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Choose the number sentence that illustrates the distributive property of multiplication over addition:

A. [tex]\(3 \times (4+7) = (3 \times 4) + (3 \times 7)\)[/tex]
B. [tex]\(3 \times (4+7) = (3 \times 4) + 7\)[/tex]
C. [tex]\(3 \times (4+7) = (3+4) \times (3+7)\)[/tex]

Sagot :

To determine which number sentence illustrates the distributive property of multiplication over addition, we need to remember what the distributive property states. The distributive property indicates that for any three numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex], the following relationship holds true:

[tex]\[ a \times (b + c) = (a \times b) + (a \times c) \][/tex]

Let’s examine each of the provided options to see which one fits this pattern.

Option A:
[tex]\[ 3 \times (4 + 7) = (3 \times 4) + (3 \times 7) \][/tex]

Here, we apply the distributive property correctly:
[tex]\[ 3 \times (4 + 7) = 3 \times 4 + 3 \times 7 \][/tex]

Option B:
[tex]\[ 3 \times (4 + 7) = (3 \times 4) + 7 \][/tex]

This does not correctly apply the distributive property. The second term should be [tex]\(3 \times 7\)[/tex], not just 7.

Option C:
[tex]\[ 3 \times (4 + 7) = (3 + 4) \times (3 + 7) \][/tex]

This is not an example of the distributive property. This sentence suggests adding 3 and 4, and also adding 3 and 7, and then multiplying the results, which is not correct.

So, based on our analysis:

The correct answer is:
[tex]\[ \boxed{A} \][/tex]