Question

6. Which expression is equivalent to 53p + (16p + 7p)?
*
2 points
(16p + 7p) ∙ 53p
(53p + 16p) + 7p
(16p ∙ 7p) + 53p
(53p ∙ 16p) ∙ 7p

Answer 1

To simplify the expression \( 53p + (16p + 7p) \), we first combine the terms within the parentheses:

\[
16p + 7p = 23p
\]

Now we can substitute this back into the original expression:

\[
53p + 23p
\]

Next, we combine the like terms:

\[
53p + 23p = (53 + 23)p = 76p
\]

Now we can evaluate the provided options to see which one is equivalent to \( 76p \):

1. \( (16p + 7p) \cdot 53p \) simplifies to:
\[
23p \cdot 53p = 1219p^2 \quad \text{(not equivalent)}
\]

2. \( (53p + 16p) + 7p \) simplifies to:
\[
(69p) + 7p = 76p \quad \text{(equivalent)}
\]

3. \( (16p \cdot 7p) + 53p \) simplifies to:
\[
112p^2 + 53p \quad \text{(not equivalent)}
\]

4. \( (53p \cdot 16p) \cdot 7p \) simplifies to:
\[
(848p^2) \cdot 7p = 5936p^3 \quad \text{(not equivalent)}
\]

The only expression that is equivalent to \( 53p + (16p + 7p) \) is:

\((53p + 16p) + 7p\)

Thus, the correct answer is:

\((53p + 16p) + 7p\)