Question

What is the reciprocal of \[-3\] ?
1). \[-3\]
2). \[-\dfrac{1}{3}\]
3). \[\dfrac{1}{3}\]
4). \[3\]
5). undefined

Answer 1

Hint: Here first of all we will go through the definition of a reciprocal of a number hence divide the given negative number by one after that to simplify it to get the required answer. Make sure that Denominator cannot be written in negative. Then check which option is correct according to the obtained result.

Complete step-by-step solution:
The inverse of a value or a number is simply stated as reciprocal in mathematics. If \[n\] is a real number, then \[\dfrac{1}{n}\] is its reciprocal.
The word reciprocal comes from the Latin word reciprocus, which means returning. When you take the reciprocal of an inverted number, you get the original number back. When the reciprocal of a given number is multiplied by that number, the result is one. As a result, it's also known as the multiplicative inverse.
We are already familiar that the reciprocal of a number is the inverse of the given number and we can easily find it for any number by writing \[1\] over it.
For any negative number \[-n\] , reciprocal will be its inverse with a minus sign with it. Also, for variable terms, such as \[-a{{x}^{2}}\] , reciprocal can be calculated and thus, reciprocal will be \[\dfrac{-1}{a{{x}^{2}}}\].
Finding the reciprocal of a decimal number is significantly simpler. Simply divide one by the decimal number or write one over it to discover the reciprocal of a decimal number. A mixed fraction, also known as a mixed number, is a number that contains both a whole number and a correct fraction. It could be a combination of integers or even variables. Mixed fractions that are reciprocal are always proper fractions.
Now according to the question we have to find out the reciprocal of a negative number that is \[-3\]
Hence \[-3\] can be written as \[\dfrac{-3}{1}\] as it is a rational number.
Now divide \[\dfrac{-3}{1}\] by \[1\] we get:
\[= \dfrac{1}{\dfrac{-3}{1}}\]
\[= \dfrac{1}{-3}\]
The value of denominator cannot be written in negative hence:
\[= \dfrac{-1}{3}\]
Hence option \[(2)\] is correct as the reciprocal of \[-3\] is \[\dfrac{-1}{3}\].

Note: The reciprocal of zero has no defined value. In reality, any positive or negative number divided by zero has no meaning. As a result, there is a number that cannot be defined as a number. It is commonly referred to as infinity. That is, \[\dfrac{x}{0}=\infty \] , where \[x\] is \[1\] or any other positive or negative number.