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.

- Express the division of the rational numbers in fraction form.
- Keep the rational number in numerator position as it is but multiply it by the reciprocal of the rational number in the denominator.
- 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.

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