The commutative property states that changing the order of the terms around an addition or multiplication symbol will not change the outcome. You can remember this because commute means to move or travel.
So, a+b is the same or equals b+a, and a*b is the same as or equal to b*a. The commutative property is only true for addition and multiplication.
Let’s look at a couple examples.
3+5 = 5+3
3+5 is 8, and 5+3 is 8. So, the order that you add the numbers doesn’t matter.
We use the same numbers for multiplication.
3*5 = 5*3
3*5 is 15, and 5*3 is 15. So, again, you can move the terms around the addition or multiplication signs, and the result will be the same.
Again, the commutative property only works for addition and multiplication. It does not work for subtraction or division.
Let’s look at that using the same numbers. So, a-b does not equal b-a. 3-5 does not equal 5-3.
3-5, you can add the inverse, that’s -2, does not equal 5-3, which is a positive 2.
The same is true for division, again, it does not work. So, a÷b does not equal b÷a.
3÷5 does not equal 5÷3. 3/5 and 5/3 are not the same.
So, the commutative property, again, commute means to move or travel, and it states that if you change the order of your terms around your addition or multiplication signs, your result will be the same. The next lesson: Distributive Property, both lessons are included in our Practice Tests.