Negative Reciprocal: Definition & Examples

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  • 0:03 What Is a Reciprocal?
  • 0:57 Negative Numbers & Reciprocals
  • 2:12 Perpendicular Slope Example
  • 3:01 Lesson Summary
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Lesson Transcript
Instructor: Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

The negative reciprocal of a number is a very fancy word for a very simple concept. In this lesson, through definition and example, we'll learn how to find a number's negative reciprocal.

What Is a Reciprocal?

Imagine that you and a friend have to sleep in a bunk bed. You want to sleep on the top bunk, so your friend takes the bottom bunk. After about 15 minutes, you remember that you often get up to use the bathroom in the middle of the night. Now that you realize the bottom bunk would be a better fit, you and your friend switch places. As you're now occupying the bottom bunk, and your friend is sleeping in the top bunk, you're reciprocals of each other.

In mathematics, finding the reciprocal of a number simply involves putting the number in fraction form and then flipping its numerator and denominator, or top and bottom numbers respectively. For example, to find the reciprocal of the number 2/3, we flip the numerator and the denominator to get 3/2. Now, consider the number 23. To find the reciprocal of 23, we first put it in fraction form (23/1) and then flip the numerator and denominator to get 1/23.

Negative Numbers & Reciprocals

Have you looked at your bank account lately? If not, let's imagine that your employer just transferred $500 into your checking account. A few days later, you transfer that $500 to your savings account. When record these transactions in your checkbook, you show the money coming in and going out as +500 and -$500 respectively; in doing this, you've just taken the negative of 500 by simply changing its sign.

Now that you understand the definition of a reciprocal and a negative number, let's define the negative reciprocal of a number. The negative reciprocal of a number is exactly what the term sounds like: the number's reciprocal preceded by a negative sign. To find the negative reciprocal of a number, we first find its reciprocal and then its negative. The phrase 'flip and switch' is a good way to remember this process.

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