Question

Estimate 5/8−1/10 . (1 point) Responses 0 1/2 1 1/2

Answer 1

To estimate \( \frac{5}{8} - \frac{1}{10} \), we can first convert both fractions to have a common denominator.

The least common multiple (LCM) of 8 and 10 is 40. We can convert both fractions:

\[
\frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40}
\]

\[
\frac{1}{10} = \frac{1 \times 4}{10 \times 4} = \frac{4}{40}
\]

Now we can perform the subtraction:

\[
\frac{25}{40} - \frac{4}{40} = \frac{25 - 4}{40} = \frac{21}{40}
\]

To estimate \( \frac{21}{40} \), we can divide 21 by 40:

\[
21 \div 40 \approx 0.525
\]

Now, looking at the response options:
- 0
- \( \frac{1}{2} \) (which is 0.5)
- 1
- \( \frac{3}{2} \) (which is 1.5)

Since \( 0.525 \) is closest to \( \frac{1}{2} \) (0.5), the best estimate for \( \frac{5}{8} - \frac{1}{10} \) is:

**Response: \( \frac{1}{2} \)**.