Division of Literals

A mathematical approach of dividing a literal number by another for calculating their quotient is called the division of literals.

Introduction

In arithmetic mathematics, you have studied how to divide any number by another number. Now, you are going to learn how to divide any literal by another literal number. In algebra, there are two cases for dividing them. So, let’s learn both the cases from some understandable examples in order to find their quotients.

Dividing the same literals

Let us learn how to divide a literal by the same literal firstly.

$a \div a$

$a$ is a literal number and divide it by the same literal. In this case, there are two $a$ symbols. In fact, the value of $a$ is unknown but their quotient is equal to one due to the equal quantities of the literals.

$\implies$ $a \div a = \dfrac{a}{a}$

$\implies$ $a \div a = \require{cancel} \dfrac{\cancel{a}}{\cancel{a}}$

$\,\,\, \therefore \,\,\,\,\,\,$ $a \div a = 1$

Examples

$(1) \,\,\,\,\,$ $d \div d \,=\, \dfrac{d}{d} \,=\, 1$

$(1) \,\,\,\,\,$ $f \div f \,=\, \dfrac{f}{f} \,=\, 1$

$(1) \,\,\,\,\,$ $z \div z \,=\, \dfrac{z}{z} \,=\, 1$

Dividing the different literals

Let’s learn how to divide two different literal numbers.

$a \div b$

$a$ and $b$ are two different literal numbers, but their values are unknown. So, it is impossible to evaluate their quotient. Therefore, the quotient of them is simply written as an expression in algebraic mathematics.

$\implies$ $a \div b$ $\,=\,$ $\dfrac{a}{b}$

Examples

$(1) \,\,\,\,\,$ $c \div d \,=\, \dfrac{c}{d}$

$(2) \,\,\,\,\,$ $j \div k \,=\, \dfrac{j}{k}$

$(3) \,\,\,\,\,$ $x \div y \,=\, \dfrac{x}{y}$

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