Writing Percents as Fractions

ClipboardProblem: One team won 18 out of every 25 games, and another team won 72% of all games played. Which team has a better winning record?

We know from previous lessons that a percent is a ratio whose second term is 100. So we get the following:

72% = 72 out of 100 = seventy2_hundredths_1.gif and

18 out of 25 = eighteen_25ths_1.gif = seventy2_hundredths_1.gif

Solution: Both teams have the same winning record.

Any percent can be written as a fraction in lowest terms. One method for reducing a fraction to lowest terms is to divide both the numerator and the denominator by their greatest common factor (GCF). Let's look at an example of this.

Example 1: Write each percent as a fraction in lowest terms:    55%,    41%,    36%

Solution
Percent Fraction Reducing Lowest Terms
55% fifty5_hundredths.gif reduce_55hundredths.gif eleven_20ths_1.gif
41% forty1_hundredths.gif reduce_41hundredths.gif forty1_hundredths_1.gif
36% thirty6_hundredths_1.gif reduce_36hundredths.gif nine_25ths_1.gif

In Example 1, the GCF of 55 and 100 is 5; the GCF of 41 and 100 is 1; and the GCF of 36 and 100 is 4. Note that when the GCF is 1, this means that the fraction is already in lowest terms. Let's look at some more examples.

Example 2: Write each percent as a fraction in lowest terms:    7%,    12.5%,    62.5%

Solution
Percent Fraction    Reducing    Lowest Terms
 7%   seven_hundredths.gif  reduce_7hundredths.gif  seven_hundredths_0.gif
12.5%  12half_hundredths.gif reduce_125hundredths.gif one_eighth_1.gif
62.5%  sixty2point5_100.gif  reduce_625hundredths.gif  five_eighths_1.gif

Example 3: Write each percent as a fraction in lowest terms:    67.5%,    56.25%,    13.1%

Solution
Percent Fraction    Reducing    Lowest Terms
67.5%   sixty7point5_100.gif reduce_675thousandths.gif twenty7_40ths_1.gif
56.25% fifty6_point25_100ths.gif reduce_5625over10000.gif nine_16ths.gif
13.1%   thirteen_point1_100ths.gif reduce_131thousandths.gif one31_1000ths.gif

Summary: To write a percent as a fraction in lowest terms, follow these steps:

  1. Write the percent as a fraction with a denominator of 100.
  2. Reduce the fraction to lowest terms.

Exercises

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

Which of the following is equal to 90%?
 
      

       eighteen_20ths_1.gif

       eighteen_25ths_2.gif

       eleven_20ths_2.gif

      None of the above.

      RESULTS BOX:
          

2.  Which of the following is equal to 16%?
 
      

       fifteen_100ths_1.gif

       eighteen_hundredths_1.gif

       four_25ths_1.gif

      None of the above.

      RESULTS BOX:
          

3.  Which of the following is equal to eighteen_25ths_2.gif?
 
      

      .72

       seventy2_hundredths_2.gif

      72%

      All of the above.

      RESULTS BOX:
          

4.  Which of the following is equal to .875?
 
      

      8.75%

       eighty7_point5_100ths_1.gif

       five_eighths_1.gif

      None of the above.

      RESULTS BOX:
          

5.  Which number has the greatest value?
 
      

      .625

      6.25%

      $6.25

      6,250 cents

      RESULTS BOX: