What Is the Associative Property of Multiplication?

# What Is the Associative Property of Multiplication?

The associative property of multiplication states that the order in which numbers are multiplied in sequence is irrelevant. In other words, if more than two numbers in an expression are multiplied together, the product is the same no matter the order in which the numbers are multiplied.

In mathematics, the associative law applies to both multiplication and addition. It is distinguished from the commutative laws of multiplication and addition by its representation. The commutative law of multiplication states that a*b = b*a. By contrast, the associative law of multiplication states that (a*b)*c = a*(b*c). The associative law means that parentheses in an expression can be moved without changing the value of the expression. This is because the associative law refers to the order of operations, whereas the commutative law refers to the order of values. Multiplication and addition are both commutative and associative.

The associative property of multiplication is clear when compared to a non-associative operation, such as division. For example, the expression 4*3*2=24 can be grouped in different ways. However, whether 4 and 3 are first multiplied or 3 and 2 are, the answer does not change. However, the expression 100/20/5 has two different answers. If 100 and 20 are divided first the answer is 5, but if 20 and 5 are divided first the answer is 25.

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