Question

How do you find the reciprocal of \[ - \dfrac{1}{5}\] ?

Answer 1

Hint:Before we start solving this solution, refer to the basic concepts for reciprocal and understand it first. Reciprocal is also known as the “Multiplicative Inverse” which is simply the pair of numbers which when multiplied together that results in a value equal to one.

Complete step by step answer:
In other simple words, the reciprocal can be well signified as the multiplicative inverse. Let us assume that - “$x$” be any number then its multiplicative inverse can be expressed as $\dfrac{1}{x}{\text{ }}$ or ${\text{ }}{{\text{x}}^{ - 1}}$. If the given number is fraction, then its reciprocal can be given by just changing numerator with the denominator and denominator with its numerator keeping its sign as it is. Now, the reciprocal of the given number:
\[ - \dfrac{1}{5} = - \dfrac{5}{1} = - 5\]
(when denominator is one then the number can be written as the numerator only)

Hence, the reciprocal of \[ - \dfrac{1}{5}\] is -5.

Additional information: Additive inverse can be stated as the number which when added to the original number then it results in a value equal to zero as the resultant value.For example; additive inverse or in simple words it is just the change in the sign of the terms where the positive term becomes negative and vice versa keeping the value of the term same.

Note: Do not get confused and be clear between the difference between the two terms additive inverse and the multiplicative inverse and apply it accordingly. Always remember that while finding the multiplicative inverse of any fraction, the numerator and the denominator are simply interchanged.