1. Ratios and Proportions
Objective
I will solve proportions using reciprocals and cross products.
I will use proportions to solve real-life problems.

2. Vocabulary
Proportion - an equation in which one ratio is set equal to another ratio
(Written in the form of , which is read as “a is to b, as c is to d”)

3. Using the Reciprocal Property
Solve the proportion
SOLUTION
Write original proportion
Use reciprocal property
Multiply each side by 4
Simplify

4. Using the Reciprocal Property
Solve the proportion
CHECK
Substitute

5. Using the Cross Product Property
Solve the proportion
Write original proportion
Use cross product property
Simplify
Take square root of both sides
The solutions are x=-8 and x=8. Check both answers.

6. Checking Solutions Solve the proportion. Use cross product property
Use distributive property
Isolate variable term
Take square root of both sides

7. Checking Solutions Check each solution. x = 4: x = -4
The solution x = -4 is extraneous because the check results in a false statement. The correct solution is x = 4.

8. Proportions in Real-Life
Archaeologists excavated three pits containing the clay army. To estimate the number of warriors in Pit 1 shown below, an archaeologist might excavate three sites. The sites at the ends together contain 450 warriors. The site in the central region contains 282 warriors. This 10-meter-wide site is thought to be representative of the 200-meter central region. Estimate the number of warriors in the central region. Then estimate the total number of warriors in Pit 1.

9. Proportions in Real-Life
282 warriors
62m
240 warriors
210 warriors
10m
Central Region
200m 5m 5m
SOLUTION Let n represent the number of warriors in the 200-meter central region. You can find the value of n by solving a proportion.

10. Proportions in Real-Life
Number of warriors found Number of meters excavated =
Total number of warriors Total number of meters
282 = 10
n 200
The solution is n = 5640, indicating that there are about 5640 warriors in the central region. With the 450 warriors at the ends, that makes a total of about 6090 warriors in Pit 1.

11. Practice