6.1
Ratios and Rates
Goal: Find ratios and unit rates.
Vocabulary
Ratio:
Equivalent
ratios:
Rate:
Unit rate:
Writing Ratios
You can write the ratio of two quantities, a and b, where b is not
equal to 0, in three ways.
a to b
a
b
a:b
Each ratio is read “the ratio of a to b.” You should write the ratio
in simplest form.
Writing Ratios
Example 1
In a recent baseball season, the Anaheim Angels played 81 home
games. Anaheim won 54 of those games and lost 27. Write the
ratio in three ways.
a. The number of losses to the number of wins
b. The number of losses to the number of games
Solution
a.
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b.
Three ways to write the ratio
Three ways to write the ratio
are
are
,
, and
.
,
, and
Chapter 6 • Pre-Algebra Notetaking Guide
.
111
6.1
Ratios and Rates
Goal: Find ratios and unit rates.
Vocabulary
Ratio: A ratio uses division to compare two quantities.
Equivalent Two ratios are called equivalent ratios when they
have the same value.
ratios:
Rate: A ratio of two quantities measured in different units.
Unit rate: A rate that has a denominator of 1 when expressed
in fraction form.
Writing Ratios
You can write the ratio of two quantities, a and b, where b is not
equal to 0, in three ways.
a to b
a
b
a:b
Each ratio is read “the ratio of a to b.” You should write the ratio
in simplest form.
Example 1
Writing Ratios
In a recent baseball season, the Anaheim Angels played 81 home
games. Anaheim won 54 of those games and lost 27. Write the
ratio in three ways.
a. The number of losses to the number of wins
b. The number of losses to the number of games
Solution
a.
Copyright © Holt McDougal. All rights reserved.
27
Number of
54
losses
Number of
wins
1
2
b.
Number of
losses
Number of
games
1
27
81 3
Three ways to write the ratio
Three ways to write the ratio
1
are 2 , 1 to 2 , and 1 : 2 .
1
are 3 , 1 to 3 , and 1 : 3 .
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Checkpoint
1. Use the information given in Example 1. Compare the number
of wins to the number of games using a ratio. Write the ratio in
three ways.
Example 2
Finding a Unit Rate
Vacation On the first day of a family vacation, you and your family
drive 392 miles. The amount of gasoline used is 16 gallons. What
is the average mileage per gallon of gasoline?
Solution
First, write a rate comparing the
to the
. Then write the rate so the denominator
is
.
Divide numerator and
denominator by
.
Simplify.
Answer: The average mileage per gallon of gasoline is
.
Checkpoint Find the unit rate.
220 mi
4h
2. 112
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$115
5 people
3. Copyright © Holt McDougal. All rights reserved.
Checkpoint
1. Use the information given in Example 1. Compare the number
of wins to the number of games using a ratio. Write the ratio in
three ways.
2
, 2 to 3, 2 : 3
3
Example 2
Finding a Unit Rate
Vacation On the first day of a family vacation, you and your family
drive 392 miles. The amount of gasoline used is 16 gallons. What
is the average mileage per gallon of gasoline?
Solution
First, write a rate comparing the total distance traveled to the
number of gallons used . Then write the rate so the denominator
is 1 .
392 miles 16
392 miles
16 gallons 16
16 gallons
24.5 miles
1 gallon
Divide numerator and
denominator by 16 .
Simplify.
Answer: The average mileage per gallon of gasoline is
24.5 miles per gallon .
Checkpoint Find the unit rate.
$115
5 people
220 mi
4h
2. 3. 55 mi
1h
112
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$23
1 person
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Example 3
Writing an Equivalent Rate
Water The amount of water used in a certain home is 728 gallons
per week. Write this rate in gallons per day.
Solution
To convert from gallons per week to gallons per day, multiply the rate
1.
by a conversion factor. There are 7 days in 1 week, so
728 gal
1 week
p
Multiply rate by conversion
factor.
p
Divide out common factor
and unit.
Simplify.
Answer: The amount of water used is
Example 4
.
Using Equivalent Rates
Weather Lightning strikes occur about 100 times per second around
the world. About how many lightning strikes occur in 3 minutes?
Solution
1. Express the rate 100 times per second in times per minute.
100 times
1 sec
p
Multiply by conversion
factor. Divide out
common unit.
Simplify.
2. Find the number of times lightning strikes occur around the
world in 3 minutes.
Number of times Rate p Time
Substitute values.
p
Divide out
common unit.
Multiply.
Answer: In 3 minutes, about
around the world.
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lightning strikes occur
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Example 3
Writing an Equivalent Rate
Water The amount of water used in a certain home is 728 gallons
per week. Write this rate in gallons per day.
Solution
To convert from gallons per week to gallons per day, multiply the rate
1 week
1.
by a conversion factor. There are 7 days in 1 week, so 7 days
728 gal
728 gal
1 week
p 1 week
7 days
1 week
Multiply rate by conversion
factor.
104
728 gal
eek
1w
1w
eek
days
7
p Divide out common factor
and unit.
1
104 gal
1 day
Simplify.
Answer: The amount of water used is 104 gallons per day .
Example 4
Using Equivalent Rates
Weather Lightning strikes occur about 100 times per second around
the world. About how many lightning strikes occur in 3 minutes?
Solution
1. Express the rate 100 times per second in times per minute.
60 se
c
100 times
100 times
p 1 sec
1 min
1 s
ec
6000 times
1 min
Multiply by conversion
factor. Divide out
common unit.
Simplify.
2. Find the number of times lightning strikes occur around the
world in 3 minutes.
Number of times Rate p Time
Substitute values.
6000 times
3
min
p
Divide out
1
min
common unit.
18,000 times
Multiply.
Answer: In 3 minutes, about 18,000 lightning strikes occur
around the world.
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