Math Doubts

Division of Rational numbers

A mathematical operation of dividing a rational number by another rational numbers is called the division of rational numbers.


A division sign is often displayed between two rational numbers and it expresses that the first rational number has to divide by the second rational number. In fact, a rational number cannot be divided directly by another one due to their complex expression. Hence, we have to use a special procedure to find the quotient of them mathematically.


There are three basic steps to find the quotient of any two rational numbers.

  1. Express the division of the rational numbers in fraction form.
  2. Keep the rational number in numerator position as it is but multiply it by the reciprocal of the rational number in the denominator.
  3. Multiply the rational numbers, then find the product of them and it is equal to the quotient of the division of the given rational numbers.


Simplify $\dfrac{3}{5} \div \dfrac{2}{7}$

Step – 1

Write the division of the rational numbers $\dfrac{3}{5}$ and $\dfrac{2}{7}$ in fraction form.

$= \,\,\,$ $\dfrac{\dfrac{3}{5}}{\dfrac{2}{7}}$

Step – 2

Write the division of the rational numbers in multiplication form as per the property of reciprocal or multiplicative inverse.

$= \,\,\,$ $\dfrac{\dfrac{3}{5} \times 1}{\dfrac{2}{7}}$

$= \,\,\,$ $\dfrac{3}{5} \times \dfrac{1}{\dfrac{2}{7}}$

$= \,\,\,$ $\dfrac{3}{5} \times \dfrac{7}{2}$

Step – 3

Now, find the product of the rational numbers by the multiplication of rational numbers.

$= \,\,\,$ $\dfrac{3 \times 7}{5 \times 2}$

$= \,\,\,$ $\dfrac{21}{10}$

$\therefore \,\,\,$ $\dfrac{3}{5} \div \dfrac{2}{7}$ $\,=\,$ $\dfrac{21}{10}$

In this way, one rational number is divided by another rational number mathematically.

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved