Question

The product of a fractional number and its multiplicative inverse is
A. 0
B. 1
C. number itself
D. none

Answer 1

Hint: Fractional numbers are those numbers which are expressed in terms of the numerator and the denominator. And multiplicative inverse can be calculated for each and every number because each number can be expressed as fractional numbers.

Complete step-by-step answer:
As we know that the fractional numbers are numbers that represent one or more parts of a unit that has been divided into equal parts. The fractional numbers are figured out by two whole numbers (the fraction terms) that are separated by a horizontal line (the fraction line).
Like $${\displaystyle \frac{p}{q}}$$ is a fractional number where p is the numerator of the number and q is the denominator of the number.
And as we know that the multiplicative inverse or reciprocal for a number x, is denoted by $${\displaystyle \frac{1}{x}}$$ or $$x^{-1}$$.
So, here we are asked to find the product of a fractional number and its multiplicative inverse.
So, the fractional number will be $${\displaystyle \frac{a}{b}}$$ (a is the numerator and b is the denominator).
So, to find the multiplicative inverse of the above assumed number we had to change the numerator of the number with the denominator and replace the denominator of the number with the numerator.
So, the multiplicative inverse of $${\displaystyle \frac{a}{b}}$$ will be $${\displaystyle \frac{b}{a}}$$.
Now the product of $${\displaystyle \frac{a}{b}}$$ and $${\displaystyle \frac{b}{a}}$$ will be equal to $${\displaystyle \frac{a}{b}}\times {\displaystyle \frac{b}{a}}=1$$
So, the product of a number and its multiplicative inverse will be equal to 1.
Hence, the correct option will be B.

Note: We should remember that the multiplicative inverse of a is a number which when multiplied by x yields the multiplicative identity 1, where x is the original number. So, the multiplicative inverse of a fraction $${\displaystyle \frac{a}{b}}$$ is $${\displaystyle \frac{b}{a}}$$. And we should understand that the Multiplicative inverses can be defined over many mathematical domains as well as numbers or in other words we can say that multiplicative inverse does not only exist for numbers it can be of any matrix also. Do not confuse with the word matrix you will come to know about matrices in higher classes.