Which property is illustrated by the following statement?
6 + (2x + 2z) = (6 + 2x) + 2z
Associative Property of Multiplication
Commutative Property of Multiplication
Inverse Property of Multiplication
Associative Property of addition******
yup
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To determine which property is illustrated by the given equation, let's break down the options and apply them to the equation:
1. Associative Property of Multiplication: This property states that changing the grouping of factors does not affect the product. However, the given equation involves addition, not multiplication. Therefore, this property is not applicable.
2. Commutative Property of Multiplication: This property states that changing the order of factors does not affect the product. Since the given equation involves addition, not multiplication, this property is also not applicable.
3. Inverse Property of Multiplication: This property states that a number multiplied by its multiplicative inverse equals 1. However, no multiplication or multiplicative inverses are involved in the given equation, so this property does not apply either.
4. Associative Property of Addition: This property states that changing the grouping of numbers does not affect the sum. In the given equation, both sides have the same terms but grouped differently. By rearranging the terms, we can show that the equation holds true: 6 + (2x + 2z) = (6 + 2x) + 2z. Therefore, the correct answer is the Associative Property of Addition.
To summarize, in the given equation, the Associative Property of Addition is illustrated.