Rates and Unit Rate
Objectives: SWBAT: 1.) determine and apply unit rate
2.) convert rates into ratios
3.) compare and use rates to solve practical problems (Lesson 6.2 text p. 276­277)
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Rate: a ratio (fraction) of two quantities that have different units of measure Rate of a per b is a/b
example: 4 miles/2 hours $ 15/3 hours
Unit Rate: ­ a rate that has a denominator of 1
­ simplest form: written with units example: 2 miles/1 hour $5/1 hour (2 miles per hour) ($ 5 per hour)
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Finding Unit Rates
To find/write a unit rate: Find an equivalent rate with a denominator of 1
Example: Write 40 feet per 5 seconds as a unit rate
40 feet (÷ 5) = 8 feet
5 seconds (÷ 5) 1 second Write each as a unit rate:
1.) 114 points 2.) $ 6 6 games 2 quarts of ice cream
3.) It rains 18 inches in 8 hours
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Comparing Rates & Solving Problems
Example: Antonio rode his bike 23 miles in 4 hours.
Maria rode her bicycle 16 miles in 3.5 hours.
Which of them rode at a faster pace?
Find each person’s unit rate (speed):
Antonio: 23 miles (÷ 4) = 5.75 miles 4 hours (÷ 4) 1 hour
Maria: 16 miles (÷ 3.5) ≈ 4.6 miles 3.5 hours (÷ 3.5) 1 hour So, Antonio rode his bike faster than Maria
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Comparing Rates
Which is the best buy?
a. 2 lb. bag of fruit for $ 1.08 b. 5 lb. bag of fruit for $ 2.10 c. 10 lb. bag of fruit for $ 3.95
Find the unit rate (cost) for 1 lb. of fruit for each:
a. $ 1.08 (÷ 2) = $0.54
2 lb. (÷ 2) 1 lb.
b. $ 2.10 (÷ 5) = $0.42
5 lb (÷ 5) 1 lb.
c. $ 3.95 (÷ 10) ≈ $ 0.40 10 lb (÷ 10) 1 lb.
So, the 10 lb. bag for $ 3.95 is the best buy
(lowest cost for 1 lb.)
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Find the unit rate:
1. 152 people for 5 classes
2. $ 7.40 for 5 pounds Oct 22­11:41 AM
Which is the better deal?
Shop Rite 3 packs of soda for $ 9
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Foodtown
5 packs of soda for $10 Which is the better buy?
a.) 20 ounce box of popcorn for $ 4.19
b.) 16 ounce box of popcorn for $ 3.79
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