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Opposite Reciprocals: Definition & Concept

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  • 0:05 What are Opposite Reciprocals?
  • 1:05 Examples
  • 2:31 Perpendicular Lines
  • 3:46 Lesson Summary
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Lesson Transcript
Instructor: DaQuita Hester

DaQuita has taught high school mathematics for six years and has a master's degree in secondary mathematics education.

An opposite reciprocal is a fun mathematic concept that can help you determine whether two lines are perpendicular. In this lesson, learn about this concept and practice finding opposite reciprocals.

What Are Opposite Reciprocals?

The term opposite reciprocals refers to two numbers that have opposite signs and are flipped fractions of each other. This term is primarily used to describe the slopes of perpendicular lines or to determine whether two lines are perpendicular or not. Lines are considered perpendicular if they meet at a right angle.

Numbers must meet two requirements to be opposite reciprocals of each other. First, to be opposite, they must have differing signs. One number should be positive and the other number should be negative. Second, to be reciprocals, one number should be the flipped fraction, or upside down version, of the other number. For example, the reciprocal or flipped fraction of 3/4 is 4/3.

Additionally, opposite reciprocals have a product of -1. Therefore, if we need to determine whether two numbers are opposite reciprocals of each other, we should multiply them together. If our answer is -1, then we can conclude that they are opposite reciprocals.

Examples

Now that we understand the term, let's practice finding the opposite reciprocal.

First, let's determine the opposite reciprocal of 2/7. Since this number is positive, our opposite reciprocal will be negative. Additionally, the flipped fraction of 2/7 is 7/2. Therefore, the opposite reciprocal of 2/7 is -7/2. Let's check our answer by multiplying these numbers together. By doing this, we see that their product is -1, meaning that we found the opposite reciprocal correctly.

You may be wondering how to find the flipped fraction of a whole number. Well, whole numbers are also fractions. The denominator for every whole number is the number 1. In other words, the number 5 can be written as the fraction 5/1.

For our second example, let's determine the opposite reciprocal of -10. Since this is a whole number, we can write it as the fraction -10/1. This number is negative, meaning that the opposite reciprocal will have to be positive. The flipped fraction will be -1/10. Therefore, in putting this all together, the opposite reciprocal of -10 is positive 1/10. Once again, let's check our answer. When we multiply -10 and 1/10, we get a product of -1, proving that these numbers are definitely opposite reciprocals of each other.

Perpendicular Lines

Now, let's go a step further. Since perpendicular lines have slopes that are opposite reciprocals, we can determine if two lines are perpendicular by examining their slopes.

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