# Commutative property

The commutative property dictates that changing the order of the two numbers used in an operation does not change the result of that operation. The commutative property applies to both addition and multiplication, but not to subtraction and division.

### commutative property of addition

The commutative property of addition dictates that changing the order in which two numbers are added does not change the sum.

Examples

Ex. 1 | Ex. 2 |

7 + 9 = 16 | + = |

9 + 7 = 16 | + = |

As can be seen from the examples above, the order does not change the outcome.

The commutative property of addition is often written as:

a + b = b + a

### commutative property of multiplication

The commutative property of multiplication dictates that changing the order in which two numbers are multiplied does not change the product.

Examples

Ex. 1 | Ex. 2 |

8 × 5 = 40 | 4 × 1.3 = 5.2 |

5 × 8 = 40 | 1.3 × 4 = 5.2 |

As can be seen from the examples above, the order of multiplication does not change the product.

The commutative property of multiplication is often written as:

a × b = b × a