Question

Which pair of expressions is equivalent using the Associative Property of Multiplication?

(a) 6(4a⋅2)=24a⋅12
(b) 6(4a⋅2)=(4a⋅2)⋅6
(c) 6(4a⋅2)=6⋅4a⋅2
(d) 6(4a⋅2)=(6⋅4a).2

Answer 1

The pair of expressions that are equivalent using the Associative Property of Multiplication is b) 6(4a\u00b72)=(4a\u00b72)\u00b76, which correctly shows the numbers can be grouped in any order without affecting the product.

Step-by-step explanation:

The Associative Property of Multiplication states that when three or more numbers are multiplied together, the grouping of the numbers does not affect the product. This implies that re-arranging parentheses in a multiplication expression does not change the result. The question given asks to identify an equivalent expression using the Associative Property of Multiplication.

The correct answer to the question is: b) 6(4a\u00b72)=(4a\u00b72)\u00b76.

This shows that the multiplication can be carried out no matter how the numbers are grouped. The expression 6(4a\u00b72) can be grouped as (4a\u00b72)\u00b76, which illustrates the Associative Property, indicating that you can multiply 4a and 2 before multiplying by 6, or you can multiply 4a by 6 before multiplying by 2, without changing the result.