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Mathematics: Applications and Concepts, Course 2 Interactive Chalkboard
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GLENCOE DIVISION
Glencoe/McGraw-Hill
8787 Orion Place
Columbus, Ohio 43240
Lesson 5-1 Prime Factorization
Lesson 5-2 Greatest Common Factor
Lesson 5-3 Simplifying Fractions
Lesson 5-4 Fractions and Decimals
Lesson 5-5 Fractions and Percents
Lesson 5-6 Percents and Decimals
Lesson 5-7 Least Common Multiple
Lesson 5-8 Comparing and Ordering Rational Numbers
Example 1 Identify Numbers as Prime or Composite
Example 2 Identify Numbers as Prime or Composite
Example 3 Find the Prime Factorization
Example 4 Factor an Algebraic Expression
Determine whether the number 63 is prime or
composite.
Answer: The number 63 has six factors: 1, 3, 7, 9, 21,
and 63. So, it is composite.
Determine whether the number 41 is prime or
composite.
Answer: prime
Determine whether the number 29 is prime or
composite.
Answer: The number 29 has only two factors, 1 and 29,
so it is prime.
Determine whether the number 24 is prime or
composite.
Answer: composite
Find the prime factorization of 100.
Method 1 Use a factor tree.
Method 2 Divide by prime numbers.
Start here.
Answer: The prime factorization of 100 is
Find the prime factorization of 72.
Answer:
ALGEBRA Factor
Answer:
ALGEBRA Factor
Answer:
Example 1 Find the GCF by Listing Factors
Example 2 Find the GCF Using Prime Factors
Example 3 Find the GCF Using Prime Factors
Example 4 Find the GCF of an Algebraic Expression
Example 5 Use the GCF to Solve a Problem
Find the GCF of 28 and 42.
First, list the factors of 28 and 42.
factors of 28: 1, 2, 4, 7, 14, 28
factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Notice that 1, 2, 7, and 14 are common
factors of 28 and 42.
So, the GCF is 14.
Check You can draw a Venn diagram to check
your answer.
Answer: 14
Find the GCF of 18 and 45.
Answer: 9
Find the GCF of 20 and 32.
Method 1 Write the prime factorization.
The common prime factors are 2 and 2.
Method 2 Divide by prime numbers.
Divide both 20 and 32 by 2. Then divide the quotients by 2.
Start here.
Answer: The GCF of 20 and
Find the GCF of 24 and 36.
Answer: 12
Find the GCF of 21, 42, and 63.
Circle the common factors.
The common prime factors are 3 and 7.
Answer: The GCF is 3  7, or 21.
Find the GCF of 24, 48, and 60.
Answer: 12
ALGEBRA Find the GCF of 12p2 and 30p3.
Factor each expression.
Circle the common factors.
Answer: The GCF is 2
ALGEBRA Find the GCF of
Answer: 7mn
ART Searra wants to cut a 15-centimeter by
25-centimeter piece of tag board into squares for an
art project. She does not want to waste any of the tag
board and she wants the largest squares possible.
What is the length of the side of the squares she
should use?
The largest length of side possible is the GCF
of the dimensions of the tag board.
The GCF of 15 and 25 is 5.
Answer: Searra should use squares with
sides measuring 5 centimeters.
CANDY Alice is making candy baskets using
chocolate hearts and lollipops. She has 32 chocolate
hearts and 48 lollipops. She wants to have an equal
number of chocolate hearts and lollipops in each
basket. Find the greatest number of chocolate hearts
and lollipops Alice can put in each basket.
Answer: 16
Example 1 Write Fractions in Simplest Form
Example 2 Write Fractions in Simplest Form
Example 3 Use Fractions to Solve a Problem
Write
in simplest form.
First, find the GCF of the numerator and denominator.
factors of 12: 1, 2, 3, 4, 6, 12
factors of 45: 1, 3, 5, 9, 15, 45
The GCF of 12
and 45 is 3.
Then, divide the numerator and the denominator
by the GCF.
Check Multiply the numerator and denominator of the
answer by the GCF. The result should be the
original fraction.
Answer: So,
written in simplest form is
Write
Answer:
in simplest form.
Write
Answer:
in simplest form.
written in simplest form is
Write
Answer:
in simplest form.
MUSIC Two notes form a perfect fifth if the simplified
fraction of the frequencies of the notes equals
note
Hertz and note
Hertz, do
they form a perfect fifth?
If
The slashes mean that part of the
numerator and part of the denominator
are both divided by the same number.
For example,
1
1
1
1
1
1
Answer: The fraction of the frequencies of the notes
D and G is
perfect fifth.
So, the two notes do form a
MARBLES In a bag of 96 marbles, 18 of the marbles
are black. Write the fraction of black marbles in
simplest form.
Answer:
Example 1 Write Fractions as Decimals
Example 2 Write Fractions as Decimals
Example 3 Write Fractions as Repeating Decimals
Example 4 Write Fractions as Repeating Decimals
Example 5 Write Decimals as Fractions
Write
as a decimal.
The fraction
indicates
Method 1 Use paper and pencil.
Division ends when
the remainder is 0.
Method 2 Use a calculator.
1
8
ENTER
Answer:
0.125
Write
as a decimal.
Answer: 0.4
Write
as a decimal.
The mixed number
Method 1 Use paper and pencil.
Write as a sum.
Add.
Method 2 Use a calculator.
3
5
Answer:
7
ENTER
7.6
Write
as a decimal.
Answer: 3.625
Write
as a decimal.
Method 1 Use paper and pencil.
Method 2 Use a calculator.
1
11
Answer:
ENTER
0.090909
Write
as a decimal.
Answer:
Write
as a decimal.
Method 1 Use paper and pencil.
Write as a sum.
Write the fraction as a decimal.
Add.
Method 2 Use a calculator.
4
9
Answer:
6
ENTER
6.4444…
Write
Answer:
as a decimal.
Write 0.72 as a fraction in simplest form.
The 2 is in the hundredths place.
Simplify.
Answer:
Write 0.85 as a fraction in simplest form.
Answer:
Example 1 Write Ratios as Percents
Example 2 Write Ratios as Percents
Example 3 Write a Fraction as a Percent
Example 4 Write a Percent as a Fraction
Example 5 Use Percent to Solve a Problem
Write the ratio as a percent.
Diana scored 63 goals out of 100 attempts.
You can represent 63 out of 100 with a model.
Answer:
Write the ratio as a percent.
Alicia sold 34 of the 100 cookies at the bake sale.
Answer:
Write the ratio as a percent.
31.9 out of 100 people bought crunchy peanut butter.
Answer:
Write the ratio as a percent.
73.4 out of 100 people preferred the chicken
instead of the roast beef.
Answer:
Write
as a percent.
.… multiply the numerator
and denominator by 4.
Answer: So,
Write
Answer:
as a percent.
Write 22% as a fraction in simplest form.
Definition of percent
Simplify.
Answer:
Write 84% as a fraction in simplest form.
Answer:
RECREATION
The graphic shows the
most popular outdoor
activities according to
parents with children
ages 4 – 14. What
fraction of parents prefer
hiking as a favorite
outdoor activity?
In the bar graph,
15 parents chose hiking.
Find the total number of responses.
Answer: So,
of the parents chose hiking.
SPORTS Each member of the football team is
supposed to get playing time in each game. By the
end of the third quarter of a game, 17 of the 25
players had already been in the game. What percent
of the players is this?
Answer:
Example 1 Write Percents as Decimals
Example 2 Write Percents as Decimals
Example 3 Write Percents as Decimals
Example 4 Write Percents as Decimals
Example 5 Write Decimals as Percents
Example 6 Write Decimals as Percents
Example 7 Write Decimals as Percents
Example 8 Write Decimals as Percents
POPULATION According to the Administration on
Aging, about 28% of the population of the United
States is 19 years of age or younger. Write 28% as a
decimal.
Write the percent as a fraction.
Write the fraction as a decimal.
Answer:
AMUSEMENT PARK A popular amusement park
reports that 17% of its visitors will return at least
three times during the year. Write 17% as a decimal.
Answer: 0.17
Write 47.8% as a decimal.
Write the percent as a fraction.
Multiply by 10 to remove
the decimal in the numerator.
Simplify.
Write the fraction as a decimal.
Answer:
Write 83.2% as a decimal.
Answer: 0.832
Write 95.3% as a decimal.
Divide by 100.
Remove the %.
Answer:
Write 38% as a decimal.
Answer: 0.38
Write
as a decimal.
Divide by 100.
Remove the %.
Answer: 0.082
Write
as a decimal.
Answer: 0.2775
POPULATION In 1790, about 0.05 of the population of
the United States lived in an urban setting. Write 0.05
as a percent.
Definition of decimal
Definition of percent
Answer:
POPULATION In 2000, the population of Illinois had
increased by 0.086 from 1990. Write 0.086 as a
percent.
Answer: 8.6%
Write 0.121 as a percent.
Definition of decimal
Divide both numerator
and denominator by 10.
Definition of percent
Answer:
Write 0.364 as a percent.
Answer: 36.4%
Write 0.33 as a percent.
Multiply by 100.
Add the %.
Answer:
Write 0.52 as a percent.
Answer: 52%
Write 0.419 as a percent.
Multiply by 100.
Add the %.
Answer:
Write 0.869 as a percent.
Answer: 86.9%
Example 1 Find the LCM by Listing Multiples
Example 2 Find the LCM Using Prime Factors
Example 3 Find the LCM by Using Prime Factors
Find the LCM of 4 and 6.
First, list the multiples of 4 and 6.
multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, . . .
multiples of 6: 6, 12, 18, 24, 30, 36, . . .
Notice that 12, 24, . . ., are common multiples.
Answer: The LCM of 4 and 6 is 12.
Find the LCM of 8 and 12.
Answer: 24
Find the LCM of 4 and 15.
Write the prime factorization.
The prime factors of 4 and 15 are 2, 3, and 5.
Multiply the greatest power of 2, 3, and 5.
Answer: The LCM of 4 and 15 is 60.
Find the LCM of 6 and 14.
Answer: 42
Find the LCM of 18, 24, and 48.
LCM:
Answer: The LCM of 18, 24, and 48 is 144.
Find the LCM of 12, 20, and 45.
Answer: 180
Example 1 Compare Fractions
Example 2 Compare Ratios
Example 3 Order Ratios
Example 4 Identify Rational Numbers
GRADES Enrique and his younger brother both had a
math test last Friday. Enrique scored 48 points out of
60 and his brother scored 55 points out of 75. Who
got the better score, Enrique or his brother?
Method 1
Rename using the LCD.
Then compare numerators.
Enrique:
Brother:
Since
The LCD of 60
and 75 is 300.
Method 2
Write each fraction as a decimal.
Then compare decimals.
Enrique:
Brother:
Since
,
Answer: Enrique got the better score.
HOCKEY During the hockey season, Kyle scored 14
goals out of 24 shots taken and his teammate David
scored 18 goals out of 30 shots taken. Who had the
higher scoring percentage?
Answer: David
DOGS According to the Pet Food Manufacturer’s
Association, 11 out of 25 people own large dogs and
13 out of 50 people own medium dogs. Do more
people own large or medium dogs?
Write
and
as decimals and compare.
Since
Answer: A greater fraction of people own large
dogs than own medium dogs.
SEASONS A survey showed that 21 out of 50 people
stated that summer is their favorite season and 13
out of 25 people stated that fall is their favorite
season. Do more people prefer summer or fall?
Answer: fall
Write
and 72% as decimals and then compare all
three decimals.
Since 0.6 < 0.7 < 0.72, 0.6 <
<72%.
Check
Answer:
You can change 0.6 and 72% to fractions,
then compare all three fractions using the LCD.
Answer:
MULTIPLE-CHOICE TEST ITEM
Find the number that is rational.
A 0.12345… B 0.123123 C 
D 0.102030…
Read the Test Item
To find the number that is rational, identify three
numbers that are not rational.
Solve the Test Item
0.12345 . . ., , and 0.102030 . . .
are all irrational numbers. So, 0.123123 . . ., a repeating
decimal, is the rational number.
Answer: B
MULTIPLE-CHOICE TEST ITEM
Find the number that is not rational.
A 0.121212…
Answer: D
B 0.75 C
D 0.61626364…
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