Question

Reciprocal of -5 is how

Answer 1

reciprocal =-5
=1/-5
=-1/5(as denominator is always positive )

Answer 2

Concept

Reciprocal is defined for rational or real numbers as the multiplicative inverse of a number. If a is a real number then its reciprocal or multiplicative inverse is the real number which when multiplied to a gives the multiplicative identity i.e. 1. The reciprocal or multiplicative inverse of a is denoted by 1/a or a⁻¹. Written mathematically,

                  a × (1/a) = 1 = (1/a) × a.

Note:

• The term reciprocal is used only for multiplicative inverse and not for the additive inverse.

• Reciprocal is not defined for an integer. 5 is an integer but 1/5 is not an integer. So, for integers or natural numbers, there are no reciprocals.

• The real number 0 doesn't have any reciprocal because there is no real number when multiplied to 0 gives 1, in fact, the multiplication always gives 0.

Given

A rational number -5

Find

The reciprocal of -5.

Solution

For the rational number -5 there exists another rational number -1/5 which is the multiplicative inverse of -5 i.e.

-5 × (-1/5) = 1.

Also, (-1/5) × (-5 ) = 1.

So, we have

-5 × (-1/5) = 1 = (-1/5) × (-5).

-1/5 satisfies the definition of the multiplicative inverse.  

So, -1/5 is the multiplicative inverse or the reciprocal of -5.

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