Question

Estimate 1012 -3/8 using benchmark values equation show the estimate for each fraction and the final estimate for expression

Answer 1

To estimate \( 1012 - \frac{3}{8} \) using benchmark values, we can round the fraction to the nearest benchmark fraction for easier calculation.

### Step 1: Estimating the Fraction

The fraction \( \frac{3}{8} \) can be estimated by determining where it stands relative to benchmark fractions:

- \( \frac{0}{8} = 0 \)
- \( \frac{2}{8} = \frac{1}{4} = 0.25 \)
- \( \frac{4}{8} = \frac{1}{2} = 0.5 \)
- \( \frac{6}{8} = \frac{3}{4} = 0.75 \)
- \( \frac{8}{8} = 1 \)

Since \( \frac{3}{8} \) is closer to \( \frac{4}{8} \) (which is 0.5) than it is to \( \frac{2}{8} \) (which is 0.25), we can round \( \frac{3}{8} \) to \( \frac{1}{2} \).

### Step 2: Performing the Estimation

Now substituting the estimated fraction back into the expression:

\[
1012 - \frac{3}{8} \approx 1012 - \frac{1}{2}
\]

Now, since \( \frac{1}{2} \) is equal to 0.5, we can rewrite it as:

\[
1012 - 0.5 \approx 1012 - 1 \quad (\text{more straightforward for estimation})
\]

This means we can round it down to:

\[
1012 - 1 = 1011
\]

### Final Estimate

Thus, the final estimate for \( 1012 - \frac{3}{8} \) is:

\[
\boxed{1011}
\]