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]
