At Thanksgiving, Mrs. Jones overcooked the turkey so all but StartFraction 4 Over 5 EndFraction of it had to be thrown away. The 8 people at dinner that night each received an equal share of the remaining turkey. To determine the amount of the turkey that each person would receive, Mrs. Jones wrote the expression below.

Question

StartFraction 4 Over 5 EndFraction divided by 8

Which expression is equivalent to Mrs Jones’s expression?
StartFraction 8 Over 10 EndFraction divided by 8
StartFraction 8 Over 5 EndFraction divided by 4
StartFraction 5 Over 4 EndFraction times 8
StartFraction 4 Over 5 EndFraction times 8

Answer 1

To find an expression equivalent to Mrs. Jones's original expression \( \frac{4}{5} \div 8 \), we can rewrite the division by 8 as multiplication by the reciprocal of 8. The reciprocal of 8 is \( \frac{1}{8} \).

So, we can express:

\[ \frac{4}{5} \div 8 = \frac{4}{5} \times \frac{1}{8} \]

This can be simplified further:

\[ \frac{4}{5} \times \frac{1}{8} = \frac{4 \times 1}{5 \times 8} = \frac{4}{40} = \frac{1}{10} \]

Now let's evaluate each of the answer choices to see if any are equivalent to \( \frac{4}{5} \div 8 \):

1. Option A: \( \frac{8}{10} \div 8 = \frac{8}{10} \times \frac{1}{8} = \frac{8 \times 1}{10 \times 8} = \frac{8}{80} = \frac{1}{10} \)

2. Option B: \( \frac{8}{5} \div 4 = \frac{8}{5} \times \frac{1}{4} = \frac{8 \times 1}{5 \times 4} = \frac{8}{20} = \frac{2}{5} \)

3. Option C: \( \frac{5}{4} \times 8 = \frac{5 \times 8}{4} = \frac{40}{4} = 10 \)

4. Option D: \( \frac{4}{5} \times 8 = \frac{4 \times 8}{5} = \frac{32}{5} \)

The only option that simplifies to the same result as \( \frac{4}{5} \div 8 = \frac{1}{10} \) is Option A:

\[ \frac{8}{10} \div 8 \]

Thus, the equivalent expression is:

\( \frac{8}{10} \div 8 \).