What is a Proportion in Math? - Definition & Practice Problems

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  • 0:00 What Is a Proportion?
  • 1:00 Proportions And…
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Mathematical proportions are often used by scientists and researchers to compare information. Anytime you hear 'one out of. . .' a mathematical proportion is being used. In this lesson, you will learn the definition of a proportion and how proportions relate to equivalent fractions. When you are finished, assess your knowledge with a short practice quiz.

What is a Proportion?

A proportion is a mathematical comparison between two numbers. Often, these numbers can represent a comparison between things or people. For example, say you walked into a room full of people. You want to know how many boys there are in comparison to how many girls there are in the room. You would write that comparison in the form of a proportion.

You can write mathematical proportions in two ways. You can compare the numbers with colons, or you can write the proportion in the form of equivalent fractions.

Writing Proportions
Writing Proportions

For example, how many black and white animals to brown/orange animals are there?

Using Proportions to Show Relationships
Using Proportions to Show Relationships

In this image, there are three black and white animals compared to six brown/orange animals. You can see this proportion written with a colon and as an equivalent fraction. When the fraction is simplified, the equivalent fraction tells us that for every two orange animals there is one black and white animal.

Proportions and Equivalent Fractions

You can tell if two fractions are proportional by using cross multiplication. Only equivalent fractions are proportional.

Finding Proportional Fractions Using Cross Multiplication
Finding Proportional Fractions Using Cross Multiplication

To do this, multiply the denominator, the bottom number in the fraction, of the first fraction with the numerator, the top number in the fraction. Do the same thing with the numerator of the first fraction and the denominator of the second fraction. If the product of the two equations are the same, then you have equivalent fractions, and they are proportional!

Another example:

Are the following fractions equivalent and proportional?

A. 4/5 = 8/10

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