2 2 Proportional Reasoning Warm Up Write as

2 -2 Proportional Reasoning Warm Up Write as a decimal and a percent. 1. 2. 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 1. 2. 3. 4. 5. 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 Solve each proportion. A. B. LG 2. 2. 1

2 -2 Proportional Reasoning 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. 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: B. At Clay High School, 434 students, or 35% of the students, play a sport. How many students does Clay High School have? METHOD 1: METHOD 2:

2 -2 Proportional Reasoning 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 ≈ 39. 37 in. ) B. Luis ran 400 meters in 297 strides. Find his stride length in inches. SIMILAR FIGURES:

2 -2 Proportional Reasoning 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?