Addition of Literals

A method of adding two or more literal numbers for calculating their sum is called the addition of literals. It is called as the summation of the literals.

Introduction

You have studied earlier how to calculate addition of the numbers in arithmetic and now, you are about to learn how to add two or more literals. There are two cases involved in adding the two or more literals. So, let’s discuss both cases to understand the procedure for the addition of the literals.

Adding same literals

Let’s learn how to add two or more same literal numbers.

$a+a$

$a$ is a literal and add it to same literal number once. There are two $a$ symbols in this case. Hence, the sum of two $a$ symbols can be written as $2a$ mathematically.

$\implies a+a = 2a$

It can also be proved from arithmetic.

$a+a$ $\,=\,$ $1 \times a + 1 \times a$

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

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

$\,\,\, \therefore \,\,\,\,\,\,$ $a+a$ $\,=\,$ $2a$

Examples

$(1) \,\,\,\,\,$ $b+b+b$ $\,=\,$ $3b$

$(2) \,\,\,\,\,$ $g+g+g+g$ $\,=\,$ $4g$

$(3) \,\,\,\,\,$ $x+x+x+x+x$ $\,=\,$ $5x$

Adding different literals

Let’s learn how to add two or more different literal numbers.

$a+b$

$a$ and $b$ are two different literals, and their values are unknown. So, it is not possible to get their sum. Hence, the summation of them is simply expressed as an expression in algebra.

Examples

$(1) \,\,\,\,\,$ $x+y+z$

$(2) \,\,\,\,\,$ $p+q+r+s$

$(3) \,\,\,\,\,$ $d+e+f+g+h$

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