1. Chapter 4
Ratios and Proportions

2. Understanding and Solving Proportions
Section 4.3
Understanding and Solving Proportions
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

3. Write a Proportion
A proportion is a mathematical statement showing that two ratios are equal.
A proportion is written as an equation with a ratio on each side of the equal sign.
Remember to include the units when writing a rate. Also, keep in mind that the order of the units is important. Be sure that like units for each rate are in the same position.

4. Example Write each sentence as a proportion.
a. 2 is to 7 as 4 is to 14
b. 12 eggs is to 3 chickens as 4 eggs is to 1 chicken

5. Solution Strategy Write each sentence as a proportion.
a. 2 is to 7 as 4 is to 14
b. 12 eggs is to 3 chickens as 4 eggs is to 1 chicken
like units

6. Determine Whether Two Ratios Are Proportional

7. Example Determine whether the ratios are proportional.
If they are, write a corresponding proportion.

8. Solution Strategy Determine whether the ratios are proportional.
If they are, write a corresponding proportion.
180
180
The ratios are proportional.

9. Solve a Proportion

10. Example
Solve for the unknown quantity. Verify your answer.

11. Solution Strategy Solve for the unknown quantity. Verify your answer.72
24 • 3 = 72 4x
18 • 4 = 72
4x = 72
It checks!
x = 18

12. Solving an Application Problem

13. Example Apply your knowledge
A cake recipe requires 5 eggs for every 4 cups of flour. If a large cake requires 12 cups of flour, how many eggs should be used?

14. Solution Strategy
A cake recipe requires 5 eggs for every 4 cups of flour. If a large cake requires 12 cups of flour, how many eggs should be used?
x = number of eggs for large cake
like units
4x = 5 • 12

15. Solution Strategy 4x = 5 • 12 4 • 15 = 60 4x = 60 5 • 12 = 60 x = 15
The large cake requires 15 eggs.

16. Solving a Geometry Application Problem
One common application of proportions is solving problems involving similar geometric figures. Similar geometric figures are geometric figures with the same shape in which the ratios of the lengths of their corresponding sides are equal. Because these ratios are equal, they are proportional.

17. Solving a Geometry Application Problem
The similar rectangles yield this proportion:

18. Solving a Geometry Application Problem
The similar triangles yield these proportions:

19. Example
Using shadow proportions to find “difficult to measure” lengths
Kyle is 5.6 feet tall. Late one afternoon while visiting the Grove Isle Lighthouse, he noticed that his shadow was 8.5 feet long. At the same time, the lighthouse cast a shadow 119 feet long. What is the height of the lighthouse?
(See the figure on the next slide.)

20. Example
Using shadow proportions to find “difficult to measure” lengths
8.5 ft shadow
119 ft shadow
5.6 ft x

21. Solution Strategy
Kyle is 5.6 feet tall. Late one afternoon while visiting the Grove Isle Lighthouse, he noticed that his shadow was 8.5 feet long. At the same time, the lighthouse cast a shadow 119 feet long. What is the height of the lighthouse?
x = height of the lighthouse

22. Solution Strategy 8.5 • 78.4 = 666.4 8.5x = 5.6 • 119 8.5x = 666.4
5.6 • 119 = 666.4
8.5x = 666.4
The height of the lighthouse is 78.4 feet.
x = 78.4