Equivalent Fractions worksheet for students to practice finding equivalent fractions.

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 — they should reduce to the starting fraction.

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