Ratio, Proportion and Similarity

Objectives:

To write ratios.

To solve proportions.

To use proportions to find the measure of a side of a similar figure.

Ratios• A ratio is a comparison of two numbers by

division

• We can compare the ratio of wins to losses for the Texas Rangers in three ways:

1. 19 to 25

2. 19: 25

3.

Team W L

California 22 26

Seattle 20 25

Texas 19 25

Oakland 13 33

19

25

Examples Team W L

California 22 26

Seattle 20 25

Texas 19 25

Oakland 13 33

1. Write the win-loss ratio for California as a fraction in simplest form.

2. Write the ratio for games won by Seattle to total games played.

Guided Practice: Write each ratio as a fraction in simplest form

1. 6 absences in 180 school days

2. 300 students to 20 teachers

3. 76 heartbeats per 60 seconds

4. 300 miles to 15 gallons

Proportions

• A proportion is a statement that two ratios are equivalent or equal. If two ratios are equivalent we say that they are proportional

• Determine if the ratios 9 to 12 and 18 to 24 are proportional.

Examples: Determine if the ratios are proportional

1. 20:8 and 16:4

2. 15 to 45 and 7 to 28

Guided Practice: Determine if the ratios are proportional

1. 3 to 6, 4 to 8

2. 12 to 18, 20 to 24

3. 9 to 3, 6 to 2

4. 20:16, 35:28

5.

4 2,

8 3

Solving proportions

• To solve a proportions, cross multiply then solve the equation

• Solve 7

8 32

p

Examples4 8

6 x

4 85

25 100

x x

3 8

4 48

x

x

9 18

1 54y

Hw: p.281/7-24, p. 285/7-18, 24-26, Worksheet