Inverse vs. Reciprocal

Difference Between Inverse and Reciprocal

Inverse and reciprocal are frequently used in mathematics, and have parallel meanings. The multiplicative inverse or reciprocal of a number ‘a’ is denoted by 1/a, and is defined as a number that when multiplied by the number yields one (1). This means, that if we have a fraction x/y, its reciprocal or multiplicative inverse would be y/x. If you have a real number, just divide 1 by the number and you get its inverse or reciprocal number. Any two numbers having 1 as their product are said to be reciprocal numbers. Though, despite such close relationship, there are differences between inverse and reciprocal that will be talked about in this article. In the case of a fraction, the task of finding its reciprocal becomes all the more easy as one just need to swap the numerator and denominator.

The idea of reciprocal is very supportive as it simplifies many math problems and one can solve the sum mentally. Take a look at the following example.

8/(1/5 ) simply becomes 8 X 5 = 40; instead of dividing 8 by 1/5, we multiply 8 by the reciprocal of 1/5, which is 5

Whilst it is true that there is very modest to choose amid multiplicative inverse and reciprocal of a number, there are also additive inverses that need to be added to the original number to get zero, and not one, which is the case in multiplicative inverse. So if the number is a, its additive inverse would be –a so that a+ (-a) = 0. Additive number is what you ought to add to it to get zero as the result.


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