# Reciprocal rule of Fractions or Rational numbers

## Formula

$\dfrac{1}{\Big(\dfrac{a}{b}\Big)} \,=\, \dfrac{b}{a}$

### Introduction

The reciprocal of a fraction or a rational number is equal to the quotient of the denominator divided by numerator of the fraction or rational number. It is called the reciprocal rule of rational numbers or fractions. It is also called the multiplicative inverse rule of fractions or rational numbers.

Let $a$ and $b$ be two literals and they represent two quantities in mathematical form. The quotient of $a$ divided by $b$ represents a fraction or a rational number in mathematical form.

$\dfrac{a}{b}$

The reciprocal of fraction or rational a divided by b is written in mathematics as follows.

$\dfrac{1}{\Big(\dfrac{a}{b}\Big)}$

It is equal to the quotient of b divided by a and it is called the reciprocal rule of the fractions or rational numbers.

$\therefore\,\,\,$ $\dfrac{1}{\Big(\dfrac{a}{b}\Big)} \,=\, \dfrac{b}{a}$

#### Examples

$(1).\,\,$ $\dfrac{1}{\Big(\dfrac{2}{5}\Big)}$ $\,=\,$ $\dfrac{5}{2}$ $\,=\,$ $2.5$

$(2).\,\,$ $\dfrac{1}{\Big(\dfrac{1}{10}\Big)}$ $\,=\,$ $\dfrac{10}{1}$ $\,=\,$ $10$

$(3).\,\,$ $\dfrac{1}{\Big(\dfrac{4}{6}\Big)}$ $\,=\,$ $\dfrac{6}{4}$ $\,=\,$ $1.5$

#### Proof

Learn how to prove the reciprocal rule of fractions to find the multiplicative inverse of any rational number or a fraction.

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