In mathematics, addition, represented by the symbol ${\displaystyle +}$, is an operation which combines two mathematical objects together into another mathematical object of the same type, called the sum.[1][2][3] Addition can occur with simple objects such as numbers, and more complex objects such as vectors and matrices.[4]

## Arithmetic

In arithmetic, addition is finding the total of two or more numbers. The sign for addition is "+", and the name for the sign "+" is "plus". Another name for the total is the sum.

### Counting examples

For example, there are objects in two groups. The objects are small circles: "o". One group has five of these objects. The other group has three of these objects. To find the total number of objects in both groups, the objects can be counted. Another way to find the number of objects in both groups is to add the numbers in each group.

Another method is to add the numbers of objects in group A and group B, since they are already counted. In symbols:

5 + 3

There are rules for adding numbers that people learn. There are also rules for adding numbers that are built into machines (binary adder). The rule says that:

5 + 3 = 8

In another counting example, Sally and Bill have 2 children. Sally and Bill get 3 more children. Sally and Bill have added three children to their two children, and now have five children.

The animation above demonstrates the addition of seven hundred and eighty six and four hundred and sixty seven, the problems digits have been separated into units, tens and hundreds (place value).

First, the units 6 and 7 are added together to make 13, so 1 ten and 3 units, with the 3 written below and the 1 ten carried to the tens column. Next, in the tens column, the 1, 8 and 6 are added together to make 15 tens, so 1 hundred and 5 tens, with the 5 written below and the 1 hundred carried to the hundreds column. Finally, in the hundreds column, 1, 7 and 4 are added together to make 12 hundreds, so 1 thousand and 2 hundreds, with the 2 written below and the 1 thousand carried to the thousand column. The final answer is thus one thousand two hundred and fifty three.

### A measurement example

Tom wants to know the distance between his house and Sally's house. Bob's house is 300 meters east of Tom's house. Sally's house is 120 meters east of Bob's house:

Tom's house ${\displaystyle \leftarrow }$ 300 meters ${\displaystyle \rightarrow }$ Bob's house ${\displaystyle \leftarrow }$ 120 meters ${\displaystyle \rightarrow }$ Sally's house

The distance from Tom's house to Sally's house can be found by adding the distances already measured. The distance from Tom's house to Bob's house, added to the distance from Bob's house to Sally's house, is the same as the distance from Tom's house to Sally's house. That is, three hundred (300) meters plus 120 meters.

300 + 120 = 420

Hence Sally's house is 420 meters to the east of Tom's house.

Addition can also mean to make bigger.

### Example of addition as increase

• For example, Tom has a house. Tom puts a new room on the house. This new room is called an addition.
• John is making food. To make the food taste better, John puts salt in the food. That is, John adds salt to the food. The salt is a food additive or addition to the food.

 1 + 0 = 1 1 + 1 = 2 1 + 2 = 3 1 + 3 = 4 1 + 4 = 5 1 + 5 = 6 1 + 6 = 7 1 + 7 = 8 1 + 8 = 9 1 + 9 = 10 1 + 10 = 11
 2 + 0 = 2 2 + 1 = 3 2 + 2 = 4 2 + 3 = 5 2 + 4 = 6 2 + 5 = 7 2 + 6 = 8 2 + 7 = 9 2 + 8 = 10 2 + 9 = 11 2 + 10 = 12
 3 + 0 = 3 3 + 1 = 4 3 + 2 = 5 3 + 3 = 6 3 + 4 = 7 3 + 5 = 8 3 + 6 = 9 3 + 7 = 10 3 + 8 = 11 3 + 9 = 12 3 + 10 = 13
 4 + 0 = 4 4 + 1 = 5 4 + 2 = 6 4 + 3 = 7 4 + 4 = 8 4 + 5 = 9 4 + 6 = 10 4 + 7 = 11 4 + 8 = 12 4 + 9 = 13 4 + 10 = 14
 5 + 0 = 5 5 + 1 = 6 5 + 2 = 7 5 + 3 = 8 5 + 4 = 9 5 + 5 = 10 5 + 6 = 11 5 + 7 = 12 5 + 8 = 13 5 + 9 = 14 5 + 10 = 15
 6 + 0 = 6 6 + 1 = 7 6 + 2 = 8 6 + 3 = 9 6 + 4 = 10 6 + 5 = 11 6 + 6 = 12 6 + 7 = 13 6 + 8 = 14 6 + 9 = 15 6 + 10 = 16
 7 + 0 = 7 7 + 1 = 8 7 + 2 = 9 7 + 3 = 10 7 + 4 = 11 7 + 5 = 12 7 + 6 = 13 7 + 7 = 14 7 + 8 = 15 7 + 9 = 16 7 + 10 = 17
 8 + 0 = 8 8 + 1 = 9 8 + 2 = 10 8 + 3 = 11 8 + 4 = 12 8 + 5 = 13 8 + 6 = 14 8 + 7 = 15 8 + 8 = 16 8 + 9 = 17 8 + 10 = 18
 9 + 0 = 9 9 + 1 = 10 9 + 2 = 11 9 + 3 = 12 9 + 4 = 13 9 + 5 = 14 9 + 6 = 15 9 + 7 = 16 9 + 8 = 17 9 + 9 = 18 9 + 10 = 19
 10 + 0 = 10 10 + 1 = 11 10 + 2 = 12 10 + 3 = 13 10 + 4 = 14 10 + 5 = 15 10 + 6 = 16 10 + 7 = 17 10 + 8 = 18 10 + 9 = 19 10 + 10 = 20

## References

1. "List of Arithmetic and Common Math Symbols". Math Vault. 2020-03-17. Retrieved 2020-08-26.