Question

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Explanation:

Step1: Analyze Fred's Work

Fred is converting $\frac{8}{5}$ to a decimal. He sets up long division with 8.0 divided by 5.

• 5 goes into 8 once (1), 1×5 = 5, subtract 5 from 8 to get 3.
• Bring down the 0 to make 30. 5 goes into 30 six times (6), 6×5 = 30, subtract 30 from 30 to get 0.
• So the result is 1.6, which is correct because $\frac{8}{5}=1.6$.

Step2: Analyze Wilma's Work

Wilma sets up long division with 5.000 divided by 8, which is for converting $\frac{5}{8}$, not $\frac{8}{5}$. So her setup is incorrect for the fraction $\frac{8}{5}$.

Step3: Confirm Correctness

To check if 1.6 is correct, we can also multiply 1.6 by 5: $1.6\times5 = 8$, which matches the numerator of the fraction $\frac{8}{5}$. So Fred's work is correct.

Answer:

Fred's work is correct. We know it's correct because when converting $\frac{8}{5}$ to a decimal, we divide 8 (the numerator) by 5 (the denominator). Fred's long division of 8.0 by 5 gives 1.6, and verifying by multiplying 1.6 by 5 gives 8 (the original numerator), confirming it's correct. Wilma incorrectly divided 5 by 8, which is for $\frac{5}{8}$, not $\frac{8}{5}$.