# Multiplicative Inverse

If the product of two numbers is 1, then each number is known as multiplicative inverse or the reciprocal of one another.

The following are the rules of multiplicative inverse of a fractional number:

(a) To find the multiplicative inverse of a proper or improper fraction, interchange the numerator and denominator.

(b) To find the reciprocal of a mixed fraction or whole number, first change it into an improper fraction, then interchange the numerator and denominator.

Multiplicative inverse is also known as reciprocal.

The important facts of multiplicative inverse of a fractional number are:

(i) The reciprocal of a proper fraction is an improper fraction.

For Example:

1. Reciprocal of $$\frac{5}{18}$$ is $$\frac{18}{5}$$.

2. Reciprocal of $$\frac{3}{13}$$ is $$\frac{13}{3}$$.

3. Reciprocal of $$\frac{19}{26}$$ is $$\frac{26}{19}$$.

4. Reciprocal of $$\frac{37}{48}$$ is $$\frac{48}{37}$$.

5. Reciprocal of $$\frac{9}{11}$$ is $$\frac{11}{9}$$.

(ii) The reciprocal of an improper fraction is a proper fraction.

For Example:

1. Reciprocal of $$\frac{15}{4}$$ is $$\frac{4}{15}$$.

2. Reciprocal of $$\frac{23}{3}$$ is $$\frac{3}{23}$$.

3. Reciprocal of $$\frac{49}{6}$$ is $$\frac{6}{49}$$.

4. Reciprocal of $$\frac{37}{18}$$ is $$\frac{18}{37}$$.

5. Reciprocal of $$\frac{27}{11}$$ is $$\frac{11}{27}$$.

(iii) The reciprocal of a whole number (except 0) will always have a numerator 1.

(i.e., it will be a unit fraction)

For Example:

1. Reciprocal of 90 is $$\frac{1}{90}$$.

2. Reciprocal of 25 is $$\frac{1}{25}$$.

3. Reciprocal of 42 is $$\frac{1}{42}$$.

4. Reciprocal of 17 is $$\frac{1}{17}$$.

5. Reciprocal of 75 is $$\frac{1}{75}$$.

(iv) The multiplicative inverse of 1 is 1.

(v) The multiplicative inverse of 0 cannot be found.