Writing Fractions as Percents

Writing Fractions as Percents

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%

GradebookSolution: 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:    [IMAGE]

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 denominatorLook 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%
 
      [IMAGE]

      [IMAGE]

      [IMAGE]

      None of the above.

      RESULTS BOX:
          

2.  Which of the following is equal to 62.5%?
 
      [IMAGE]

      [IMAGE]

      

      None of the above.

      RESULTS BOX:
          

3.  Which of the following is equal to [IMAGE]?
 
      .583%
      5.83%
      58.3%
      None of the above.

      RESULTS BOX:
          

4.  Which of the following is equal to [IMAGE] ?
 
      11%
      5.5%
      200%
      None of the above.

      RESULTS BOX:
          

5.  What fraction is equal to .42%?
 
      [IMAGE]

      [IMAGE]

      [IMAGE]

      All of the above.

      RESULTS BOX: