# Commutative Properties of Multiplication ••• Liquidlibrary/liquidlibrary/Getty Images

Simply put, the commutative property of multiplication means that no matter how you order the numbers you are multiplying, you will get the same answer. Addition also shares the commutative property with multiplication, whereas division and subtraction do not. For example, if you multiply 3 by 5 or 5 by 3, you will get the same answer of 15.

## Commutative Property Basics

The root word for "commutative" is "commute." You can remember the meaning of commutative by thinking of the definition of "commute," which means to move around, change places, travel or interchange. The product will be the same no matter the order of the factors. In the operation of addition, if you add 5 and 3 or 3 and 5, you get the same sum of 8. The same applies in multiplication: The order of factors makes no difference.

## Example Problems

The examples of 3 x 5 = 15 and 5 x 3 = 15 are numerical examples of the commutative property associated with multiplication. This can also be illustrated by an array. Draw on a piece of paper 15 circles, but arrange them in columns and rows. Whether you created three rows of five circles or five rows of three circles, both arrangements equal 15 circles. The same logic applies for algebraic terms, such as ab = ba or (4x)(2y) = (2y)(4x).

## Word Problems

Although both addition and multiplication have the commutative property, when you must perform such operations after reading word problems, the interpretations are somewhat different. If you are reading a word problem that involves adding 112 houses with 134 houses, the meaning does not change whatever order you add the numbers. Suppose you are asked to determine the total number of flowers: If the word problem states that there are five groups of four flowers, you should interpret the equation as 5 x 4; if the problem states four groups of five, you should multiply 4 x 5. Although the answers are the same, it is worthwhile to take the time to read a word problem slowly to understand the exact question. You can even draw the groupings before producing your final answer.

## Related Properties

Some mathematical properties go hand in hand with the commutative property. The associative property also pertains to both addition and multiplication. In multiplication, if you have three or more factors, the order and groupings of the factors does not matter -- the product will always be the same. For example, (2 x 3) x 4 is the same as (3 x 4) x 2, and each equals 24. The distributive property only pertains to multiplication. According to this property, the sum of two numbers multiplied by a third number is the same as multiplying each of the numbers being added by that factor. In algebraic terms, this can be represented by x (y + z) = xy + xz.

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