English

# How to do Commutative Operations?

## Commutative Property Tutorial

###### Definition:

The commutative property (or commutative law) is a property generally associated with binary operations and functions. If the commutative property holds for a pair of elements under a certain binary operation then the two elements are said to commute under that operation.

###### Commutative Addition Rule:

The addition of numbers is commutative.

a + b = b + a

###### Commutative Multiplication Rule:

The multiplication of numbers is commutative.

a × b = b × a

###### Commutative Subtraction Rule:

The subtraction of numbers is non-commutative.

a - b ≠ b - a

###### Commutative Division Rule:

The division of numbers is non-commutative.

a / b ≠ b / a

##### Commutative Law Example Problems:
###### Example: 1

Justify commutative addition rule when a is 12 and b is 3. Solution: 12 + 3 = 15 3 + 12 = 15 15 = 15

###### Example: 2

Justify commutative multiplication rule when a is 12 and b is 3. Solution: 12 × 3 = 36 3 × 12 = 36 36 = 36

###### Example: 3

Justify commutative subtraction rule when a is 12 and b is 3. Solution: 12 - 3 = 9 3 - 12 = -9 9 ≠ -9

###### Example: 4

Justify commutative division rule when a is 12 and b is 3. Solution: 12 / 3 = 4 3 / 12 = 1 / 4 = 0.25 4 ≠ 0.25