Algebra 2.6 Rates, Ratios, and Proportions

Learning Targets Language Goal  Students will be able to write and use ratios, rates, and unit rates. Math Goal  Students will be able to write and solve proportions. Essential Question  Where do you see ratios, rates, and proportions in real-life situations?

Warm-up

Go over Quiz

Vocabulary  Ratio:  Rate:  Scale:  Unit Rate: A comparison of two quantities. A ratio of two quantities with different units Ex. 34 mi/2 gal A ratio between two sets of measurement. Ex. 1 in : 5 mi A rate with a second quantity of 1 unit. Ex. 17 mi / 1 gal

Vocabulary  Conversion Factor:  Proportion:  Cross Products:  Scale Drawings/Scale Model: Two quantities are equal but use different units Ex. 12 in / 1 ft Uses a scale to represent an object as smaller or larger than the actual object Ex. A map

Cross Product Property WordsNumbersAlgebra In a proportion, cross products are equal.

Example 4: Solving Proportions

Extra Whiteboard Practice!

Example 1: Using Ratios  A. The ratio of faculty members to students at a college is 1:15. There are 675 students how many faculty members are there?

Example 1: Using Ratios  B. The ratio of games won to games lost for a baseball team is 3:2. The team won 18 games. How many games did the team lose

Example 1: Using Ratios  C. The ratio of the number of bones in the human skull to the number of bones in the ears is 11:3. There are 22 bones in the skull. How many bones are in the ears?

Example 2: Finding Unit Rates  A. Takeru Kobayashi of Japan ate 53.5 hotdogs in 12 minutes to win a contest. Find the unit rate. Round your answer to the nearest hundredth.

Example 2: Finding Unit Rates  B. Cory earns $52.50 in 7 hours. Find the unit rate.

Example 2: Finding Unit Rates  C. Ralf Laue of Germany flipped a pancake 416 times in 120 seconds to set the world record. Find the unit rate. Round your answer to the nearest hundredth.

Example 3: Converting Rates  A. As you go deeper underground, the earth’s temperature increases. In some places, it may increase by 25  C per kilometer. What is this rate in degrees per meter?

Example 3: Converting Rates  B. The dwarf sea horse swims at a rate of feet per hour. What is this speed in inches per minute?

Example 3: Converting Rates  C. A cyclist travels 56 miles in 4 hours. What is the cyclist’s speed in feet per second? Round your answer to the nearest tenth.

Practice B WS (if time)

Lesson Quiz