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% |
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% |
2. Which of the following is equal to 62.5%? |
3. Which of the following is equal to ? |
4. Which of the following is equal to ? |
5. What fraction is equal to .42%? |