Question

How do you find the additive and multiplicative inverse of $ - 0.125$?

Answer 1

Hint: In order to determine the additive and multiplicative inverse of the given number , assume $a = - 0.125$. Now by assuming that $b$ as additive inverse, calculate it using the expression $a + b = b + a = 0$ and similarly by assuming $b$ as multiplicative inverse of $a$, obtain the value of $b$ using expression $a \times b = 1$.

Complete step by step answer:
We are given a decimal number $ - 0.125$
To find the additive and multiplicative inverse, first let us understand what are actually additive and multiplicative inverse for any value.
So, Additive number of a number is a number which when added to the original number, the result is always equal to zero. In other words if numbers $a\,and\,b$ are additive inverse of each other , then their sum $a + b = b + a = 0$
Let $a = - 0.125$and $b$is its additive inverse, so
\[
   \Rightarrow a + b = 0 \\
   \Rightarrow - 0.125 + b = 0 \\
 \]
Transposing the terms such that we get only variable $b$ on the left-hand side of the equation and other terms on RHS, by using the concept of transposition of terms. In our expression $ - 0.125$ will become $0.125$ in the RHS.
\[ \Rightarrow b = 0.125\]
Hence, we got $b = 0.125$ as the additive inverse of number $ - 0.125$
Now,
Multiplicative inverse of a number is a number which when multiplied to the original number, the result is equal to 1. In other words if numbers $a\,and\,b$ are multiplicative inverse of each other , then their multiplication $a \times b = 1$
Let $a = - 0.125$and $b$ is its multiplicative inverse, so
$
   \Rightarrow a \times b = 1 \\
   \Rightarrow \left( { - 0.125} \right) \times b = 1 \\
 $
Dividing both sides of the equation with the value $\left( { - 0.125} \right)$, we get
\[ \Rightarrow \dfrac{{\left( { - 0.125} \right) \times b}}{{\left( { - 0.125} \right)}} = \dfrac{1}{{\left( { - 0.125} \right)}}\]
Simplifying it further we get
\[ \Rightarrow b = \dfrac{1}{{ - 0.125}}\]
hence, we got \[b = \dfrac{1}{{ - 0.125}}\]as the multiplicative inverse of number $ - 0.125$
Therefore, the additive and multiplicative inverse of the number $ - 0.125$ is equal to $0.125$\[\dfrac{1}{{ - 0.125}}\] respectively.

Note: 1. Remember, the additive and multiplicative inverse of zero does not exist.
2.multiplcative inverse is nothing but the reciprocal of the number.
3. Shortest way to calculate additive inverse is to simply reverse the sign of the number .