Which of the following shows the Commutative Property of Multiplication?
A. a×b=b×a
B. a×(b×c)=(a×b)×c
C. a×1=a
D. a×(-1)=-a
A. a×b=b×a
The correct answer that shows the Commutative Property of Multiplication is A. a×b=b×a. The Commutative Property states that the order of the numbers being multiplied does not affect the result.
The Commutative Property of Multiplication states that the order in which you multiply two numbers does not affect the result. In other words, if you swap the order of the numbers being multiplied, you will get the same product.
Let's analyze the options given:
A. a×b=b×a - This option represents the Commutative Property of Multiplication. Swapping the order of a and b does not change the result of the multiplication.
B. a×(b×c)=(a×b)×c - This option represents the Associative Property of Multiplication, not the Commutative Property. It states that the grouping of numbers being multiplied does not affect the result.
C. a×1=a - This option represents the Identity Property of Multiplication. Multiplying any number by 1 does not change its value.
D. a×(-1)=-a - This option represents the Multiplicative Inverse Property, where multiplying any number by its multiplicative inverse gives the multiplicative identity (1). It does not demonstrate the Commutative Property.
Therefore, the answer is A. a×b=b×a, as it shows the Commutative Property of Multiplication.