Multiplication of Rational numbers

A mathematical operation of multiplying two or more rational numbers is called the multiplication of rational numbers.

Introduction

The two or more rational numbers are expressed in some cases by displaying a multiplication sign between every two rational numbers. It is impossible to multiply a rational number by another rational number directly but there is a procedure to find the multiplication of two or more rational numbers.

Steps

The multiplication of the rational numbers can be calculated in two simple steps.

Multiply the numerators and write the product of them as the numerator.
Multiply the denominators and write the product of them as the denominator.

Example

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

Step – 1

$3$ and $2$ are numerators. Express the multiplication of the numerators by displaying a multiplication sign between them. Now, write it in numerator.

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

Step – 2

$7$ and $5$ are the denominators. So, express the multiplication of both denominators by displaying a multiplication sign between them but write it as denominator.

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

Step – 3

Now, find the product of the expression in the numerator and also the product of the expression in the denominator for evaluating the multiplication of the rational numbers.

$= \,\,\,$ $\dfrac{6}{35}$

$\therefore \,\,\,$ $\dfrac{3}{7} \times \dfrac{2}{5}$ $\,=\,$ $\dfrac{6}{35}$

Thus, the rational numbers are multiplied in the mathematics.