Math Doubts

Literals addition

Definition

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

What is the Addition of Literals?

A literal can be added to another literal number to find their sum, and this is one of the basic operations in algebra. The process involves combining one literal with another in a systematic way. This mathematical procedure is known as the addition of literals.

There are two distinct cases in the addition of literals, as explained below.

  1. Addition of Literals in the Same Form
  2. Addition of Literals in Different Forms

Quantities are expressed as numbers in elementary mathematics, but in algebra, they are represented by literals. You have already learned how to add numbers in arithmetic, and now it’s time to learn how to add one literal to another in algebra.

As a beginner, let’s learn each method of adding literals with easy-to-understand examples.

Case1

How to add Literals in the Same Form

Let’s first understand the addition of numbers in the same form using a numerical example.

Example

Evaluate $3+3$

$\implies$ $3+3$ $\,=\,$ $6$

In this case, the number $3$ appears twice, so it can be written as $2$ times that number.

$\implies$ $3+3$ $\,=\,$ $2 \times 3$

$\implies$ $3+3$ $\,=\,$ $6$

The above arithmetic example shows that adding a number to itself multiple times equals multiplying it by that number of times. The same arithmetic property can be applied when adding a literal to itself, as shown in the example below.

Example

Evaluate $a+a$

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

$\implies$ $a+a$ $\,=\,$ $2a$

The examples below show how to find the sum of literals in the same form.

  1. $x+x+x$ $\,=\,$ $3x$
  2. $y+y+y+y$ $\,=\,$ $4y$
  3. $z+z+z+z+z$ $\,=\,$ $5z$
Case2

How to add Literals in Different Forms

Now, let’s learn the addition of different numbers through a numerical example.

Example

Evaluate $3+4$

$\implies$ $3+4$ $\,=\,$ $7$

The numbers are different in this case, but their sum can be calculated because their values are known.

Example

Evaluate $a+b$

The literal numbers are different and their values are unknown. Therefore, their sum cannot be calculated and is simply written as an expression.

The examples below show how to find the sum of literals in different forms.

  1. $x+y+z$
  2. $a+b+c+d$

The two cases above and their examples show how to add one literal to another. You can now easily find the sum of any two literals.