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

Question

Line 1: =(4x)(6y)
Line 2: 4⋅(x⋅6)⋅y
Line 3: 4⋅(6⋅x)⋅y
Line 4: (4⋅6)(x⋅y)
Line 5: 24xy

Answer 1

Here are the properties that justify each step in the transformation from Line 1 to Line 5:

1. Line 1 to Line 2: (4x)(6y) = 4 ⋅ (x ⋅ 6) ⋅ y

   • Property: Associative Property of Multiplication (specifically grouping the factors)

2. Line 2 to Line 3: 4 ⋅ (x ⋅ 6) ⋅ y = 4 ⋅ (6 ⋅ x) ⋅ y

   • Property: Commutative Property of Multiplication (rearranging the factors)

3. Line 3 to Line 4: 4 ⋅ (6 ⋅ x) ⋅ y = (4 ⋅ 6)(x ⋅ y)

   • Property: Associative Property of Multiplication (grouping the factors together)

4. Line 4 to Line 5: (4 ⋅ 6)(x ⋅ y) = 24xy

   • Property: Simplification and the definition of multiplication (calculating the product)

This step-by-step justification illustrates how different properties of multiplication are applicable throughout the transformation of the expression.