Question

What is the multiplicative inverse of $ \dfrac{{ - 2}}{3} $ ?

Answer 1

Hint: We have to find the multiplicative inverse of the given number. The multiplicative inverse of a number in mathematical terms can be said to be the number which when multiplied by a given number yields the number $ 1 $ . This is unlike the additive inverse where we add something to a number to make it equal to $ 0 $ . The multiplicative inverse of a number can be obtained by changing its numerator to the denominator and its denominator to the numerator.
So the multiplicative inverse of number $ \dfrac{a}{b} $ would be ,
 $ \to \dfrac{b}{a} $

Complete step-by-step answer:
We have to find the multiplicative inverse of $ \dfrac{{ - 2}}{3} $
The numerator of the number is given as $ - 2 $ , while the denominator of the number is given as,
 $ 3 $ . We will interchange the numerator and denominator to get the value of the multiplicative inverse of a number.
So the number $ \dfrac{{ - 2}}{3} $ transforms as :
 $ \dfrac{{ - 2}}{3} \to \dfrac{3}{{ - 2}} $
This fraction however has a negative number in its denominator so we will multiply both the numerator and denominator by $ - 1 $ , doing we get,
 $ \Rightarrow \dfrac{3}{{ - 2}} = \dfrac{{3 \times - 1}}{{ - 2 \times - 1}} $
Which yields,
 $ \dfrac{{ - 3}}{2} $ which is the desired answer.
So, the correct answer is “ $ \dfrac{{ - 3}}{2} $ ”.

Note: The above result can be very easily verified by multiplying the multiplicative inverse of the number calculated and the original number given in the question. If the multiplication of these two numbers yields the number $ 1 $ , we can say that the answer is correct. So multiplying the original number $ \dfrac{{ - 2}}{3} $ with the calculated multiplicative inverse we proceed as follows,
 $ \Rightarrow \dfrac{{ - 2}}{3} \times \dfrac{{ - 3}}{2} $
 $ \Rightarrow - 1 \times - 1 $
 $ \Rightarrow 1 $
Hence we can say that the number we calculated was correct.