QuestionIdentify the property that justifies the statement $z(2 w+y)=(2 w+y) z$ . A associative property of multiplication B commutative property of multiplication C multiplication property of equality D symmetric property of equality

Studdy Solution

STEP 1

1. The problem involves identifying a property of real numbers.
2. The expression given is $z(2w + y) = (2w + y)z$ .
3. The properties to consider are associative, commutative, multiplication property of equality, and symmetric property of equality.

STEP 2

1. Understand each property.
2. Analyze the given expression.
3. Match the expression to the correct property.

STEP 3

Understand each property:
- Associative Property of Multiplication: This property states that the way in which numbers are grouped in multiplication does not change their product. For example, $(a \times b) \times c = a \times (b \times c)$ .
- Commutative Property of Multiplication: This property states that the order of numbers in multiplication does not affect the product. For example, $a \times b = b \times a$ .
- Multiplication Property of Equality: This property states that if you multiply both sides of an equation by the same number, the equality holds. For example, if $a = b$ , then $a \times c = b \times c$ .
- Symmetric Property of Equality: This property states that if one quantity equals another, then the second quantity equals the first. For example, if $a = b$ , then $b = a$ .

STEP 4

Analyze the given expression:
The expression is $z(2w + y) = (2w + y)z$ .
Notice that the terms $z$ and $(2w + y)$ have swapped places on either side of the equation.

STEP 5

Match the expression to the correct property:
The expression $z(2w + y) = (2w + y)z$ shows that the order of multiplication does not affect the product. This is a direct application of the Commutative Property of Multiplication.
Therefore, the property that justifies the statement is:
B commutative property of multiplication
The correct answer is $\boxed{B}$ .

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