Question

Use the distributive property to find the product of the rational numbers.
-5(-2/3 - 5/3)
25/3
12/3
5/3
35/3

Answer 1

To use the distributive property to find the product of \(-5\) and the expression \(-\frac{2}{3} - \frac{5}{3}\), we first need to simplify the expression inside the parentheses.

1. Combine the fractions:
\[
-\frac{2}{3} - \frac{5}{3} = -\left(\frac{2}{3} + \frac{5}{3}\right) = -\frac{2 + 5}{3} = -\frac{7}{3}
\]

2. Now, substitute back into the expression:
\[
-5 \left(-\frac{7}{3}\right)
\]

3. Calculate the product:
\[
-5 \cdot -\frac{7}{3} = \frac{35}{3}
\]

Thus, the final answer is:

\[
\boxed{\frac{35}{3}}
\]