Commutative Property

The word commuttative (com-mute-a-tive) comes from the Latin word commutare which means to change or to move around. (Think of the word commute meaning to travel to work.)

The property says that the position of numbers can be changed when adding or multiplying them.

Here is an example for addition:

$5 + 3 = 8$ and $3 + 5 = 8$ .

The order of the 3 and 5 was changed but the answers are the same.

The general rule, where a and b represent numbers is:

$a + b = b + a$ .

Here is an example for multiplication:

$5 \times 3=15$ and $3 \times 5=15$ .

The order of the 3 and 5 was changed but the answers are the same.

The general rule, where a and b represent and number is:

$a \times b = b \times a$ .

Let’s look at this property not applying to examples for subtraction and for division.

$5 - 3 = 2$ and $3 - 5 = -2$ .

The order of the 3 and 5 was changed and the answers are different.

$5 \div 3 = 1$ $\frac{2}{5}$ and $3\div 5 =$ $\frac{3}{5}$ .

The order of the 3 and 5 was changed and the answers are different.

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