Question

Expand
5/8(-8-3f)
A. 15/8f-5
B. 15/8f+5
C. -15/8f-5
D.-15/8+5

Answer 1

To expand the expression \( \frac{5}{8}(-8 - 3f) \), we will distribute \( \frac{5}{8} \) to both terms inside the parentheses.

1. Distributing \( \frac{5}{8} \) to \(-8\):
\[
\frac{5}{8} \times -8 = -\frac{40}{8} = -5
\]

2. Distributing \( \frac{5}{8} \) to \(-3f\):
\[
\frac{5}{8} \times -3f = -\frac{15}{8}f
\]

Now combine the two results:

\[
\frac{5}{8}(-8 - 3f) = -5 - \frac{15}{8}f
\]

This can be rearranged as:

\[
-\frac{15}{8}f - 5
\]

Now, looking at the options provided:
A. \( \frac{15}{8}f - 5 \)
B. \( \frac{15}{8}f + 5 \)
C. \( -\frac{15}{8}f - 5 \)
D. \( -\frac{15}{8} + 5 \)

The correct answer is:

**C. \( -\frac{15}{8}f - 5 \)**