Which property of multiplication states that changing the order of the factors does not change the product?
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Associative property
Right.
The property of multiplication that states changing the order of the factors does not change the product is called the Commutative Property of Multiplication.
To understand this property, one way to think about it is by considering a multiplication problem. Let's take an example: 3 multiplied by 5, which can be written as 3 x 5.
According to the Commutative Property of Multiplication, if we change the order of the factors and write it as 5 x 3, the product will still be the same. In this case, both 3 x 5 and 5 x 3 give us a product of 15.
To prove this property for any two numbers, we can consider the general form of a multiplication operation: a x b. If we interchange the values of a and b and multiply them, we'll always obtain the same product. In mathematical notation, it can be written as a x b = b x a, where "=" denotes equality.
The Commutative Property of Multiplication is particularly useful when evaluating expressions with multiple factors, as it allows us to rearrange the order and simplify calculations.