Question

Which expression uses the commutative property of addition and the associative property of multiplication to rewrite theexpression (3•2) . 5 + 7?

Answer 1

The commutative property of addition states that the order of the values being added doesn't affect the final result:

$a+b=b+a$

The associative property of multiplication states that the order of the products being calculated doesn't affect the final result:

$(a\cdot b)\operatorname{\cdot}c=a\operatorname{\cdot}(b\operatorname{\cdot}c)$

Using these properties, we can rewrite the given expression with the following steps:

$\begin{gathered} (3\operatorname{\cdot}2)\operatorname{\cdot}5+7 \\ \text{ using the commutative property of addition:} \\ 7+(3\operatorname{\cdot}2)\operatorname{\cdot}5 \\ \text{ using the associative property of multiplication:} \\ 7+3\operatorname{\cdot}(2\operatorname{\cdot}5) \end{gathered}$

Therefore the correct option is the third one.