which of the following show the Commutative Property of Multiplication
responses
a x 1 = a
a x b = b x a
a x (b x c) = (a x b) x c
a x (-1) = -a
The correct response showing the Commutative Property of Multiplication is: a x b = b x a
The Commutative Property of Multiplication states that the order of factors does not affect the product.
Out of the responses you mentioned:
- "a x 1 = a" does not show the Commutative Property because the order is not being changed.
- "a x (-1) = -a" does not show the Commutative Property because the order is not being changed.
- "a x (b x c) = (a x b) x c" does not show the Commutative Property because this is an example of the Associative Property, which deals with grouping.
- "a x b = b x a" is the correct equation that represents the Commutative Property of Multiplication. It states that the product of a and b is equal to the product of b and a, regardless of the order of the factors.
So, the correct response that shows the Commutative Property of Multiplication is:
a x b = b x a
The Commutative Property of Multiplication states that changing the order of the factors in a multiplication equation does not change the result.
To determine which of the following options demonstrate the Commutative Property of Multiplication, we need to check if the equations remain true when we swap the order of the factors.
Let's go through each option one by one:
a x 1 = a
This equation is showing the property of multiplication by the identity element (1) rather than the Commutative Property. It does not involve swapping the order of the factors, so it is not an example of the Commutative Property of Multiplication.
a x b = b x a
This equation directly shows the Commutative Property of Multiplication because it demonstrates that the order of the factors (a and b) can be interchanged without affecting the result. So, this option represents the Commutative Property of Multiplication.
a x (b x c) = (a x b) x c
This equation exhibits the Associative Property of Multiplication, which states that changing the grouping of factors does not change the result. It does not involve swapping the order of the factors, so it does not show the Commutative Property of Multiplication.
a x (-1) = -a
This equation involves multiplying a number by -1, which is the additive inverse element. This property is called the Additive Inverse Property rather than the Commutative Property of Multiplication.
In conclusion, the option that demonstrates the Commutative Property of Multiplication is:
a x b = b x a