Question

What is the multiplicative inverse of -6?
A.-6
B.6
C. \[\dfrac{1}{6}\]
D. \[\dfrac{-1}{6}\]

Answer 1

Hint: In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by \[\dfrac{1}{x}\] or \[{{x}^{-1}}\], is a number which when multiplied by x gives the number 1. The multiplicative inverse of a fraction \[\dfrac{a}{b}\] is \[\dfrac{b}{a}\].

Complete step-by-step answer:
Before proceeding with the solution, let’s understand the concept of multiplicative inverse. The multiplicative inverse of a number is that number, which, when multiplied with the given number, gives the product as 1. It is also known as the reciprocal of a number. For example: The multiplicative inverse of the number 2 is $\dfrac{1}{2}$ , because $2\times \dfrac{1}{2}=1$ .
Now, coming to the question, we are asked to find the multiplicative inverse of -6. We know that the multiplicative inverse of a number is its reciprocal. So, the multiplicative inverse of -6 is equal to \[\dfrac{-1}{6}\].

Note: In the real numbers, zero does not have reciprocals because no real number multiplied by 0 produces 1 (the product of any number with zero is zero). With the exception of zero, reciprocals of every real number are real, reciprocals of every rational number are rational, and reciprocals of every complex number are complex. The property that every element other than zero has a multiplicative inverse is part of the definition of a field, of which these are all examples. On the other hand, no integer other than 1 and −1 has an integer reciprocal, and so the integers are not a field.
Students generally get confused with multiplicative inverse and additive inverse. For multiplicative inverse, the product of the numbers should be equal to 1, whereas in additive inverse, the sum of the numbers should be equal to 0.