The reciprocal of a negative number is also a negative number because when the two numbers are multiplied the answer is 1. For example, the reciprocal of -6 is -1/6, and the product of these two numbers is -6 x (-1/6)= 1.
The reciprocal of a number is also known as a multiplicative inverse, and it is defined as that number which when multiplied by the given number gives the result as unity, in other words 1. A reciprocal is determined by exchanging the position of the numerator and denominator in a given number. For example, the reciprocal of -2/3 is -3/2.