To select the number sentence that correctly illustrates the distributive property of multiplication over addition, let’s recall what this property states. The distributive property of multiplication over addition allows you to distribute the multiplication over the terms inside the parentheses. Mathematically, it is represented as:
[tex]\[ a \times (b + c) = (a \times b) + (a \times c) \][/tex]
Now, let's analyze each of the given options to see which one matches this form.
### Option A:
[tex]\[ 4 \times (3 + 7) = (4 + 3) \times (4 + 7) \][/tex]
This equation is not correct because instead of distributing the multiplication, it adds 4 and 3, and also 4 and 7, which does not follow the distributive property.
### Option B:
[tex]\[ 4 \times (3 + 7) = (4 \times 3) + (4 \times 7) \][/tex]
This equation follows the distributive property correctly. The 4 is multiplied by both 3 and 7, then the products are added together. This matches the form:
[tex]\[ a \times (b + c) = (a \times b) + (a \times c) \][/tex]
### Option C:
[tex]\[ 4 \times (3 + 7) = (4 \times 3) + 7 \][/tex]
This equation is incorrect because it only multiplies 4 by 3 and then adds 7, instead of multiplying 4 by both 3 and 7.
Therefore, the correct choice that illustrates the distributive property of multiplication over addition is:
[tex]\[ \boxed{B} \][/tex]
[tex]\[ 4 \times (3 + 7) = (4 \times 3) + (4 \times 7) \][/tex]
