The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 2.13: Writing Ratios Correctly

When students write ratios, they may inadvertently switch the order of the terms, use a wrong

label, or use faulty data. Each of these mistakes will result in writing an incorrect ratio.

1. Explain to your students that order matters when working with ratios. The ratio of 3 to 4 is
   different from the ratio of 4 to 3. The first quantity must be the first term; the second quan-
   tity must be the second term.


2. Explain that ratios must be written in the same units or measurements. If one unit of mea-
   sure can be expressed in terms of another, students should rewrite the larger in terms of the
   smaller. For example, because 1 yard equals 36 inches, the ratio of 3 inches to 1 yard can be
   rewritten as 3 inches to 36 inches or

3

36

or

1

12

. In this example, caution your students not to
make the mistake of writing the ratio as 3 to 1, which is incorrect because the units—inches
and yards—are different.
3. Review the information and examples on the worksheet with your students. Remind them to
make certain that they are using the correct information when writing ratios.

EXTRA HELP:

Be sure that ratios are expressed in simplest form.

ANSWER KEY:

(1)

3

4

(2)

20

1

(3)

2

3

(4)

2

1

(5)

1

4

(6)

1

100

(7)

2

5

(8)

1

20

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(Challenge)Because 15 is the least common denominator of 3 and 15,

2

3

canbewrittenas

10

15

. This means that the team won 10 games if they played 15 games because

10

15

is the ratio

of games won to games played. Because the problem states the ratio of games lost to games

played is

4

15

, the team lost 4 games. If they played 15 games, won 10, and lost 4, they tied 1

game. The ratio of games tied to games played is

1

15

. If a larger common denominator was

used, the ratio of games tied to games played would be a ratio equivalent to

1

15

.

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72 THE ALGEBRA TEACHER’S GUIDE