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Fractions

The Reciprocal

Assume d is an integer and d ≠ 0. Then the reciprocal of d is 1/d.

The reciprocal of a nonzero fraction a/b is b/a.

Any number multiplied by its reciprocal is 1. a over b times b over a equals 1

Examples

The reciprocal of 1/3 is 3 over 1 or simply 3.

The reciprocal of 22/7 is 7/22.

The reciprocal of 18=18/1 is 1/18.

More Examples

 

Exercise

Practice finding the reciprocals.

The reciprocal of  

   is  
 

Reciprocals of real numbers

All real numbers except 0 have reciprocals. The reciprocal of a negative number must itself be a negative number so that the number and its reciprocal multiply to 1.

Example

The reciprocal of negative 1 over 5 is negative 5. Checking by multiplying

Now try finding the reciprocal of some signed numbers:

The reciprocal of  

   is  
 

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