To determine which property of operations is demonstrated by the given expression:
[tex]\[
3[5(4)]+3=[3(5)] 4+3
\][/tex]
we can break down each side and compare the steps mathematically.
1. Evaluate the Left Side:
[tex]\[
3[5(4)]+3
\][/tex]
- First, evaluate the expression inside the brackets:
[tex]\[
5 \times 4 = 20
\][/tex]
- Then multiply this result by 3:
[tex]\[
3 \times 20 = 60
\][/tex]
- Finally, add 3:
[tex]\[
60 + 3 = 63
\][/tex]
So the left side evaluates to 63.
2. Evaluate the Right Side:
[tex]\[
[3(5)] 4 + 3
\][/tex]
- First, evaluate the expression inside the brackets:
[tex]\[
3 \times 5 = 15
\][/tex]
- Then multiply this result by 4:
[tex]\[
15 \times 4 = 60
\][/tex]
- Finally, add 3:
[tex]\[
60 + 3 = 63
\][/tex]
So the right side also evaluates to 63.
Since both sides of the expression evaluate to 63, we see that they are equal:
[tex]\[
3[5(4)]+3 = [3(5)] 4 + 3
\][/tex]
This equality shows the associative property of multiplication at work, which states that the way in which factors are grouped in multiplication does not affect the product:
[tex]\(
a \times (b \times c) = (a \times b) \times c
\)[/tex]
Therefore, the property demonstrated by the expression [tex]\(3[5(4)]+3=[3(5)] 4+3\)[/tex] is the associative property of multiplication.
