Question

Which shows the correct way to use the rule “multiply by the reciprocal” for the expression below?

7 divided by StartFraction 5 Over 8 EndFraction
StartFraction 1 Over 7 EndFraction times StartFraction 5 Over 8 EndFraction = StartFraction 5 Over 56 EndFraction
StartFraction 7 Over 1 EndFraction times StartFraction 5 Over 8 EndFraction = StartFraction 35 Over 8 EndFraction
StartFraction 1 Over 7 EndFraction times StartFraction 8 Over 5 EndFraction = StartFraction 8 Over 35 EndFraction
StartFraction 7 Over 1 EndFraction times StartFraction 8 Over 5 EndFraction = StartFraction 56 Over 5 EndFraction

Answer 1

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:

1. Write \( 7 \) as a fraction: \( \frac{7}{1} \).
2. Multiply by the reciprocal of \( \frac{5}{8} \):

\[
\frac{7}{1} \times \frac{8}{5}
\]

3. 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:

1. \( \frac{1}{7} \times \frac{5}{8} = \frac{5}{56} \) (incorrect approach)
2. \( \frac{7}{1} \times \frac{5}{8} = \frac{35}{8} \) (incorrect because it does not use the reciprocal)
3. \( \frac{1}{7} \times \frac{8}{5} = \frac{8}{35} \) (incorrect approach)
4. \( \frac{7}{1} \times \frac{8}{5} = \frac{56}{5} \) (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**.