1.
Chapter 14
Decimals
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2.
Decimals
14
Lesson 14-1 Tenths and Hundredths
Lesson 14-2 Relate Mixed Numbers and
Decimals
Lesson 14-3 Problem-Solving Strategy: Make
a Model
Lesson 14-4 Compare and Order Decimals
Lesson 14-5 Problem-Solving Investigation:
Choose a Strategy
Lesson 14-6 Fraction and Decimal Equivalents
Lesson 14-7 Decimals, Fractions, and Mixed
Numbers
3.
14-1 Tenths and Hundredths
Five-Minute Check (over Chapter 13)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Fractions and Decimals
4.
14-1 Tenths and Hundredths
• I will identify, read, and write tenths and
hundredths as decimals and fractions.
• decimal • tenth
• decimal point • hundredth
5.
14-1 Tenths and Hundredths
Standard 4NS1.6 Write tenths and hundredths
in decimal and fraction notations and know the
fraction and decimal equivalents for halves and
fourths (i.e., = 0.5 or 0.50; =1 = 1.75).
6.
14-1 Tenths and Hundredths
Write 39 cents as a fraction and as a decimal.
The amount 39 cents means 39 pennies out of 1 dollar.
7.
14-1 Tenths and Hundredths
One Way: Model
Draw a hundreds
model. Shade 39 out
of 100 parts to show
39 cents.
Read thirty-nine hundredths
39
Write or 0.39
100
8.
14-1 Tenths and Hundredths
Another Way: Place Value
0 3 9
Read thirty-nine hundredths
39
Write or 0.39
100
9.
14-1 Tenths and Hundredths
Write 71 cents as a fraction and a decimal.
7
A. ; 0.07
100
71
B. ; 0.71
100
17
C. ; 0.17
100
710
D. ; 0.710
100
10.
14-1 Tenths and Hundredths
4
Write as two different decimals.
10
One Way: Write Tenths
Read four tenths
Write 0.4
11.
14-1 Tenths and Hundredths
Another Way: Write Hundredths
Read forty-hundredths
Write 0.40
The decimals 0.4 and 0.40 are equivalent decimals.
12.
14-1 Tenths and Hundredths
7
Write as two different decimals.
10
A. 0.7; 0.8
B. 0.07; 0.070
C. 0.7; 0.70
D. 0.7; 0.10
13.
14-2 Relate Mixed Numbers and Decimals
Five-Minute Check (over Lesson 14-1)
Main Idea
California Standards
Example 1
Example 2
14.
14-2 Relate Mixed Numbers and Decimals
• I will identify, read, and write decimals greater
than 1.
15.
14-2 Relate Mixed Numbers and Decimals
Standard 4NS1.6 Write tenths and hundredths
in decimal and fraction notations and know the
fraction and decimal equivalents for halves and
fourths (i.e., = 0.5 or 0.50; =1 = 1.75).
16.
14-2 Relate Mixed Numbers and Decimals
4
Write 3 as a decimal.
10
One Way: Model
17.
14-2 Relate Mixed Numbers and Decimals
One Way: Model
4
Mixed Number 3
10
Read three and four tenths
Write 3.4
18.
14-2 Relate Mixed Numbers and Decimals
Another Way: Place Value
3 4
4
Answer: So, 3 as a decimal is 3.4.
10
19.
14-2 Relate Mixed Numbers and Decimals
1
Write 2 as a decimal.
10
A. 2.1
B. 2.01
C. 2.001
D. 1.2
20.
14-2 Relate Mixed Numbers and Decimals
The length of a chameleon is 6 78 inches. Write
100
6 78 as a decimal.
100
6 7 8
21.
14-2 Relate Mixed Numbers and Decimals
78
Mixed Number 6
100
Read six and seventy-eight hundredths
Write 6.78
22.
14-2 Relate Mixed Numbers and Decimals
89
Write 5 as a decimal.
100
A. 8.59
B. 9.58
C. 5.89
D. 5.98
23.
14-3 Problem-Solving Strategy: Make a Model
Five-Minute Check (over Lesson 14-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
24.
14-3 Problem-Solving Strategy: Make a Model
• I will solve problems by making a model.
25.
14-3 Problem-Solving Strategy: Make a Model
Standard 4MR2.3 Use a variety of
methods, such as words, numbers, symbols,
charts, graphs, tables, diagrams, and models,
to explain mathematical reasoning.
26.
14-3 Problem-Solving Strategy: Make a Model
Standard 4NS3.0 Students solve problems
involving
addition, subtraction, multiplication, and
division of whole numbers and understand
the relationships among the operations.
27.
14-3 Problem-Solving Strategy: Make a Model
Luisa’s mom has asked her to find seating for
22 guests for her birthday party. They have an
oval table that can seat 10 people. They also
have card tables that each seat 4 people. What
is the fewest number of card tables to seat the
guests?
28.
14-3 Problem-Solving Strategy: Make a Model
Understand
What facts do you know?
• An oval table seats 10 people.
• There will be 22 guests altogether.
• Each card table seats 4 people.
What do you need to find?
• The fewest number of card tables needed to seat
the guests.
29.
14-3 Problem-Solving Strategy: Make a Model
Plan
You can draw a model of the tables to see how
many tables are needed.
30.
14-3 Problem-Solving Strategy: Make a Model
Solve
The oval table can 12 people will sit at
seat 10 people. card tables.
22 – 10 = 12 12 – 12 = 0
Answer: So, three is the fewest number of card
tables needed to seat the guests.
31.
14-3 Problem-Solving Strategy: Make a Model
Check
Look back at the problem. The fewest number of
card tables needed is 3. This makes sense
because 22 – 10 – (3 × 4) = 0. The answer is
correct.
32.
14-4 Compare and Order Decimals
Five-Minute Check (over Lesson 14-3)
Main Idea
California Standards
Example 1
Example 2
33.
14-4 Compare and Order Decimals
• I will compare and order decimals.
34.
14-4 Compare and Order Decimals
Standard 4NS1.2 Order and compare
whole numbers and decimals to two decimal
places.
Standard 4NS1.9 Identify on a number line
the relative position of positive fractions, positive
mixed numbers, and positive decimals to two
decimal places.
35.
14-4 Compare and Order Decimals
Jun’s time in the 100 meter dash was 13.6
seconds and Manuel’s was 13.3 seconds. Who
ran the race in the least time?
Use a place value chart. Line up the decimal points.
Then compare the digits in each place value
position.
36.
14-4 Compare and Order Decimals
1 3 6 0
1 3 3 0
In the tenths place, 6 > 3. So, 13.6 is greater than 13.3.
Answer: Manuel ran the race in the least time.
37.
14-4 Compare and Order Decimals
Corina’s time in the 400 meter dash was 64.1
seconds and Tara’s was 64.4 seconds. Who ran
the race in the least time?
A. Corina
B. Tara
C. Both ran the race in the least time.
D. Neither ran the race in the least time.
38.
14-4 Compare and Order Decimals
Order 4.56, 4.32, and 5.23 from least to greatest.
4.56 4.56 4.32
4.32 4.32 4.56
5.23 5.23 5.23
39.
14-4 Compare and Order Decimals
Answer: So, the order from least to greatest is
4.32, 4.56, and 5.23.
40.
14-4 Compare and Order Decimals
Order 3.53, 3.49, and 3.64 from least to greatest.
A. 3.53, 3.49, 3.64
B. 3.49, 3.64, 3.53
C. 3.49, 3.53, 3.64
D. 3.64, 3.49, 3.53
41.
14-5 Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 14-4)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
42.
14-5 Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
43.
14-5 Problem-Solving Investigation: Choose a Strategy
Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing
relevant from irrelevant
information, sequencing and prioritizing
information, and observing patterns.
44.
14-5 Problem-Solving Investigation: Choose a Strategy
Standard 4NS3.0 Students solve
problems involving addition, subtraction,
multiplication, and division of whole numbers
and understand relationships among the
operations.
45.
14-5 Problem-Solving Investigation: Choose a Strategy
1
XING: My father and I each ate
4
of a pizza. My brother ate 1 more
slice than I did and twice as many
as my mother. She ate two slices.
YOUR MISSION: Find the number of
slices of pizza Xing’s family ate.
46.
14-5 Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• You know how much pizza each person ate.
What do you need to find?
• Find the total number of slices of pizza the
family ate.
47.
14-5 Problem-Solving Investigation: Choose a Strategy
Plan
Use logical reasoning to determine the answer.
48.
14-5 Problem-Solving Investigation: Choose a Strategy
Solve
Start with what is known.
• mother: 2 slices
• brother: twice as much as his mother or
2×2=4
• Xing: 1 less than his brother or 4 – 1 = 3
• father: 3 slices
49.
14-5 Problem-Solving Investigation: Choose a Strategy
Solve
Answer: So, Xing’s family ate 2 + 4 + 3 + 3 = 12
slices of pizza.
50.
14-5 Problem-Solving Investigation: Choose a Strategy
Check
Look back at the problem.
1
Xing and his father of 12 = 3
4
Xing’s brother 3+1=4
Xing’s mother 4÷2=2
3 + 3 + 4 + 2 = 12. So, the answer is correct.
51.
14-6 Fraction and Decimal Equivalents
Five-Minute Check (over Lesson 14-5)
Main Idea and Vocabulary
California Standards
Key Concept: Fraction-Decimal Equivalents
Example 1
Example 2
52.
14-6 Fraction and Decimal Equivalents
• I will learn about fractions that have decimal
equivalents.
• decimal equivalent
53.
14-6 Fraction and Decimal Equivalents
Standard 4NS1.6 Write tenths and hundredths in
decimal and fraction notation and know the
fraction and decimal equivalents for halves and
fourths (e.g., = 0.5 or 0.50; = = 1.75).
54.
14-6 Fraction and Decimal Equivalents
Standard 4NS1.7 Write the fraction represented by
a drawing of parts of a figure; represent a given
fraction by using drawings; and relate a fraction to
a simple decimal on a number line.
56.
14-6 Fraction and Decimal Equivalents
4
Determine whether 12.7 and 12 are equivalent.
5
57.
14-6 Fraction and Decimal Equivalents
4
The number lines show that 12 is further to the right
5
than 12.7.
4
Answer: So, 12.7 and 12 are not equivalent.
5
58.
14-6 Fraction and Decimal Equivalents
1
Determine whether 8.4 and 8 are equivalent.
2
A. equivalent
B. not equivalent
59.
14-6 Fraction and Decimal Equivalents
Write a fraction and a decimal to describe the
shaded part of the model.
4 20 80
× =
5 20 100
60.
14-6 Fraction and Decimal Equivalents
80 80
= 0.80 Write as a decimal.
100 100
Answer: So, 4 and 0.80 describe the shaded part of
5
the model.
61.
14-6 Fraction and Decimal Equivalents
Write a fraction and a decimal to describe the
shaded part of the model.
2
A. 4 ; 0.50
2
B. 5 ; 0.40
4
C. 4 ; 0.40
4
D. 5 ; 0.50
62.
14-7 Decimals, Fractions, and Mixed Numbers
Five-Minute Check (over Lesson 14-6)
Main Idea
California Standards
Example 1
63.
14-7 Decimals, Fractions, and Mixed Numbers
• I will compare and order decimals, fractions, and
mixed numbers.
64.
14-7 Decimals, Fractions, and Mixed Numbers
Standard 4NS1.2 Order and compare
whole numbers and decimals to two decimal
places.
65.
14-7 Decimals, Fractions, and Mixed Numbers
Standard 4NS1.9 Identify on a number
line the relative position of positive
fractions, positive mixed numbers, and
positive decimals to two decimal places.
66.
14-7 Decimals, Fractions, and Mixed Numbers
Order 17.35, 17 1 , 17.2, and 17 6 from least to
2 8
greatest.
1 6
Step 1 Write 17 and 17 as decimals.
2 8
1 6
17 = 17.5 17 = 17.75
2 8
67.
14-7 Decimals, Fractions, and Mixed Numbers
1 6
Step 2 Compare 17.35, 17 , 17.2, and 17 .
2 8
Answer: The order from least to greatest is 17.2,
17.35, 17 1 , and 17 6 .
2 8
68.
14-7 Decimals, Fractions, and Mixed Numbers
Order 12.4, 12 3 , and 12 1 from least to greatest.
4 5
3 1
A. 12.4, 12 , 12
4 5
3 1
B. 12 , 12.4, 12
4 5
1 3
C. 12 , 12.4, 12
5 4
3 1
D. 12 , 12 , 12.4
4 5
69.
Decimals
14
Five-Minute Checks
Fractions and Decimals
71.
Decimals
14
(over Chapter 13)
Write 2 2 as an improper fraction.
5
4
A. 5
7
B. 5
12
C. 5
2
D. 7
72.
Decimals
14
(over Chapter 13)
Write 3 7 as an improper fraction.
8
31
A.
8
7
B.
11
10
C. 8
24
D. 8
73.
Decimals
14
(over Chapter 13)
Write 5 1 as an improper fraction.
10
50
A.
10
6
B.
10
51
C. 15
51
D. 10
74.
Decimals
14
(over Chapter 13)
Write 28 as a mixed number.
9
3
A. 9
1
B. 3 9
9
C. 3
3
D. 3 9
75.
Decimals
14
(over Chapter 13)
Write 34 as a mixed number.
6
2
A. 5 6
3
B. 4 2
1
C. 6 3
2
D. 5 3
76.
Decimals
14
(over Chapter 13)
Write 23 as a mixed number.
5
3
A. 4 5
1
B. 5 5
2
C. 4 5
3
D. 4 4
77.
Decimals
14
(over Lesson 14-1)
Write six tenths as a fraction and a decimal.
1
A. ; 0.167
6
1
B. ; 0.063
16
6
C. 10 ; 0.60
10
D. 6 ; 1.67
78.
Decimals
14
(over Lesson 14-1)
Write fifty-four hundredths as a fraction and a
decimal.
A. 50 ; 0.125
400
B. 54 ; 0.54
100
54
C. ; 0.135
400
100
D. ; 1.85
54
79.
Decimals
14
(over Lesson 14-1)
Write three hundredths as a fraction and a decimal.
300
A. 1000 ; 0.30
B. 100 ; 33.33
3
3
C. ; 0.01
300
3
D. ; 0.03
100
80.
Decimals
14
(over Lesson 14-1)
Write forty hundredths as a fraction and a decimal.
A. 40 ; 0.40
100
B. 40 ; 0.10
400
100
C. ; 2.5
40
4
D. ; 0.04
100
81.
Decimals
14
(over Lesson 14-2)
Write sixteen and three tenths as a mixed number
and a decimal.
A. 16 1 ; 16.003
310
10
B. 3 ; 3.625
16
3
C. 16 ; 16.3
10
3
D. 16 ; 16.01
310
82.
Decimals
14
(over Lesson 14-2)
Write four and seventy-five hundredths as a mixed
number and a decimal.
A. 4 475 ; 4.75
100
75
B. 4 ; 4.75
100
4
C. 100 ; 100.05
75
1
D. 7500 ; 7500.25
4
83.
Decimals
14
(over Lesson 14-2)
Write thirty-three and seven hundredths as a mixed
number and a decimal.
A. 33 7 ; 33.07
100
B. 33 33 ; 33.047
700
C. 33 7 ; 33.01
700
D. 33 33 ; 33.07
700
84.
Decimals
14
(over Lesson 14-2)
Write nine and one half as a mixed number and a
decimal.
9
A. ; 4.5
2
2
B. 9 ; 9.5
1
12
C. ; 45.5
12
1
D. 9 ; 45.5
2
85.
Decimals
14
(over Lesson 14-3)
Use the Make a Model strategy to solve the problem.
Tenaya is playing a card game with her brother. One
half of her cards are hearts, one fourth are diamonds
and the rest are clubs. If she has 12 cards in her
hand, how many are hearts and diamonds?
A. 3 cards
B. 6 cards
C. 9 cards
D. 10 cards
86.
Decimals
14
(over Lesson 14-4)
Order 9.65, 9.68, 9.52, and 9.59 from greatest to
least.
A. 9.59, 9.52, 9.65, 9.68
B. 9.52, 9.59, 9.65, 9.68
C. 9.68, 9.65, 9.59, 9.52
D. 9.65, 9.68, 9.59, 9.52
87.
Decimals
14
(over Lesson 14-4)
Order 51.21, 53.45, 53.54, and 51.54 from greatest
to least.
A. 53.54, 51.54, 53.45, 51.21
B. 51.54, 53.54, 53.45, 51.21
C. 53.45, 51.54, 53.45, 51.21
D. 53.54, 53.45, 51.54, 51.21
88.
Decimals
14
(over Lesson 14-4)
Order 17.05, 17.50, 17.55, and 17.45 from greatest
to least.
A. 17.55, 17.50, 17.45, 17.05
B. 17.50, 17.55, 17.45, 17.05
C. 17.05, 17.45, 17.50, 17.55
D. 17.50, 17.45, 17.55, 17.05
89.
Decimals
14
(over Lesson 14-4)
Order 22.62, 22.17, 22.06, and 22.68 from greatest
to least.
A. 22.17, 22.68, 22.62, 22.06
B. 22.68, 22.62, 22.17, 22.06
C. 22.68, 22.17, 22.62, 22.06
D. 22.06, 22.17, 22.62, 22.68
90.
Decimals
14
(over Lesson 14-5)
Use any strategy to solve. Five students sold
tickets for the school play. Paige and Selena each
sold 6 more than Lexi. Lexi sold one half as many
as Alonzo. Alonzo sold 11 more than John who
sold 17 tickets. How many tickets did the 5
students sell in all?
A. 93 tickets
B. 99 tickets
C. 109 tickets
D. 141 tickets
91.
Decimals
14
(over Lesson 14-6)
Write thirty-fiftieths as a fraction and a decimal.
A. 30 ; 0.06
500
30
B. ; 0.35
50
3
C. ; 0.06
50
30
D. ; 0.60
50
92.
Decimals
14
(over Lesson 14-6)
Write five twenty-fifths as a fraction and a decimal.
A. 520 ; 104.0
5
5
B. ; 0.20
25
5
C. 5 ; 5.25
20
5
D. 250 ; 0.02
93.
Decimals
14
(over Lesson 14-6)
Write one-fourth as a fraction and a decimal.
1
A. 1 ; 1.25
4
1
B. ; 0.025
40
1
C. 4 ; 0.25
14
D. ; 0.35
40
94.
Decimals
14
(over Lesson 14-6)
Write thirteen-twentieths as a fraction and a decimal.
30
A. ; 1.5
20
13
B. ; 0.65
20
13
C. ; 1.54
20
20
D. ; 1.54
13
95.
Decimals
14
(over Lesson 14-6)
Write four-fifths as a fraction and a decimal.
A. 4 ; 0.8
5
40
B. ; 8.0
5
5
C. 4 ; 1.25
4
D. ; 0.08
50