = 2 $ → $ \frac{2}{18} $
- 9 to 45: ×5 → $ 1 \times 5 = 5 $ → $ \frac{5}{45} $

✔ Answer: $ \frac{1}{9} = \frac{2}{18} = \frac{5}{45} $

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9. $ \frac{2}{5} = \frac{\square}{15} = \frac{\square}{20} $

- 5 to 15: ×3 → $ 2 \times 3 = 6 $ → $ \frac{6}{15} $
- 5 to 20: ×4 → $ 2 \times 4 = 8 $ → $ \frac{8}{20} $

✔ Answer: $ \frac{2}{5} = \frac{6}{15} = \frac{8}{20} $

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10. $ \frac{1}{10} = \frac{\square}{20} = \frac{\square}{50} $

- 10 to 20: ×2 → $ 1 \times 2 = 2 $ → $ \frac{2}{20} $
- 10 to 50: ×5 → $ 1 \times 5 = 5 $ → $ \frac{5}{50} $

✔ Answer: $ \frac{1}{10} = \frac{2}{20} = \frac{5}{50} $

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✔ Final Answers:

1. $ \frac{1}{2} = \frac{3}{6} = \frac{4}{8} $
2. $ \frac{1}{4} = \frac{3}{12} = \frac{5}{20} $
3. $ \frac{1}{8} = \frac{2}{16} = \frac{4}{32} $
4. $ \frac{3}{4} = \frac{6}{8} = \frac{12}{16} $
5. $ \frac{5}{6} = \frac{10}{12} = \frac{20}{24} $
6. $ \frac{3}{5} = \frac{6}{10} = \frac{9}{15} $
7. $ \frac{4}{5} = \frac{20}{25} = \frac{24}{30} $
8. $ \frac{1}{9} = \frac{2}{18} = \frac{5}{45} $
9. $ \frac{2}{5} = \frac{6}{15} = \frac{8}{20} $
10. $ \frac{1}{10} = \frac{2}{20} = \frac{5}{50} $

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🔍 Explanation:

To find equivalent fractions:
- Multiply both numerator and denominator by the same number.
- This keeps the value of the fraction unchanged.

For example:
$ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} $

You can always check your answer by simplifying the new fraction back to see if it equals the original.

Let me know if you'd like a printable version or visual models!