Answer
397.2k+ views
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$.
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$.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)