Question

complete the expressions and select the missing properties. write each answer as a number, a variable, or the product of a number and a variable. (y·6)5 = y(6·5) distributive property = y·30 multiply = 30 y dropdown with options: commutative property of addition, commutative property of multiplication, associative property of addition, associative property of multiplication, distributive property

Explanation:

Step1: Identify the property for reordering multiplication

The step from \( y \cdot 30 \) to \( 30y \) involves reordering the factors of multiplication. The commutative property of multiplication states that \( a \cdot b = b \cdot a \) for any numbers \( a \) and \( b \). Here, \( a = y \) and \( b = 30 \), so we use the commutative property of multiplication.

Step2: Confirm the property

Since we are swapping the order of \( y \) and \( 30 \) in the multiplication \( y \cdot 30 \) to get \( 30y \), this matches the definition of the commutative property of multiplication.

Answer:

Commutative property of multiplication