1.2 Learn Basic Properties and Operations

This lesson will help you learn the basic properties and rules that govern math problem-solving.


The commutative property applies to addition and multiplication. It states that you can add or multiply numbers in any order without changing the result.

Note: We use letters when we write a property so that it is clear that the property will work for all numbers.

Commutative property

$$a + b = b + a$$ and $$ab = ba$$


1. eight + negative 3 = 5 and negative 3 + 8 = 5

We can add the numbers in any order, and the result will be 5.

2.   negative 4 times 5 = negative 20 and positive 5 times negative 4 = negative 20

Changing the order of the numbers being multiplied doesn’t change the answer.
Remember, subtraction and division are not commutative operations. Changing the order changes the result.