Equivalent Fractions worksheet with 15 practice problems for finding missing values in equivalent fractions.

To solve the problem of finding equivalent fractions, we need to determine the missing numerators or denominators in each fraction so that the fractions remain equivalent. This involves understanding how to scale fractions by multiplying or dividing both the numerator and the denominator by the same number.

Step-by-Step Solution:

#### 1) $\frac{1}{4} = \frac{\_\_}{16}$
- The denominator changes from 4 to 16. To find the scaling factor:
$$
\frac{16}{4} = 4
$$
- Multiply the numerator by 4:
$$
1 \times 4 = 4
$$
- Therefore, $\frac{1}{4} = \frac{4}{16}$.

#### 2) $\frac{5}{10} = \frac{\_\_}{20}$
- The denominator changes from 10 to 20. To find the scaling factor:
$$
\frac{20}{10} = 2
$$
- Multiply the numerator by 2:
$$
5 \times 2 = 10
$$
- Therefore, $\frac{5}{10} = \frac{10}{20}$.

#### 3) $\frac{3}{4} = \frac{\_\_}{12}$
- The denominator changes from 4 to 12. To find the scaling factor:
$$
\frac{12}{4} = 3
$$
- Multiply the numerator by 3:
$$
3 \times 3 = 9
$$
- Therefore, $\frac{3}{4} = \frac{9}{12}$.

#### 4) $\frac{4}{7} = \frac{\_\_}{21}$
- The denominator changes from 7 to 21. To find the scaling factor:
$$
\frac{21}{7} = 3
$$
- Multiply the numerator by 3:
$$
4 \times 3 = 12
$$
- Therefore, $\frac{4}{7} = \frac{12}{21}$.

#### 5) $\frac{2}{8} = \frac{\_\_}{80}$
- The denominator changes from 8 to 80. To find the scaling factor:
$$
\frac{80}{8} = 10
$$
- Multiply the numerator by 10:
$$
2 \times 10 = 20
$$
- Therefore, $\frac{2}{8} = \frac{20}{80}$.

#### 6) $\frac{1}{2} = \frac{\_\_}{16}$
- The denominator changes from 2 to 16. To find the scaling factor:
$$
\frac{16}{2} = 8
$$
- Multiply the numerator by 8:
$$
1 \times 8 = 8
$$
- Therefore, $\frac{1}{2} = \frac{8}{16}$.

#### 7) $\frac{6}{12} = \frac{\_\_}{\_\_}$
- Simplify the fraction $\frac{6}{12}$ by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 6:
$$
\frac{6 \div 6}{12 \div 6} = \frac{1}{2}
$$
- Therefore, $\frac{6}{12} = \frac{1}{2}$.

#### 8) $\frac{5}{9} = \frac{\_\_}{36}$
- The denominator changes from 9 to 36. To find the scaling factor:
$$
\frac{36}{9} = 4
$$
- Multiply the numerator by 4:
$$
5 \times 4 = 20
$$
- Therefore, $\frac{5}{9} = \frac{20}{36}$.

#### 9) $\frac{1}{3} = \frac{\_\_}{15}$
- The denominator changes from 3 to 15. To find the scaling factor:
$$
\frac{15}{3} = 5
$$
- Multiply the numerator by 5:
$$
1 \times 5 = 5
$$
- Therefore, $\frac{1}{3} = \frac{5}{15}$.

#### 10) $\frac{5}{10} = \frac{\_\_}{50}$
- The denominator changes from 10 to 50. To find the scaling factor:
$$
\frac{50}{10} = 5
$$
- Multiply the numerator by 5:
$$
5 \times 5 = 25
$$
- Therefore, $\frac{5}{10} = \frac{25}{50}$.

#### 11) $\frac{5}{6} = \frac{\_\_}{42}$
- The denominator changes from 6 to 42. To find the scaling factor:
$$
\frac{42}{6} = 7
$$
- Multiply the numerator by 7:
$$
5 \times 7 = 35
$$
- Therefore, $\frac{5}{6} = \frac{35}{42}$.

#### 12) $\frac{1}{5} = \frac{\_\_}{25}$
- The denominator changes from 5 to 25. To find the scaling factor:
$$
\frac{25}{5} = 5
$$
- Multiply the numerator by 5:
$$
1 \times 5 = 5
$$
- Therefore, $\frac{1}{5} = \frac{5}{25}$.

#### 13) $\frac{2}{7} = \frac{\_\_}{35}$
- The denominator changes from 7 to 35. To find the scaling factor:
$$
\frac{35}{7} = 5
$$
- Multiply the numerator by 5:
$$
2 \times 5 = 10
$$
- Therefore, $\frac{2}{7} = \frac{10}{35}$.

#### 14) $\frac{3}{4} = \frac{\_\_}{28}$
- The denominator changes from 4 to 28. To find the scaling factor:
$$
\frac{28}{4} = 7
$$
- Multiply the numerator by 7:
$$
3 \times 7 = 21
$$
- Therefore, $\frac{3}{4} = \frac{21}{28}$.

#### 15) $\frac{3}{8} = \frac{\_\_}{48}$
- The denominator changes from 8 to 48. To find the scaling factor:
$$
\frac{48}{8} = 6
$$
- Multiply the numerator by 6:
$$
3 \times 6 = 18
$$
- Therefore, $\frac{3}{8} = \frac{18}{48}$.

Final Answer:

$$
\boxed{
\begin{array}{lll}
1) & \frac{1}{4} = \frac{4}{16} & \\
2) & \frac{5}{10} = \frac{10}{20} & \\
3) & \frac{3}{4} = \frac{9}{12} & \\
4) & \frac{4}{7} = \frac{12}{21} & \\
5) & \frac{2}{8} = \frac{20}{80} & \\
6) & \frac{1}{2} = \frac{8}{16} & \\
7) & \frac{6}{12} = \frac{1}{2} & \\
8) & \frac{5}{9} = \frac{20}{36} & \\
9) & \frac{1}{3} = \frac{5}{15} & \\
10) & \frac{5}{10} = \frac{25}{50} & \\
11) & \frac{5}{6} = \frac{35}{42} & \\
12) & \frac{1}{5} = \frac{5}{25} & \\
13) & \frac{2}{7} = \frac{10}{35} & \\
14) & \frac{3}{4} = \frac{21}{28} & \\
15) & \frac{3}{8} = \frac{18}{48} & \\
\end{array}
}
$$