Question

Is $\dfrac{4}{5}$ the multiplicative inverse of $ - 1\dfrac{1}{4}$? Why or why not?

Answer 1

Hint: Here, we have to find that $\dfrac{4}{5}$ is the multiplicative inverse of $ - 1\dfrac{1}{4}$ or not. Multiplicative inverse of a number can be defined as a number which when multiplied with the original number equals to $1$ and it can also be termed as the reciprocal of a number. In order to solve this question we first convert $ - 1\dfrac{1}{4}$ into a proper fraction and after that we will find its multiplicative inverse.

Complete step by step answer:
The multiplicative inverse of a number is a number which when multiplied with the original number equals to $1$ and here the original number can never be equal to $0$. We can represent the multiplicative inverse of a number $X$ by ${X^{ - 1}}$ or $\dfrac{1}{X}$.The multiplicative inverse of a fraction number can be obtained by flipping its numerator and denominator. So, the multiplicative inverse of the fraction $\dfrac{x}{y}$ is $\dfrac{y}{x}$ and the multiplicative inverse of a negative number $ - Y$ is $ - {Y^{ - 1}}$ or $ - \dfrac{1}{Y}$.

Now, we will find the multiplicative inverse of $ - 1\dfrac{1}{4}$.Firstly, convert the mixed fraction into proper fraction. So,
$ \Rightarrow - 1\dfrac{1}{4} = - \dfrac{5}{4}$
Now, we will find the multiplicative inverse of $ - \dfrac{5}{4}$.We can find the multiplicative inverse of $ - \dfrac{5}{4}$ by flipping its numerator and denominator. So, the multiplicative inverse of $ - \dfrac{5}{4}$ is $ - \dfrac{4}{5}$.Therefore, $\dfrac{4}{5}$ is not the multiplicative inverse of $ - 1\dfrac{1}{4}$ as by definition the multiplicative inverse of a negative number also have a negative sign and in $\dfrac{4}{5}$ there is no negative sign.

Hence, $\dfrac{4}{5}$ is not the multiplicative inverse of $ - 1\dfrac{1}{4}$.

Note: In multiplicative inverse we do not change the sign of a number we only flip the numerator and denominator of fraction it is the additive inverse where we change the sign of a number. The multiplicative inverse property of a number states that when a number $N$is multiplied with its multiplicative inverse gives the result as one. Note that the multiplicative inverse of $0$ does not exist as when we divide some number by $0$ the result is not defined.