Which of the following demonstrates the Associative Property of Multiplication?(1 point)
Responses
(3⋅5)+2=(3+5)⋅2
left parenthesis 3 times 5 right parenthesis plus 2 equals left parenthesis 3 plus 5 right parenthesis times 2
(3⋅5)⋅2=(3⋅5)⋅2
left parenthesis 3 times 5 right parenthesis times 2 equals left parenthesis 3 times 5 right parenthesis times 2
(3⋅5)⋅2=3⋅(5⋅2)
left parenthesis 3 times 5 right parenthesis times 2 equals 3 times left parenthesis 5 times 2 right parenthesis
(3+5)⋅2=3+(5⋅2)
left parenthesis 3 plus 5 right parenthesis times 2 equals 3 plus left parenthesis 5 times 2 right parenthesis
The option that demonstrates the Associative Property of Multiplication is:
(3⋅5)⋅2=3⋅(5⋅2)
This equation shows that when multiplying three numbers together, the grouping can be changed without affecting the result.
To determine which of the given options demonstrates the Associative Property of Multiplication, we need to understand what the Associative Property of Multiplication actually means.
The Associative Property of Multiplication states that when multiplying three or more numbers, the grouping of the numbers does not affect the final result. In other words, you can change the grouping of the numbers being multiplied, and the product will remain the same.
Let's examine each option and apply the Associative Property of Multiplication:
Option 1: (3⋅5)+2=(3+5)⋅2
In this option, the numbers 3, 5, and 2 are grouped differently on each side of the equation. The left side multiplies 3 and 5 together and then adds 2, while the right side adds 3 and 5 together and then multiplies the sum by 2. Since the grouping is different, this does not demonstrate the Associative Property of Multiplication.
Option 2: (3⋅5)⋅2=(3⋅5)⋅2
In this option, the numbers are grouped the same on both sides of the equation. The left side multiplies 3 and 5 together and then multiplies the product by 2. The right side also multiplies 3 and 5 together and then multiplies the product by 2. Since the grouping is the same and the product remains the same, this demonstrates the Associative Property of Multiplication.
Option 3: (3⋅5)⋅2=3⋅(5⋅2)
In this option, the numbers are grouped differently on each side of the equation. The left side multiplies 3 and 5 together and then multiplies the product by 2. The right side multiplies 5 and 2 together and then multiplies the product by 3. Since the grouping is different, this does not demonstrate the Associative Property of Multiplication.
Option 4: (3+5)⋅2=3+(5⋅2)
This option does not involve multiplication, so it does not demonstrate the Associative Property of Multiplication.
Therefore, the only option that demonstrates the Associative Property of Multiplication is Option 2: (3⋅5)⋅2=(3⋅5)⋅2.