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1.2 Learn Basic Properties and Operations

Properties

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 $$ab = ba$$

Examples

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.