Addition is one of the oldest and the most basic arithmetic operation. It is known to mathematician since more than 6000 years. The ‘counting’ was considered as an early form of addition.

The first official evidence of addition is that it was used by Egyptians and Babylonians in 2000 BC. The symbols of addition and subtraction were invented in around 16^{th} century, but before that, the equations were written in words, which makes it really time consuming to solve the problems.

**Addition Definition**

Generally, addition is defined as combining two or more groups of objects into a single group. Mathematically, addition can be defined as an arithmetic operation in which the sum or total of two or more numbers is determined.

The addition symbol is a plus (+) and is inserted between numbers being added. Performing addition is one of the simplest numerical tasks. Addition is an important skill in all aspects of life including: at home, school and work.

Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or *sum* of those values combined.

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## Parts of Addition

There are 3 parts of addition, the addend, the equal sign, and the sum.

**The Addend**

In addition, the addends or the summands are numbers or terms being added together. For example, 10 + 6 = 16, 10 and 6 are the addends of this equation.

**The Equal Sign**

The equal sign indicates that the two halves of the equation are equivalent. For example, in the addition sentence, 10 + 6 = 16, the is equal is denoted with two short horizontal strokes.

**The Sum**

The sum in addition sentence is the totals of the addends. For example, in 10 + 6 = 16, the sum is 16.

## How addition works

The addition is taking two or more numbers and adding them together, that is, it is the total sum of 2 or more numbers. We clarify these two examples –

#### Example One:

#### Example Two:

## Place Value review

We are introduced to the concept of using “*place value review*” (the *value* of where the digit is in the number, based on the location of the digit) in order to add and subtract numbers. At this age, she will likely become stronger at taking numbers apart and putting them back together.

#### Example:

## Number line Addition

To add a positive number means that we move the point to the right of the number line. Similarly, to add a negative number implies that we move the point to the left of the number line.

#### Example:

## Column addition

What is Column Addition? The Column Addition method is one of the most common written methods of addition taught in schools. To add numbers using the column addition method you line up the digits in their place value columns and add the digits together form left to right.

#### Example:

## Properties of Addition

**Addition is commutative**

This property states that the positions of numbers in an equation does not affect the final answer. For example, 4 + 5 is the same as 5 + 4. This property applies to addition of numbers, no matter how large the group of numbers is.

**Associative Property**

This property applies to complex equations that involve the use of brackets, braces and parenthesis to separate group of numbers. In addition, we can move the brackets around without affecting the ultimate answer. For example, (4 + 6) + 2 = 4 + (6 + 2).

**Identity Property**

The identity property states that the sum of a number with zero is equivalent to the number itself. For example, 5+ 0 = 5. The number zero is called identity number because it does affect other numbers during the addition.

When a student is adding large groups of numbers, remind them that the number zero does not affect other numbers in the equation.

**Inverse Operations**

The inverse operation implies that the addition and subtraction are opposites. For instance, two plus three minus three is equal to two. Adding and subtracting same numbers is similar to cancelling out the numbers.

For this reason, you should look for numbers that cancels out when performing addition and subtraction on large groups of numbers.