Equivalent Fractions Worksheet with 10 Problems for Students to Solve

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}{3} = \frac{\square}{9} = \frac{\square}{12} $

- To get from 3 to 9: multiply by 3 → numerator: $1 \times 3 = 3$ → $ \frac{3}{9} $
- To get from 3 to 12: multiply by 4 → numerator: $1 \times 4 = 4$ → $ \frac{4}{12} $

✔ Answer: $ \frac{1}{3} = \frac{3}{9} = \frac{4}{12} $

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2. $ \frac{1}{2} = \frac{\square}{8} = \frac{\square}{10} $

- From 2 to 8: multiply by 4 → $1 \times 4 = 4$ → $ \frac{4}{8} $
- From 2 to 10: multiply by 5 → $1 \times 5 = 5$ → $ \frac{5}{10} $

✔ Answer: $ \frac{1}{2} = \frac{4}{8} = \frac{5}{10} $

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3. $ \frac{1}{5} = \frac{\square}{10} = \frac{\square}{15} $

- From 5 to 10: ×2 → $1 \times 2 = 2$ → $ \frac{2}{10} $
- From 5 to 15: ×3 → $1 \times 3 = 3$ → $ \frac{3}{15} $

✔ Answer: $ \frac{1}{5} = \frac{2}{10} = \frac{3}{15} $

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4. $ \frac{2}{3} = \frac{\square}{9} = \frac{\square}{18} $

- From 3 to 9: ×3 → $2 \times 3 = 6$ → $ \frac{6}{9} $
- From 3 to 18: ×6 → $2 \times 6 = 12$ → $ \frac{12}{18} $

✔ Answer: $ \frac{2}{3} = \frac{6}{9} = \frac{12}{18} $

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5. $ \frac{1}{6} = \frac{\square}{12} = \frac{\square}{36} $

- From 6 to 12: ×2 → $1 \times 2 = 2$ → $ \frac{2}{12} $
- From 6 to 36: ×6 → $1 \times 6 = 6$ → $ \frac{6}{36} $

✔ Answer: $ \frac{1}{6} = \frac{2}{12} = \frac{6}{36} $

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6. $ \frac{3}{4} = \frac{\square}{12} = \frac{\square}{20} $

- From 4 to 12: ×3 → $3 \times 3 = 9$ → $ \frac{9}{12} $
- From 4 to 20: ×5 → $3 \times 5 = 15$ → $ \frac{15}{20} $

✔ Answer: $ \frac{3}{4} = \frac{9}{12} = \frac{15}{20} $

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

- From 5 to 15: ×3 → $2 \times 3 = 6$ → $ \frac{6}{15} $
- From 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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8. $ \frac{1}{4} = \frac{\square}{8} = \frac{\square}{16} $

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

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

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9. $ \frac{4}{5} = \frac{\square}{10} = \frac{\square}{15} $

- From 5 to 10: ×2 → $4 \times 2 = 8$ → $ \frac{8}{10} $
- From 5 to 15: ×3 → $4 \times 3 = 12$ → $ \frac{12}{15} $

✔ Answer: $ \frac{4}{5} = \frac{8}{10} = \frac{12}{15} $

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10. $ \frac{1}{7} = \frac{\square}{14} = \frac{\square}{49} $

- From 7 to 14: ×2 → $1 \times 2 = 2$ → $ \frac{2}{14} $
- From 7 to 49: ×7 → $1 \times 7 = 7$ → $ \frac{7}{49} $

✔ Answer: $ \frac{1}{7} = \frac{2}{14} = \frac{7}{49} $

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✔ Final Answers:

1. $ \frac{1}{3} = \frac{3}{9} = \frac{4}{12} $
2. $ \frac{1}{2} = \frac{4}{8} = \frac{5}{10} $
3. $ \frac{1}{5} = \frac{2}{10} = \frac{3}{15} $
4. $ \frac{2}{3} = \frac{6}{9} = \frac{12}{18} $
5. $ \frac{1}{6} = \frac{2}{12} = \frac{6}{36} $
6. $ \frac{3}{4} = \frac{9}{12} = \frac{15}{20} $
7. $ \frac{2}{5} = \frac{6}{15} = \frac{8}{20} $
8. $ \frac{1}{4} = \frac{2}{8} = \frac{4}{16} $
9. $ \frac{4}{5} = \frac{8}{10} = \frac{12}{15} $
10. $ \frac{1}{7} = \frac{2}{14} = \frac{7}{49} $

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🔍 Explanation:

To find equivalent fractions, you multiply both the numerator and denominator by the same number (the scaling factor). For example:
- $ \frac{1}{3} \to \frac{1 \times 3}{3 \times 3} = \frac{3}{9} $
- Always check that the ratio stays the same.

This method ensures the fractions are equivalent.

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