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Using the Proportion Method to Find a Percent

Instructor: David Karsner

David holds a Master of Arts in Education

When one fraction equals another fraction it is called a proportion. In this lesson, we will learn how to cross multiply and use proportions to turn fractions into a percentage.

The Same But Different

Brenden, Kayla, and Stan
threecartoons

Kayla, Brenden, and Stan are all in the same class and are very competitive with each other. They just received their grade for the last quiz; however, they can't tell who got the best grade. Their teacher used a different way to show their grade on each of their quizzes. Kayla received a 17/23, Brenden received a 0.08, and Stan received a 75%. All three of them want to know who got the best grade.

In math, information is often presented in fractional, decimal, or percentage form. In fact, the same number can be represented in these three different forms. For example, we can use 50%, 0.50 and 50/100 - all which represent the same number, in different ways. However, since percentages (based on being out of 100) are used quite frequently, it is important to be able to convert the information from fractional and decimal form to a percentage.

In this lesson, we will review the process of converting from fractional form to a percentage using the proportion method. We will view several examples and will test our knowledge at the end by converting Kayla and Brenden's scores to percentages and comparing them to Stan's.

Cross Multiplying

Example of Proportion
proportion

A proportion occurs when one fraction is equivalent, equal, to another fraction. The Example of Proportion image shows that 1/2 = 2/4. A characteristic of proportions is that they can be cross multiplied. This means when you multiply the numerator of the first fraction by the denominator of the second fraction, it will be equal to the denominator of the first fraction multiplied by the numerator of the second fraction. Look at How to Cross Multiply to see this.

I will illustrate this using the 1/2 = 2/4 proportion.


Cross multiply


Now that we know how to cross multiply, we are going to use this knowledge to change fractions into percentages.

From Fraction to Percent

Remember, percent means out of one hundred. For example, 17% means 17 out of 100 and can be written in fraction form as 17/100. To convert a fraction to a percent, you will need to set up a proportion, a/b = c/d. The left side of the proportion will be the fraction we are converting. The right side will be the unknown percentage/100. Let's look at an example:


Using Proportion Method to Convert from Fraction to Percent
Fraction to Percent


To convert 4/5 to a percentage, set up the proportion 4/5 = x%/100. Proportions will cross multiply. Multiply the numerator of the fraction on the left by the denominator of the fraction on the right: 4*100 = 400. Then, continue cross multiplying by multiplying the denominator of the fraction on the left by the numerator of the fraction on the right: 5*x = 5x. Get the variable on one side by itself by dividing both sides (400 and 5x) by 5, which leaves you with x = 400/5. Divide 400 by 5 to solve for x. 400/5 = 80 - so, x = 80. 4/5 = 80/100 = 80%.

As you may have noticed, there is a shortcut. Once you have done step one of the cross multiplying, you can then actually just divide that answer (in this case, 400), by the first fraction's denominator (5). This is a shortcut as you eventually get to this point after performing step two of the cross multiplication. But, let's save time where we can, right?

Examples

OK. Time for you to get out your pencil and paper. I have two practice problems for you. Don't scroll down until you have tried to solve both of them!

Problem 1: Convert 3/12 to a percent

Problem 2: Convert 16/40 to a percent

Again, don't go any further until you try these on your own!

You are not peeking, are you?

OK. Let's look at the solutions.


Example 1

Example 2


Related Activities

As was stated earlier, decimals can also be changed into percentages. This does not require the proportion method or cross multiplying, so let's just do a quick review.

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