To correct your friend's calculation, let's first find the correct quotient of the fractions given.
(a) To calculate \( \frac{3}{8} \div \frac{1}{8} \), you multiply by the reciprocal of the second fraction:
\[ \frac{3}{8} \div \frac{1}{8} = \frac{3}{8} \times \frac{8}{1} \]
Now, multiply:
\[ \frac{3 \times 8}{8 \times 1} = \frac{24}{8} = 3 \]
So the correct quotient is \( 3 \).
(b) Now, let's analyze what mistake your friend likely made. The options provided are:
A. Your friend multiplied \( \frac{8}{3} \times 8 \)
B. Your friend multiplied with the reciprocal of the first fraction, not the second fraction.
C. Your friend multiplied \( \frac{3}{8} \times \frac{1}{8} \)
D. Your friend added the fractions instead of dividing.
From your friend's claim that \( \frac{3}{8} \div \frac{1}{8} = \frac{1}{3} \) and that it equals \( 1 \frac{3}{8} \), it seems that they did not apply the correct operation. Since they ended up with an incorrect quotient of \( 1 \frac{3}{8} \), it indicates they may have tried to add or misunderstood how to divide fractions.
The best fit among the options is: D. Your friend added the fractions instead of dividing.
This error would lead to a different outcome, as addition of the two fractions would not yield the correct division result.