Chapter 9
Percent
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9
Percent
Lesson 9-1
Lesson 9-2
Lesson 9-3
Lesson 9-4
Lesson 9-5
Lesson 9-6
Lesson 9-7
Lesson 9-8
Lesson 9-9
Lesson 9-10
Percents and Fractions
Circle Graphs
Percents and Decimals
Problem-Solving Strategy: Solve a
Simpler Problem
Estimating with Percents
Percent of a Number
Problem-Solving Investigation:
Choose the Best Strategy
Probability
Sample Spaces
Making Predictions
9-1
Percents and Fractions
Five-Minute Check (over Chapter 8)
Main Idea and Vocabulary
California Standards
Key Concept: Percent
Example 1
Example 2
Example 3
Example 4
Example 5
9-1
Percents and Fractions
• I will express percents as fractions and fractions
as percents.
• percent
9-1
Percents and Fractions
Standard 5NS1.2 Interpret percents as a
part of a hundred; find decimal and percent
equivalents for common fractions and explain
why they represent the same value; compute a
given percent of a whole number.
Standard 5SDAP1.3 Use fractions and percentages
to compare data sets of different sizes.
9-1
Percents and Fractions
Percents and Fractions
9-1
Write 60% as a fraction in simplest form.
60% means 60 out of 100.
60
60% =
100
3
60 or 3
100
5
5
Definition of percent
Simplify. Divide the
numerator and the
denominator by the
GCF, 20.
9-1
Percents and Fractions
Choose the fraction in simplest form that
represents 75%.
A.
3
4
B.
1
2
C.
75
100
D.
15
20
9-1
Percents and Fractions
Write 140% as a mixed number in simplest form.
140% means 140 for every 100.
140% =
140
100
=1
40
100
Definition of percent
Write as a mixed number.
9-1
Percents and Fractions
2
40
2
=1
or 1
100
5
5
Divide the numerator and
denominator by the GCF, 20.
9-1
Percents and Fractions
Choose 160% as a mixed number in simplest form.
60
A. 1 100
B. 1 30
50
3
1
C.
5
D. 2
9-1
Percents and Fractions
Use the table below. What fraction of the class
members preferred spaghetti for the school lunch?
The table shows that 25%
of those surveyed prefer
spaghetti.
9-1
Percents and Fractions
25% =
=
25
100
1
4
Definition of percent
Simplify.
Answer: So, 1 of those surveyed prefer spaghetti.
4
9-1
Percents and Fractions
Use the table below. What fraction of the fifth
graders preferred football?
20
A.
100
B. 1
5
C. 1
2
D.
1
20
9-1
Percents and Fractions
Write
7
as a percent.
10
7
n
=
10
100
Write an equation using ratios. One ratio
is the fraction. The other is an unknown
value compared to 100.
7
70
=
10
100
Since 10 × 10 = 100, multiply 7 by 10
to find n.
Answer: So,
7
70
=
or 70%.
10 100
9-1
Percents and Fractions
Write
14
as a percent.
25
A. 50%
B. 60%
C. 56%
D. 14%
9-1
Percents and Fractions
42
of the students
600
24
study Spanish. At Foothills Middle School,
480
of the students study Spanish. Which school has
At Boulder Middle School,
the greater percent of students that study Spanish?
Write each fraction as a percent. Then compare.
9-1
Percents and Fractions
Boulder MS
Foothills MS
42
n
=
600
100
28
n
=
480
100
42
7
=
or 7%
600
100
28
5
=
or 5%
480
100
Answer: Since 7% > 5%, Boulder MS has the greater
percent of students that study Spanish.
9-1
Percents and Fractions
45
of the students
300
has their driver’s license. At Grove City High School,
At Franklin Heights High School,
36
of the students has their driver’s license. Which
360
school has the greater percent of students with their
driver’s license and with what percent?
A. Franklin Heights HS; 15% > 10%
B. Franklin Heights HS; 20% > 15%
C. Grove City HS; 15% > 10%
D. Grove City HS; 20% > 15%
9-2
Circle Graphs
Five-Minute Check (over Lesson 9-1)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
Example 4
Circle Graphs
9-2
Circle Graphs
• I will sketch and analyze circle graphs.
• circle graph
9-2
Circle Graphs
Standard 5SDAP1.2 Organize and display
single-variable data in appropriate graphs and
representations (e.g., histogram, circle graphs)
and explain which types of graphs are appropriate
for various data sets.
Standard 5SDAP1.3 Use fractions and percentages
to compare data sets of different sizes.
9-2
Circle Graphs
The table shows how many hours a group of
teenagers spent playing video games in one
week. Sketch a circle graph to display the data.
9-2
Circle Graphs
• Write a fraction for each percent.
35% =
10% =
25% =
30% =
35
100
10
100
25
100
30
100
7
or
20
1
or
10
1
or 4
or
3
10
• Use a compass to draw a circle with at least a
1-inch radius.
9-2
Circle Graphs
1
of the circle, shade about
3
a third of the circle for 3 or more.
• Since 30% is about
• Since 25% is 1 of the circle, shade 1 of the
4
4
circle for 2–3.
• Since 35% is a little more than 1 , shade a little
3
more than 1 of the circle for 0–1.
3
• Shade the remaining small piece or 10% for 1–2.
9-2
Circle Graphs
• Label each section of the circle graph. Then give
the graph a title.
9-2
Circle Graphs
Choose the circle graph
that represents the data
in the table.
A.
B.
9-2
Circle Graphs
Choose the circle graph
that represents the data
in the table.
C.
D.
9-2
Circle Graphs
Choose the circle graph
that represents the data
in the table.
C.
9-2
Circle Graphs
Use the circle graph
to the right that
shows the method of
transportation
students use to get
to Martin Luther
King, Jr., Middle
School. Which
method of
transportation do
most students use?
Method of Transportation
Used by Students to
Arrive at School
9-2
Circle Graphs
The largest section of
the graph is the
section that represents
taking the bus.
Answer: So, most
students arrive
at school by
bus.
Method of Transportation
Used by Students to
Arrive at School
9-2
Circle Graphs
Use the graph to the right
that shows the favorite
fruit of students in Ms.
Bradley’s fifth grade class
to determine the fruit
most students prefer.
A. orange
B. banana
C. mango
D. apple
Favorite Fruits
9-2
Circle Graphs
Use the circle graph
to the right that
shows the method of
transportation
students use to get to
Martin Luther King,
Jr., Middle School.
Which two methods
of transportation are
used by the least
amount of students?
Method of Transportation
Used by Students to
Arrive at School
9-2
Circle Graphs
The smallest section of
the graph represents
riding a moped. The
next smallest section of
the graph represents
walking to school.
Answer: So, the least
amount of
students arrive at
school by moped
and by walking.
Method of Transportation
Used by Students to
Arrive at School
9-2
Circle Graphs
Use the graph to the right
that shows the favorite
fruit of students in Ms.
Bradley’s fifth grade class
to determine the fruit the
fewest students prefer.
A. orange
B. banana
C. mango
D. apple
Favorite Fruits
9-2
Circle Graphs
Use the circle graph
to the right that shows
the method of
transportation
students use to get to
Martin Luther King,
Jr., Middle School.
How does the number
of students who ride
mopeds compare to
the number of
students who take the
bus?
Method of Transportation
Used by Students to
Arrive at School
9-2
Circle Graphs
The section representing
taking the bus is about 5
times larger than the
section representing
riding a moped.
Answer: So, 5 times as
many students
take the bus.
Method of Transportation
Used by Students to
Arrive at School
9-2
Circle Graphs
Use the graph to the
right that shows the
favorite fruit of
students in Ms.
Bradley’s fifth grade
class to compare the
number of students
who preferred mango
to the number of
students who preferred
apple.
Favorite Fruits
9-2
Circle Graphs
Use the graph on the previous slide that shows
compare the number of students who preferred
mango to the number of students who preferred
apple.
A. 4 times as many students prefer apples.
B. 4 times as many students prefer mangoes.
C. 3 times as many students prefer apples.
D. 3 times as many students prefer mangoes.
9-3
Percents and Decimals
Five-Minute Check (over Lesson 9-2)
Main Idea
California Standards
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
9-3
Percents and Decimals
• I will express percents as decimals and decimals
as percents.
9-3
Percents and Decimals
Standard 5NS1.2 Interpret percents as a
part of a hundred; find decimal and percent
equivalents for common fractions and explain
why they represent the same value; compute a
given percent of a whole number.
9-3
Percents and Decimals
Write 86% as a decimal.
86
86% =
100
= 0.86
Rewrite the percent as a fraction
with a denominator of 100.
Write 86 hundredths as a decimal.
9-3
Percents and Decimals
Write 75% as a decimal.
A. 7.5
B. 0.075
C. 0.75
D. 7.05
9-3
Percents and Decimals
Write 1% as a decimal.
1
1% =
100
= 0.01
Rewrite the percent as a fraction
with a denominator of 100.
Write 1 hundredths as a decimal.
9-3
Percents and Decimals
Write 7% as a decimal.
A. 0.7
B. 0.007
C. 7.0
D. 0.07
9-3
Percents and Decimals
Write 110% as a decimal.
110
110% =
100
Rewrite the percent as a fraction
with a denominator of 100.
10
= 1
100
Write as a mixed number.
= 1.10
Write 1 and 10 hundredths as a decimal.
= 1.1
9-3
Percents and Decimals
Write 130% as a decimal.
A. 1.3
B. 13.0
C. 0.113
D. 1.13
9-3
Percents and Decimals
Write 0.44 as a percent.
44
0.44 =
100
= 44%
Write 44 hundredths as a fraction.
Write the fraction as a percent.
9-3
Percents and Decimals
Write 0.65 as a percent.
A. 65%
B. 6.5%
C. 650%
D. 0.65%
9-3
Percents and Decimals
Write 1.81 as a percent.
81
1.81 = 1
100
Write 1 and 81 hundredths as a
mixed number.
181
=
100
Write the mixed number as an
improper fraction.
= 181%
Write the fraction as a percent.
9-3
Percents and Decimals
Write 2.37 as a percent.
A. 2.37%
B. 23.7%
C. 237%
D. 23%
9-3
Percents and Decimals
Write 0.09 as a percent.
0.09 =
9
100
= 9%
Write 9 hundredths as a fraction.
Write the fraction as a percent.
9-3
Percents and Decimals
Write 0.03 as a percent.
A. 30%
B. 300%
C. 3%
D. 0.3%
9-3
Percents and Decimals
During a particularly rainy June in Boston, it rained
0.8 of the days in the month. Write 0.8 as a percent.
0.8 =
8
10
Write 8 tenths as a fraction.
=
8 × 10
10 × 10
Multiply the numerator and denominator
by 10 so that the denominator is 100.
=
80
100
Simplify.
= 80%
Write the fraction as a percent.
9-3
Percents and Decimals
Write 0.5 as a percent.
A. 5%
B. 50%
C. 0.5%
D. 500%
9-4
Problem-Solving Strategy: Solve a Simpler Problem
Five-Minute Check (over Lesson 9-3)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
9-4
Problem-Solving Strategy: Solve a Simpler Problem
• I will solve problems by solving a simpler problem.
9-4
Problem-Solving Strategy: Solve a Simpler Problem
Standard 5MR2.2 Apply strategies and results
from simpler problems to more complex
problems.
Standard 5NS1.2 Interpret percents as a
part of a hundred; find decimal and percent
equivalents for common fractions and explain why
they represent the same value; compute a given
percent of a whole number.
9-4
Problem-Solving Strategy: Solve a Simpler Problem
A total of 400 students at
Liberty Elementary voted on
whether a tiger or a dolphin
should be the new school’s
mascot. The circle graph
shows the results. How many
students voted for the tiger
for the school mascot?
9-4
Problem-Solving Strategy: Solve a Simpler Problem
Understand
What facts do you know?
• 400 students voted.
• 70% of the students voted for the tiger.
What do you need to find?
• How many students voted for the tiger for the
school mascot?
9-4
Problem-Solving Strategy: Solve a Simpler Problem
Plan
Solve a simpler problem by finding 10% of the
number of students that voted. Then use that result
to find 70% of the number of students that voted.
9-4
Problem-Solving Strategy: Solve a Simpler Problem
Solve
Since 10% =
or
, 1 out of every 10
students voted for the tiger.
400 ÷ 10 = 40 students.
Since 70% is equal to 7 times 10%, multiply 40 by 7.
40 × 7 = 280 students.
Answer: So, 280 students voted for the tiger.
9-4
Problem-Solving Strategy: Solve a Simpler Problem
Check
Look back at the problem. You know that 70% is close
to 75%, which is
. Since
of 400 is 100,
300. So, 280 is a reasonable answer.
of 400 is
9-5
Estimating with Percents
Five-Minute Check (over Lesson 9-4)
Main Idea
California Standards
Key Concept: Percent-Fraction Equivalents
Example 1
Example 2
Example 3
Example 4
Estimating with Percents
9-5
Estimating with Percents
• I will estimate the percent of a number.
9-5
Estimating with Percents
Standard 5MR2.2 Apply strategies and results
from simpler problems to more complex
problems.
Standard 5NS2.5 Compute and perform simple
multiplication and division of fractions and apply
these procedures to solving problems.
9-5
Estimating with Percents
9-5
Estimating with Percents
Estimate 49% of 302.
49% is close to 50% or
1
. Round 302 to 300.
2
1
of 300 is 150.
2
1
or half means to divide by 2.
2
Answer: So, 49% of 302 is about 150.
9-5
Estimating with Percents
Estimate 51% of 599.
A. 300
B. 250
C. 350
D. 200
9-5
Estimating with Percents
Estimate 80% of 42.
80% is
4
. Round 42 to 40 since it is divisible by 5.
5
4
4
of 40 = × 40 or 32
5
5
Answer: Thus, 80% of 42 is about 32.
9-5
Estimating with Percents
Estimate 75% of 41.
A. 40
B. 35
C. 30
D. 32
9-5
Estimating with Percents
A CD that originally cost $11.90 is on sale for 30%
off. If you have $7, would you have enough money
to buy the CD?
To determine whether you have enough money to buy
the CD, you need to estimate 30% of $11.90.
9-5
Estimating with Percents
One Way: Use an equation.
1
30% is about and $11.90 is about $12.
3
x
1
=
12
3
Write the equation.
x
1
=
12
3
Since 3 × 4 = 12, multiply 1 by 4.
x=4
9-5
Estimating with Percents
Another Way: Use mental math.
1
30% is about and $11.90 is about $12.
3
1
of $12 is about $4.
3
Answer: Since 30% off or $11.90 – $4.00 =
$7.90, you would not have enough
money for the CD.
9-5
Estimating with Percents
Admission to the theme park was originally $50. Lou
has a coupon for 25% off. His mom gave him $40.
Does he have enough money to buy the ticket?
A. Yes
B. No
C. Maybe
D. Not enough information
9-5
Estimating with Percents
Claire surveyed her classmates about their favorite
national park in California. Predict the number of
students out of 234 who prefer the Redwood
National Forest.
9-5
Estimating with Percents
You need to estimate the number of students out of 234
that preferred Redwood National Forest. 26% of the
students surveyed chose Redwood National Forest.
26% is about 25% or
1
.
4
Round 234 to 240 since it is divisible by 4.
1
1
4 of 240 = 4 × 240 or 60.
Answer: So, about 60 students would prefer
Redwood National Forest.
9-5
Estimating with Percents
Claire surveyed her classmates about their favorite
national park in California. Predict the number of
students out of 234 who prefer the Yosemite
National Park.
A. 80 students
B. 75 students
C. 60 students
D. 85 students
9-6
Percent of a Number
Five-Minute Check (over Lesson 9-5)
Main Idea
California Standards
Example 1
Example 2
Example 3
9-6
Percent of a Number
• I will find the percent of a number.
9-6
Percent of a Number
Standard 5NS1.2 Interpret percents as a
part of a hundred; find decimal and percent
equivalents for common fractions and explain why
they represent the same value; compute a given
percent of a whole number.
9-6
Percent of a Number
Find 7% of 400.
To find 7% of 400, you can use either method.
One Way: Write the percent as a fraction.
7% = 7
100
7
7
of 400 =
× 400 or 28
100
100
9-6
Percent of a Number
Another Way: Write the percent as a decimal.
7% = 7
or 0.07
100
0.07 of 400 = 0.07 × 400 or 28
Answer: So, 7% of 400 is 28.
9-6
Percent of a Number
Find 5% of 400.
A. 20
B. 25
C. 22
D. 30
9-6
Percent of a Number
Find 130% of 80.
9-6
Percent of a Number
One Way: Write the percent as a fraction.
130% = 130 or 13
100
10
13
13
of 80 =
× 80
10
10
13
80
or 104
×
10
1
9-6
Percent of a Number
Another Way: Write the percent as a decimal.
130% = 130 or 1.3
100
1.3 of 80 = 1.3 × 80 or 104
Answer: So, 130% of 80 is 104.
9-6
Percent of a Number
Find 140% of 20.
A. 30
B. 28
C. 70
D. 15
9-6
Percent of a Number
The Adams School raised money for a field trip by
selling the items shown in the circle graph. If the
school collected $596, how much did the school
raise with the book sale?
9-6
Percent of a Number
You need to find 28% of $596.
28% =
28
100
= 0.28
Definition of a percent
Write 28 hundredths as a decimal.
0.28 of $596 = 0.28 × 596
= 166.88
Multiply.
Answer: So, the school raised $166.88 with the
book sale.
9-6
Percent of a Number
If the school raised $455, how much did the school
raise with the baked goods sale?
A. $109.20
B. $110
C. $108.98
D. $111.15
9-7
Problem-Solving Investigation: Choose the Best Strategy
Five-Minute Check (over Lesson 9-6)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
9-7
Problem-Solving Investigation: Choose the Best Strategy
• I will choose the best strategy to solve a problem.
9-7
Problem-Solving Investigation: Choose the Best Strategy
Standard 5MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.
Standard 5NS1.2 Interpret percents as a part
of a hundred; . . . compute a given percent of a
whole number.
9-7
Problem-Solving Investigation: Choose the Best Strategy
TYRA: I’m going to the mall with $75
to buy a shirt, a pair of jeans, and
a hat. The hat costs $15, which is
50% of the cost of one shirt. The
shirt costs $10 less than the jeans.
If I spend more than $50, I get a
15% discount off of the total price.
YOUR MISSION: Determine if Tyra has
enough money to buy all three items.
9-7
Problem-Solving Investigation: Choose the Best Strategy
Understand
What facts do you know?
• Tyra has $75 to spend.
What do you need to find?
• You need to determine if Tyra has enough
money to buy all three items.
9-7
Problem-Solving Investigation: Choose the Best Strategy
Plan
You can work backward to find the amount that each
item costs. Then find out how much she spent.
9-7
Problem-Solving Investigation: Choose the Best Strategy
Solve
The hat is 50% of the cost of one shirt. So, one shirt
costs $15 × 2 or $30. The cost of the jeans is $10
more than the cost of the shirt. So, the jeans cost
$30 + $10 or $40. So, Tyra spent $15 + $30 + $40
or $85.
Since she spent a total of $85, she gets a 15%
discount.
85 × 15% → 85 × 0.15 = $12.75
The discount is $12.75.
9-7
Problem-Solving Investigation: Choose the Best Strategy
Solve
Answer: So, Tyra spent $85 – $12.75 or
$72.25. Since $72.25 is less than
$75, Tyra has enough money.
9-7
Problem-Solving Investigation: Choose the Best Strategy
Check
Start with the cost of the jeans. The jeans cost
$40. The shirt costs are $40 – $10 or $30. The
hat is 50% of the cost of the shirt, so the hat is
$30 ÷ 2 or $15.
9-8
Probability
Five-Minute Check (over Lesson 9-7)
Main Idea and Vocabulary
California Standards
Key Concept: Probability
Example 1
Example 2
Example 3
Example 4
9-8
Probability
• I will find and interpret the probability of a simple
event.
• outcomes
• random
• simple event
• complementary events
• probability
9-8
Probability
Preparation for Standard 6SDAP3.3 Represent
probabilities as ratios, proportions, decimals
between 0 and 1, and percentages between 0
and 100 and verify that the probabilities computed
are reasonable; know that if P is the probability
of an event, 1 – P is the probability of an event
not occurring.
9-8
Probability
9-8
Probability
There are six equally
likely outcomes on the
spinner to the right.
Find the probability of
landing on 1.
There is one section of
the spinner labeled 1.
9-8
Probability
P(1) =
number of favorable outcomes
number of possible outcomes
1
=
6
1
Answer: The probability of landing on 1 is ,
6
0.167, or 16.7%.
9-8
Probability
There are six equally likely outcomes on the
spinner below. Find the probability of landing
on an even number.
A. 50%
B. 40%
C. 25%
D. 75%
9-8
Probability
There are six equally
likely outcomes on the
spinner to the right.
Find the probability of
landing on 2 or 4.
The word or indicates that
the favorable outcomes
are the 2 and 4 sections.
There is one section of
the spinner that is a 2 and
one section that is a 4.
9-8
Probability
P(2 or 4) =
number of favorable outcomes
number of possible outcomes
2
=
6
1
=
3
Simplify.
1
Answer: The probability of landing on 2 or 4 is ,
3
0.33, or 33%.
9-8
Probability
There are six equally likely outcomes on the spinner
below. Find the probability of landing on a number
greater than 2.
3
A. 4
1
A. 4
3
A. 6
2
A. 3
9-8
Probability
The spinner is spun
once. Find the
probability of not
landing on a 6.
The probability of not
landing on a 6 and the
probability of landing on a
6 are complementary.
9-8
Probability
P(6) + P(not 6) =
1
The sum of the probabilities is 1.
1
+ P(not 6) =
6
1
Replace P(6) with
– 1
6
= –1
6
5
P(not 6) =
6
Subtract
1
.
6
1
from each side.
6
5
Answer: So, the probability of not landing on 6 is ,
6
0.8333…, or 83.33%.
9-8
Probability
The spinner is spun once. Find the probability of
not landing on an even number.
A. 30%
B. 50%
C. 40%
D. 25%
9-8
Probability
A sportscaster predicted that the Tigers have a
75% chance of winning tonight. Describe the
complement of the event and find its probability.
The complement of winning is not winning. The sum of
the probabilities is 100%.
9-8
Probability
P(winning) + P(not winning) = 100%
75% + P(not winning) = 100%
– 75%
= – 75%
P(not winning) =
25%
Replace P(winning)
with 75%.
Subtract 75% from
each side.
Answer: So, the probability that the Tigers will not win
1
is 25%, , or 0.25.
4
9-8
Probability
The weathercaster reported a 40% chance of
thunderstorms. Identify the complement. Then
find its probability.
A. 60% chance of not storming
B. 40% chance of not storming
C. 50% chance of not storming
D. 45% chance of not storming
9-9
Sample Spaces
Five-Minute Check (over Lesson 9-8)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
9-9
Sample Spaces
• I will construct sample spaces using tree diagrams
or lists.
• sample space
• tree diagram
9-9
Sample Spaces
Preparation for Standard 6SDAP3.1 Represent all
possible outcomes for compound events in an
organized way (e.g. tables, grids, tree diagrams)
and express the theoretical probability of each
outcome.
9-9
Sample Spaces
While on vacation, Carlos can snorkel, boat, and
paraglide. In how many ways can Carlos do the
three activities?
Make an organized list to show the sample space.
Let S = snorkel, B = boat, and P = paraglide.
SBP
BPS
PBS
SPB
BSP
PSB
Answer: So, there are 6 ways to do the three activities.
9-9
Sample Spaces
While shopping at the store, Louisa must get toilet
paper, milk, bread, and cat food. How many different
ways can she collect these items?
A. 16
B. 64
C. 24
D. 30
9-9
Sample Spaces
A car can be purchased with either two doors or
four doors. You may also choose leather, fabric, or
vinyl seats. Use a tree diagram to find all the buying
options.
List each door choice. Then pair each door choice with
each seat choice.
9-9
Sample Spaces
Car
2-door (2)
4-door (4)
Seat
Outcome
leather (L)
2L
fabric (F)
2F
vinyl (V)
2V
leather (L)
4L
fabric (F)
4F
vinyl (V)
4V
Answer: There are 6 possible combinations.
9-9
Sample Spaces
At the ice cream store, you can order either a sugar
cone or a cake cone. You may also choose from
chocolate, strawberry, vanilla, or orange sherbet ice
cream flavors. How many combinations of cone and
ice cream can I get?
A. 6
B. 8
C. 10
D. 16
9-9
Sample Spaces
Dayo rolls two number cubes. What is the
probability that she will roll a 5 on the first cube
and a 2 on the second cube?
Use a tree diagram to find all of the possible outcomes.
Sample Spaces
9-9
1
2
3
4
5
6
123456 123456 123456 123456 123456 123456
Notice there is only one combination of 5 first then 2.
Answer: Since there are 36 possible outcomes and
only one favorable outcome, the probability
of rolling a 5 on the first cube and a 2 on the
second is 1 .
36
9-9
Sample Spaces
Joy rolls two number cubes. What is the probability
that she will roll a 3 and a 4?
1
A. 36
1
B. 18
2
C. 36
1
D. 63
9-10
Making Predictions
Five-Minute Check (over Lesson 9-9)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
9-10
Making Predictions
• I will predict the actions of a larger group using
a sample.
• survey
• population
• sample
9-10
Making Predictions
Standard 5AF1.2 Use a letter to represent
an unknown number; write and evaluate simple
algebraic expressions in one variable by substitution.
9-10
Making Predictions
Bonne asked every sixth person in the school
cafeteria to name the kind of activity he or she
would like to do for the school’s spring outing.
What is the probability that a student will prefer an
amusement park?
9-10
Making Predictions
P(amusement park) =
=
number of students that prefer
the amusement park
number of students surveyed
15
40
Answer: So, 15 out of 40 or 15 , 0.375, or 37.5%
40
will prefer the amusement park.
9-10
Making Predictions
Use the table below to answer the following
question. What is the probability that a student
prefers chocolate ice cream?
22
A. 55
2
B. 5
11
C. 25
22
D. 50
9-10
Making Predictions
There are 400 students
at Julia’s school.
Predict how many
students prefer going
to an amusement park.
Let s represent the
number of students that
prefer going to an
amusement park.
9-10
Making Predictions
s
400
15
40
=
15
40
s
=
400
Since 40 × 10 = 400, multiply
15 by 10 to find s.
15
40
150
=
400
s = 150
Write an equation.
Answer: Of 400 students, about 150 will prefer the
amusement park.
9-10
Making Predictions
There are 550 students at Corbin’s school. Predict
how many of the students will prefer strawberry.
A. 170 students
B. 55 students
C. 130 students
D. 155 students
9
Percent
Five-Minute Checks
Circle Graphs
Estimating with Percents
9
Percent
Lesson 9-1
(over Chapter 8)
Lesson 9-2
(over Lesson 9-1)
Lesson 9-3
(over Lesson 9-2)
Lesson 9-4
(over Lesson 9-3)
Lesson 9-5
(over Lesson 9-4)
Lesson 9-6
(over Lesson 9-5)
Lesson 9-7
(over Lesson 9-6)
Lesson 9-8
(over Lesson 9-7)
Lesson 9-9
(over Lesson 9-8)
Lesson 9-10 (over Lesson 9-9)
9
Percent
(over Chapter 8)
While driving on a vacation, the Nguyen family
traveled at an average speed of 60 miles per hour.
Make a table to show the relationship between the
total distance d the family traveled in h hours.
A.
9
Percent
(over Chapter 8)
While driving on a vacation, the Nguyen family
traveled at an average speed of 60 miles per hour.
Make a table to show the relationship between the
total distance d the family traveled in h hours.
B.
9
Percent
(over Chapter 8)
While driving on a vacation, the Nguyen family
traveled at an average speed of 60 miles per hour.
Make a table to show the relationship between the
total distance d the family traveled in h hours.
C.
9
Percent
(over Chapter 8)
While driving on a vacation, the Nguyen family
traveled at an average speed of 60 miles per hour.
Make a table to show the relationship between the
total distance d the family traveled in h hours.
D.
9
Percent
(over Chapter 8)
While driving on a vacation, the Nguyen family
traveled at an average speed of 60 miles per hour.
Make a table to show the relationship between the
total distance d the family traveled in h hours.
D.
9
Percent
(over Chapter 8)
While driving on a vacation, the Nguyen family
traveled at an average speed of 60 miles per hour.
Write an equation to find the total distance d that
the Nguyen family traveled in h hours.
A. d = 30h2
B. d = 60h
C. d = 20h3
9
Percent
(over Chapter 8)
While driving on a vacation, the Nguyen family
traveled at an average speed of 60 miles per hour.
How many miles did the Nguyen family travel in 4
hours?
A. 120 miles
B. 100 miles
C. 240 miles
9
Percent
(over Lesson 9-1)
Write 35% as a fraction or a mixed number in
simplest form.
A.
7
20
B. 3
5
1
C. 3
D. 1
3
4
9
Percent
(over Lesson 9-1)
Write 4% as a fraction or a mixed number in
simplest form.
A.
4
10
40
B. 100
C. 1
3
5
1
D.
25
9
Percent
(over Lesson 9-1)
Write 175% as a fraction or a mixed number in
simplest form.
A. 1
3
4
17
B. 150
C. 1
D. 2
3
5
6
9
Percent
(over Lesson 9-1)
Write 2 as a percent.
5
A. 25%
B. 40%
C. 35%
2
D. 1
5
9
Percent
(over Lesson 9-1)
Write 3 as a percent.
25
A. 15%
B. 2
3
5
C. 40%
D. 12%
9
Percent
(over Lesson 9-1)
Write 2 3 as a percent.
5
A. 260%
B. 35%
C. 125%
3
D. 2
5
9
Percent
(over Lesson 9-2)
Sketch a circle graph of this data: In a survey of
preferences of four careers, 14% of students chose
teacher, 25% chose doctor, 25% chose lawyer, and
36% chose musician.
A.
9
Percent
(over Lesson 9-2)
Sketch a circle graph of this data: In a survey of
preferences of four careers, 14% of students chose
teacher, 25% chose doctor, 25% chose lawyer, and
36% chose musician.
B.
9
Percent
(over Lesson 9-2)
Sketch a circle graph of this data: In a survey of
preferences of four careers, 14% of students chose
teacher, 25% chose doctor, 25% chose lawyer, and
36% chose musician.
C.
9
Percent
(over Lesson 9-2)
Sketch a circle graph of this data: In a survey of
preferences of four careers, 14% of students chose
teacher, 25% chose doctor, 25% chose lawyer, and
36% chose musician.
D.
9
Percent
(over Lesson 9-2)
Sketch a circle graph of this data: In a survey of
preferences of four careers, 14% of students chose
teacher, 25% chose doctor, 25% chose lawyer, and
36% chose musician.
B.
9
Percent
(over Lesson 9-3)
Write 98% as a decimal.
A. 0.98
B. 1.98
C. 0.02
D. 0.20
9
Percent
(over Lesson 9-3)
Write 7% as a decimal.
A. 0.70
B. 1.03
C. 0.07
D. 0.93
9
Percent
(over Lesson 9-3)
Write 135% as a decimal.
A. 13.5
B. 1.035
C. 1.35
D. 0.65
9
Percent
(over Lesson 9-3)
Write 0.79 as a percent.
A. 21%
B. 79%
C. 7.9%
D. 0.79%
9
Percent
(over Lesson 9-3)
Write 0.03 as a percent.
A. 3%
B. 93%
C. 30%
D. 1.3%
9
Percent
(over Lesson 9-3)
Write 1.09 as a percent.
A. 1.9%
B. 19%
C. 0.19%
D. 109%
9
Percent
(over Lesson 9-4)
Use the solve a simpler problem strategy to solve
this problem. A team needs to assemble 1,200
boxes. They can assemble 45 boxes every 30
minutes. If they work 8 hours a day, can they
assemble all the boxes in one day? Explain.
A. No; they can make only 720 boxes in one day.
B. Yes; they can make 1,200 boxes.
9
Percent
(over Lesson 9-5)
Estimate 19% of $78.
A.
1
of $80; $16
5
B.
1
of $70; $15
6
2
C.
of $90; $20
8
9
Percent
(over Lesson 9-5)
Estimate 53% of 220.
2
A.
of 200; 150
5
B.
3
of 250; 225
5
1
C.
of 200; 100
2
9
Percent
(over Lesson 9-5)
Estimate 69% of 20.
7
A.
of 20; 14
10
B.
6
of 20; 16
10
8
C.
of 20; 8
10
9
Percent
(over Lesson 9-5)
Estimate 4% of 20.
1
A.
of 20; 1
20
B.
4
of 20; 16
5
1
C.
of 20; 6
4
9
Percent
(over Lesson 9-6)
Find 50% of 786.
A. 409
B. 343
C. 410
D. 393
9
Percent
(over Lesson 9-6)
Find 100% of 150.
A. 75
B. 150
C. 100
D. 1,500
9
Percent
(over Lesson 9-6)
Find 8% of 25.
A. 2
B. 12
C. 4
D. 20
9
Percent
(over Lesson 9-6)
Find 75% of 84.
A. 75
B. 24
C. 63
D. 76
9
Percent
(over Lesson 9-6)
Find 105% of 40.
A. 42
B. 65
C. 60
D. 105
9
Percent
(over Lesson 9-7)
Use any strategy to solve this problem. Explain how
you used the strategy. Tickets for a town fair cost
$25 for adults and $10 for students. The town
collected $2,045 for 107 tickets. How many student
tickets were sold?
A. 107 student tickets
B. 2,045 student tickets
C. 42 student tickets
D. 35 student tickets
9
Percent
(over Lesson 9-8)
Find each probability for a spinner with 8 sections
that are marked 1, 2, 3, 4, 5, 6, 7, and 8.
P(even number)
A.
1
3
B.
1
7
1
C. 8
D.
1
2
9
Percent
(over Lesson 9-8)
Find each probability for a spinner with 8 sections
that are marked 1, 2, 3, 4, 5, 6, 7, and 8.
P(number > 3)
A.
1
9
B.
3
8
5
C. 8
D.
6
8
9
Percent
(over Lesson 9-8)
Find each probability for a spinner with 8 sections
that are marked 1, 2, 3, 4, 5, 6, 7, and 8.
P(not an even number)
A.
3
8
B.
3
5
1
C. 2
D.
3
7
9
Percent
(over Lesson 9-8)
Find each probability for a spinner with 8 sections
that are marked 1, 2, 3, 4, 5, 6, 7, and 8.
P(number not > 3)
A.
3
8
B.
1
2
3
C. 8
D.
1
3
9
Percent
(over Lesson 9-9)
An ice cream wagon offers chocolate, strawberry,
and vanilla ice cream cones. You can have a waffle
cone or a sugar cone with one scoop of ice cream.
Find the sample space and tell how many outcomes
are possible.
A. 3 outcomes: WC, WS, WV
B. 3 outcomes: SC, SS, SV
C. 6 outcomes: WC, WS, WV, SC, SS, SV
9
Percent
(over Lesson 9-9)
You roll a number cube twice. You record one
number from the first roll and another number from
the second roll. Tell how many outcomes are
possible.
A. 24 outcomes
B. 36 outcomes
C. 12 outcomes
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