Concept of Reciprocal or Multiplicative Inverse

Reciprocal of a fraction: The non-zero numbers whose product with each other is 1, are called the reciprocals of each other.

Reciprocal of a fraction:

The number ${\displaystyle \frac{2}{1}}$ can be obtained by interchanging the numerator and denominator of ${\displaystyle \frac{1}{2} \text{or by inverting} \frac{1}{2}}$.

A reciprocal of a fraction is obtained by inverting it upside down.

The reciprocal of ${\displaystyle \frac{9}{5}\text{is}\frac{5}{9}}$.

The non-zero numbers whose product with each other is 1, are called the reciprocals of each other.

${\displaystyle \frac{2}{3}\times \frac{3}{2}=\frac{2\times 3}{3\times 2}=\frac{6}{6}=1}$.

Reciprocal Or Multiplicative Inverse of Rational Numbers:

${\displaystyle \frac{-5}{7}\text{must be multiplied by}\frac{7}{-5}}$ so as to get the product 1.

${\displaystyle \frac{7}{-5}\text{is the reciprocal of}\frac{-5}{7}}$.

${\displaystyle \frac{7}{-5}\times -\frac{5}{7}=1}$.

The reciprocal or multiplicative inverse of  another non-zero rational number ${\displaystyle \frac{a}{b}}$ if ${\displaystyle \frac{a}{b}\times \frac{c}{d}=1}$.