Question

How do you find the additive and multiplicative inverse of $-11$?

Answer 1

Hint: We will use the concept that if the sum of two numbers is equal to zero then these numbers are called additive inverse. If a product of two numbers is 1 then these numbers are called multiplicative inverse. We will use these concepts to find the additive and multiplicative inverse of $-11$.

Complete step by step answer:
We have to find the additive and multiplicative inverse of $-11$.
We know that two numbers are called additive inverses when their sum is equal to 0.
So, let us assume that the additive inverse of $-11$ is $a$. Then we will get
$\Rightarrow -11+a=0$
On simplifying the above obtained equation we will get
$\Rightarrow a=11$
Hence the additive inverse of $-11$ is $11$.
Now, we know that two numbers are called multiplicative inverses when their product is equal to 1.
So, let us assume that the multiplicative inverse of $-11$ is $b$. Then we will get
$\Rightarrow -11\times b=1$
On simplifying the above obtained equation we will get
\[\Rightarrow b=-\dfrac{1}{11}\]

So the multiplicative inverse of $-11$ is \[-\dfrac{1}{11}\].

Note: In additive inverse the sum of two integers is equal to zero, so the zero is known as the additive identity. Similarly when the product of two numbers is equal to one then the numbers are multiplicative inverses and 1 is known as the multiplicative identity. The multiplicative inverse of a number is also called the reciprocal of that number.