Question
Simplify the expression. Write your answers using integers or improper fractions.
start fraction, 4, divided by, 5, end fraction, left parenthesis, 10, p, minus, 30, right parenthesis, minus, 8, p
5
4
(10p−30)−8p
start fraction, 4, divided by, 5, end fraction, left parenthesis, 10, p, minus, 30, right parenthesis, minus, 8, p
5
4
(10p−30)−8p
Answers
Answered by
GPT-4o mini
To simplify the expression \(\frac{4}{5}(10p - 30) - 8p\), follow these steps:
1. Distribute \(\frac{4}{5}\) into the parentheses:
\[
\frac{4}{5} \cdot 10p - \frac{4}{5} \cdot 30
\]
Calculating each term:
\[
\frac{4}{5} \cdot 10p = \frac{40}{5}p = 8p
\]
\[
\frac{4}{5} \cdot 30 = \frac{120}{5} = 24
\]
So, we have:
\[
8p - 24
\]
2. Now, substitute back into the expression:
\[
8p - 24 - 8p
\]
3. Combine like terms:
\[
8p - 8p - 24 = 0 - 24 = -24
\]
Thus, the simplified expression is:
\[
\boxed{-24}
\]
1. Distribute \(\frac{4}{5}\) into the parentheses:
\[
\frac{4}{5} \cdot 10p - \frac{4}{5} \cdot 30
\]
Calculating each term:
\[
\frac{4}{5} \cdot 10p = \frac{40}{5}p = 8p
\]
\[
\frac{4}{5} \cdot 30 = \frac{120}{5} = 24
\]
So, we have:
\[
8p - 24
\]
2. Now, substitute back into the expression:
\[
8p - 24 - 8p
\]
3. Combine like terms:
\[
8p - 8p - 24 = 0 - 24 = -24
\]
Thus, the simplified expression is:
\[
\boxed{-24}
\]