Question

Caitlyn evaluates the expression 5 7/9 - 5/8 and gets an answer of 5 11/72.

Answer 1

To verify Caitlyn's evaluation of the expression \( 5 \frac{7}{9} - \frac{5}{8} \), let's first convert the mixed number \( 5 \frac{7}{9} \) into an improper fraction.

1. **Convert \( 5 \frac{7}{9} \)**:
\[
5 \frac{7}{9} = \frac{5 \times 9 + 7}{9} = \frac{45 + 7}{9} = \frac{52}{9}
\]

2. **Now subtract \( \frac{5}{8} \)**:
We need a common denominator for \( \frac{52}{9} \) and \( \frac{5}{8} \). The least common multiple (LCM) of 9 and 8 is 72.

3. **Convert \( \frac{52}{9} \) and \( \frac{5}{8} \) to have a denominator of 72**:
- For \( \frac{52}{9} \):
\[
\frac{52}{9} = \frac{52 \times 8}{9 \times 8} = \frac{416}{72}
\]

- For \( \frac{5}{8} \):
\[
\frac{5}{8} = \frac{5 \times 9}{8 \times 9} = \frac{45}{72}
\]

4. **Now we can perform the subtraction**:
\[
\frac{416}{72} - \frac{45}{72} = \frac{416 - 45}{72} = \frac{371}{72}
\]

5. **Convert \( \frac{371}{72} \) back to a mixed number**:
- Divide 371 by 72:
\[
371 \div 72 = 5 \quad \text{(since } 72 \times 5 = 360\text{)}
\]
- The remainder is:
\[
371 - 360 = 11
\]
- Therefore,
\[
\frac{371}{72} = 5 \frac{11}{72}
\]

The final result of the calculation \( 5 \frac{7}{9} - \frac{5}{8} \) is indeed \( 5 \frac{11}{72} \). Caitlyn's answer is correct!