Question

When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step?
Original Equation:
Original Equation:
5, left parenthesis, 4, x, right parenthesis, equals, 5
5(4x)=
5
First Step:
First Step:
left parenthesis, 5, dot, 4, right parenthesis, x, equals, 5
(5⋅4)x=
5
Answer
Multiple Choice Answers
associative property of multiplication
commutative property of addition
addition property of equality
associative property of addition

Answer 1

Carmen's first step rewrites the original equation \(5(4x) = 5\) as \((5 \cdot 4)x = 5\). This step involves factoring the coefficient of \(4x\) into two parts, \(5\) and \(4\).

The property that justifies this first step is the **associative property of multiplication**, which allows us to group factors in different ways when multiplying. In the context of Carmen's equation, it's not directly changing the operation, but it involves how we pair numbers in multiplication, keeping the product the same.

So the answer is:
**associative property of multiplication.**