Question

which expression uses the commutative property of addition and the associative property of multiplication to rewrite the expression $5 + 3 cdot (3 cdot 8)$?

• $3 cdot (3 cdot 8) + 5$
• $(3 cdot 3) cdot 8 + 5$
• $3 cdot (8 cdot 3) + 5$
• $5 + 3 cdot (24)$

Explanation:

Step1: Recall commutative addition property

The commutative property of addition states $a + b = b + a$. For $5 + 3 \cdot (3 \cdot 8)$, we can rewrite it as $3 \cdot (3 \cdot 8) + 5$.

Step2: Recall associative multiplication property

The associative property of multiplication states $a \cdot (b \cdot c) = (a \cdot b) \cdot c$. Applying this to $3 \cdot (3 \cdot 8)$, we get $(3 \cdot 3) \cdot 8$.

Step3: Combine both transformations

Substitute the transformed multiplication part into the rearranged addition expression: $(3 \cdot 3) \cdot 8 + 5$.

Answer:

$(3 \cdot 3) \cdot 8 + 5$