Which of the following shows the Commutative Property of Multiplication?

Responses

a×(−1)=−a
A times negative 1 is equal to negative A - no response given

a×b=b×a
a×b=b×a
𝑎
×
𝑏
=
𝑏
×
𝑎
- not selected, this is the correct answer

a×(b×c)=(a×b)×c
a×(b×c)=(a×b)×c
𝑎
×
(
𝑏
×
𝑐
)
=
(
𝑎
×
𝑏
)
×
𝑐
- incorrect

a×1=a
A times 1 is equal to A - no response given
Score

1 answer

The Commutative Property of Multiplication states that changing the order of the factors does not change the product. In this case, the correct response that demonstrates this property is:

a × b = b × a

This shows that multiplying \( a \) by \( b \) yields the same result as multiplying \( b \) by \( a \).

The other expressions you listed represent different properties:

  • \( a \times (-1) = -a \): This demonstrates how multiplication by -1 works but is not the commutative property.
  • \( a \times (b \times c) = (a \times b) \times c \): This is the Associative Property of Multiplication.
  • \( a \times 1 = a \): This shows the Identity Property of Multiplication.

So, the correct answer to show the Commutative Property of Multiplication is indeed:

a × b = b × a.