To answer the question of which property is represented by the equation [tex]\(4(6 + 7) = 24 + 28\)[/tex], let's analyze it step by step.
1. Start with the given expression:
[tex]\[
4(6 + 7)
\][/tex]
2. Apply the property to break down the expression:
[tex]\[
4(6 + 7) = 4 \cdot 6 + 4 \cdot 7
\][/tex]
3. Perform the multiplication:
[tex]\[
4 \cdot 6 = 24
\][/tex]
[tex]\[
4 \cdot 7 = 28
\][/tex]
4. Combine the results:
[tex]\[
4(6 + 7) = 24 + 28
\][/tex]
This sequence of steps shows that multiplying 4 by each term inside the parentheses separately and then adding the products gives the same result as multiplying 4 by the sum of the terms inside the parentheses.
The property applied here is the distributive property, which states that for any numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex],
[tex]\[
a(b + c) = ab + ac.
\][/tex]
Thus, the correct property represented by the equation [tex]\(4(6 + 7) = 24 + 28\)[/tex] is the distributive property. Therefore, the correct answer is:
distributive.
