Which property of multiplication is shown? $\newline$ $g \cdot (h \cdot j) = (g \cdot h) \cdot j$ $\newline$ Choices: $\newline$ (A)associative $\newline$ (B)identity $\newline$ (C)zero $\newline$ (D)commutative

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Algebra 1

Properties of addition and multiplication

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Q. Which property of multiplication is shown?

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g \cdot (h \cdot j) = (g \cdot h) \cdot j

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Choices:

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(A)associative

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(B)identity

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(C)zero

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(D)commutative

Identify Property of Multiplication: Identify the property of multiplication by examining the equation $g \cdot (h \cdot j) = (g \cdot h) \cdot j$ . In this equation, the placement of the parentheses is changed, but the order of the multiplication remains the same. This indicates that the property being used is one that allows us to regroup the factors without changing the product.
Compare with Property Definitions: Compare the given equation with the definitions of the properties listed in the choices. $\newline$ (A) Associative Property: This property states that when three or more numbers are multiplied, the product is the same regardless of the grouping of the factors. In other words, $(a \cdot b) \cdot c = a \cdot (b \cdot c)$ . $\newline$ (B) Identity Property: This property states that any number multiplied by one gives the number itself, which is not what is being shown in the equation. $\newline$ (C) Zero Property: This property states that any number multiplied by zero is zero, which is also not what is being shown in the equation. $\newline$ (D) Commutative Property: This property states that the order in which two numbers are multiplied does not change the product, i.e., $a \cdot b = b \cdot a$ , which is not the case here as the order of the factors is not being changed.
Determine Exemplified Property: Determine which property the equation $g \cdot (h \cdot j) = (g \cdot h) \cdot j$ exemplifies based on the comparison in the previous step. $\newline$ The equation shows that the grouping of factors can be changed without affecting the product, which is a characteristic of the Associative Property of multiplication.