Equivalent Fractions Worksheets - 15 Worksheets Library - Free Printable

Let's solve the Equivalent Fractions worksheet step by step. The goal is to find five equivalent fractions for each given fraction by multiplying both the numerator and denominator by the same number (i.e., scaling up the fraction).

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🔷 Rule:

To find an equivalent fraction:
Multiply both the numerator and denominator by the same non-zero number.

For example:
$$
\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}
$$

We'll do this for each problem.

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✔ Problem 1: $ \frac{1}{6} $

Multiply numerator and denominator by 2, 3, 4, 5, 6:

- $ \frac{1 \times 2}{6 \times 2} = \frac{2}{12} $
- $ \frac{1 \times 3}{6 \times 3} = \frac{3}{18} $
- $ \frac{1 \times 4}{6 \times 4} = \frac{4}{24} $
- $ \frac{1 \times 5}{6 \times 5} = \frac{5}{30} $
- $ \frac{1 \times 6}{6 \times 6} = \frac{6}{36} $

✔ Answer:
$$
\frac{1}{6} = \frac{2}{12} = \frac{3}{18} = \frac{4}{24} = \frac{5}{30} = \frac{6}{36}
$$

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✔ Problem 2: $ \frac{2}{5} $

Multiply by 2, 3, 4, 5, 6:

- $ \frac{2 \times 2}{5 \times 2} = \frac{4}{10} $
- $ \frac{2 \times 3}{5 \times 3} = \frac{6}{15} $
- $ \frac{2 \times 4}{5 \times 4} = \frac{8}{20} $
- $ \frac{2 \times 5}{5 \times 5} = \frac{10}{25} $
- $ \frac{2 \times 6}{5 \times 6} = \frac{12}{30} $

✔ Answer:
$$
\frac{2}{5} = \frac{4}{10} = \frac{6}{15} = \frac{8}{20} = \frac{10}{25} = \frac{12}{30}
$$

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✔ Problem 3: $ \frac{5}{6} $

Multiply by 2, 3, 4, 5, 6:

- $ \frac{5 \times 2}{6 \times 2} = \frac{10}{12} $
- $ \frac{5 \times 3}{6 \times 3} = \frac{15}{18} $
- $ \frac{5 \times 4}{6 \times 4} = \frac{20}{24} $
- $ \frac{5 \times 5}{6 \times 5} = \frac{25}{30} $
- $ \frac{5 \times 6}{6 \times 6} = \frac{30}{36} $

✔ Answer:
$$
\frac{5}{6} = \frac{10}{12} = \frac{15}{18} = \frac{20}{24} = \frac{25}{30} = \frac{30}{36}
$$

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✔ Problem 4: $ \frac{2}{9} $

Multiply by 2, 3, 4, 5, 6:

- $ \frac{2 \times 2}{9 \times 2} = \frac{4}{18} $
- $ \frac{2 \times 3}{9 \times 3} = \frac{6}{27} $
- $ \frac{2 \times 4}{9 \times 4} = \frac{8}{36} $
- $ \frac{2 \times 5}{9 \times 5} = \frac{10}{45} $
- $ \frac{2 \times 6}{9 \times 6} = \frac{12}{54} $

✔ Answer:
$$
\frac{2}{9} = \frac{4}{18} = \frac{6}{27} = \frac{8}{36} = \frac{10}{45} = \frac{12}{54}
$$

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✔ Problem 5: $ \frac{4}{7} $

Multiply by 2, 3, 4, 5, 6:

- $ \frac{4 \times 2}{7 \times 2} = \frac{8}{14} $
- $ \frac{4 \times 3}{7 \times 3} = \frac{12}{21} $
- $ \frac{4 \times 4}{7 \times 4} = \frac{16}{28} $
- $ \frac{4 \times 5}{7 \times 5} = \frac{20}{35} $
- $ \frac{4 \times 6}{7 \times 6} = \frac{24}{42} $

✔ Answer:
$$
\frac{4}{7} = \frac{8}{14} = \frac{12}{21} = \frac{16}{28} = \frac{20}{35} = \frac{24}{42}
$$

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✔ Problem 6: $ \frac{3}{8} $

Multiply by 2, 3, 4, 5, 6:

- $ \frac{3 \times 2}{8 \times 2} = \frac{6}{16} $
- $ \frac{3 \times 3}{8 \times 3} = \frac{9}{24} $
- $ \frac{3 \times 4}{8 \times 4} = \frac{12}{32} $
- $ \frac{3 \times 5}{8 \times 5} = \frac{15}{40} $
- $ \frac{3 \times 6}{8 \times 6} = \frac{18}{48} $

✔ Answer:
$$
\frac{3}{8} = \frac{6}{16} = \frac{9}{24} = \frac{12}{32} = \frac{15}{40} = \frac{18}{48}
$$

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✔ Problem 7: $ \frac{1}{7} $

Multiply by 2, 3, 4, 5, 6:

- $ \frac{1 \times 2}{7 \times 2} = \frac{2}{14} $
- $ \frac{1 \times 3}{7 \times 3} = \frac{3}{21} $
- $ \frac{1 \times 4}{7 \times 4} = \frac{4}{28} $
- $ \frac{1 \times 5}{7 \times 5} = \frac{5}{35} $
- $ \frac{1 \times 6}{7 \times 6} = \frac{6}{42} $

✔ Answer:
$$
\frac{1}{7} = \frac{2}{14} = \frac{3}{21} = \frac{4}{28} = \frac{5}{35} = \frac{6}{42}
$$

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✔ Problem 8: $ \frac{7}{12} $

Multiply by 2, 3, 4, 5, 6:

- $ \frac{7 \times 2}{12 \times 2} = \frac{14}{24} $
- $ \frac{7 \times 3}{12 \times 3} = \frac{21}{36} $
- $ \frac{7 \times 4}{12 \times 4} = \frac{28}{48} $
- $ \frac{7 \times 5}{12 \times 5} = \frac{35}{60} $
- $ \frac{7 \times 6}{12 \times 6} = \frac{42}{72} $

✔ Answer:
$$
\frac{7}{12} = \frac{14}{24} = \frac{21}{36} = \frac{28}{48} = \frac{35}{60} = \frac{42}{72}
$$

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✔ Final Answers:

1) $ \frac{1}{6} = \frac{2}{12} = \frac{3}{18} = \frac{4}{24} = \frac{5}{30} = \frac{6}{36} $
2) $ \frac{2}{5} = \frac{4}{10} = \frac{6}{15} = \frac{8}{20} = \frac{10}{25} = \frac{12}{30} $
3) $ \frac{5}{6} = \frac{10}{12} = \frac{15}{18} = \frac{20}{24} = \frac{25}{30} = \frac{30}{36} $
4) $ \frac{2}{9} = \frac{4}{18} = \frac{6}{27} = \frac{8}{36} = \frac{10}{45} = \frac{12}{54} $
5) $ \frac{4}{7} = \frac{8}{14} = \frac{12}{21} = \frac{16}{28} = \frac{20}{35} = \frac{24}{42} $
6) $ \frac{3}{8} = \frac{6}{16} = \frac{9}{24} = \frac{12}{32} = \frac{15}{40} = \frac{18}{48} $
7) $ \frac{1}{7} = \frac{2}{14} = \frac{3}{21} = \frac{4}{28} = \frac{5}{35} = \frac{6}{42} $
8) $ \frac{7}{12} = \frac{14}{24} = \frac{21}{36} = \frac{28}{48} = \frac{35}{60} = \frac{42}{72} $

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📝 Summary:

Each fraction has been multiplied by integers from 2 to 6 to generate five equivalent fractions. You can verify any of them by simplifying back to the original fraction — they should all reduce to the starting value.

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