Ask a New Question
Menu

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

Line 1: , left parenthesis, 4, x, right parenthesis, left parenthesis, 7, y, right parenthesis
Line 1: =
(4x)(7y)
Line 2: , 4, dot, left parenthesis, x, dot, 7, right parenthesis, dot, y
Line 2: =
4⋅(x⋅7)⋅y
Line 3: , 4, dot, left parenthesis, 7, dot, x, right parenthesis, dot, y
Line 3: =
4⋅(7⋅x)⋅y
Line 4: , left parenthesis, 4, dot, 7, right parenthesis, left parenthesis, x, dot, y, right parenthesis
Line 4: =
(4⋅7)(x⋅y)
Line 5: , 28, x, y
Line 5: =
28xy

1 answer

Let's identify the property that justifies each step in the sequence provided:

Line 1:
\( (4x)(7y) \)
Justification: Associative Property of Multiplication (which states that the way in which numbers are grouped in multiplication does not change their product).

Line 2:
\( 4 \cdot (x \cdot 7) \cdot y \)
Justification: Associative Property of Multiplication (again, the multiplication grouping changes but the product remains the same).

Line 3:
\( 4 \cdot (7 \cdot x) \cdot y \)
Justification: Commutative Property of Multiplication (the order of multiplication does not change the result; in this case, the position of 7 and x is swapped).

Line 4:
\( (4 \cdot 7)(x \cdot y) \)
Justification: Associative Property of Multiplication (factors are grouped differently, which does not impact the product).

Line 5:
\( 28xy \)
Justification: Multiplication (performing the multiplication of \( 4 \cdot 7 \) gives 28, or simply stating that it's the product of the numbers).

So, the justifications for each corresponding line are as follows:

  • Line 1: Associative Property of Multiplication
  • Line 2: Associative Property of Multiplication
  • Line 3: Commutative Property of Multiplication
  • Line 4: Associative Property of Multiplication
  • Line 5: Multiplication (or just simplifying the product)