Math Doubts

Literals division

Definition

The process of dividing one literal by another to obtain their quotient is called the division of literals.

What is the Division of Literals?

A literal number can be divided by another literal to find their quotient, and this is one of the basic operations in algebra. The process involves dividing one literal quantity by another in a systematic way. This mathematical procedure is known as the division of literals.

There are two different cases in the division of literals, as shown below.

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

In elementary mathematics, quantities are expressed using numbers, whereas in advanced mathematics, they are represented by literals. You have already learned how to divide one number by another in arithmetic, and now it’s time to understand how to divide one literal by another in algebra.

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

Case1

How to Divide Literals in the Same Form

Let’s first understand the division of numbers in the same form through a numerical example.

Example

Evaluate $5 \div 5$

$=\,\,\,$ $\dfrac{5}{5}$

$=\,\,\,$ $\dfrac{\cancel{5}}{\cancel{5}}$

$=\,\,\,$ $1$

The above arithmetic example shows that when a number is divided by itself, the quotient is always equal to one. Similarly, when a literal is divided by itself, the quotient is also equal to one.

Example

Evaluate $x \div x$

$=\,\,\,$ $\dfrac{x}{x}$

$=\,\,\,$ $\dfrac{\cancel{x}}{\cancel{x}}$

$=\,\,\,$ $1$

Case2

How to Divide Literals in Different Forms

Now, let’s study the division of numbers in different forms using an arithmetic example.

Example

Evaluate $6 \div 2$

$=\,\,\,$ $\dfrac{6}{2}$

$=\,\,\,$ $\dfrac{\cancel{6}}{\cancel{2}}$

$=\,\,\,$ $3$

In arithmetic, the quantities are known, so a number can be easily divided by any other number. In algebra, the quantities are literals, which are unknown, so it is not possible to directly divide one literal by another. However, their quotient is written as an expression.

Example

Evaluate $x \div y$

$=\,\,\,$ $\dfrac{x}{y}$

The examples above clearly explain how to divide a literal number by another literal. You can now divide a literal number by any other literal number to get the quotient.