Identify the property that justifies each step asked about in the answer area below.

Question

Line 1: , left parenthesis, a, c, right parenthesis, b
Line 1: =
(ac)b
Line 2: , a, left parenthesis, c, b, right parenthesis
Line 2: =
a(cb)
Line 3: , a, left parenthesis, b, c, right parenthesis
Line 3: =
a(bc)
Answer
Attempt 1 out of 2

Line 1 to Line 2:
Line 2 to Line 3:

Answer 1

To identify the properties that justify each step:

Line 1 to Line 2:

• The property used is the Associative Property of Multiplication. This property states that when multiplying three or more numbers, the way in which the numbers are grouped does not change the product. In this case, \( (ac)b \) can be regrouped to \( a(cb) \).

Line 2 to Line 3:

• The property used again is the Associative Property of Multiplication. Here, \( a(cb) \) is being rearranged to \( a(bc) \). Since the grouping of the factors does not change their product, this step is justified by the same property.

So, the properties that justify the steps are:

• Line 1 to Line 2: Associative Property of Multiplication
• Line 2 to Line 3: Associative Property of Multiplication