Equivalent Fractions Worksheets - 15 Worksheets Library - Free Printable

Let's solve each of the equivalent fractions step by step. The goal is to find missing numerators or denominators so that the fractions are equivalent (equal in value).

We'll use the concept:
If two fractions are equivalent, then their cross-products are equal, or we can multiply both numerator and denominator by the same number to get an equivalent fraction.

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1) $\frac{2}{5} = \frac{\square}{10} = \frac{\square}{15}$

- To go from 5 to 10: multiply by 2 → $2 \times 2 = 4$ → $\frac{4}{10}$
- To go from 5 to 15: multiply by 3 → $2 \times 3 = 6$ → $\frac{6}{15}$

✔ Answer: $\frac{2}{5} = \frac{4}{10} = \frac{6}{15}$

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2) $\frac{3}{5} = \frac{\square}{15} = \frac{\square}{25}$

- From 5 to 15: ×3 → $3 \times 3 = 9$ → $\frac{9}{15}$
- From 5 to 25: ×5 → $3 \times 5 = 15$ → $\frac{15}{25}$

✔ Answer: $\frac{3}{5} = \frac{9}{15} = \frac{15}{25}$

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3) $\frac{5}{9} = \frac{\square}{18} = \frac{\square}{45}$

- From 9 to 18: ×2 → $5 \times 2 = 10$ → $\frac{10}{18}$
- From 9 to 45: ×5 → $5 \times 5 = 25$ → $\frac{25}{45}$

✔ Answer: $\frac{5}{9} = \frac{10}{18} = \frac{25}{45}$

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4) $\frac{1}{6} = \frac{\square}{24} = \frac{\square}{30}$

- From 6 to 24: ×4 → $1 \times 4 = 4$ → $\frac{4}{24}$
- From 6 to 30: ×5 → $1 \times 5 = 5$ → $\frac{5}{30}$

✔ Answer: $\frac{1}{6} = \frac{4}{24} = \frac{5}{30}$

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5) $\frac{4}{9} = \frac{\square}{18} = \frac{\square}{27}$

- From 9 to 18: ×2 → $4 \times 2 = 8$ → $\frac{8}{18}$
- From 9 to 27: ×3 → $4 \times 3 = 12$ → $\frac{12}{27}$

✔ Answer: $\frac{4}{9} = \frac{8}{18} = \frac{12}{27}$

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6) $\frac{1}{4} = \frac{\square}{24} = \frac{\square}{40}$

- From 4 to 24: ×6 → $1 \times 6 = 6$ → $\frac{6}{24}$
- From 4 to 40: ×10 → $1 \times 10 = 10$ → $\frac{10}{40}$

✔ Answer: $\frac{1}{4} = \frac{6}{24} = \frac{10}{40}$

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7) $\frac{2}{3} = \frac{\square}{6} = \frac{\square}{15}$

- From 3 to 6: ×2 → $2 \times 2 = 4$ → $\frac{4}{6}$
- From 3 to 15: ×5 → $2 \times 5 = 10$ → $\frac{10}{15}$

✔ Answer: $\frac{2}{3} = \frac{4}{6} = \frac{10}{15}$

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8) $\frac{2}{7} = \frac{\square}{21} = \frac{\square}{35}$

- From 7 to 21: ×3 → $2 \times 3 = 6$ → $\frac{6}{21}$
- From 7 to 35: ×5 → $2 \times 5 = 10$ → $\frac{10}{35}$

✔ Answer: $\frac{2}{7} = \frac{6}{21} = \frac{10}{35}$

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9) $\frac{5}{12} = \frac{\square}{36} = \frac{\square}{60}$

- From 12 to 36: ×3 → $5 \times 3 = 15$ → $\frac{15}{36}$
- From 12 to 60: ×5 → $5 \times 5 = 25$ → $\frac{25}{60}$

✔ Answer: $\frac{5}{12} = \frac{15}{36} = \frac{25}{60}$

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10) $\frac{6}{11} = \frac{\square}{22} = \frac{\square}{33}$

- From 11 to 22: ×2 → $6 \times 2 = 12$ → $\frac{12}{22}$
- From 11 to 33: ×3 → $6 \times 3 = 18$ → $\frac{18}{33}$

✔ Answer: $\frac{6}{11} = \frac{12}{22} = \frac{18}{33}$

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11) $\frac{4}{15} = \frac{\square}{60} = \frac{\square}{90}$

- From 15 to 60: ×4 → $4 \times 4 = 16$ → $\frac{16}{60}$
- From 15 to 90: ×6 → $4 \times 6 = 24$ → $\frac{24}{90}$

✔ Answer: $\frac{4}{15} = \frac{16}{60} = \frac{24}{90}$

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12) $\frac{3}{10} = \frac{\square}{20} = \frac{\square}{30}$

- From 10 to 20: ×2 → $3 \times 2 = 6$ → $\frac{6}{20}$
- From 10 to 30: ×3 → $3 \times 3 = 9$ → $\frac{9}{30}$

✔ Answer: $\frac{3}{10} = \frac{6}{20} = \frac{9}{30}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | $\frac{2}{5} = \frac{4}{10} = \frac{6}{15}$ |
| 2) | $\frac{3}{5} = \frac{9}{15} = \frac{15}{25}$ |
| 3) | $\frac{5}{9} = \frac{10}{18} = \frac{25}{45}$ |
| 4) | $\frac{1}{6} = \frac{4}{24} = \frac{5}{30}$ |
| 5) | $\frac{4}{9} = \frac{8}{18} = \frac{12}{27}$ |
| 6) | $\frac{1}{4} = \frac{6}{24} = \frac{10}{40}$ |
| 7) | $\frac{2}{3} = \frac{4}{6} = \frac{10}{15}$ |
| 8) | $\frac{2}{7} = \frac{6}{21} = \frac{10}{35}$ |
| 9) | $\frac{5}{12} = \frac{15}{36} = \frac{25}{60}$ |
|10) | $\frac{6}{11} = \frac{12}{22} = \frac{18}{33}$ |
|11) | $\frac{4}{15} = \frac{16}{60} = \frac{24}{90}$ |
|12) | $\frac{3}{10} = \frac{6}{20} = \frac{9}{30}$ |

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🔍 Explanation Summary:

To find equivalent fractions, you multiply both the numerator and denominator by the same number. For example:
- $\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$
- $\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}$

This ensures the value of the fraction stays the same.

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