Math Doubts

Division of Unlike Algebraic Terms

A mathematical operation of dividing an algebraic term by its unlike term is called the division of unlike algebraic terms.


The unlike algebraic terms have different literal factors. So, the quotient of division of two unlike algebraic terms is also an algebraic term.

The quotient rules of exponents are used when the unlike algebraic terms contain one or more literals commonly.


$6xy$ and $3x^2$ are two unlike algebraic terms.


Divide an algebraic term by another

Take, the algebraic term $6xy$ is divided by the algebraic term $3x^2$. The division of them is written in mathematical form as follows.


The literal factor of the term $6xy$ is $xy$ and the literal factor of $3x^2$ is $x^2$. The literal factors of both terms are different but $x$ is a common factor in both terms.


Get Quotient of them

It can be written in product form to understand the division easily.

$\implies \dfrac{6xy}{3x^2} \,=\, \dfrac{6 \times x \times y}{3 \times x^2}$

$\implies \dfrac{6xy}{3x^2} \,=\, \dfrac{6}{3} \times \dfrac{x}{x^2} \times y$

$\implies \dfrac{6xy}{3x^2} \,=\, \require{cancel} \dfrac{\cancel{6}}{\cancel{3}} \times \dfrac{\cancel{x}}{\cancel{x^2}} \times y$

$\implies \dfrac{6xy}{3x^2} \,=\, 2 \times \dfrac{1}{x} \times y$

$\therefore \,\,\,\,\,\, \dfrac{6xy}{3x^2} \,=\, \dfrac{2y}{x} \,\,$ (or) $\,\, 2x^{-1}y$

The example has proved that the division of two unlike algebraic terms is an algebraic term.

More Examples

Look at the following examples to learn how to divide an algebraic term by its unlike term.

$(1) \,\,\,\,\,\,$ $\dfrac{-b}{2a}$ $\,=\,$ $-\dfrac{1}{2}a^{-1}b$

$(2) \,\,\,\,\,\,$ $\dfrac{5cd^2}{cd}$ $\,=\,$ $\require{cancel} \dfrac{5 \times \cancel{c} \times \cancel{d^2}}{\cancel{c} \times \cancel{d}}$ $\,=\, 5d$

$(3) \,\,\,\,\,\,$ $\dfrac{14e}{7f^2}$ $\,=\,$ $\require{cancel} \dfrac{\cancel{14}}{\cancel{7}} \times \dfrac{e}{f^2}$ $\,=\,$ $2ef^{-2}$

$(4) \,\,\,\,\,\,$ $\dfrac{0.5gh}{5g}$ $\,=\,$ $\require{cancel} \dfrac{\cancel{0.5}}{\cancel{5}} \times \dfrac{\cancel{g}}{\cancel{g}} \times h$ $\,=\,$ $0.1h$

$(5) \,\,\,\,\,\,$ $\dfrac{ij^4}{k}$ $\,=\,$ $ij^4k^{-1}$

Follow us
Email subscription
Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Mobile App for Android users Math Doubts Android App
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more