Question

What is the multiplicative inverse of the $-\left( -\dfrac{4}{7} \right)$?

Answer 1

Hint: In this problem we need to calculate the multiplicative inverse of the given number. We know that the multiplicative inverse of a number is nothing but a number whose product is equal to $1$. So, we will first consider the given number and simplify it by removing the parenthesis. After that we will assume the multiplicative inverse of the number as $x$. By the rule of multiplicative inverse, we will equate the product of both the numbers to $1$ and simplify the equation by using the basic mathematical operation to calculate the value of $x$ which is our required result.

Complete step by step answer:
Given number is $-\left( -\dfrac{4}{7} \right)$.
When we multiply a negative sign with the negative sign, we will get the positive sign, so we can write the given number as
$-\left( -\dfrac{4}{7} \right)=\dfrac{4}{7}$
Now considering the number $\dfrac{4}{7}$.
Let us assume the multiplicative inverse of the above number is $x$.
We know that the product of a number with its multiplicative inverse will be equal to $1$. Then we can write
$\dfrac{4}{7}\times x=1$
Multiplying the above equation with $7$ on both sides of the above equation, then we will have
$\begin{align}
  & 7\times \dfrac{4}{7}\times x=7\times 1 \\
 & \Rightarrow 4\times x=7 \\
\end{align}$
Dividing the above equation with $4$ on both sides of the above equation, then we will get
$\begin{align}
  & \dfrac{4\times x}{4}=\dfrac{7}{4} \\
 & \Rightarrow x=\dfrac{7}{4} \\
\end{align}$

Hence the multiplicative inverse of the given number $-\left( -\dfrac{4}{7} \right)$ is $\dfrac{7}{4}$.

Note: In this problem they have only asked to calculate the multiplicative inverse. Apart from this we also have the additive inverse of the number with which the number is added we will get zero as result. So, when they have asked to calculate the additive inverse then we will equate the sum of the number to zero and simplify the equation to get the solution.