# Addition

Addition is a way of finding the amount of two sets or quantities that are put together. It is an arithmetic operation. The four basic arithmetic operations are addition, subtraction, multiplication, and division.

The addition of two numbers, objects, etc, is the total number of each of the numbers being added.

Generally, it is easier to learn addition after first learning how to count. After learning to count, addition can be practiced by learning to add by using objects to represent the addition problem, then counting how many objects there are in total.

Example:

If John has 1 ball and Jane has 1 ball, how many balls do John and Jane have in total?

Since each of them had 1 ball each, combining each ball results in a total of 2 balls.

### Properties of addition

Two of the main properties of addition are the commutative property and the associative property:

- Commutative property of addition - This property means that the order that you add some numbers doesn't change the result of the addition
- 2 + 3 = 3 + 2 = 5
- Associative property of addition - This property means that how the numbers are grouped when you are adding 3 or more numbers doesn't change the result. In other words, order of operations does not matter
- 2 + 3 + 5 = (2 + 3) + 5 = 2 + (3 + 5) = 10

Using both the properties above, 5 + 2 + 3 would still equal 10 since both the order you add the numbers in and which numbers you add first don't matter. Knowing this, when learning to add, it is often easier to start with the bigger number then add the smaller number; it is easier to add 2 to 8 than adding 8 to 2.

### Addition table

+ | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

2 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |

3 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

4 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |

5 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |

6 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |

7 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

8 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |

9 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

See also addition facts, addition sentence.

Related words add, addend additive, additional.