Fractions and Equivalent Recurring-Terminating Decimals worksheet ... - Free Printable

To solve the problem, we need to convert each fraction into its decimal form and determine whether the resulting decimal is terminating or recurring. Let's go through each fraction step by step.

1. \( \frac{1}{2} \)

- Decimal: Perform the division \( 1 \div 2 \).
\[
1 \div 2 = 0.5
\]
- Recurring/Terminating: The decimal \( 0.5 \) terminates.
- Result:
- Decimal: \( 0.5 \)
- Recurring/Terminating: Terminating

2. \( \frac{3}{5} \)

- Decimal: Perform the division \( 3 \div 5 \).
\[
3 \div 5 = 0.6
\]
- Recurring/Terminating: The decimal \( 0.6 \) terminates.
- Result:
- Decimal: \( 0.6 \)
- Recurring/Terminating: Terminating

3. \( \frac{4}{6} \)

- Simplify the fraction: \( \frac{4}{6} = \frac{2}{3} \) (divide numerator and denominator by 2).
- Decimal: Perform the division \( 2 \div 3 \).
\[
2 \div 3 = 0.666\ldots = 0.\overline{6}
\]
- Recurring/Terminating: The decimal \( 0.\overline{6} \) is recurring.
- Result:
- Decimal: \( 0.\overline{6} \)
- Recurring/Terminating: Recurring

4. \( \frac{1}{13} \)

- Decimal: Perform the division \( 1 \div 13 \).
\[
1 \div 13 = 0.076923076923\ldots = 0.\overline{076923}
\]
- Recurring/Terminating: The decimal \( 0.\overline{076923} \) is recurring.
- Result:
- Decimal: \( 0.\overline{076923} \)
- Recurring/Terminating: Recurring

5. \( \frac{8}{16} \)

- Simplify the fraction: \( \frac{8}{16} = \frac{1}{2} \) (divide numerator and denominator by 8).
- Decimal: Perform the division \( 1 \div 2 \).
\[
1 \div 2 = 0.5
\]
- Recurring/Terminating: The decimal \( 0.5 \) terminates.
- Result:
- Decimal: \( 0.5 \)
- Recurring/Terminating: Terminating

6. \( \frac{7}{9} \)

- Decimal: Perform the division \( 7 \div 9 \).
\[
7 \div 9 = 0.777\ldots = 0.\overline{7}
\]
- Recurring/Terminating: The decimal \( 0.\overline{7} \) is recurring.
- Result:
- Decimal: \( 0.\overline{7} \)
- Recurring/Terminating: Recurring

7. \( \frac{24}{25} \)

- Decimal: Perform the division \( 24 \div 25 \).
\[
24 \div 25 = 0.96
\]
- Recurring/Terminating: The decimal \( 0.96 \) terminates.
- Result:
- Decimal: \( 0.96 \)
- Recurring/Terminating: Terminating

Final Answer

Putting all the results together, the completed table is:

| Fractions | Decimals | Recurring/Terminating |
|-----------|----------|-----------------------|
| \( \frac{1}{2} \) | \( 0.5 \) | Terminating |
| \( \frac{3}{5} \) | \( 0.6 \) | Terminating |
| \( \frac{4}{6} \) | \( 0.\overline{6} \) | Recurring |
| \( \frac{1}{13} \) | \( 0.\overline{076923} \) | Recurring |
| \( \frac{8}{16} \) | \( 0.5 \) | Terminating |
| \( \frac{7}{9} \) | \( 0.\overline{7} \) | Recurring |
| \( \frac{24}{25} \) | \( 0.96 \) | Terminating |

Thus, the final answer is:
\[
\boxed{
\begin{array}{|c|c|c|}
\hline
\text{Fractions} & \text{Decimals} & \text{Recurring/Terminating} \\
\hline
\frac{1}{2} & 0.5 & \text{Terminating} \\
\frac{3}{5} & 0.6 & \text{Terminating} \\
\frac{4}{6} & 0.\overline{6} & \text{Recurring} \\
\frac{1}{13} & 0.\overline{076923} & \text{Recurring} \\
\frac{8}{16} & 0.5 & \text{Terminating} \\
\frac{7}{9} & 0.\overline{7} & \text{Recurring} \\
\frac{24}{25} & 0.96 & \text{Terminating} \\
\hline
\end{array}
}
\]