Question

Write additive inverse and multiplicative inverse of $ \dfrac{1}{5} $

Answer 1

Hint: For additive inverse, the sign of the term is changed keeping the value as the same. Positive term becomes negative and the negative term becomes positive. For the multiplicative inverse of the fraction, the numerator is moved to the denominator and the denominator to the numerator keeping the sign as it is.

Complete step by step solution:
Given term: $ \dfrac{1}{5} $
For additive inverse, Let us assume that - “x” be any number then its additive inverse can be expressed as $ - x $ .
Additive inverse can be expressed as the number which when added to the original number gives zero as the resultant value.
Therefore, the additive inverse of the given term $ \dfrac{1}{5} $ is $ - \dfrac{1}{5} $ …… (A)
Now, for the multiplicative inverse –
Let us suppose that - “x” be any number then its multiplicative inverse can be given as $ $ $ \dfrac{1}{x}{\text{ and }}{{{x}}^{ - 1}} $ .
For the multiplicative inverse of any fraction, the numerator and the denominator are interchanged keeping the sign of the term as it is.
Now, the multiplicative inverse of the given number: $ \dfrac{1}{5} = \dfrac{5}{1} = 5 $ ……. (B)
This is the required solution.

Note: In additive inverse, the term and its additive inverse sum up and give resultant value as zero and in multiplicative inverse the product of the term and its multiplicative inverse gives value as one. Do not get confused with the terms additive and multiplicative inverse and apply the fundamentals accordingly.