Math Background

Lesson: Using Ratios and Percents
Developing the Concept

Help with Opening PDF Files

Now that students are familiar with ratios, decimals, and percents, they can apply this knowledge when solving problems.

Materials: overhead projector; Music Styles (PDF file) worksheet for each student or group of students

Preparation: Make a transparency of the worksheet. Distribute copies of the worksheet to each student or group of students.

  • Say: In the lesson today you will learn how to write numerical data in an organized table using ratios, fractions, decimals, and percents. (Display the worksheet on the overhead.) A survey was conducted in a school lunchroom and 60 students were asked about their favorite music style. You can see that 6 students chose jazz, 33 chose rock and roll, 18 chose country, and 3 had no opinion.
  • Say: The task is to use ratios to show the results of the survey. Let's complete the table by writing the ratios as a fraction, decimal, and percent for each type of music preferred.
  • Ask: What is the ratio of students choosing jazz to the total number of students surveyed?
    Students may reply 6 to 60.
    How do you write the ratio? (6 to 60, or 6:60)
    Have students write the ratio on their worksheets, using the colon format.
  • Ask: How can you write the ratio as a fraction?
    Students may respond six-sixtieths ; have them write the fraction in simplest form: one-tenth . On the overhead, show how to write the fraction in simplest form:
    six-sixtieths = six-sixtieths ÷ six-sixths = one-tenth
  • Ask: Who can tell me how to write one-tenth as a decimal?
    Students may respond one-tenth = 0.10.
  • Ask: How do you write 0.10 as a percent?
    Students may respond 0.10 = 10%.

    Have students complete the rest of the table. The ratio column should reflect the ratio of the number of students preferring the music style to the total number of students. Remind them that when changing a fraction to a decimal it helps to find an equivalent fraction with a denominator of 100. The completed table should look like the one below.

    Number of
    Ratio Fraction Decimal Percent
    Jazz 6 6:60 six-sixtieths = one-tenth 0.10 10%
    Rock &
    3333:60 thirty-three-sixtieths = eleven-twentieths 0.55 55%
    Country 18 18:60 eighteen-sixtieths = three-tenths 0.30 30%
    No Opinion 3 3:60 three-sixtieths = one-twentieth 0.05 5%

Wrap-Up and Assessment Hints
Make sure students understand that a ratio of 1 to 4, even though it can be written in fraction form, doesn't always mean the same as the fraction one-fourth .
Discuss the example of a paint mixture of 1 part yellow and 4 parts red, a ratio of 1 to 4, yet the mixture contains one-fifth yellow paint.

To assess whether students understand the meaning of fractions, decimals, and percents, ask them to do mental math exercises to pick the greater number of a pair of numbers. Following are a few examples.

1. six-twentieths or 50% (50% > 30%)
2. 73% or three-fourths (75% > 73%)
3. 0.45 or twelve-twenty-fifths (0.48 > 0.45)

Houghton Mifflin Math Grade 5