What is a Reciprocal? - Definition & Examples

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  • 0:01 Definition of Reciprocal
  • 1:34 Examples of Reciprocals
  • 1:56 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

Do you know what a reciprocal is in math? Well, in this lesson, you'll learn how to define the term, go give some examples and provide some key facts about reciprocals. You'll also have the chance to answer some questions and solve some problems about reciprocals.

Definition of Reciprocal

The reciprocal of a number is 1 divided by that number. So, for example, the reciprocal of 3 is 1 divided by 3, which is 1/3. A reciprocal is also a number taken to the power of -1. So, 1/8 is the same as 8 to the power of -1.

A Reciprocal is a -1 Power
Reciprocal is a Negative One Power

You can also take the reciprocal of a fraction by flipping the fraction. For instance, the reciprocal of 2/3 is 3/2:

Reciprocal of a Fraction is That Fraction Flipped
Reciprocal of a Fraction is That Fraction Flipped

This operation allows us to come to an interesting conclusion, one that's especially important for using reciprocals in algebra. The reciprocal of a reciprocal is the original number. To understand this principle more fully, let's take the number 23. The reciprocal of 23 is 1/23.

But if we take the reciprocal again and flip that fraction, 1/23 becomes 23/1. And 23 divided by 1 is just 23. By taking the reciprocal twice, we got back to where we started.

Reciprocal of a Reciprocal is the Original Number
Reciprocal of a Reciprocal is the Original Number

To reverse a reciprocal, you take the reciprocal all over again. Additionally, if you multiply a number by its reciprocal, you always get 1. For example, 16 multiplied by 1/16 is just 1. Pretty simple, right?

Multiplying a Number by its Reciprocal Gives 1
Multiplying a Number by its Reciprocal Gives 1

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