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# The multiplicative inverse of $- 1 \times \dfrac{{ - 2}}{5}$ is $\dfrac{p}{2}$. Then the value of $p$ is

Last updated date: 14th Jun 2024
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Hint: We have to find the multiplicative inverse of $- 1 \times \dfrac{{ - 2}}{5}$. Multiplicative inverse of a number is obtained when $1$ is divided by the given number that is, the multiplicative inverse of a number $x$ is $\dfrac{1}{x}$. After getting the value of the inverse of the given number, we have to equate the result with the $\dfrac{p}{2}$. Then solving the equation we will get the required value of $p$.

Complete step-by-step solution:
It is given that the multiplicative inverse of $- 1 \times \dfrac{{ - 2}}{5}$ is $\dfrac{p}{2}$. And we have to find the value of $p$.
First of all, find the multiplicative inverse of the given number $- 1 \times \dfrac{{ - 2}}{5}$.
As multiplication of two negative numbers gives the positive number so, $- 1 \times \dfrac{{ - 2}}{5}$ can be written as $\dfrac{2}{5}$.
Now, to get the multiplicative inverse of $\dfrac{2}{5}$, divide $1$ by $\dfrac{2}{5}$. That is
$= 1 \div \dfrac{2}{5} \\ = 1 \times \dfrac{5}{2} \\ = \dfrac{5}{2}$
So, we get the multiplicative inverse of $- 1 \times \dfrac{{ - 2}}{5}$ is $\dfrac{5}{2}$.
Now, to find the value of $p$equate the obtained multiplicative inverse to the $\dfrac{p}{2}$ because it is given that $\dfrac{p}{2}$ is the multiplicative inverse of given number$- 1 \times \dfrac{{ - 2}}{5}$.
$\Rightarrow \dfrac{5}{2} = \dfrac{p}{2} \\$
Solving this by cross multiplication, we get
$\Rightarrow p \times 2 = 5 \times 2 \\ \Rightarrow p = \dfrac{{5 \times 2}}{2} \\ \therefore p = 5$

Thus, the required value of $p$ is $5$.

Note: The multiplicative inverse of the number is a particular number which when multiplied with the given number we get one as a result. That is, if the multiplicative inverse of the number $x$ is a number $y$ then $xy = 1$.
Similarly, we can find the additive inverse of a number which is obtained by subtracting the given number from zero.
Additive inverse of a number is a particular number which when added with the given number we get zero as a resultant. That is, if the additive inverse of a number $x$is a number $y$then $x + y = 0$.
Simply, we can say the additive inverse of $x$ is $- x$.