Convert Fractions to Decimals using Equivalent Fractions ... - Free Printable

To solve the problem of converting fractions to decimals using equivalent fractions, we will follow these steps:

1. Identify the denominator: Determine if the denominator can be converted to a power of 10 (e.g., 10, 100, 1000) by finding an equivalent fraction.
2. Find the equivalent fraction: Multiply both the numerator and the denominator by the same number to make the denominator a power of 10.
3. Convert to decimal: Once the denominator is a power of 10, the numerator will directly give the decimal value.

Let's solve each fraction step by step:

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1. $\frac{15}{20}$

- Simplify the fraction: $\frac{15}{20} = \frac{3}{4}$.
- Convert $\frac{3}{4}$ to a denominator of 100: $\frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100}$.
- Decimal: $0.75$.

2. $\frac{12}{25}$

- Convert $\frac{12}{25}$ to a denominator of 100: $\frac{12}{25} = \frac{12 \times 4}{25 \times 4} = \frac{48}{100}$.
- Decimal: $0.48$.

3. $\frac{12}{25}$

- Same as above: $\frac{12}{25} = \frac{48}{100} = 0.48$.

4. $\frac{1}{2}$

- Convert $\frac{1}{2}$ to a denominator of 10: $\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$.
- Decimal: $0.5$.

5. $\frac{13}{25}$

- Convert $\frac{13}{25}$ to a denominator of 100: $\frac{13}{25} = \frac{13 \times 4}{25 \times 4} = \frac{52}{100}$.
- Decimal: $0.52$.

6. $\frac{3}{5}$

- Convert $\frac{3}{5}$ to a denominator of 10: $\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$.
- Decimal: $0.6$.

7. $\frac{19}{50}$

- Convert $\frac{19}{50}$ to a denominator of 100: $\frac{19}{50} = \frac{19 \times 2}{50 \times 2} = \frac{38}{100}$.
- Decimal: $0.38$.

8. $\frac{17}{20}$

- Convert $\frac{17}{20}$ to a denominator of 100: $\frac{17}{20} = \frac{17 \times 5}{20 \times 5} = \frac{85}{100}$.
- Decimal: $0.85$.

9. $\frac{6}{20}$

- Simplify the fraction: $\frac{6}{20} = \frac{3}{10}$.
- Decimal: $0.3$.

10. $\frac{1}{4}$

- Convert $\frac{1}{4}$ to a denominator of 100: $\frac{1}{4} = \frac{1 \times 25}{4 \times 25} = \frac{25}{100}$.
- Decimal: $0.25$.

11. $\frac{24}{25}$

- Convert $\frac{24}{25}$ to a denominator of 100: $\frac{24}{25} = \frac{24 \times 4}{25 \times 4} = \frac{96}{100}$.
- Decimal: $0.96$.

12. $\frac{9}{25}$

- Convert $\frac{9}{25}$ to a denominator of 100: $\frac{9}{25} = \frac{9 \times 4}{25 \times 4} = \frac{36}{100}$.
- Decimal: $0.36$.

13. $\frac{2}{5}$

- Convert $\frac{2}{5}$ to a denominator of 10: $\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$.
- Decimal: $0.4$.

14. $\frac{7}{20}$

- Convert $\frac{7}{20}$ to a denominator of 100: $\frac{7}{20} = \frac{7 \times 5}{20 \times 5} = \frac{35}{100}$.
- Decimal: $0.35$.

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Final Answers:

\[
\begin{aligned}
&\frac{15}{20} = 0.75, \quad \frac{12}{25} = 0.48, \\
&\frac{12}{25} = 0.48, \quad \frac{1}{2} = 0.5, \\
&\frac{13}{25} = 0.52, \quad \frac{3}{5} = 0.6, \\
&\frac{19}{50} = 0.38, \quad \frac{17}{20} = 0.85, \\
&\frac{6}{20} = 0.3, \quad \frac{1}{4} = 0.25, \\
&\frac{24}{25} = 0.96, \quad \frac{9}{25} = 0.36, \\
&\frac{2}{5} = 0.4, \quad \frac{7}{20} = 0.35.
\end{aligned}
\]

\boxed{
\begin{aligned}
&0.75, \, 0.48, \, 0.48, \, 0.5, \, 0.52, \, 0.6, \, 0.38, \, 0.85, \, 0.3, \, 0.25, \, 0.96, \, 0.36, \, 0.4, \, 0.35
\end{aligned}
}