Equivalent Fractions Worksheets - 15 Worksheets Library - Free Printable

To solve the problem of finding equivalent fractions, we need to multiply both the numerator and the denominator of each given fraction by different integers. This will generate fractions that are equivalent to the original ones. Let's go through each problem step by step.

Problem 1: $\frac{1}{6}$

We can find equivalent fractions by multiplying both the numerator and the denominator by the same number (e.g., 2, 3, 4, etc.).

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

So, the equivalent fractions are:
$$
\frac{1}{6} = \frac{2}{12} = \frac{3}{18} = \frac{4}{24} = \frac{5}{30} = \frac{6}{36}
$$

Problem 2: $\frac{2}{5}$

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

So, the equivalent fractions are:
$$
\frac{2}{5} = \frac{4}{10} = \frac{6}{15} = \frac{8}{20} = \frac{10}{25} = \frac{12}{30}
$$

Problem 3: $\frac{5}{6}$

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

So, the equivalent fractions are:
$$
\frac{5}{6} = \frac{10}{12} = \frac{15}{18} = \frac{20}{24} = \frac{25}{30} = \frac{30}{36}
$$

Problem 4: $\frac{2}{9}$

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

So, the equivalent fractions are:
$$
\frac{2}{9} = \frac{4}{18} = \frac{6}{27} = \frac{8}{36} = \frac{10}{45} = \frac{12}{54}
$$

Problem 5: $\frac{4}{7}$

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

So, the equivalent fractions are:
$$
\frac{4}{7} = \frac{8}{14} = \frac{12}{21} = \frac{16}{28} = \frac{20}{35} = \frac{24}{42}
$$

Problem 6: $\frac{3}{8}$

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

So, the equivalent fractions are:
$$
\frac{3}{8} = \frac{6}{16} = \frac{9}{24} = \frac{12}{32} = \frac{15}{40} = \frac{18}{48}
$$

Problem 7: $\frac{1}{7}$

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

So, the equivalent fractions are:
$$
\frac{1}{7} = \frac{2}{14} = \frac{3}{21} = \frac{4}{28} = \frac{5}{35} = \frac{6}{42}
$$

Problem 8: $\frac{7}{12}$

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

So, the equivalent fractions are:
$$
\frac{7}{12} = \frac{14}{24} = \frac{21}{36} = \frac{28}{48} = \frac{35}{60} = \frac{42}{72}
$$

Final Answer

The completed worksheet looks like this:

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

The final answer is:
$$
\boxed{
\begin{array}{l}
1) \frac{1}{6} = \frac{2}{12} = \frac{3}{18} = \frac{4}{24} = \frac{5}{30} = \frac{6}{36} \\
2) \frac{2}{5} = \frac{4}{10} = \frac{6}{15} = \frac{8}{20} = \frac{10}{25} = \frac{12}{30} \\
3) \frac{5}{6} = \frac{10}{12} = \frac{15}{18} = \frac{20}{24} = \frac{25}{30} = \frac{30}{36} \\
4) \frac{2}{9} = \frac{4}{18} = \frac{6}{27} = \frac{8}{36} = \frac{10}{45} = \frac{12}{54} \\
5) \frac{4}{7} = \frac{8}{14} = \frac{12}{21} = \frac{16}{28} = \frac{20}{35} = \frac{24}{42} \\
6) \frac{3}{8} = \frac{6}{16} = \frac{9}{24} = \frac{12}{32} = \frac{15}{40} = \frac{18}{48} \\
7) \frac{1}{7} = \frac{2}{14} = \frac{3}{21} = \frac{4}{28} = \frac{5}{35} = \frac{6}{42} \\
8) \frac{7}{12} = \frac{14}{24} = \frac{21}{36} = \frac{28}{48} = \frac{35}{60} = \frac{42}{72}
\end{array}
}
$$