Addition

Addition (usually denoted by the plus symbol +) is one of the four basic arithmetic operations. When 2 whole numbers are added, the total value or sum of those values is obtained. The example is that a total of five apples are made up of three apples and two apples. The mathematical equation “3 + 2 = 5” is identical to this observation (that is, “3 plus 2 is equal to 5”).

The term “addition” means the process of putting things together or together. When we add two numbers together or together, we are counting them as one larger number. In actual life, addition occurs frequently.

History of addition: –

One of the earliest and most fundamental arithmetic operations is addition. Mathematicians have known about it for about 6000 years. ‘Counting’ was sometimes thought to be an early form of addition.

In the year 2000 B.C., Egyptians and Babylonians used addition for the first time. The addition and subtraction symbols were established in the 16th century, but before that, equations were expressed in words, which made solving problems extremely time-consuming.

Components of addition: –

The addend, the equal sign, and the sum are the three parts of addition.

• The Addend

Furthermore, addends or summands are numbers or phrases that are added together. The addends of the equation 10 + 6 = 16 are, for example, 10 and 6.

• The Sign of Equality

The equal sign denotes that the equation’s two parts are equivalent. The equal sign is represented by two short horizontal strokes in the addition statement 10 + 6 = 16.

• The Sum 

The totals of the addends are the sum in the addition statement. For example, the sum of 10 + 7 = 17 ;   here 17 is the sum

Notation: –

Usually, addition is written in infix notation, with the plus sign “+” between the terms. An equals symbol is used to denote the result.

Few of the examples are as follows;

1 + 1 = 2

3 + 4 = 7

11 + 9 = 20 

5 + 5 + 4 = 14

6.8 + 7.3 = 14.1

Basic properties of addition:-

• Commutative Property:

Basically we can say that addition is commutative or changing the order of addends has no effect on the sum.

Example: 4 + 3 = 3 + 4 ; Here the sum of both left hand side and right hand side is the same i.e., 7 although the order is reversed.

• Associative Property:

Just similar to commutative, addition is also associative i.e.,  changing the order in which the addends are grouped has no effect on the sum.

Example: (3 + 4) + 3 = 3 + (4 + 3) ;

              LHS =  (3 + 4) + 3 

                      = 7 + 3

                      = 10

              RHS = 3 + (4 + 3)

                      = 3 + 7

                      = 10

 Here the sum of both sides is the same i.e., equals to 10 although the groupings are different.

(N.B.- The parentheses indicate which part to solve first.)

• Identity Property:

According to the identity property of addition, the sum of 0 and any number equals that number. Here’s an illustration:

0 + 8 = 8

This is accurate since the definition of 0 is “no quantity,” so adding 0 to 8 has no effect on the quantity of 8

It should be in mind that, it doesn’t matter if the 0 appears before or after the number, according to the commutative property of addition. With the 0 after the number, here’s an example of the identity feature of addition:

8 + 0 = 8

• Additive Inverse:

A number’s opposite is its additive inverse. When you add a number to its additive inverse, the answer is 0. The basic rule is to turn a positive number into a negative number and vice versa.

For example, we know that 

                            6 + (-6) = 0

That means we can say that -6 is the additive inverse of 6 and also 6 is the additive inverse of -6 .

Conclusion: –

The process of adding two or more integers to obtain a final result is known as an addition. Commutative, distributive, associative, and additive identity are the four main features of addition. The commutative term refers to the fact that the result of addition remains the same regardless of the order of that term. The associative property states that the order in which three integers are added has no bearing on the final result. If the 2nd and 3rd numbers are multiplied and added by the 1st, the distributive property states that adding two integers and multiplying with a third number will result in constant solutions. Additive identity states that any number multiplied by 0 produces the same integer.