1. LEARNING GOALS FOR LESSON 2.2
Warm Up
Write as a decimal and a percent.
3. The distance from Max’s house to the park is 3.5 mi. What is the distance in feet? (1 mi = 5280 ft)
LEARNING GOALS FOR LESSON 2.2
Solve proportion equations
Solve percent problems
Apply proportional relationships to rate problems
Scaling figures in the coordinate plane
Write and solve real world similarity problems
RATIO:
PROPORTION:
CROSS PRODUCTS PROPERTY:
Example 1: Solving Proportions
LG 2.2.1
Solve each proportion. A. B.

2. Example 2: Solving Percent Problems
Because percents can be expressed as ratios, you can use the proportion below to solve percent problems.
Percent problems can also be represented with this basic equation:
(whole) × (percent as a decimal) = (part)
Example 2: Solving Percent Problems
LG 2.2.2
A poll taken one day before an election showed that 22.5% of voters planned to vote for a certain candidate. If 1800 voters participated in the poll, how many indicated that they planned to vote for that candidate?
METHOD 1: METHOD 2:
At Clay High School, 434 students, or 35% of the students, play a sport. How many students does Clay High School have?

3. Example 3: Fitness Application
RATE:
Example 3: Fitness Application
LG 2.2.3
A. Ryan ran 600 meters and counted 482 strides. How long is Ryan’s stride in inches? (Hint: 1 m ≈ in.)
B. Luis ran 400 meters in 297 strides. Find his stride length in inches.
SIMILAR FIGURES:

4. Example 4: Scaling Geometric Figures in the Coordinate Plane LG 2.2.4
∆XYZ has vertices X(0, 0), Y(–6, 9) and Z(0, 9).
∆XAB is similar to ∆XYZ with a vertex at B(0, 3).
Graph ∆XYZ and ∆XAB on the same grid.
Example 5: Nature Application
LG 2.2.5
A The tree in front of Luka’s house casts a 6-foot shadow at the same time as the house casts a 22-fot shadow. If the tree is 9 feet tall, how tall is the house?
B. A 6-foot-tall climber casts a 20-foot long shadow at the same time that a tree casts a 90-foot long shadow. How tall is the tree?