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Difference Between Inverse and Reciprocal

Inverse vs Reciprocal

The terms reciprocal and inverse are used mostly in mathematics, and have similar 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. However, 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 transpose the numerator and denominator.

The concept of reciprocal is very helpful 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

While it is true that there is very little to choose between 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 should add to it to get zero as the result.

In brief:

Difference Between Inverse and Reciprocal

• Inverse and reciprocal are similar concepts in mathematics that have similar meaning, and in general refer to the opposite of an identity

• Multiplicative inverse is identical to reciprocal as it needs to be multiplied with a number to get one as the result.

• However, there is also additive inverse that needs to be added to a number to get zero as the result.


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