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.
Simplify $\dfrac{3}{5} \div \dfrac{2}{7}$
Write the division of the rational numbers $\dfrac{3}{5}$ and $\dfrac{2}{7}$ in fraction form.
$= \,\,\,$ $\dfrac{\dfrac{3}{5}}{\dfrac{2}{7}}$
Write the division of the rational numbers in multiplication form as per the property of reciprocal or multiplicative inverse.
$= \,\,\,$ $\dfrac{\dfrac{3}{5} \times 1}{\dfrac{2}{7}}$
$= \,\,\,$ $\dfrac{3}{5} \times \dfrac{1}{\dfrac{2}{7}}$
$= \,\,\,$ $\dfrac{3}{5} \times \dfrac{7}{2}$
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.
A best free mathematics education website for students, teachers and researchers.
Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.
Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.
Copyright © 2012 - 2022 Math Doubts, All Rights Reserved