Which equation shows the distributive property of multiplication? $\newline$ Choices: $\newline$ (A) $j \cdot 0 = 0$ $\newline$ (B) $(j \cdot k) \cdot m = j \cdot (k \cdot m)$ $\newline$ (C) $m = j \cdot k$ $\newline$ (D) $j \cdot k + j \cdot m = j \cdot (k + m)$

Full solution

Q. Which equation shows the distributive property of multiplication?

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Choices:

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(A)

j \cdot 0 = 0

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(B)

(j \cdot k) \cdot m = j \cdot (k \cdot m)

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(C)

m = j \cdot k

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(D)

j \cdot k + j \cdot m = j \cdot (k + m)

Understand Distributive Property: Understand the distributive property of multiplication. The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products. Mathematically, it can be expressed as $a(b + c) = ab + ac$ .
Examine Choices: Examine each choice to see which one matches the distributive property. $\newline$ (A) $j \cdot 0 = 0$ does not show the distributive property; it shows the multiplication property of zero. $\newline$ (B) $(j \cdot k) \cdot m = j \cdot (k \cdot m)$ shows the associative property of multiplication, not the distributive property. $\newline$ (C) $m = j \cdot k$ is just an equation and does not show the distributive property. $\newline$ (D) $j \cdot k + j \cdot m = j \cdot (k + m)$ matches the format of the distributive property, where $j$ is distributed over the sum of $k$ and $m$ .
Identify Correct Choice: Identify the correct choice that demonstrates the distributive property. From Step $2$ , we can see that choice (D) $j \cdot k + j \cdot m = j \cdot (k + m)$ is the correct representation of the distributive property.