Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Divide. Round answers to the nearest
tenth. 1. 2. 3. 4.
23.3
3.5
23.9
23.8
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Problem of the Day There are 3 bags of flour for
every 2 bags of sugar in a freight truck. A bag
of flour weighs 60 pounds, and a bag of sugar
weighs 80 pounds. Which part of the trucks
cargo is heavier, the flour or the sugar?
flour
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Learn to work with rates and ratios.
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Vocabulary
rate unit rate unit price
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A rate is a comparison of two quantities that
have different units.
90 3
Ratio
Read as 90 miles per 3 hours.
90 miles 3 hours
Rate
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Unit rates are rates in which the second quantity
is 1.
90 3
30 1

30 miles, 1 hour
unit rate
or 30 mi/h
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Additional Example 1 Finding Unit Rates
Geoff can type 30 words in half a minute. How
many words can he type in 1 minute?
Write a rate.
Multiply to find words per minute.
60 words 1 minute

Geoff can type 60 words in one minute.
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Check It Out Example 1
Penelope can type 90 words in 2 minutes. How many
words can she type in 1 minute?
90 words 2 minutes
Write a rate.
Divide to find words per minute.
90 words 2 2 minutes 2
45 words 1 minute

Penelope can type 45 words in one minute.
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Additional Example 2A Chemistry Application
Five cubic meters of copper has a mass of 44,800
kilograms. What is the density of copper?
44,800 kg 5 m3
Write a rate.
Divide to find kilograms per 1 m3.
44,800 kg 5 5 m3 5
8,960 kg 1 m3
Copper has a density of 8,960 kg/m3.
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Additional Example 2B Chemistry Application
A piece of gold with a volume of 0.5 cubic meters
weighs 9650 kilograms. What is the density of
gold?
9650 kg 0.5 m3
Write a rate.
Multiply to find kilograms per 1 m3.
9650 kg 2 0.5 m3 2
19,300 kg 1 m3
Gold has a density of 19,300 kg/m3.
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Check It Out Example 2A
Four cubic meters of precious metal has a mass of
18,128 kilograms. What is the density of the
precious metal?
18,128 kg 4 m3
Write a rate.
Divide to find kilograms per 1 m3.
18,128 kg 4 4 m3 4
4,532 kg 1 m3
Precious metal has a density of 4,532 kg/m3.
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Check It Out Example 2B
A piece of gem stone with a volume of 0.25 cubic
meters weighs 3540 kilograms. What is the density
of the gem stone?
3540 kg 0.25 m3
Write a rate.
Multiply to find kilograms per 1 m3.
3540 kg 4 0.25 m3 4
14,160 kg 1 m3
The gem stone has a density of 14,160 kg/m3.
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Additional Example 3A Estimating Unit Rates
Estimate each unit rate.
468 students to 91 computers
Choose a number close to 468 that is divisible by
91.
Divide to find students per computer.
468 students to 91 computers is approximately 5
students per computer.
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Additional Example 3B Estimating Unit Rates
Estimate each unit rate.
313 feet in 8 seconds
Choose a number close to 313 that is divisible by
8.
Divide to find feet per second.
313 feet to 8 seconds is approximately 39 feet
per second.
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Check It Out Example 3A
Estimate each unit rate.
583 soccer players to 85 soccer balls.
Choose a number close to 583 that is divisible by
85.
Divide to find players per soccer ball.
583 soccer players to 85 soccer balls is
approximately 7 players per soccer ball.
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Check It Out Example 3B
Estimate each unit rate.
271 yards in 3 hours
Choose a number close to 271 that is divisible by
3.
Divide to find yards per hour.
271 yards to 3 hours is approximately 92 yards
per hour.
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Unit price is a unit rate used to compare price
per item.
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Additional Example 4A Finding Unit Prices to
Compare Costs
Pens can be purchased in a 5-pack for 1.95 or a
15-pack for 6.20. Which is the better buy?
Divide the price by the number of pens.
price for package number of pens
1.95 5
?

0.39
price for package number of pens
6.20 15

?
0.41
The better buy is the 5-pack for 1.95.
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Additional Example 4B Finding Unit Prices to
Compare Costs
Jamie can buy a 15-oz jar of peanut butter for
2.19 or a 20-oz jar for 2.78. Which is the
better buy?
Divide the price by the number of ounces.
2.19 15

?
0.15
2.78 20

?
0.14
The better buy is the 20-oz jar for 2.78.
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Check It Out Example 4A
Golf balls can be purchased in a 3-pack for 4.95
or a 12-pack for 18.95. Which is the better buy?
Divide the price by the number of balls.
price for package number of balls
4.95 3
?

1.65
price for package number of balls
18.95 12
?

1.58
The better buy is the 12-pack for 18.95.
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Check It Out Example 4B
John can buy a 24 oz bottle of ketchup for 2.19
or a 36 oz bottle for 3.79. Which is the better
buy?
Divide the price by the number of ounces.
2.19 24

?
0.09
3.79 36

?
0.11
The better buy is the 24-oz jar for 2.19.
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Lesson Quiz Part 1
1. A penny has a mass of 2.5 g and a volume of
approximately 0.360 cm3. What is the approximate
density of a penny? 2. Meka can make 6 bracelets
per half hour. How many bracelets can she make in
1 hour? Estimate the unit rate. 3. 2.22 for 6
stamps 4. 8 heartbeats in 6 seconds
6.94 g/cm3
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0.37 per stamp
? 1.3 beats/s
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Lesson Quiz Part 2
Determine the better buy. 5. A half dozen
carnations for 4.75 or a dozen for 9.24 6. 4
pens for 5.16 or a ten-pack for 12.90.
a dozen
They cost the same.