Which property is demonstrated?

[tex]\[
3[5(4)] + 3 = [3(5)] 4 + 3
\][/tex]

A. Associative property of addition
B. Associative property of multiplication
C. Commutative property of addition
D. Commutative property of multiplication



Answer :

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.