Which property is used in the problem below, the commutative property or the associative property?(4 x 2) x 3 = (2 x 4) x 3The  property is being used.

1. Break Down the Problem

To determine whether the commutative property or the associative property is used in the equation $(4 \times 2) \times 3 = (2 \times 4) \times 3$, let's analyze it more closely.

2. Relevant Concepts

• Commutative Property: States that changing the order of the numbers in an operation does not change the result. For multiplication, $a \times b = b \times a$.
• Associative Property: States that changing the grouping of numbers in an operation does not change the result. For multiplication, $(a \times b) \times c = a \times (b \times c)$.

3. Analysis and Detail

In the provided equation, we have:

• The left side: $(4 \times 2) \times 3$
• The right side: $(2 \times 4) \times 3$

The left side shows that $4$ and $2$ are multiplied first, while the right side shows that $2$ and $4$ are multiplied first before being combined with $3$.

This indicates a change in the order of multiplication, which aligns with the definition of the commutative property, since $a \times b$ (where $a=4$ and $b=2$) can be rearranged without affecting the outcome.

4. Verify and Summarize

In this case, both expressions yield the same final product (which can be computed), but they demonstrate the use of the commutative property since the order of the factors $4$ and $2$ has been switched.

Final Answer

The property being used is the commutative property.