What is the reciprocal of a number ? Definition and examples


The reciprocal of a nonzero rational number a/b is b/a. For example, the reciprocal of 4/5 is 5/4.

Reciprocal of a number
Reciprocal of a number


Notice that 4/5 × 5/4 = 20/20 = 1

Therefore, you can also define the reciprocal of a number a as the number b such that a × b =  1.

Rational number

1/5

4/7

4/1

9

Reciprocal

5/1

7/4

1/4

1/9

Equation

1/5 × 5/1 = 1

4/7 × 4/7 = 1

4/1 × 1/4 = 1

9  × 1/9 = 1

The reciprocal of a number is also called multiplicative inverse.


Zero does not have a reciprocal.

For example, what is the reciprocal of 0/b?

If this was possible, it would be b/0. However, division by zero is undefined or has no answer.

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