Math Doubts

Addition of Literals

Definition

The process of adding a literal to another literal number to find their sum is called the addition of literals.

What is the Addition of Literals?

A literal number can be connected to another literal mathematically by a plus sign. It is a basic math operation and mainly used to find the summation of the literals in algebra. There is a mathematical procedure to find the sum of two or more literal numbers and it is called the addition of literals.

As a beginner, you must firstly know how to add the literals. In algebra, there are two different cases in adding the literals numbers. So, let’s understand each case for adding the literal numbers from simple examples.

Case1

How to add Like literals

Let’s denote a quantity by a literal number $x$. Now, add the literal $x$ to same literal number by a plus sign.

$x+x$

The literals are in same form and we need to find their sum mathematically. Each literal number is written once in each term of the expression. So, every literal can be written as one time $x$.

$\implies$ $x+x$ $\,=\,$ $1 \times x$ $+$ $1 \times x$

Now, $x$ is a common factor in each term. So, the common factor can be taken out from the terms for simplifying the expression further on the right-hand side of the equation.

$\implies$ $x+x$ $\,=\,$ $(1+1) \times x$

$\implies$ $x+x$ $\,=\,$ $(2) \times x$

$\implies$ $x+x$ $\,=\,$ $2 \times x$

$\,\,\,\therefore\,\,\,\,\,\,$ $x+x$ $\,=\,$ $2x$

Therefore, it is proved that the sum of the literals in same form is equal to the number of times the literal number is added. Now, you can add the like literals by following this principle in algebra.

Examples
  1. $a+a+a$ $\,=\,$ $3a$
  2. $b+b+b+b$ $\,=\,$ $4b$
  3. $c+c+c+c+c$ $\,=\,$ $5c$
Case2

How to add Unlike literals

Let’s represent a quantity by a literal $x$ and add it to another literal number $y$ by a plus symbol to find their sum.

$x+y$

The values of both literals $x$ and $y$ are unknown, and they are not in same form. So, it is not possible to combine them mathematically but the sum of them is only written as an expression in algebra.

Examples
  1. $a+b+c$
  2. $p+q+r+s$
  3. $k+l+m+n+o$

The above two cases explain you the basic mathematical operation with literals to know how to add the literal numbers of same kind and different. According to above two cases, you can now add two or more literal numbers to find their summation in algebra.