Multiplicative Inverse and Identity

Multiplicative inverse or (reciprocal) for a number is that number which when multiplied by the number yields the Multiplicative identity 1. Therefore, 1 is the identity for multiplication  e.g.

⇒ \( \scriptsize 5 \: \times \normalsize \frac{1}{5} \scriptsize = 1 \)

The multiplicative inverse  of  5 = \( \frac{1}{5} \)

The  multiplicative inverse of \( \frac{1}{5} \) = 5

Example 4.3.1:

Find the  reciprocal or multiplicative inverse of the following 

a. \( \frac{1}{7} \)

b. \( \: – \frac{1}{5} \)

c. 8

d. \( \frac{4}{5} \)

e. 0.2

f. \( \scriptsize \: -1 \frac{5}{7} \)

g. 2^-3

h. \( \frac{1}{10^8} \)

Solution