Addition

The word “Addition” means the grouping of two or more things together. When coming to numbers, we have the first operation as counting. Counting two or more groups of things together is nothing but the “addition operation”. Thus, addition is an arithmetic operation. If we consider the different groups as different numbers, to make them together, we need to do the sum of those numbers. Here the word “sum” represents the addition operation. So, we can say the meaning of addition is “the sum of two or more numbers together”. The addition operation is represented by a plus (+) sign. The words, sum, plus, making together are synonyms of the word “addition”. This is the basic operation in mathematics, which is essential in every topic. For example, the addition of 4 and 5 is represented by “4+5” and it is read as “four plus five”. The result of this addition is 9. I.e., after 4 we need to count 5 more numbers. So, we get the resulting number as 9. There are different methods for dealing with additions in mathematics and different concepts based on the process of addition.

Meaning of addition

The meaning of addition is “making together”. Consider three boxes filled with three different colours of balls. First, we need to count the total number of balls according to their colour. Then, counting all together gives the total count of the balls irrespective of their colour. So, to know the “total”, we use the operation called “addition” or “sum”. The addition operation is denoted by the plus (+) symbol. The same procedure is applied to the numeral too. So, the digits or the numbers before and after the “plus” symbol is known as “addend” and the result is represented after an equal (=) symbol. That result is said to be the “sum”.

I.e., addend (1) + addend (2) = Sum

Process Of Addition On The Number Line

Here the addition operation is explained by the number line. A number line is the pictorial representation of numbers on a line. The addition of two numbers is calculated by different methods. One of the easiest methods for class 1, class 2, and the other primary classes is to perform addition operations between two numbers or more than two numbers.

Here,

• The addition of four and five is explained by the number line

• The number line has numbers from zero to 15. Even we can increase more as per the requirement.

• The number 4 is represented by pointing a dot at its place.

• Now, we need to add 5 to the 4. So, after 4 we need to count 5 more places to the right.

• Thus, we get the number 9. That means the sum of 4 and 5 is 9.

• In such a way, the addition is calculated between any two numbers or more than two numbers.

Horizontal Addition

• This is also one of the methods of addition operation.

• For understanding the basic concepts for class 1, 2, 3, and 4 students, this is the best way of teaching addition operations for smaller numbers (with a smaller number of digits).

• Here the Horizontal addition means, the appends are written Horizontally i.e., writing them one after the other by a plus sign separating them and an equal sign after them with the result in a single line.

• This is the general representation of the addition operation.

• Example: \[4+5=9\]

Vertical Addition

• This is the contrast method of horizontal addition.

• This is also used for the students in pre-primary and primary classes to make them understand the addition process for bigger numbers (with a greater number of digits).

• Here, in the vertical addition operation, the appends are written one below the other and are framed in a structural format. So, that one can add the appends easily by counting.

• This is also mostly used representation and this method provides a way for the concepts like “addition with carry and without carry”.

• Example:

\begin{array}{r}

4 \\

+\quad 5 \\

\hline 9

\end{array}

Addition Without Carry

The appends when added, if the result is less than or equal to 9, then they do not produce any carry which is to be forwarded to its predecessor append. Here the vertical addition method clearly explains this concept. Here the carry is nothing but the digit in the tens place of the sum obtained by two appends.

Example:

\begin{array}{r}

42 \\

+\quad 53 \\

\hline 95

\end{array}

Addition With Carry

The appends when added, if the result is more than 9, i.e., tens (10, 11, 12, …), then they produce a carry which is to be forwarded to its predecessor append. Here also the vertical addition method clearly explains this concept. This will happen mostly for the bigger numbers.

Example:

Different Properties Based On Addition

• There are different properties established by the basic addition operation

• Such as commutative, associative, additive identity, etc.

• The commutative property is shown as \[4+5=5+4=9\].

• The associative property is shown as \[4+\left( 2+3 \right)=\left( 4+2 \right)+3=9\].

• The additive identity property is shown as \[0+9=9+0=9\].

Applications Of Additions

The addition operation is not only permitted for numerals or numbers. But also applied to all the other numbers such as decimals, fractions, and algebraic expressions. The addition operation is also framed in words that are called word problems. One must and should learn addition operations to understand the entire mathematics.