Equivalent fractions practice worksheet for students, featuring 14 problems to find missing numerators or denominators, ideal for math education.

To solve the problem of finding equivalent fractions, we need to determine the missing numbers in each fraction so that both sides of the equation are equal. Equivalent fractions are fractions that represent the same value but have different numerators and denominators. This is achieved by multiplying or dividing both the numerator and the denominator by the same non-zero number.

Let's solve each problem step by step:

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1. \(\frac{4}{?} = \frac{28}{70}\)

- Simplify \(\frac{28}{70}\):
\[
\frac{28}{70} = \frac{28 \div 14}{70 \div 14} = \frac{2}{5}
\]
- Now, we need \(\frac{4}{?} = \frac{2}{5}\). To find the missing denominator:
\[
\frac{4}{?} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
\]
- Therefore, the missing number is \(10\).

Answer: \(\frac{4}{10}\)

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2. \(\frac{?}{2} = \frac{4}{8}\)

- Simplify \(\frac{4}{8}\):
\[
\frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
- Now, we need \(\frac{?}{2} = \frac{1}{2}\). The numerator must be \(1\).

Answer: \(\frac{1}{2}\)

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3. \(\frac{2}{3} = \frac{?}{27}\)

- To find the missing numerator, note that the denominator \(3\) is multiplied by \(9\) to get \(27\). Therefore, the numerator \(2\) must also be multiplied by \(9\):
\[
\frac{2}{3} = \frac{2 \times 9}{3 \times 9} = \frac{18}{27}
\]
- Therefore, the missing number is \(18\).

Answer: \(\frac{18}{27}\)

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4. \(\frac{4}{6} = \frac{16}{?}\)

- Simplify \(\frac{4}{6}\):
\[
\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}
\]
- Now, we need \(\frac{2}{3} = \frac{16}{?}\). To find the missing denominator, note that the numerator \(2\) is multiplied by \(8\) to get \(16\). Therefore, the denominator \(3\) must also be multiplied by \(8\):
\[
\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}
\]
- Therefore, the missing number is \(24\).

Answer: \(\frac{16}{24}\)

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5. \(\frac{1}{8} = \frac{?}{64}\)

- To find the missing numerator, note that the denominator \(8\) is multiplied by \(8\) to get \(64\). Therefore, the numerator \(1\) must also be multiplied by \(8\):
\[
\frac{1}{8} = \frac{1 \times 8}{8 \times 8} = \frac{8}{64}
\]
- Therefore, the missing number is \(8\).

Answer: \(\frac{8}{64}\)

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6. \(\frac{2}{4} = \frac{?}{16}\)

- Simplify \(\frac{2}{4}\):
\[
\frac{2}{4} = \frac{2 \div 2}{4 \div 2} = \frac{1}{2}
\]
- Now, we need \(\frac{1}{2} = \frac{?}{16}\). To find the missing numerator, note that the denominator \(2\) is multiplied by \(8\) to get \(16\). Therefore, the numerator \(1\) must also be multiplied by \(8\):
\[
\frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16}
\]
- Therefore, the missing number is \(8\).

Answer: \(\frac{8}{16}\)

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7. \(\frac{1}{?} = \frac{10}{50}\)

- Simplify \(\frac{10}{50}\):
\[
\frac{10}{50} = \frac{10 \div 10}{50 \div 10} = \frac{1}{5}
\]
- Now, we need \(\frac{1}{?} = \frac{1}{5}\). The denominator must be \(5\).

Answer: \(\frac{1}{5}\)

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8. \(\frac{?}{6} = \frac{4}{12}\)

- Simplify \(\frac{4}{12}\):
\[
\frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}
\]
- Now, we need \(\frac{?}{6} = \frac{1}{3}\). To find the missing numerator, note that the denominator \(3\) is multiplied by \(2\) to get \(6\). Therefore, the numerator \(1\) must also be multiplied by \(2\):
\[
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
\]
- Therefore, the missing number is \(2\).

Answer: \(\frac{2}{6}\)

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9. \(\frac{7}{12} = \frac{?}{24}\)

- To find the missing numerator, note that the denominator \(12\) is multiplied by \(2\) to get \(24\). Therefore, the numerator \(7\) must also be multiplied by \(2\):
\[
\frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24}
\]
- Therefore, the missing number is \(14\).

Answer: \(\frac{14}{24}\)

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10. \(\frac{3}{?} = \frac{6}{10}\)

- Simplify \(\frac{6}{10}\):
\[
\frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5}
\]
- Now, we need \(\frac{3}{?} = \frac{3}{5}\). The denominator must be \(5\).

Answer: \(\frac{3}{5}\)

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11. \(\frac{2}{10} = \frac{?}{40}\)

- To find the missing numerator, note that the denominator \(10\) is multiplied by \(4\) to get \(40\). Therefore, the numerator \(2\) must also be multiplied by \(4\):
\[
\frac{2}{10} = \frac{2 \times 4}{10 \times 4} = \frac{8}{40}
\]
- Therefore, the missing number is \(8\).

Answer: \(\frac{8}{40}\)

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12. \(\frac{?}{4} = \frac{18}{24}\)

- Simplify \(\frac{18}{24}\):
\[
\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}
\]
- Now, we need \(\frac{?}{4} = \frac{3}{4}\). The numerator must be \(3\).

Answer: \(\frac{3}{4}\)

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13. \(\frac{7}{8} = \frac{?}{72}\)

- To find the missing numerator, note that the denominator \(8\) is multiplied by \(9\) to get \(72\). Therefore, the numerator \(7\) must also be multiplied by \(9\):
\[
\frac{7}{8} = \frac{7 \times 9}{8 \times 9} = \frac{63}{72}
\]
- Therefore, the missing number is \(63\).

Answer: \(\frac{63}{72}\)

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14. \(\frac{1}{?} = \frac{9}{18}\)

- Simplify \(\frac{9}{18}\):
\[
\frac{9}{18} = \frac{9 \div 9}{18 \div 9} = \frac{1}{2}
\]
- Now, we need \(\frac{1}{?} = \frac{1}{2}\). The denominator must be \(2\).

Answer: \(\frac{1}{2}\)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \frac{4}{10} \\
2. & \frac{1}{2} \\
3. & \frac{18}{27} \\
4. & \frac{16}{24} \\
5. & \frac{8}{64} \\
6. & \frac{8}{16} \\
7. & \frac{1}{5} \\
8. & \frac{2}{6} \\
9. & \frac{14}{24} \\
10. & \frac{3}{5} \\
11. & \frac{8}{40} \\
12. & \frac{3}{4} \\
13. & \frac{63}{72} \\
14. & \frac{1}{2}
\end{array}
}
\]