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

Full solution

Q. Which equation shows the commutative property of multiplication?

\newline

Choices:

\newline

(A)

b \cdot c = c \cdot b

\newline

(B)

b \cdot c + b \cdot d = b \cdot (c + d)

\newline

(C)

b \cdot (c - d) = b \cdot c - b \cdot d

\newline

(D)

b \cdot c - b \cdot d = b \cdot (c - d)

Understand Commutative Property: Understand the commutative property of multiplication. The commutative property of multiplication 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.
Analyze Choices: Analyze each choice to see which one represents the commutative property. $\newline$ (A) $b \cdot c = c \cdot b$ $\newline$ This choice shows two numbers being multiplied in different orders and set equal to each other, which is exactly what the commutative property describes.
Eliminate Incorrect Choices: Eliminate the other choices that do not represent the commutative property. $\newline$ (B) $b \cdot c + b \cdot d = b \cdot (c + d)$ $\newline$ This choice represents the distributive property, not the commutative property. $\newline$ (C) $b \cdot (c - d) = b \cdot c - b \cdot d$ $\newline$ This choice also represents the distributive property. $\newline$ (D) $b \cdot c - b \cdot d = b \cdot (c - d)$ $\newline$ This choice is another representation of the distributive property.
Conclude Correct Representation: Conclude which choice correctly represents the commutative property. Based on the analysis, choice (A) $b \cdot c = c \cdot b$ is the correct representation of the commutative property of multiplication.