Question

What is the best estimate of the sum of the fractions?

StartFraction 31 over 4 EndFraction + StartFraction 17 over 3 EndFraction + StartFraction 8 over 18 EndFraction
12 and one-half
13
14 and one-half
15

Answer 1

To estimate the sum of the fractions \( \frac{31}{4} + \frac{17}{3} + \frac{8}{18} \), we can first convert these fractions to decimal approximations to make the addition simpler.

1. **Calculate \( \frac{31}{4} \)**:
\[
\frac{31}{4} = 7.75
\]

2. **Calculate \( \frac{17}{3} \)**:
\[
\frac{17}{3} \approx 5.67 \quad (\text{since } 3 \text{ goes into } 17, 5 \text{ times with a remainder of } 2)
\]

3. **Calculate \( \frac{8}{18} \)**:
\[
\frac{8}{18} = \frac{4}{9} \approx 0.44
\]

Now, let's sum these approximate values:
\[
7.75 + 5.67 + 0.44 \approx 7.75 + 5.67 = 13.42
\]
Then adding \( 0.44 \):
\[
13.42 + 0.44 \approx 13.86
\]

This sum approaches about 14 when rounded to the nearest whole number.

Thus, the best estimate of the sum of the fractions is:
\[
\boxed{14\text{ and } \frac{1}{2}}
\]

Considering the options available (12 and one-half, 13, 14 and one-half, 15), the closest answer is \( 14 \text{ and one-half} \).

The correct answer is \( 14 \text{ and one-half} \).