Which equation shows the commutative property of multiplication? $\newline$ Choices: $\newline$ (A) $a \cdot b = c + d$ $\newline$ (B) $b \cdot a = a \cdot b$ $\newline$ (C) $a \cdot 1 = a$ $\newline$ (D) $(a \cdot b) \cdot c = a \cdot (b \cdot c)$

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Algebra 1

Properties of addition and multiplication

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Q. Which equation shows the commutative property of multiplication?

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Choices:

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(A)

a \cdot b = c + d

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(B)

b \cdot a = a \cdot b

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(C)

a \cdot 1 = a

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(D)

(a \cdot b) \cdot c = a \cdot (b \cdot c)

Identify Property: Identify the commutative property of multiplication. $\newline$ The commutative property states that changing the order of the factors does not change the product. In other words, for any numbers $a$ and $b$ , the equation $a \cdot b = b \cdot a$ demonstrates the commutative property.
Examine Choices: Examine each choice to see which one represents the commutative property. (A) $a \cdot b = c + d$ does not show the commutative property because it involves both multiplication and addition, and the order of the factors is not changed.
Check for Commutative Property: (B) $b \cdot a = a \cdot b$ directly shows the commutative property because the order of the factors $a$ and $b$ is reversed, yet the equation states that they are equal.
Determine Correct Choice: (C) $a \cdot 1 = a$ shows the identity property of multiplication, not the commutative property, because it states that any number multiplied by $1$ equals itself.
Determine Correct Choice: (C) $a \cdot 1 = a$ shows the identity property of multiplication, not the commutative property, because it states that any number multiplied by $1$ equals itself.(D) $(a \cdot b) \cdot c = a \cdot (b \cdot c)$ shows the associative property of multiplication, not the commutative property, because it demonstrates that the grouping of factors does not affect the product.
Determine Correct Choice: (C) $a \cdot 1 = a$ shows the identity property of multiplication, not the commutative property, because it states that any number multiplied by $1$ equals itself.(D) $(a \cdot b) \cdot c = a \cdot (b \cdot c)$ shows the associative property of multiplication, not the commutative property, because it demonstrates that the grouping of factors does not affect the product.Determine the correct choice that represents the commutative property. $\newline$ From the examination of the choices, only choice (B) $b \cdot a = a \cdot b$ represents the commutative property of multiplication.