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Question

Which of the following is an example of the distributive property of multiplication over addition for rational numbers.


A

-14×23+-47=-14×23+-14×-47

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B

-14×23+-47=23+-14×-47

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C

-14×23+-47=14×23--47

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D

-14×23+-47=23+-47-14

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Solution

The correct option is A

-14×23+-47=-14×23+-14×-47


Explanation for the correct answer:

Option A. -14×23+-47=-14×23+-14×-47

The distributive property splits the expression a×b+c into a×b+a×c.

So, the split expression for -14×23+-47 is shown below

-14×23+-14×-47

This corresponds to option A.

So, Option A is correct.

Explanation for incorrect answers:

Option B. -14×23+-47=23+-14×-47

The expression a×b+a×c involves the product of the term outside the bracket with each term inside the bracket.

However, in the expression -14×23+-47=23+-14×-47 , the term -14 is not multiplied by each term inside the bracket.

So, the option (B) is incorrect.

Option C. -14×23+-47=14×23--47

The expression a×b+a×c involves the product of the term outside the bracket with each term inside the bracket.

However, in the expression-14×23+-47=14×23--47, the term -14 is not multiplied by each term inside the bracket.

So, the option (C) is incorrect.

Option D. -14×23+-47=23+-47-14
The expression -14×23+-47=23+-47-14 does not involve any multiplication.

So, option (D) is incorrect.

Hence, the correct option is A.


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