Which equation shows the associative property of multiplication? $\newline$ Choices: $\newline$ (A) $1 \cdot u = u$ $\newline$ (B) $(u \cdot v) \cdot w = u \cdot (v \cdot w)$ $\newline$ (C) $(u - v) \cdot w = u \cdot w - v \cdot w$ $\newline$ (D) $u \cdot v = w \cdot y$

Full solution

Q. Which equation shows the associative property of multiplication?

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Choices:

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(A)

1 \cdot u = u

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(B)

(u \cdot v) \cdot w = u \cdot (v \cdot w)

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(C)

(u - v) \cdot w = u \cdot w - v \cdot w

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(D)

u \cdot v = w \cdot y

Identify Property: Identify the associative property of multiplication. $\newline$ The associative property states that when three or more numbers are multiplied, the way in which they are grouped does not affect the product.
Examine Choice (A): Examine choice (A) $1 \cdot u = u$ . This is an example of the identity property of multiplication, which states that any number multiplied by $1$ equals the number itself.
Examine Choice (B): Examine choice (B) $(u \cdot v) \cdot w = u \cdot (v \cdot w)$ . This equation shows that no matter how we group the numbers when multiplying, the result is the same. This is the associative property of multiplication.
Examine Choice (C): Examine choice (C) $(u - v) \cdot w = u \cdot w - v \cdot w$ . This is an example of the distributive property of multiplication over subtraction, not the associative property.
Examine Choice (D): Examine choice (D) $u \cdot v = w \cdot y$ . This equation does not demonstrate any property of multiplication with respect to associativity; it simply states that the product of $u$ and $v$ is equal to the product of $w$ and $y$ .