Chapter 4
Fractions and Decimals
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4
Fractions and Decimals
Lesson 4-1
Lesson 4-2
Lesson 4-3
Lesson 4-4
Lesson 4-5
Lesson 4-6
Lesson 4-7
Lesson 4-8
Lesson 4-9
Lesson 4-10
Greatest Common Factor
Problem-Solving Strategy: Make an
Organized List
Simplifying Fractions
Mixed Numbers and Improper
Fractions
Least Common Multiple
Problem-Solving Investigation: Choose
the Best Strategy
Comparing Fractions
Writing Decimals as Fractions
Writing Fractions as Decimals
Algebra: Ordered Pairs and Functions
4-1
Greatest Common Factor
Five-Minute Check (over Chapter 3)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
Example 4
Example 5
Greatest Common Factor
4-1
Greatest Common Factor
• I will find the greatest common factor of two or
more numbers.
• common factor
• greatest common factor (GCF)
4-1
Greatest Common Factor
Preparation for Standard 6NS2.4 Determine the
least common multiple and the greatest common
divisor of whole numbers; use them to solve
problems with fractions (e.g., to find a common
denominator to add two fractions or to find the
reduced form for a fraction).
4-1
Greatest Common Factor
Identify the common factors of 20 and 36.
First, list the factors by pairs for each number.
Answer: The common factors of 20 and 36 are
1, 2, and 4.
4-1
Greatest Common Factor
Identify the common factors of 12 and 18.
A. 1, 2, 3, 6
B. 1, 2, 6
C. 1, 2, 4, 6
D. 1, 2, 3, 4, 6
4-1
Greatest Common Factor
Find the GCF of 36 and 48.
Write the prime factorization.
36
48
12 × 3
4 × 3
3
2×2×3 ×3
2
×
24
2 × 2 × 12
2 × 2 × 3 × 4
2 × 2 × 3×2 × 2
Answer: The GCF of 36 and 48 is 2 × 3 or 6.
4-1
Greatest Common Factor
Check
Use a Venn diagram to show the factors. Notice that
the factors 1, 2, 3, 4, 6, and 12 are common factors of
36 and 48 and the GCF is 12.
4-1
Greatest Common Factor
Find the GCF of 14 and 21.
A. 1
B. 2
C. 3
D. 7
4-1
Greatest Common Factor
Find the GCF of 21 and 28.
21
28
7 × 3
2 × 14
2
2×7
Answer: The GCF of 21 and 28 is 7.
4-1
Greatest Common Factor
Check
Use a Venn diagram to show the factors. Notice that
the factors 1 and 7 are common factors of 21 and 28
and the GCF is 7.
4-1
Greatest Common Factor
Find the GCF of 15 and 25.
A. 1
B. 2
C. 5
D. 15
4-1
Greatest Common Factor
Ana sells bags of different
kinds of cookies. She
made $27 selling bags of
peanut butter cookies,
$18 from chocolate chip
cookies, and $45 selling
bags of oatmeal cookies.
Each bag of cookies
costs the same amount.
What is the most that Ana
could have charged for
each bag of cookies?
4-1
Greatest Common Factor
Factors of 27:
1, 3, 9, 27
Factors of 18:
1, 2, 3, 6, 9, 18
Factors of 45:
1, 3, 5, 9, 15, 45
Answer: The GCF of 27, 18, and 45 is 9. So, the most
Ana could have charged for each bag of
cookies is $9.
4-1
Greatest Common Factor
Joy bought presents for her three friends. She spent
$48 on Jonah, $36 on Louise, and $60 on Brenden.
Each gift cost the same amount. What is the most
each gift could have cost?
A. $1
B. $4
C. $18
D. $12
4-1
Greatest Common Factor
Refer to Example 4 of this lesson. How many bags
could Ana have sold if each bag cost $9?
There is a total of $27 + $18 + $45 or $90.
Answer: So, the number of bags of cookies is
$90 ÷ $9 or 10.
4-1
Greatest Common Factor
If Joy spent $48 on Jonah, $36 on Louise, and $60
on Brenden, and each gift cost $12, how many gifts
did she buy?
A. 48
B. 36
C. 12
D. 60
4-2
Problem-Solving Strategy: Make an Organized List
Five-Minute Check (over Lesson 4-1)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
4-2
Problem-Solving Strategy: Make an Organized List
• I will solve problems by making an organized list.
4-2
Problem-Solving Strategy: Make an Organized List
Standard 5MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.
Standard 5NS1.4 Determine the prime
factors of all numbers through 50 and write the
numbers as the product of their prime factors.
4-2
Problem-Solving Strategy: Make an Organized List
Jessica is setting up four booths in a row for the
school carnival. There will be a dart game booth,
a ring toss booth, a face-painting booth, and a
virtual football booth. In how many ways can the
four booths be arranged for the school carnival?
4-2
Problem-Solving Strategy: Make an Organized List
Understand
What facts do you know?
• There are four different booths: dart game, ring
toss, face-painting, and virtual football.
• The booths will be set up in a row.
What do you need to find?
• Find how many different ways the booth can be
arranged.
4-2
Problem-Solving Strategy: Make an Organized List
Plan
Make a list of all the different possible arrangements.
Use D for darts, R for ring toss, F for face-painting, and
V for virtual football. Organize your list by listing each
booth first as shown below.
D_
__
R_
__
F_
__
V_
__
4-2
Problem-Solving Strategy: Make an Organized List
Plan
Then fill in the remaining three positions with the
other booths. Continue this process until all the
different arrangements are listed in the second,
third, and fourth positions.
4-2
Problem-Solving Strategy: Make an Organized List
Solve
Listing D first:
Listing R first:
DRFV
RFVD
DRVF
RFDV
DFRV
RVDF
DFVR
RVFD
DVRF
RDFV
DVFR
RDVF
4-2
Problem-Solving Strategy: Make an Organized List
Solve
Listing F first:
Listing V first:
FVDR
FVRD
FDRV
FDVR
FRVD
FRDV
VDRF
VDFR
VRFD
VRDF
VFDR
VFRD
Answer: There are 24 different ways the booths can
be arranged.
4-2
Problem-Solving Strategy: Make an Organized List
Check
Look back. Is each booth accounted for six times in
the first, second, third, and fourth positions?
4-3
Simplifying Fractions
Five-Minute Check (over Lesson 4-2)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
Example 4
4-3
Simplifying Fractions
• I will express fractions in simplest form.
• ratio
• equivalent fractions
• simplest form
4-3
Simplifying Fractions
Preparation for Standard 5NS2.3 Solve
simple problems, including ones arising in concrete
situations, involving the addition and subtraction of
fractions and mixed numbers (like and unlike
denominators of 20 or less), and express answers
in the simplest form.
4-3
Simplifying Fractions
Replace the x with a number so the fractions are
equivalent.
x
6
=
52
13
x
6
=
52
13
Since 13 × 4 = 52, multiply the
numerator and denominator by 4.
Answer: So, x = 24.
4-3
Simplifying Fractions
Solve for x. Choose the correct answer.
x
7
=
48
12
A. 24
B. 28
C. 30
D. 7
4-3
Simplifying Fractions
Replace the x with a number so the fractions are
equivalent.
24
=
40
3
x
24
=
40
3
x
Since 24 ÷ 8 = 3, divide the numerator
and denominator by 8.
Answer: So, x = 5.
4-3
Simplifying Fractions
Solve for x. Choose the correct answer.
1
5
=
x
25
A. 5
B. 10
C. 20
D. 15
4-3
Simplifying Fractions
14
Write
in simplest form.
42
One Way: Divide by common factors.
7
14
=
=
21
42
1
3
A common factor of 14 and 42 is 2.
A common factor of 7 and 21 is 7.
4-3
Simplifying Fractions
Another Way: Divide by the GCF.
factors of 14: 1, 2, 7, 14
factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
The GCF of 14 and 42 is 14.
14
=
42
1
3
Divide the numerator and
denominator by the GCF, 14.
4-3
Simplifying Fractions
48
Write
in simplest form.
50
24
A. 25
9
B.
10
14
C. 15
D. 48
50
4-3
Simplifying Fractions
Lin practices gymnastics 3 hours each day. There
are 24 hours in a day. Express the fraction 3 in
24
simplest form.
The GCF of 3 and 24 is 3.
1
3
=
24
1
8
Mentally divide both the numerator and
denominator by 3.
8
1
or 1 out of every 8
8
hours practicing gymnastics.
Answer: So, Lin spends
Simplifying Fractions
4-3
Mark spends $10 of the $50 bill his mom gave him.
Express 10 in simplest form.
50
5
A. 10
B.
C.
D.
1
2
1
5
1
25
4-4
Mixed Numbers and Improper Fractions
Five-Minute Check (over Lesson 4-3)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
4-4
Mixed Numbers and Improper Fractions
• I will write mixed numbers as improper fractions
and vice versa.
• mixed number
• proper fraction
• improper fraction
4-4
Mixed Numbers and Improper Fractions
Standard 5NS1.5 Identify and represent
on a number line decimals, fractions, mixed
numbers, and positive and negative integers.
4-4
Mixed Numbers and Improper Fractions
If a spaceship lifts off the Moon, it must travel at
a speed of 2 2 kilometers per second in order to
5
escape the pull of the Moon’s gravity. Write this
speed as an improper fraction. Then graph the
improper fraction on a number line.
4-4
Mixed Numbers and Improper Fractions
(2 × 5) + 2
12
2
2 =
= 5
5
5
2
12
Answer: So, 2 =
.
5
5
4-4
Mixed Numbers and Improper Fractions
Since 12 is between 2 and 3, draw a number line
5
12
using increments of one fifth. Then, draw a dot at 5 .
4-4
Mixed Numbers and Improper Fractions
The average height of an adult man is 5 9 feet tall.
12
9
Choose the answer that shows 5
as an improper
12
fraction.
59
A. 12
9
B. 108
9
C. 60
D. 69
60
4-4
Mixed Numbers and Improper Fractions
Write 23 as a mixed number. Then graph the mixed
4
number on a number line.
3
5 4
4 23
– 20
3
3
23
Answer: So,
= 5 .
4
4
4-4
Mixed Numbers and Improper Fractions
3
Since 5 is between 5 and 6, draw a number line
4
from 5 to 6 using increments of one fourth. Then, draw
a dot at 5 3 .
4
Mixed Numbers and Improper Fractions
4-4
Choose the answer that shows 47 as a mixed
6
number.
5
7
5
76
A. 6
B.
C.
D.
6
57
7
78
4-5
Least Common Multiple
Five-Minute Check (over Lesson 4-4)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
4-5
Least Common Multiple
• I will find the least common multiple of two or
more numbers.
• multiple
• common multiples
• least common multiple (LCM)
4-5
Least Common Multiple
Preparation for Standard 5SDAPS1.3 Use
fractions and percentages to compare data
sets of different sizes.
4-5
Least Common Multiple
Identify the first three common multiples of 3 and 9.
First, list the multiples of each number.
Multiples of 3: 3, 6, 9, 12, 15, 18, …
1 × 3, 2 × 3, 3 × 3, …
Multiples of 9: 9, 18, 27, 36, 45, 49, … 1 × 9, 2 × 9, 3 × 9, …
Notice that 9, 18, and 27 are multiples common to
both 3 and 9.
Answer: So, the first three common multiples of 3
and 9 are 9, 18, and 27.
4-5
Least Common Multiple
Identify the first three multiples of 6 and 12.
A. 6, 12, 18
B. 6, 12, 24
C. 12, 24, 36
D. 12, 24, 48
Least Common Multiple
4-5
Find the LCM of 8 and 18.
Write the prime factorization of each number.
8
18
2 × 4
3 × 6
2 2×2
3 2×3
4-5
Least Common Multiple
Identify all common prime factors.
8=2×2×2
18 = 3 × 2 × 3
Find the product of the prime factors using each
common prime factor only once and any remaining
factors.
Answer: The LCM is 2 × 2 × 2 × 3 × 3 or 72.
4-5
Least Common Multiple
Find the LCM of 7 and 21.
A. 7
B. 42
C. 21
D. 14
4-5
Least Common Multiple
Liam, Eva, and Bansi each have the same amount of
money. Liam has only nickels, Eva has only dimes,
and Bansi has only quarters. What is the least
amount of money that each of them could have?
Find the LCM using prime factors.
5
10
25
5
2×5
5×5
Answer: The least amount of money they could all
have is 5 × 5 × 2 or $0.50.
4-5
Least Common Multiple
Samuel, John, and Uma were all paid the same
amount in ones, fives, and tens, respectively.
What is the least they could have been paid?
A. $10
B. $20
C. $25
D. $5
4-6
Problem-Solving Investigation: Choose the Best Strategy
Five-Minute Check (over Lesson 4-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
4-6
Problem-Solving Investigation: Choose the Best Strategy
• I will choose the best strategy to solve a problem.
4-6
Problem-Solving Investigation: Choose the Best Strategy
Standard 5MR2.6 Make precise calculations
and check the validity of the results from the
context of the problem.
4-6
Problem-Solving Investigation: Choose the Best Strategy
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.
4-6
Problem-Solving Investigation: Choose the Best Strategy
TROY: This weekend, my family went
to the zoo. We spent a total of $42
on admission tickets. We purchased
at least 2 adult tickets for $9
each and no more than three
children’s tickets for $5 each.
YOUR MISSION: Find how many adult
and children’s tickets Troy’s
family purchased.
4-6
Problem-Solving Investigation: Choose the Best Strategy
Understand
What facts do you know?
• You know that the family spent a total of $42.
• At least 2 adult tickets were purchased for $9
each.
• No more than three children’s tickets were
purchased for $5 each.
4-6
Problem-Solving Investigation: Choose the Best Strategy
Understand
What do you need to find?
• You need to find how many of each ticket Troy’s
family purchased.
4-6
Problem-Solving Investigation: Choose the Best Strategy
Plan
Guess and check to find the number of adult and
children’s tickets purchased.
4-6
Problem-Solving Investigation: Choose the Best Strategy
Solve
Answer: So, Troy’s family bought 3 adult and
3 children’s tickets.
4-6
Problem-Solving Investigation: Choose the Best Strategy
Check
Look back. Three adult tickets cost 3 × $9, or $27
and three children’s tickets cost 3 × $5 or $15.
Since $27 + $15 = $42, the answer is correct.
4-7
Comparing Fractions
Five-Minute Check (over Lesson 4-6)
Main Idea and Vocabulary
California Standards
Key Concept: Compare Two Fractions
Example 1
Example 2
Example 3
Example 4
4-7
Comparing Fractions
• I will compare fractions.
• least common denominator (LCD)
4-7
Comparing Fractions
Standard 5SDAP1.3 Use fractions and percentages
to compare data sets of different sizes.
4-7
Comparing Fractions
4-7
Comparing Fractions
Replace the
true sentence.
8
with <, >, or = in
21
3
to make a
7
Step 1 The LCM of the denominators is 21. So,
the LCD is 21.
Step 2 Write an equivalent fraction with a denominator
of 21 for each fraction.
8
8
=
21
21
3
7
9
=
21
4-7
Comparing Fractions
8
9
Step 3
<
, since 8 < 9.
21 21
Answer: So,
8
3
<
.
21
7
4-7
Comparing Fractions
Which answer below makes 3
4
sentence?
A. >
B. <
C. =
D. +
2 a true
3
4-7
Comparing Fractions
1
Replace the
with <, >, or = in 2
3
a true sentence.
2
2 to make
6
Since the whole numbers are the same, compare
and
.
Step 1 The LCM of the denominators is 6. So, the
LCD is 6.
4-7
Comparing Fractions
Step 2 Write an equivalent fraction with a denominator
of 6 for each fraction.
2
6
Step 3
=
=
2
6
1
3
, since 2 = 2.
1
2
Answer: So, 2 = 2 .
3
6
=
2
6
4-7
Comparing Fractions
3
Replace the
with <, >, or = to make 4
8
a true sentence.
A. >
B. <
C. =
D. +
4
4
5
4-7
Comparing Fractions
Ginny had 3 out of 4 hits in a baseball game. Belinda
had 4 out of 6 hits in that game. Who has the greater
fraction of hits?
Step 1 Write each quantity as a fraction.
Ginny:
Belinda:
4-7
Comparing Fractions
Step 2 The LCD of the fractions is 12. So, rewrite each
fraction with a denominator of 12.
3
4
9
=
12
4
6
8
=
12
9
8
Answer: Since
>
, the fraction of hits Ginny
12
12
made is greater.
4-7
Comparing Fractions
Heidi got 10 out of 12 answers right on the math
quiz. Tiffany got 5 out of 6 right on her math quiz.
Who has the greater fraction of correct answers?
A. Tiffany
B. Heidi
C. They got the same fraction.
D. neither
4-7
Comparing Fractions
Use the table to answer the following question.
What did the least number of people say should
be done with a penny?
You need to compare
the fractions. The LCD
of the fractions is 100.
4-7
Comparing Fractions
Rewrite the fractions with the LCD, 100.
32
8
=
100
25
3
3
=
100
100
65
13
=
100
20
Answer: Since the least number is 3, the least number
of people were undecided.
4-7
Comparing Fractions
According to the data in the table, who walked
the shortest distance?
A. Kayla
B. Nora
C. Mercedes
D. They all walked the same distance.
4-8
Writing Decimals as Fractions
Five-Minute Check (over Lesson 4-7)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
Example 4
Example 5
4-8
Writing Decimals as Fractions
• I will write decimals as fractions or mixed numbers
in simplest form.
• rational number
4-8
Writing Decimals as 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.
4-8
Writing Decimals as Fractions
Write 0.4 as a fraction in simplest form.
In the place-value chart, the last nonzero digit, 4, is
in the tenths place. Say four tenths.
0
0
0
0
4
0
0
0
4-8
Writing Decimals as Fractions
4
0.4 =
10
Write as a
fraction.
2
4
=
10
5
=
2
5
Simplify.
Divide the
numerator and
denominator by
the GCF, 2.
Writing Decimals as Fractions
4-8
Choose the answer below that shows 0.8 as a
fraction in simplest form.
B.
4
5
8
10
C.
6
8
D.
2
3
A.
4-8
Writing Decimals as Fractions
Write 0.38 as a fraction in simplest form.
In the place-value chart, the last nonzero digit, 8, is
in the hundredths place. Say thirty-eight hundredths.
0
0
0
0
3
8
0
0
4-8
Writing Decimals as Fractions
0.38 =
38
100
Write as a
fraction.
19
=
38
100
50
19
=
50
Simplify.
Divide the
numerator and
denominator by
the GCF, 2.
Writing Decimals as Fractions
4-8
Choose the answer below that shows 0.75 as a
fraction in simplest form.
A.
B.
C.
D.
5
7
7
5
3
4
75
100
4-8
Writing Decimals as Fractions
Write 0.07 as a fraction in simplest form.
In the place-value chart, the last nonzero digit, 7, is
in the hundredths place. Say seven hundredths.
0
0
0
0
0
7
0
0
4-8
Writing Decimals as Fractions
7
0.07 =
100
7
=
100
=
7
100
Write as a
fraction.
Simplify.
Divide by the
GCF, 1.
Writing Decimals as Fractions
4-8
Choose the answer below that shows 0.04 as a
fraction in simplest form.
A.
B.
C.
D.
4
100
2
50
4
10
1
25
4-8
Writing Decimals as Fractions
Write 0.264 as a fraction in simplest form.
In the place-value chart, the last nonzero digit, 4, is
in the thousandths place. Say two hundred sixty-four
thousandths.
0
0
0
0
2
6
4
0
4-8
Writing Decimals as Fractions
264
0.264 =
1,000
Write as a
fraction.
33
264
=
1,000
125
33
=
125
Simplify.
Divide by the
GCF, 8.
Writing Decimals as Fractions
4-8
Choose the answer below that shows 0.246 as a
fraction in simplest form.
A.
B.
C.
D.
246
1,000
123
500
17
40
41
67
4-8
Writing Decimals as Fractions
In 1955, Hurricane Diane moved through New
England and produced one of the region’s heaviest
rainfalls in history. In a 24-hour period, 18.15 inches
of rain were recorded in one area. Express this
amount as a mixed number in simplest form.
15
18.15 = 18
100
Write as a fraction.
3
15
= 18
100
20
3
= 18
20
Simplify.
4-8
Writing Decimals as Fractions
Lee Redmond is the world record holder for the
longest fingernails. Her thumbnail is 30.2 inches
long. Choose the answer below that shows 30.2
inches written as a mixed number in simplest form.
A.
B.
C.
D.
1
5
1
30 2
30
3
30 4
1
30 4
4-9
Writing Fractions as Decimals
Five-Minute Check (over Lesson 4-8)
Main Idea
California Standards
Example 1
Example 2
Example 3
Example 4
4-9
Writing Fractions as Decimals
• I will write fractions as decimals.
4-9
Writing Fractions as 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.
4-9
Writing Fractions as Decimals
7
Write
as a decimal.
10
7 has a denominator of 10, it can be written as
10
a decimal using place value.
Since
= 0.7
Answer: 0.7
4-9
Writing Fractions as Decimals
29
Choose the answer below that shows
written
100
as a decimal.
A. 0.029
B. 0.29
C. 2.9
D. 0.0029
4-9
Writing Fractions as Decimals
Write
as a decimal.
Divide 1 by 4.
0. 2 5
4 1.00
– 8
20
– 20
0
Answer: Therefore,
1
= 0.25.
4
4-9
Writing Fractions as Decimals
Choose the answer below that shows 5 written
8
as a decimal.
A. 0.58
B. 0.675
C. 0.625
D. 0.526
4-9
Writing Fractions as Decimals
3
Write
as a decimal.
8
3
8
0. 3 7 5
8 3.000
–24
60
– 56
40
– 40
0
Answer: Therefore,
3
= 0.375.
8
4-9
Writing Fractions as Decimals
2
Choose the answer below that shows
written
5
as a decimal.
A. 0.5
B. 0.2
C. 0.25
D. 0.4
4-9
Writing Fractions as Decimals
At a meeting, people drank 25 bottles of water. The
water came in packs of 8. This makes 3
packs.
Write the number as a decimal.
3
= 3 +
125
= 3 + 1,000
Definition of a mixed number
Since 8 × 125 = 1,000,
multiply the numerator and
the denominator by 125.
= 3 + 0.125 or 3.125
Answer: The number of packs is 3.125.
4-9
Writing Fractions as Decimals
At the party, kids drank 18 juice boxes. The juice
came in packs of 10. This makes 1 8 packs. Choose
10
the answer below that shows the number of packs
written as a decimal.
A. 1.8
B. 1.10
C. 1.18
D. 1.08
4-10
Algebra: Ordered Pairs and Functions
Five-Minute Check (over Lesson 4-9)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
Example 4
Example 5
Ordered Pairs and Functions
4-10
Algebra: Ordered Pairs and Functions
• I will use ordered pairs to locate points and
organize data.
• coordinate plane • y-axis
• origin
• ordered pair
• x-axis
• x-coordinate
• y-coordinate
• graph
4-10
Algebra: Ordered Pairs and Functions
Standard 5SDAP1.5 Know how to write
ordered pairs correctly; for example, (x, y).
4-10
Algebra: Ordered Pairs and Functions
Write the ordered pair that names the point S.
Step 1 Start at the origin.
Move right along
the x-axis until
you are under
point S. The xcoordinate of the
ordered pair is 1.
S
4-10
Algebra: Ordered Pairs and Functions
Step 2 Now move up
until you reach
point S. The ycoordinate is 2.
S
Answer: So, point S is named by the ordered
pair (1, 2).
4-10
Algebra: Ordered Pairs and Functions
Write the ordered pair
that names the point T.
A. (2, 1)
B. (1, 2)
C. (1, 1)
D. (2, 2)
4-10
Algebra: Ordered Pairs and Functions
Graph the point T(2, 2).
• Start at the origin.
• Move 2 units to the right
on the x-axis.
• Then move 2 units up to
locate the point.
• Draw a dot and label the
dot T.
T
4-10
Algebra: Ordered Pairs and Functions
Which of the graphs show point N at (4, 3)?
A.
4-10
Algebra: Ordered Pairs and Functions
Which of the graphs show point N at (4, 3)?
B.
4-10
Algebra: Ordered Pairs and Functions
Which of the graphs show point N at (4, 3)?
C.
4-10
Algebra: Ordered Pairs and Functions
Which of the graphs show point N at (4, 3)?
D.
4-10
Algebra: Ordered Pairs and Functions
Which of the graphs show point N at (4, 3)?
B.
4-10
Algebra: Ordered Pairs and Functions
Graph the point U(1 , 0).
• Start at the origin.
• Move 1
units to the
right on the x-axis.
• Then move 0 units up to
locate the point.
• Draw a dot and label the
dot U.
U
4-10
Algebra: Ordered Pairs and Functions
Which of the graphs show point U at (2, 4 )?
A.
4-10
Algebra: Ordered Pairs and Functions
Which of the graphs show point U at (2, 4 )?
B.
4-10
Algebra: Ordered Pairs and Functions
Which of the graphs show point U at (2, 4 )?
C.
4-10
Algebra: Ordered Pairs and Functions
Which of the graphs show point U at (2, 4 )?
D.
4-10
Algebra: Ordered Pairs and Functions
Which of the graphs show point U at (2, 4 )?
C.
4-10
Algebra: Ordered Pairs and Functions
Amazi feeds her dog,
Buster, 2 cups of food
each day. Amazi made
this table to show how
much food Buster eats
for 1, 2, 3, and 4 days.
List the information as
ordered pairs (days,
food).
Answer: The ordered pairs are (1, 2), (2, 4),
(3, 6), (4, 8).
4-10
Algebra: Ordered Pairs and Functions
Below is the continuation of the table in Example 4.
Choose the answer that shows the information in
ordered pairs.
A. (10, 5) (12, 6) (14, 7) (16, 8)
B. (5, 10) (6, 12) (7, 14) (8, 16)
C. (5, 6) (7, 8) (10, 12) (14, 16)
D. (5, 5) (6, 6) (7, 7) (8, 8)
4-10
Algebra: Ordered Pairs and Functions
D
Graph the ordered pairs from
Example 4. Then describe the
graph.
The ordered pairs (1,
2), (2, 4), (3, 6), and (4,
8) correspond to the
points A, B, C, and D in
the coordinate plane.
Answer: The points appear to lie on a line.
C
B
A
4-10
Algebra: Ordered Pairs and Functions
Choose the graph that has the ordered pairs (5, 3),
(4, 2), (3, 1), and (2, 0) plotted correctly.
A.
4-10
Algebra: Ordered Pairs and Functions
Choose the graph that has the ordered pairs (5, 3),
(4, 2), (3, 1), and (2, 0) plotted correctly.
B.
4-10
Algebra: Ordered Pairs and Functions
Choose the graph that has the ordered pairs (5, 3),
(4, 2), (3, 1), and (2, 0) plotted correctly.
C.
4-10
Algebra: Ordered Pairs and Functions
Choose the graph that has the ordered pairs (5, 3),
(4, 2), (3, 1), and (2, 0) plotted correctly.
D.
4-10
Algebra: Ordered Pairs and Functions
Choose the graph that has the ordered pairs (5, 3),
(4, 2), (3, 1), and (2, 0) plotted correctly.
B.
4
Fractions and Decimals
Five-Minute Checks
Greatest Common Factor
Ordered Pairs and Functions
4
Fractions and Decimals
Lesson 4-1
(over Chapter 3)
Lesson 4-2
(over Lesson 4-1)
Lesson 4-3
(over Lesson 4-2)
Lesson 4-4
(over Lesson 4-3)
Lesson 4-5
(over Lesson 4-4)
Lesson 4-6
(over Lesson 4-5)
Lesson 4-7
(over Lesson 4-6)
Lesson 4-8
(over Lesson 4-7)
Lesson 4-9
(over Lesson 4-8)
Lesson 4-10 (over Lesson 4-9)
4
Fractions and Decimals
(over Chapter 3)
Find each sum or difference.
0.5 + 4.6
A. 4.1
B. 9.6
C. 0.4
D. 5.1
4
Fractions and Decimals
(over Chapter 3)
Find each sum or difference.
2.91 + 5.75
A. 8.76
B. 2.84
C. 8.66
D. 7.66
4
Fractions and Decimals
(over Chapter 3)
Find each sum or difference.
8.5 – 5.8
A. 2.7
B. 14.3
C. 3.7
D. 3.3
4
Fractions and Decimals
(over Chapter 3)
Find each sum or difference.
9.01 – 0.45
A. 9.46
B. 8.66
C. 9.44
D. 8.56
4
Fractions and Decimals
(over Chapter 3)
Find each sum or difference.
4.3 + 8.99
A. 8.56
B. 13.29
C. 9.42
D. 12.29
4
Fractions and Decimals
(over Chapter 3)
Find each sum or difference.
20 – 11.78
A. 9.32
B. 19.32
C. 8.22
D. 11.98
4
Fractions and Decimals
(over Lesson 4-1)
Identify the common factors of each set of numbers.
9, 15
A. 3
B. 3 and 6
C. 1 and 6
D. 1 and 3
4
Fractions and Decimals
(over Lesson 4-1)
Identify the common factors of each set of numbers.
6, 42
A. 1 and 3
B. 1, 2, 3, and 6
C. 1, 2, and 3
D. 1, 3, and 6
4
Fractions and Decimals
(over Lesson 4-1)
Find the GCF of each set of numbers.
13, 15
A. 3
B. 5
C. 1
D. 2
4
Fractions and Decimals
(over Lesson 4-1)
Find the GCF of each set of numbers.
22, 104
A. 2
B. 4
C. 1
D. 11
4
Fractions and Decimals
(over Lesson 4-1)
Find the GCF of each set of numbers.
24, 42, 72
A. 3
B. 2
C. 6
D. 12
4
Fractions and Decimals
(over Lesson 4-2)
Solve. Use the make an organized list strategy.
Luis is displaying sports balls for sale. He has a
soccer ball, a baseball, and a basketball. How many
different ways can he arrange these balls on a table?
A. 3
B. 6
C. 12
D. 9
4
Fractions and Decimals
(over Lesson 4-3)
Write 18 in simplest form. If the fraction is already
24
in simplest form, write simplest form.
9
A.
12
3
B. 24
3
C. 4
D. simplest form
4
Fractions and Decimals
(over Lesson 4-3)
Write 35 in simplest form. If the fraction is already
49
in simplest form, write simplest form.
15
A.
17
B. 5
7
C.
10
14
D. simplest form
4
Fractions and Decimals
(over Lesson 4-3)
Write 4 in simplest form. If the fraction is already
11
in simplest form, write simplest form.
8
A.
22
B.
2
5
1
C. 3
D. simplest form
4
Fractions and Decimals
(over Lesson 4-3)
Write 19 in simplest form. If the fraction is already
105
in simplest form, write simplest form.
8
A.
13
B.
1
5
38
C. 210
D. simplest form
4
Fractions and Decimals
(over Lesson 4-3)
Write 30 in simplest form. If the fraction is already
102
in simplest form, write simplest form.
10
A.
34
B. 5
17
C.
15
51
D. simplest form
4
Fractions and Decimals
(over Lesson 4-4)
Write 4
9
A.
6
B.
24
6
C.
29
6
D.
25
6
5
as an improper fraction.
6
4
Fractions and Decimals
(over Lesson 4-4)
Write 3 as an improper fraction.
3
A.
3
B.
3
9
1
C. 3
D. 9
3
4
Fractions and Decimals
(over Lesson 4-4)
Write 19 as a mixed number in simplest form.
5
A. 3
4
5
B. 2
9
5
C. 2
4
5
D. 1
14
5
4
Fractions and Decimals
(over Lesson 4-4)
Write 24 as a mixed number in simplest form.
6
A.
12
3
B. 2
12
6
C. 4
D. 3
6
6
4
Fractions and Decimals
(over Lesson 4-4)
Write 17 as a mixed number in simplest form.
17
1
A. 1
17
B. 1
C. 2
D. 0
1
7
4
Fractions and Decimals
(over Lesson 4-5)
Find the LCM of 9, 12.
A. 3
B. 72
C. 1
D. 36
4
Fractions and Decimals
(over Lesson 4-5)
Find the LCM of 5, 9.
A. 3
B. 90
C. 45
D. 14
4
Fractions and Decimals
(over Lesson 4-5)
Find the LCM of 3, 11.
A. 33
B. 99
C. 3
D. 66
4
Fractions and Decimals
(over Lesson 4-5)
Find the LCM of 4, 6, 12.
A. 24
B. 12
C. 6
D. 36
4
Fractions and Decimals
(over Lesson 4-5)
Find the LCM of 2, 4, 7.
A. 14
B. 21
C. 56
D. 28
4
Fractions and Decimals
(over Lesson 4-6)
Solve this problem. A clothing store sells 4 different
styles of shoes in 3 different colors. How many
combinations of style and color are possible?
A. 24
B. 7
C. 12
D. 4
Fractions and Decimals
4
(over Lesson 4-7)
Replace each
sentence.
5
8
A. <
B. >
C. =
5
6
with <, >, or = to make a true
4
Fractions and Decimals
(over Lesson 4-7)
Replace each
sentence.
7
2
3
3
12
3
A. <
B. >
C. =
with <, >, or = to make a true
4
Fractions and Decimals
(over Lesson 4-7)
Replace each
sentence.
4
13
5
16
A. <
B. >
C. =
with <, >, or = to make a true
4
Fractions and Decimals
(over Lesson 4-7)
Replace each
sentence.
1
7
2
3
3
A. <
B. >
C. =
with <, >, or = to make a true
4
Fractions and Decimals
(over Lesson 4-8)
Write 0.55 as a fraction in simplest form.
55
A. 100
B. 5
10
11
C. 100
D.
11
20
4
Fractions and Decimals
(over Lesson 4-8)
Write 0.08 as a fraction in simplest form.
A.
8
100
B.
2
25
8
C. 10
D.
4
5
4
Fractions and Decimals
(over Lesson 4-8)
Write 3.125 as a mixed number in simplest form.
5
A. 3
40
3125
B. 1000
C. 3
1
8
D. 3
125
1000
4
Fractions and Decimals
(over Lesson 4-8)
Write 4.04 as a mixed number in simplest form.
A.
404
100
B. 4 1
25
C. 4 4
100
D. 4
2
50
4
Fractions and Decimals
(over Lesson 4-9)
Write 7 as a decimal.
10
A. 0.7
B. 0.07
C. 7.10
D. 0.71
4
Fractions and Decimals
(over Lesson 4-9)
Write 11 as a decimal.
20
A. 0.505
B. 5.50
C. 0.55
D. 0.055
4
Fractions and Decimals
(over Lesson 4-9)
Write 2
5
as a decimal.
8
A. 0.625
B. 2.625
31
C. 8
D. 8.25
4
Fractions and Decimals
(over Lesson 4-9)
Write 3
5
as a decimal.
11
A. 3.5
B.
38
11
C. 0.4545
D. 3.4545...
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