Which equation shows the distributive property of multiplication? $\newline$ Choices: $\newline$ (A) $m \cdot (n \cdot p) = (m \cdot n) \cdot p$ $\newline$ (B) $0 = 0 \cdot m$ $\newline$ (C) $m \cdot n - m \cdot p = m \cdot (n - p)$ $\newline$ (D) $m \cdot 1 = m$

Full solution

Q. Which equation shows the distributive property of multiplication?

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Choices:

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(A)

m \cdot (n \cdot p) = (m \cdot n) \cdot p

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(B)

0 = 0 \cdot m

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(C)

m \cdot n - m \cdot p = m \cdot (n - p)

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(D)

m \cdot 1 = m

Understand Distributive Property: Understand the distributive property. The distributive property of multiplication over addition or subtraction states that multiplying a sum or difference by a number is the same as multiplying each addend or subtrahend by the number and then adding or subtracting the products. Mathematically, it can be expressed as $a(b + c) = ab + ac$ or $a(b - c) = ab - ac$ .
Examine Choice (A): Examine choice (A) $m \cdot (n \cdot p) = (m \cdot n) \cdot p$ . This choice represents the associative property of multiplication, not the distributive property. It shows that the grouping of factors does not affect the product.
Examine Choice (B): Examine choice (B) $0 = 0 \cdot m$ . This choice represents the multiplication property of zero, which states that any number multiplied by zero is zero. It does not demonstrate the distributive property.
Examine Choice (C): Examine choice (C) $m \cdot n - m \cdot p = m \cdot (n - p)$ . This choice correctly represents the distributive property of multiplication over subtraction. It shows that multiplying $m$ by the difference of $n$ and $p$ is the same as multiplying $m$ by $n$ and $m$ by $p$ separately, and then subtracting the two products.
Examine Choice (D): Examine choice (D) $m \cdot 1 = m$ . This choice represents the identity property of multiplication, which states that any number multiplied by one is the number itself. It does not demonstrate the distributive property.