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Mathematics: Applications and Concepts, Course 1 Interactive Chalkboard
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Lesson 10-1
Ratios
Lesson 10-2
Solving Proportions
Lesson 10-3
Scale Drawings and Models
Lesson 10-4
Modeling Percents
Lesson 10-5
Percents and Fractions
Lesson 10-6
Percents and Decimals
Lesson 10-7
Percent of a Number
Lesson 10-8
Estimating with Percents
Example 1 Write a Ratio in Simplest Form
Example 2 Use Ratios to Compare Parts of a Whole
Example 3 Find Unit Rate
RECREATION Write the ratio
that compares the number of
unicycles to the number of
scooters.
For every 11 unicycles, there
are 5 scooters.
Answer: The ratio of unicycles to scooters is
11 to 5, or 11:5.
FRUIT Write the ratio that compares the number of
apples to the number of oranges.
Answer:
BOOKS Write the ratio that compares the number of
books about sports to the total number of books.
For every five sports books, there are eight total books.
Answer: The ratio of books about sports to the total
number of books is
5 to 8, or 5:8.
SPORTS Write the ratio that compares the number of
basketballs to the total number of sports balls.
Answer:
FOOD Find the cost per ounce of a 16-ounce jar of
salsa that costs $2.88.
Divide the numerator and
denominator by 16 to get a
denominator of 1.
Answer: So, the cost per ounce of the salsa is $0.18.
TEMPERATURE The outside temperature rises 32
degrees in four hours. Find the temperature increase
for one hour.
Answer:
Example 1 Solve a Proportion
Example 2 Solve a Proportion
Example 3 Use a Proportion to Solve a Problem
Solve
Cross products
Multiply.
Divide each side by 4.
Answer: The solution is 35.
Solve
Answer: 24
Solve
Cross products
Multiply.
Divide each side by 1.2.
Answer: The solution is 0.5.
Solve
Answer: 3
SPORTS Out of the 40 students in a gym class, 12 rate
soccer as their favorite sport. Based on this result,
how many of the 4,200 students in the community will
rate soccer as their favorite sport?
Write and solve a proportion. Let s represent the number of
students who can be expected to rate soccer as their
favorite sport.
soccer as favorite sport 
total students in class 
 soccer as favorite sport
total students in community
Cross products
Multiply.
Divide.
Answer: So, 1,260 of the students in the community can
be expected to rate soccer as their favorite sport.
BUSINESS Out of 50 people in one department of a
large corporation, 35 stated that they enjoy their job.
Based on this result, how many of the 2,400 employees
of this corporation can be expected to say that they
enjoy their job?
Answer: 1,680 employees
Example 1 Find Actual Measurements
Example 2 Find Actual Measurements
MONUMENTS A scale model of the Washington
Monument has a scale of
If the height
of the model is 5.55 feet, what is the actual height of
the monument?
Let x represent the actual height.
Scale Model
Monument
 model height
model height 
actual height 
 actual height
Find the cross products.
Multiply.
Answer: The actual height of the monument is 555 feet.
CARS A scale model of a car has a scale of
inches. If the length of the car model
is 5 inches, what is the actual length of the car?
Answer: 120 in.
STATES On a map of Pennsylvania, the distance
between Pittsburgh and Harrisburg is 2.5 inches. If the
scale on the map is
what is the
actual distance between Pittsburgh and Harrisburg?
Let d represent the actual distance.
Map Scale
Actual Distance
 map distance
map distance 
actual distance 
 actual distance
Find the cross products.
Multiply.
Answer: The actual distance is 155 miles.
MAPS On a map, the distance between two small
towns is 8.5 inches. If the scale on the map is
what is the actual distance
between the two small towns?
Answer: 340 mi
Example 1 Model a Percent
Example 2 Identify a Percent
Example 3 Identify a Percent
60% means 60 out of 100. So, shade 60 of the 100 squares.
Answer:
Answer:
Identify the percent that is modeled.
There are 75 out of 100 squares shaded.
Answer: So, the model shows 75%.
Identify the percent that is modeled.
Answer: 45%
Identify the percent that is modeled.
There are 30 out of 100 squares shaded.
Answer: So, the model shows 30%.
Identify the percent that is modeled.
Answer: 5%
Example 1 Write a Percent as a Fraction
Example 2 Write a Percent as a Fraction
Example 3 Write a Percent as a Fraction
Example 4 Write a Fraction as a Percent
Example 5 Write a Fraction as a Percent
Write 60% as a fraction in simplest form.
60% means 60 out of 100.
Write the percent as
a fraction with a
denominator of 100.
3
5
Answer:
Simplify. Divide the
numerator and
denominator by the
GCF, 20.
Write 30% as a fraction in simplest form.
Answer:
Write 140% as a fraction in simplest form.
140% means 140 for every 100.
Write the percent as a fraction with
a denominator of 100.
2
Simplify. Divide the numerator and
denominator by the GCF, 20.
5
Answer:
Write 180% as a fraction in simplest form.
Answer:
LUNCH Use the table below. What fraction of the class
members preferred spaghetti for the school lunch?
School Lunch Choices
Lunch
pizza
spaghetti
hamburger
chicken strips
soup
Percent
30%
25%
20%
15%
10%
The table shows that 25% of the class members preferred
spaghetti.
Write the percent as a fraction with
a denominator of 100.
Simplify.
Answer: So,
of the class members preferred spaghetti
for the school lunch.
ICE CREAM Use the table below. What fraction of the
students chose chocolate as their favorite flavor?
Students Favorite Ice
Cream Flavor
Flavor
Percent
vanilla
37%
Answer:
chocolate
chocolate chip
Strawberry
28%
20%
8%
Other
7%
Write
as a percent.
Set up a proportion.
Write the cross products.
Multiply.
Divide each side by 10.
Simplify.
Answer: So,
is equivalent to 70%.
Write
as a percent.
Answer: 40%
Write
as a percent.
Set up a proportion.
Write the cross products.
Multiply.
Divide each side by 5.
Simplify.
Answer: So,
is equivalent to 240%.
Write
as a percent.
Answer: 225%
Example 1 Write a Percent as a Decimal
Example 2 Write a Percent as a Decimal
Example 3 Write a Percent as a Decimal
Example 4 Write a Decimal as a Percent
Example 5 Write a Decimal as a Percent
Write 86% as a decimal.
Rewrite the percent as a fraction
with a denominator of 100.
Write the fraction as a decimal.
Answer: 0.86
Write 34% as a decimal.
Answer: 0.34
Write 112% as a decimal.
Rewrite the percent as a fraction
with a denominator of 100.
Write the fraction as a decimal.
Answer: 1.12
Write 154% as a decimal.
Answer: 1.54
Write 0.9% as a decimal.
0.9% means nine-tenths of one percent.
Rewrite the percent as a fraction
with a denominator of 100.
Multiply by
to eliminate the
decimal in the numerator.
Write the fraction as a decimal.
Answer: 0.009
Write 0.2% as a decimal.
Answer: 0.002
Write 0.44 as a percent.
Write the decimal as a fraction.
Write the fraction as a percent.
Answer: 44%
Write 0.82 as a percent.
Answer: 82%
Write 0.254 as a percent.
Write the decimal as a fraction.
Divide the numerator and
denominator by 10.
Write the fraction as a percent.
Answer: 25.4%
Write 0.683 as a percent.
Answer: 68.3%
Example 1 Find the Percent of a Number
Example 2 Find the Percent of a Number
Example 3 Find the Percent of a Number
Find 8% of 125.
Method 1
Write the percent as a fraction.
Method 2
Write the percent as a decimal.
So, 8% of 125 is 10. Use a model to check the answer.
Answer: The model confirms that 8% of 125 is 10.
Find 6% of 150.
Answer: 9
Find 125% of 64.
Method 1
Write the percent as a fraction.
Method 2
Write the percent as a decimal.
So, 125% of 64 is 80. Use a model to check your answer.
Answer: The model confirms that 125% of 64 is 80.
Find 175% of 240.
Answer: 420
LANGUAGES The graph to the
right shows that 30% of the
people in a community speak
Spanish as their first language.
If a community has 800 people,
how many people can be
expected to speak Spanish as
their first language?
Answer: So, 240 people can be expected to speak
Spanish as their first language.
SPORTS The graph below shows that 22% of the
students stated that baseball was their favorite sport. If
the seventh grade class has 300 students, how many
can be expected to consider baseball their favorite
sport?
Answer: 66
Example 1 Estimate the Percent of a Number
Example 2 Estimate the Percent of a Number
Example 3 Use Estimation to Solve a Problem
Example 4 Estimate the Percent of a Figure
Estimate 49% of 302.
49% is close to 50% or
Round 302 to 300.
of 300 is 150.
Answer: So, 49% of 302 is about 150.
Estimate 26% of 122.
Sample answer: 30
Estimate 80% of 1,605.
80% is
Round 1,605 to 1,600.
160
1
Answer: So, 80% of 1,605 is about 1,280.
Estimate 40% of 1,207.
Sample answer: 480
MONEY 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 70% of $11.90.
70% of $11.90
Answer: Since $8.40 is $1.40 more than $7, you would
not have enough money.
MONEY A poster that originally cost $14.90 is on sale
for 40% off. If you have $10, would you have enough to
buy the poster?
Answer: yes
MULTIPLE-CHOICE TEST ITEM Which of the following
is a reasonable percent for the percent of the figure
that is shaded?
A 30%
B 50%
C 60%
D 75%
Read the Test Item
You need to find what percent of the circles are shaded.
Solve the Test Item
12 out of 16 circles are shaded.
So, 75% of the circles are shaded.
Answer: D
MULTIPLE-CHOICE TEST ITEM Which of the following
is a reasonable percent for the percent of the figure
that is shaded?
A 75%
Answer: B
B 40%
C 20%
D 9%
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