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Algebra 2.6Rates, Ratios, and Proportions
Learning TargetsLanguage 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 unitsEx. 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 unitsEx. 12 in / 1 ft
A statement that two ratios are equivalent.Ex.
In proportion ,
Uses a scale to represent an object as smaller or larger than the actual object
Ex. A map
Cross Product PropertyWords Numbers Algebra
In a proportion, cross products
are equal.
Example 4: Solving ProportionsA. B.
C. D.
Extra Whiteboard Practice!A.
Extra Whiteboard Practice!B.
Extra Whiteboard Practice!C.
Extra Whiteboard Practice!D.
Extra Whiteboard Practice!E.
Extra Whiteboard Practice!F.
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 25C per kilometer. What is this rate in degrees per meter?
Example 3: Converting Rates B. The dwarf sea horse swims at a rate
of 52.68 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