To evaluate the expression \( 7 \div \frac{5}{8} \) using the rule "multiply by the reciprocal," you need to multiply \( 7 \) by the reciprocal of \( \frac{5}{8} \), which is \( \frac{8}{5} \).
So, the steps are as follows:
- Write \( 7 \) as a fraction: \( \frac{7}{1} \).
- Multiply by the reciprocal of \( \frac{5}{8} \):
\[ \frac{7}{1} \times \frac{8}{5} \]
- Multiply the numerators and the denominators:
\[ \frac{7 \times 8}{1 \times 5} = \frac{56}{5} \]
Now, let's compare this with the options you provided:
- \( \frac{1}{7} \times \frac{5}{8} = \frac{5}{56} \) (incorrect approach)
- \( \frac{7}{1} \times \frac{5}{8} = \frac{35}{8} \) (incorrect because it does not use the reciprocal)
- \( \frac{1}{7} \times \frac{8}{5} = \frac{8}{35} \) (incorrect approach)
- \( \frac{7}{1} \times \frac{8}{5} = \frac{56}{5} \) (correct approach)
Therefore, the correct way to use the rule “multiply by the reciprocal” is:
StartFraction 7 Over 1 EndFraction times StartFraction 8 Over 5 EndFraction = StartFraction 56 Over 5 EndFraction.
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