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5-Minute Check
Use with Lesson
4-1
(over Chapter 3)
Write the sentence as an algebraic equation.
1. Seven years more than Tom’s age is 35.
Solve.
2. n - 7 = -10
3. 6s = 42
5. Copy and complete the function
table. Identify the domain
and range.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6.
4. r + 4 ≤ -3
y = 3x - 2
x 3x - 2 y
1
2
3
Which algebraic expression
matches the phrase below? 15 less than the
product of n and 4
Test Practice
A 4n - 15
C 15 - 4 + n
B 15 - 4n
D 4 + n - 15
ANSWERS
1. t + 7 = 35
3. 7
5. x 3x − 2
1
2
3
Chapter 4
y
1
3(2) − 2 4
3(3) − 2 7
3(1) − 2
domain: {1, 2, 3};
range: {1, 4, 7}
2. -3
4. r ≤ -7
6. A
Glencoe Math Connects, Course 2
4–1
Prime Factorization
GLE: NO:1C
BUILD YOUR VOCABULARY (pages 77–78)
MAIN IDEA
• Find the prime
factorization of a
composite number.
A prime number is a whole number greater than 1 that
factors,
has exactly
and
.
A composite number is a whole number greater than
that has more than
Every
factors.
number can be written as a product
of prime numbers exactly one way called the prime
factorization.
A factor tree can be used to find the factorization.
®
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
ORGANIZE IT
Under the tab for
Lesson 4-1, give examples
of prime and composite
numbers. Be sure to
explain how to tell a
prime number from a
composite number.
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EXAMPLES
Identify Numbers as Prime or Composite
Determine whether each number is prime or composite.
63
63 has six factors: 1,
So, it is
, 7,
, 21, and
.
.
29
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So, it is
.
Check Your Progress Determine whether each number
is prime or composite.
a. 41
b. 24
Math Connects, Course 2
79
4–1
EXAMPLE
REMEMBER IT
Multiplication is
commutative, so the
order of factors does
not matter.
Find the Prime Factorization
Find the prime factorization of 100.
To find the prime factorization, you can use a factor tree or
divide by prime numbers. Let’s use a factor tree.
100
×
25
×
×
100 =
EXAMPLE
×
2
×
×
×
×
×
or
×
.
Find an Algebraic Expression
ALGEBRA Factor 21m 2n.
×
21
×
7 ×
×
×
×
×
Check Your Progress
HOMEWORK
ASSIGNMENT
a. Find the prime factorization of 72.
Page(s):
Exercises:
80
b. Factor 15xy 3.
Math Connects, Course 2
×
n
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
21m 2n
Score:________/________
30-Square Answer Sheet-----MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
5-Minute Check
Use with Lesson
(over Lesson 4-1)
4-2
Determine whether each number is prime or
composite.
1. 47
2. 63
Find the prime factorization of each number.
3. 54
4. 32
5. Evaluate 2p2 + 5 for p = 0, 1, 2, 3. List the
resulting numbers that are prime numbers.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6.
Zoran needs to rent storage space
to store his furniture. He thinks he will need a
floor space of 9 ft × 12 ft. What is the prime
factorization of this area?
Test Practice
A 32 × 22
C 32 × 23
B 33 × 22
D 33 × 23
ANSWERS
1. prime
2. composite
3. 2 × 33
4. 25
5. The resulting numbers 5, 7, 13, and 23 are all
prime.
6. B
Chapter 4
Glencoe Math Connects, Course 2
4–2
Greatest Common Factor
GLE: NO:1C
BUILD YOUR VOCABULARY (pages 77–78)
MAIN IDEA
• Find the greatest
common factor of two
or more numbers.
A Venn diagram uses
to show how elements
among sets of numbers or objects are related.
The
number that is a common
to two or more numbers is called the greatest common
factor (GCF).
EXAMPLE
®
ORGANIZE IT
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Under the tab for
Lesson 4-2, take notes
on finding the greatest
common factor of two or
more numbers.
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Find the Greatest Common Factor
Find the GCF of 28 and 42.
METHOD 1 First, list the factors of 28 and 42.
factors of 28:
factors of 42:
The common factors are
So, the GCF is
.
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METHOD 2 Use prime factorization.
28 = 2 × 2 ×
42 = 2 × 3 ×
The greatest common factor or GCF is 2 × 7 or
.
Check Your Progress Find the GCF of 18 and 45.
Math Connects, Course 2
81
4–2
EXAMPLE
WRITE IT
Which method of finding
the GCF of two or more
numbers do you prefer
using to find the GCF of
small numbers? for large
numbers?
Find the GCF of Three Numbers
Find the GCF of 21, 42, and 63.
METHOD 1 First, list the factors of 21, 42, and 63.
factors of 21: 1, 3, 7,
factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
, 9, 21, 63
factors of 63: 1, 3,
The common factors of 21, 42, and 63 are
,
So, the greatest common factor or GCF is
.
, and
.
METHOD 2 Use prime factorization.
21 =
3×7
42 = 2 × 3 × 7
Circle the common factors.
63 = 3 × 3 × 7
The common prime factors are 3 and 7.
The GCF is
×
, or
.
24, 48, and 60
EXAMPLE
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?
82
Math Connects, Course 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Check Your Progress Find the GCF of each set
of numbers.
4–2
The largest length of side possible is the GCF of the dimensions
of the tag board.
15 =
×
25 =
×
The
of 15 and 25 is
squares with sides measuring
. So, Searra should use
centimeters.
EXAMPLE
How many squares can she make if the sides are
5 centimeters?
÷ 5 = 5 squares can fit along the length.
÷ 5 = 3 squares can fit along the width.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
So, 5 × 3 =
squares can be made from the tag board.
Check Your Progress CANDY Alice is making candy
baskets using chocolate hearts and lollipops. She is tying each
piece of candy with either a red piece of string or a green piece
of string. She has 64 inches of red string and 56 inches of green
string. She wants to cut the pieces of string equal lengths and
use all of the string she has.
a. What is the length of the longest piece of string that
can be cut?
HOMEWORK
ASSIGNMENT
b. How many pieces of string can be cut if the pieces are
8 inches long?
Page(s):
Exercises:
Math Connects, Course 2
83
Score:________/________
30-Square Answer Sheet-----MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
5-Minute Check
Use with Lesson
4-3
(over Lesson 4-2)
Find the GCF of each set of numbers.
1. 12, 36
2. 27, 45
Find the GCF of each set of algebraic
expressions.
3. 8b, 12b
4. 36r2, 18rq
5. What is the GCF of 24 × 3 and 23 × 32?
6.
Test Practice
Which set of numbers has
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
a GCF of 9?
A 49, 18, 81
C 27, 58, 63
B 72, 117, 153
D 9, 45, 98
ANSWERS
1. 12
2. 9
3. 4b
4. 18r
5. 24
6. B
Chapter 4
Glencoe Math Connects, Course 2
4–4
Simplifying Fractions
GLE: NO:1B
BUILD YOUR VOCABULARY (pages 77–78)
MAIN IDEA
• Write fractions in
simplest form.
Fractions having the same
equivalent fractions.
are called
A fraction is in simplest form when the greatest common
and the denominator is 1.
factor of the
EXAMPLES
®
ORGANIZE IT
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Under the tab for
Lesson 4-4, take notes
about simplifying
fractions. Be sure to
include an example.
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Write Fractions in Simplest Form
Write each fraction in simplest form.
12
_
45
To write a fraction in simplest form, you can divide by common
factors or divide by the
. Let’s divide by the GCF.
and
First, find the GCF of the
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factors of 12:
factors of 45:
The GCF of 12 and 45 is
.
Then, divide the numerator and the denominator by
.
12 ÷
12
_
= __ =
45
45 ÷
12
4
So, _
written in simplest form is _
.
45
15
Math Connects, Course 2
85
4–4
40
_
64
factors of 40: 1, 2,
, 5, 8, 10, 20,
factors of 64: 1, 2, 4, 8,
, 32, 64
The GCF of 40 and 64 is
.
40 ÷
40
_
= __ =
64
64 ÷
40
So, _
written in simplest form is
.
64
Check Your Progress Write each fraction in
simplest form.
32
a. _
28
b. _
40
49
EXAMPLE
MUSIC Two notes form a perfect fifth if the simplified
3
fraction of the frequencies of the notes equals _
. If note
frequency of note D
____
=
frequency of note G
1
1
1
2×3×7×7
= ____
=
2×2×2×7×7
1
1
1
The fraction of the frequency of the notes D and G is
So, the two notes do form a perfect fifth.
HOMEWORK
ASSIGNMENT
Page(s):
Check Your Progress In a bag of 96 marbles, 18 of the
marbles are black. Write the fraction of black marbles in
simplest form.
Exercises:
86
Math Connects, Course 2
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4
D = 294 Hertz and note G = 392 Hertz, do they form a
perfect fifth?
Score:________/________
30-Square Answer Sheet-----MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
Use with Lesson
5-Minute Check
4-5
(over Lesson 4-4)
Write each fraction in simplest form.
8
1. _
20
12
2. _
21
11
3. _
121
Write two fractions that are equivalent to each
fraction.
5
4. _
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7
3
5. _
11
6.
Which fraction is not equivalent to
the other fractions?
Test Practice
32
A_
48
14
B_
37
38
C_
57
18
D_
27
ANSWERS
2
1. _
5
10 _
; 15
4. _
14 21
Chapter 4
4
2. _
7
6 _
5. _
; 9
22 33
1
3. _
11
6. B
Glencoe Math Connects, Course 2
4–5
Fractions and Decimals
GLE: NO:1B
EXAMPLES
MAIN IDEA
• Write fractions
as terminating or
repeating decimals
and write decimals as
fractions.
Use Mental Math
Write each fraction or mixed number as a decimal.
9
_
10
× 10
THINK
9
_
=
10
× 10
9
So, _
=
10
.
3
7_
5
3
7_
=7+
Think of it as a sum.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5
=7+
3
You know that _
= 0.6.
= 7.6
Add mentally.
3
=
So, 7 _
5
5
.
Check Your Progress Write each fraction or mixed
number as a decimal.
®
7
a. _
25
ORGANIZE IT
Under the tab for
Lesson 4-5, take notes
on writing fractions as
decimals and writing
decimals as fractions.
Include examples.
1
b. 9 _
5
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Math Connects, Course 2
87
4–5
EXAMPLE
Use Pencil and Paper or a Calculator
1
Write _
as a decimal.
8
METHOD 1 Use paper and pencil.
0.125
1.000
8 8
__
20
- 16
___
40
40
___
0
Divide
by
Division ends when the remainder is 0.
WRITE IT
METHOD 2 Use a calculator.
Write the following
1 8
decimal equivalents:
1
So, _
=
1 _
_1 , _1 , _2 , _1 , _3 , _1 , _
, 1.
.
ENTER
8
.
2 3 3 4 4 5 10 8
Check Your Progress Write each fraction or mixed
number as a decimal.
2
a. _
5
20
BUILD YOUR VOCABULARY (pages 77–78)
A terminating decimal is a decimal whose digits
Repeating decimals have a pattern in the digits that
repeats
.
Bar notation is used to indicate that a number repeats
forever by writing a
that repeat.
88
Math Connects, Course 2
over the
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7
b. 1 _
4–5
EXAMPLES
Write Fractions as Repeating Decimals
1
Write _
as a decimal.
11
METHOD 1 Use paper and pencil.
0.0909...
11 1.0000
0
__
100
____
10
0
__
99
____
METHOD 2 Use a calculator.
1 11
ENTER
1
=
So, _
11
0.0909...
.
5
Check Your Progress Write 2 _
as a decimal.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11
EXAMPLE
Use a Power of 10
CEREAL Jorge read that 0.72 of his favorite cereal was
whole-grain wheat. Find what fraction of his cereal, in
simplest form, is whole-grain wheat.
72
0.72 = _
100
18
=_
25
HOMEWORK
ASSIGNMENT
Page(s):
Exercises:
So,
The final digit,
, is in the hundredths place.
Simplify.
of the cereal is whole-grain wheat.
Check Your Progress EXERCISE Jeanette ran 0.86 of a
mile. What fraction of a mile did she run?
Math Connects, Course 2
89
Score:________/________
20-Square Answer Sheet------MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
Use with Lesson
5-Minute Check
4-6
(over Lesson 4-5)
Write each repeating decimal using bar
notation.
1. 1.22222
2. 0.15151515
Write each fraction or mixed number as a
decimal. Use bar notation if the decimal is a
repeating decimal.
3
3. 2_
5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5
4. _
8
1
5. _
9
6.
Test Practice
Write 2.65 as a fraction in
simplest form.
13
A 2_
2
C 2_
25
3
B 2_
5
ANSWERS
_
1. 1.2
4. 0.625
Chapter 4
3
13
D 2_
20
__
2. 0.15
_
5. 0.1
3. 2.6
6. D
Glencoe Math Connects, Course 2
4–6
Fractions and Percents
GLE: NO:1B
BUILD YOUR VOCABULARY (pages 77–78)
MAIN IDEA
A ratio is a
• Write fractions as
percents and percents
as fractions.
of two numbers by
.
When a
compares a number to
, it can
be written as a percent.
EXAMPLES
Write Ratios as Percents
Write each ratio as a percent.
KEY CONCEPT
Percent A percent is a
ratio that compares a
number to 100.
Diana scored 63 goals out of 100 attempts.
You can represent 63 out
of 100 with a model.
63
_
=
100
31.9
__
=
Check Your Progress Write each ratio as a percent.
a. Alicia sold 34 of the 100 cookies at the bake sale.
b. On average, 73.4 out of 100 people preferred the chicken
instead of the roast beef.
90
Math Connects, Course 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
In a survey, 31.9 out of 100 people on average preferred
crunchy peanut butter.
4–6
EXAMPLE
®
ORGANIZE IT
Under the tab for
Lesson 4-6, take notes
on writing fractions as
percents and percents
as fractions. Include
examples.
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Write a Fraction as a Percent
16
Write _
as a percent.
25
×4
16
64
_
=_
Since 100 ÷ 25 = 4, . . .
25
100
. . . multiply the
numerator and
denominator by 4.
×4
64
_
= 64%
100
16
So, _
= 64%.
24
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11
Check Your Progress Write _
as a percent.
20
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
EXAMPLE
FISHING William caught and released 20 trout on his
fishing trip. Twelve of them were rainbow trout. What
percent of the trout he caught were rainbow trout?
William caught
12
_
=
20
= 60%
So,
HOMEWORK
ASSIGNMENT
Page(s):
rainbow trout out of 20 trout.
Write an equivalent fraction with a
denominator of 100.
60
_
= 60%
100
of the trout William caught were rainbow trout.
Check Your Progress READING Mitchell read 18 out of
25 chapters of a book during his winter vacation. What percent
of chapters did he read?
Exercises:
Math Connects, Course 2
91
Score:________/________
30-Square Answer Sheet-----MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
Use with Lesson
5-Minute Check
4-7
(over Lesson 4-6)
Write each ratio as a percent.
67
1. _
100
2. 32 per 100
Write each fraction as a percent.
2
3. _
8
17
4. _
20
5. Write 55% as a fraction in simplest form.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6.
There are 200 people in the
audience of a game show. Fifty are chosen to
participate. What percent of the audience will be
chosen to participate?
Test Practice
A 25 percent
C 50 percent
B 40 percent
D 75 percent
ANSWERS
1. 67%
2. 32%
3. 25%
4. 85%
11
5. _
6. A
Chapter 4
20
Glencoe Math Connects, Course 2
4–7
Percents and Decimals
GLE: NO:1B
EXAMPLES
MAIN IDEA
• Write percents as
decimals and decimals
as percents.
Write Percents as Decimals
Write 47.8% as a decimal.
To write a percent as a decimal, you can either first write
the percent as a
mentally.
47.8% = 47.8
= 0.478
So, 47.8% =
or divide mentally. Let’s divide
Remove the % symbol and divide by 100.
Add leading zero.
.
POPULATION According to the Administration on Aging,
1
about 28 _
% of the population of the United States is
5
1
19 years of age or younger. Write 28 _
% as a decimal.
1
% = 28.2%
28 _
5
Writing Percents as
Decimals To write a
percent as a decimal,
divide the percent by 100
and remove the percent
symbol.
5
5
= 28.2
Remove the % symbol and divide by 100.
=
Add leading zero.
1
So, 28 _
% = 0.282.
5
Check Your Progress
a. Write 83.2% as a decimal.
b. AMUSEMENT PARKS A popular amusement park reports
1
% of its visitors will return at least three times
that 17_
10
1
% as a decimal.
during the year. Write 17_
10
92
Math Connects, Course 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
KEY CONCEPT
1
Write _
as 0.2.
4–7
EXAMPLE
Write Decimals as Percents
Write 0.33 as a percent.
METHOD 1 Write the decimal as a fraction.
33
0.33 = _
100
=
Write the fraction as a percent.
METHOD 2 Multiply mentally.
0.33 = 33.0
= 33%
So, 0.33 =
Multiply by 100.
Add the % symbol.
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Check Your Progress Write 0.7 as a percent.
EXAMPLE
POPULATION In 1790, about 0.05 of the population of the
United States lived in an urban setting. Write 0.05 as a
percent.
0.05 =
=
HOMEWORK
ASSIGNMENT
Definition of decimal
Definition of
Check Your Progress In 2000, the population of Illinois
had increased by 0.086 from 1990. Write 0.086 as a percent.
Page(s):
Exercises:
Math Connects, Course 2
93
Score:________/________
45-Square Answer Sheet------MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
Use with Lesson
5-Minute Check
4-8
(over Lesson 4-7)
Write each percent as a decimal.
1. 13.7%
1
%
2. 7_
4
Write each decimal as a percent.
3. 0.183
4. 0.07
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Assuming every student placed a vote, if 0.83 of
the student body voted for Afsheen and 0.17
voted for Neal, what percent of the student body
voted for Neal?
6.
Test Practice
1
What is 32 _
% written as a
2
decimal?
A 0.32
B 3.2
1
C 0.32 _
2
D 0.325
ANSWERS
1. 0.137
2. 0.725
3. 18.3%
4. 7%
5. 17%
6. D
Chapter 4
Glencoe Math Connects, Course 2
Least Common Multiple
4–8
GLE: NO:1C
BUILD YOUR VOCABULARY (pages 77–78)
MAIN IDEA
A multiple is the
• Find the least common
multiple of two or
more numbers.
of a number and any
number.
The least common multiple (LCM) of two or more
numbers is the
excluding
EXAMPLES
of their common multiples,
.
Find the LCM
Find the LCM of 4 and 6.
®
ORGANIZE IT
METHOD 1 List the nonzero multiples.
multiples of 4:
iVˆ“>Ã]
À>V̈œ˜ÃÊVi˜ÌÃ
>˜`Ê*iÀ
multiples of 6:
œÀˆâ>̈œ˜
{‡£Ê*Àˆ“iÊ>VÌ
̜ÀÃ
ÃÌÊ
œ““œ˜Ê>V
{‡ÓÊÀi>Ìi
À}>˜ˆâi`ʈÃÌ
{‡ÎÊ>ŽiÊ>˜Ê"
ÊÀ>V̈œ˜Ã
{‡{Ê-ˆ“«ˆvވ˜}
Ã
Ê>˜`ÊiVˆ“>
>˜`Ê*iÀVi˜ÌÃ
{‡ÈÊÀ>V̈œ˜ÃÊ
˜`ÊiVˆ“>Ã
{‡ÇÊ*iÀVi˜ÌÃÊ>
“œ˜ÊՏ̈«i
{‡nÊi>ÃÌÊ
œ“
{‡xÊÀ>V̈œ˜Ã
Ã
̈œ˜>Ê ՓLiÀ
`Ê"À`iÀˆ˜}Ê,>
{‡™Ê
œ“«>Àˆ˜}Ê>˜
The common multiples are
The LCM of 4 and 6 is
, 24, 36, ... .
.
METHOD 2 Use prime factorization.
4=
·
6=
·
The LCM is 2 · 2 · 3 or
94
Math Connects, Course 2
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Under the tab for
Lesson 4-8, take notes
about least common
multiples. Be sure to
include examples.
4–8
Find the LCM of 4 and 15.
Use Method 2. Find the prime factorization of each number.
4=
15 =
× 2 or
×
The prime factors of 4 and 15 are
.
× 3 × 5, or
The LCM of 4 and 15 is
.
Check Your Progress Find the LCM of each set
of numbers.
a. 8, 12
b. 6, 14
EXAMPLE
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
WORK On an assembly line, machine A must be oiled
every 18 minutes, machine B every 24 minutes, and
machine C every 48 minutes. If all three machines are
turned on at the same time, in how many minutes will
all three machines need to be oiled at the same time?
First find the LCM of 18, 24, and 48.
18 = 2 × 3 × 3 or 2 × 3 2
24 = 2 × 2 × 2 × 3 or 2 3 × 3
48 = 2 × 2 × 2 × 2 ×
or 2 4 × 3
The LCM of 18, 24, and 48 is 2 4 × 3 2 or
× 9, which is 144.
So, all three machines will need to be oiled at the same time in
minutes.
HOMEWORK
ASSIGNMENT
Page(s):
Exercises:
Check Your Progress LIGHTS Brenda put up three
different strands of decorative blinking lights. The first strand
blinks every 6 seconds while the second strand blinks every 8
seconds. The third strand blinks every 4 seconds. If all strands
blink at the same time, in how many seconds will they again
blink at the same time?
Math Connects, Course 2
95
Score:________/________
30-Square Answer Sheet-----MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
Use with Lesson
5-Minute Check
4-9
(over Lesson 4-8)
Find the LCM of each set of numbers.
1. 4, 12
2. 3, 13
3. 12, 15
4. 4, 6, 8
5. Find the LCM of 42 × 2 and 22 × 4.
6.
Test Practice
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A 54
Find the LCM of 54 and 90.
B 90
C 270
D 540
ANSWERS
1. 12
2. 39
3. 60
4. 24
5. 32
6. C
Chapter 4
Glencoe Math Connects, Course 2
4–9
Comparing and Ordering Rational Numbers
GLE: NO:1A
BUILD YOUR VOCABULARY (pages 77–78)
MAIN IDEA
Rational numbers are numbers that can be written as
fractions and include fractions, terminating and repeating
• Compare and order
fractions, decimals, and
percents.
.
decimals, and
A common denominator is a common multiple of two or
more
.
The least common denominator (LCD) is the
of the denominators.
EXAMPLES
Compare Rational Numbers
Replace each with <, >, or = to make a true sentence.
-3
_3 -3 _7
8
8
Graph each rational number on a number line.
REVIEW IT
48
Explain how to write _
60
as a decimal.
(Lesson 4-5)
{
Ç
È
x
{
Î
Ó
£
Î n Î n Î n Î n Î n Î n Î n
3
The number line shows that -3 _
Î
7
-3 _
.
8
8
5
7
_
_
12
16
The LCD of the denominators, 12 and 16, is 48.
5
5·
_
= __
=
_
7·
7
_
= __
=
_
12
16
Since
96
Math Connects, Course 2
12 ·
16 ·
<
48
48
5
, then _
12
7
_
.
16
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
between -4 and
Mark off equal size increments of
4–9
Check Your Progress Replace each with <, >, or = to
make a true sentence.
5
7
4
3
a. -2 _
-2 _
b. _
_
5
5
8
12
EXAMPLE
KEY CONCEPT
Rational Numbers
Rational numbers are
numbers that can be
written as fractions.
®
Takes notes on
rational numbers. Be sure
to include examples.
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?
13
11
Write _
and _
as decimals and compare.
25
11
_
=
25
50
13
_
=
50
11
Since 0.44 > 0.26, _
25
13
_
.
50
So, a greater fraction of people own
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
own
dogs than
dogs.
Check Your Progress A survey showed that 21 out of 50
people stated that summer is their favorite season and 13 out of
25 people prefer fall. Do more people prefer summer or fall?
HOMEWORK
ASSIGNMENT
Page(s):
Exercises:
Math Connects, Course 2
97
Score:________/________
30-Square Answer Sheet-----MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________