What Is a Reciprocal of a Number?

The equal sign.

In Mathematics there are several classifications of numbers such as fractions, prime, even, odd and more. Reciprocal numbers are another classification of numbers that pertain to the opposite of the primary number given. Often these are called multiplicative inverse numbers and are easy to identify.

The Product of 1

Every reciprocal number is a number that when multiplied against the primary number will result in the product 1. This reciprocal is often considered a reverse of the number. For instance the reciprocal of 3 is 1/3, by multiplying against one another the answer is 1. Every reciprocal multiplied by the primary number must result in the product of 1 otherwise it is wrong.

Fractions

Generally the best way to identify the reciprocal number is to turn the first number into a fraction. For whole numbers this is done by simply placing the number on top of the number 1 in a fraction. As all numbers divided by the number 1 is the primary number itself, this fraction is exactly the same as the primary number.

8 = 8/1

Flip the Fraction

By flipping the fraction you will have the answer to the product 1. With whole numbers this refers to taking the whole number over the product 1 and flipping it to 1 over the whole number. By multiplying these two fractions you now have the product 1.

8=8/1

8/1 flipped is 1/8

8/1*1/8= 1

Mixed Numbers

The reciprocal of the mixed number is again the opposite or reverse of the fraction, however with mixed numbers another step is needed to obtain the goal product of 1. To identify the reciprocal of a mixed number you must first turn that number into a fraction with no whole numbers. For instance the number 3 1/8 would actually have to be converted to 25/8 to then find the reciprocal. 8/25 would be the reciprocal to produce the product of 1.

Uses for Reciprocals

Reciprocal numbers are used most often in the theory of mathematics. Reciprocal numbers allow a machine to multiple to get an answer instead of divide because dividing is a slower process. Most particularly you will find that reciprocal numbers are used in computer science more than anything else.

References

• Math: Reciprocal
• MathsTeacher: The Reciprocal of a Number