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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 inverse. If $x$ 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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