Name_____________________________________ Class____________________________ Date ________________
Lesson 3-4
Ratio and Proportion
Lesson Objectives
1 Find ratios and rates
2 Solve proportions
NAEP 2005 Strand: Number Properties and Operations;
Measurement
Topics: Ratios and Proportional Reasoning; Measuring
Physical Attributes
Local Standards: ____________________________________
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Vocabulary and Key Concepts.
Cross Products of a Proportion
If ba dc then ad =
.
8 , so 2 ? 12 = 3 ? 8
Example 32 12
A ratio is
A rate is
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A unit rate is
Unit analysis is
A proportion is
In the proportion ba dc , the extremes of proportion are
In the proportion ba dc , the means of a proportion are
In the proportion ba dc , the cross products are
Examples.
1 Using Unit Rates A brand of grapefruit juice costs $1.56 for 48 oz. Find the unit rate.
cost
ounces
oz
The unit rate is
Daily Notetaking Guide
$
/oz
per oz.
Algebra 1 Lesson 3-4
49
Name_____________________________________ Class____________________________ Date ________________
2 Applying Proportions In 2000, Lance Armstrong completed the 3,630-km Tour
de France course in 92.5 hours. Traveling at his average speed, how long would it
take Lance Armstrong to ride 295 km?
t time needed to ride 295 km.
Relate
Tour de France equals
average speed
295-km trip
average speed
kilometers
Write
hours
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Define Let
t
(
(
t
t
)
)
t Write cross products.
Divide each side by
.
Simplify. Round to the nearest tenth.
Traveling at his average speed, it would take Lance approximately
3 Converting Rates The fastest recorded speed for an eastern gray kangaroo
is 40 mi per hour. What is the kangaroo’s speed in feet per second?
mi
1h
ft
?
1 mi
mi
1h
?
1h
?
?
1 min
ft
1 mi
?
1h
?
min
1 min
Divide the common units.
s
Simplify.
ft/s
The kangaroo’s speed is about
Use appropriate conversion factors.
s
min
ft/s.
Quick Check.
1. Main Street Florist sells two dozen roses for $24.60. Flowers for You Florist sells
six roses for $7.50. Find the unit rate for each. Which florist has the lower cost
per rose?
50
Algebra 1 Lesson 3-4
Daily Notetaking Guide
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
hours to cycle 295 km.
Name_____________________________________ Class____________________________ Date ________________
Example.
4 Solving Multi-Step Proportions Solve the proportion.
z3 z4
4
6
)
( ) 4(
(z 3)
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6z 16
Write cross products.
Use the Distributive Property.
18 16
Subtract
from each side.
2z Subtract
from each side.
2z
z
Divide each side by
.
Simplify.
Quick Check.
2. Suppose you walk 2 miles in 35 minutes.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
a. Find the average walking speed. Write a
rule to describe the distance d you walk
as a function of the time t you walk.
b. Use the function to find how far you would
walk in an hour.
3. A sloth travels 0.15 miles per hour. Convert this speed to feet per minute.
4. Solve each proportion.
12 x
a. x 14
10
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y 2 15
b. y 1 4 35
7
c.
3 5
w16 w24
Algebra 1 Lesson 3-4
51