Writing Fractions as Percentages Lesson

Learn About Writing Fractions as Percents With The Following Examples And Interactive Exercises

Problem: Last marking period, Ms. Jones gave an A grade to 15 out of every 100 students and Mr. McNeil gave an A grade to 3 out of every 20 students. What percent of each teacher’s students received an A?

Solution
Teacher	Ratio	Fraction	Percent
Ms. Jones	15 to 100		15%
Mr. McNeil	3 to 20		15%

Gradebook Solution: Both teachers gave 15% of their students an A last marking period.

In the problem above, the fraction for Ms. Jones was easily converted to a percent. This is because It is easy to convert a fraction to a percent when the denominator is 100. If a fraction does not have a denominator of 100, you can convert it to an equivalent fraction with a denominator of 100, and then write the equivalent fraction as a percent. This is what was done in the problem above for Mr. McNeil. Let’s look at some problems in which we use equivalent fractions to help us convert a fraction to a percent.

Example 1: Write each fraction as a percent:

Solution
Fraction	Equivalent Fraction	Percent
		50%
		90%
		80%

Example 2: One team won 19 out of every 20 games played, and a second team won 7 out of every 8 games played. Which team has a higher percentage of wins?

Solution
Team	Fraction	Equivalent Fraction	Percent
1			95%
2			87.5%

Solution: The first team has a higher percentage of wins.

In Examples 1 and 2, we used equivalent fractions to help us convert each fraction to a percent. Another way to do this is to convert each fraction to a decimal, and then convert each decimal to a percent. To convert a fraction to a decimal, divide its numerator by its denominator. Look at Example 3 below to see how this is done.

Example 3: Write each fraction as a percent:

Solution
Fraction	Decimal	Percent
		87.5%
		95%
		1.5%

Now that you are familiar with writing fractions as percents, do you see a pattern in the problem below?

Problem:

If 165% equals

, and 16.5% equals

, then what fraction is equal to 1.65%?

Solution
Percent	Fraction
165%
16.5%
1.65%

Summary: To write a fraction as a percent, we can convert it to an equivalent fraction with a denominator of 100. Another way to write a fraction as a percent is to divide its numerator by its denominator, then convert the resulting decimal to a percent.

Exercises

Directions: Read each question below. Select your answer by clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If you make a mistake, choose a different button.

1. Which of the following is equal to 36%