# What is a reciprocal?

There are two ways to think about a reciprocal:

1.  A reciprocal is the number that you would multiply against another number and the resulting product (multiplication) would be 1.

2. The fractional opposite of any number or fraction; to find this you simply reverse the numerator and denominator of a fraction.

### Version 1

What is the reciprocal of  1/2?

Solve for X          1 = 1/2 * x

Multiply both sides by 2          1 * 2 = 1/2 * 2

Complete equation          2 = 1 * x

2 = x

### Version 2

What is the reciprocal of 1/2?

To solve you would simply “flip” the fraction over:

1/2     FLIPPED        2/1 or 2

## Both techniques will get your the correct answer and both can be used for differing learning styles.

In the event that the problem consists of a complex fraction, you will need to convert the complex fraction into an “improper” fraction. This improper fraction can then be applied to the above techniques to find the reciprocal of the number. Let look at how to convert a complex fraction into an improper fraction:

### Convert 2 1/4 to improper fraction

#### -    9/4 is the converted “improper” fraction of 2 1/4

Version 1

What is the reciprocal of 2 1/4?

Convert fraction into “improper” fraction  :  9/4

Solve for x  :  1 = 9/4 * x

Multiply both sides by 4/9 : 1 * 4/9 = 9/4 * 4/9 * x

Complete Equation  :  4/9 = 1 * x

4/9 = x

Version 2

What is the reciprocal of 2 1/4?

First convert to improper fraction: 9/4

9/4   FLIPPED   4/9

# RECIPROCALS RECAP

• Two ways to find a reciprocal – Solve or Flip Technique
• Be sure to convert COMPLEX fractions to IMPROPER fractions
• Flip Technique is fast way to find a reciprocal!

If you have any questions please comment and good luck on your studying for the ASVAB exam!

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