What is Additive inverse and Multiplicative inverse?


Additive inverse:

The additive inverse of a number is the number that, when added to the original number gives zero.

For example,

Find the additive inverse of $-10$.

Let $x$ be the additive inverseIf $x$ is the additive inverse of $-10$ then the following equation must be true:

$x + (-10) = 0$

Add $10$ to both sides

$x + (-10) +10 = 10$

$x = 10$

So, $10$ is the additive inverse of $-10$.

Multiplicative inverse:

The multiplicative inverse is nothing but the number which makes the existing number and makes it equal to unity.

Multiplicative inverse of a is $\frac{1}{a}$.

For example,

The multiplicative inverse of $\frac{-3}{6}=\frac{1}{\frac{-3}{6}}$ 

$=\frac{6}{-3}$ $=\frac{-6}{3}$ $=-2$.

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Updated on: 10-Oct-2022

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