To use the rule "multiply by the reciprocal" for the expression \( 7 \div \frac{5}{8} \), you first need to convert the division into a multiplication by the reciprocal of the fraction you are dividing by.
So, we start with: \[ 7 \div \frac{5}{8} \]
This can be rewritten as: \[ 7 \times \frac{8}{5} \]
Now, we can express 7 as a fraction: \[ \frac{7}{1} \times \frac{8}{5} = \frac{7 \times 8}{1 \times 5} = \frac{56}{5} \]
Now we can evaluate the given options:
- \( \frac{1}{7} \times \frac{5}{8} = \frac{5}{56} \) (incorrect)
- \( \frac{7}{1} \times \frac{5}{8} = \frac{35}{8} \) (incorrect)
- \( \frac{1}{7} \times \frac{8}{5} = \frac{8}{35} \) (incorrect)
- \( \frac{7}{1} \times \frac{8}{5} = \frac{56}{5} \) (correct)
Therefore, the correct way to apply the rule "multiply by the reciprocal" for the expression \( 7 \div \frac{5}{8} \) is:
\( \frac{7}{1} \times \frac{8}{5} = \frac{56}{5} \)