SkillSkill 17

Skill 17
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Read: is less than.
↓
On the number line, 0.7 is to the
left of 0.9.
So, 0.7 � 0.9
0
0.9
2
2
ones
.
.
.
6
0
6>0
hundredths
7
7
tenths
Read: is greater than.
• Since the ones and tenths are
the same, compare hundredths.
6 hundredths are greater than
0 hundredths.
So, 2.76 � 2.70.
Ones are Tenths are Hundredths
the same. the same. are different.
↓
0.7
least
greatest
• Compare two numbers at a time.
0.94
0.50
0.98
0.50
0.98
0.94
Order Decimals
Order from least to greatest: 1.38,
0.94, 0.5, 0.98.
• Write the numbers in a list.
Align the digits.
Write zeros if needed.
1.38
This number is greatest.
0.94
None of the other
0.50
numbers has ones.
0.98
?
?
?
1.38
same 5 � 9
same 8 � 4
0.5 ,
least
0.94 ,
1.38
greatest
Go to the next side.
0.98 ,
0.94 � 0.5 0.5 � 0.98 0.98 � 0.94
In order from least to greatest,
the numbers are:
same 9 � 5
↓ ↓
↓
79
↓ ↓
Use Place Value
Compare: 2.76 � 2.7.
Use a place value table.
• Align the digits by place values.
• Then compare digits starting
with the ones place.
• Write a zero to the right of 7 in
2.7 so both numbers have the
same number of places.
↓
↓↓↓
↓
Use a Number Line
Compare: 0.7 � 0.9.
The number line is labeled in
intervals of tenths from 0 to 1.
Find 0.7 and 0.9 on the number
line.
A decimal is a number with one or more digits to the right of the decimal point.There are different ways to compare decimals.
Compare and Order Decimals
© Houghton Mifflin Harcourt Publishing Company
Name
Skill
Holt McDougal Mathematics
Name
Skill
Skill 17
Practice on Your Own
Order the numbers from greatest to least: 1.37, 1.56, 1.23, 1.59.
List the numbers. Compare two numbers at a time.
↓
�2
1.37 � 1.56
↓
3
�5
↓
1.56 � 1.59
The ones digits
are the same.
↓
6
�9
1.37
� 1.23
1.37
� 1.56
1.56
� 1.59
↓
1.59
3
↓
↓
1.23
1.37 � 1.23
Compare these
first. Their
tenths digits
are different.
1.56
↓
↓
1.37
Ordered from greatest to least: 1.59, 1.56, 1.37, 1.23
Use the number line. Write �, �, or � for �.
0.09
� 0.02
0.25
� 0.30
2
3
0.5
0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30
� 0.1
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Use place value. Write �, �, or � for
4
2.06
5
� 2.10
4.8
ones . tenths hundredths
�.
6
� 4.19
ones . tenths hundredths
7.36
� 7.36
ones . tenths hundredths
Order the numbers from least to greatest, or greatest to least.
7
8
3.42, 0.89, 0.91
,
least
9
2.65, 0.03, 2.4, 0.5
,
,
greatest
,
least
1.18, 1.27, 1.11, 1.3
,
greatest
,
greatest
,
,
least
Check
In Exercises 10 and 11, write �, �, or � for �.
10
11
0.72
� 0.7
5.28
� 5.29
12
Order from greatest to least.
2.83, 1.7, 2.48, 2.38
80
13
Order from least to
greatest.
1.38, 0.5, 1.83, 1.18
Holt McDougal Mathematics
© Houghton Mifflin Harcourt Publishing Company
1
9
��
4
+
9
4
4
1
�� � �� � �� � ��
4
4
4
4
+
with circles for
95
1
��.
4
Step 2
Group the
parts.
1
�
�
3
2
1
�� � �� � ��
2
2
2
1
� �2�
+
2
�
�
2
� �3�
1
� 1 � 1 � �4�
+
parts as wholes and
2 3 4 5 6 7 8
�� �� �� �� �� �� ��
2 3 4 5 6 7 8
Skill 21
3
�
�
+
Go to the next side.
3
� �4�
+
written as a mixed number is 21�4�.
11
4
4 3
�� � �� � �� � ��
4
4
4 4
9
��
4
�
So,
9
1
�� � 1 � 1 � ��
4
4
1
� 2 � �4�
1
� 2�4�
Step 3
Write the sum as a mixed
number.
These are some different names for 1:
9
4
4
1
�� � �� � �� � ��
4
4
4
4
1
��
4
5
3
2
�� � �� � ��
3
3
3
Write each improper fraction as a mixed number.
Try These
Step 1
Model
You can write an improper fraction as a mixed
number. Write the fraction 9�4� as a mixed number.
Write an Improper Fraction as a Mixed Number
© Houghton Mifflin Harcourt Publishing Company
Name
Skill
Holt McDougal Mathematics
Name
Skill
Skill 21
Practice on Your Own
Think:
+
Find the names for 1 in fraction form.
Then add the names for 1 and the
fraction.
Write the sum as a mixed number.
+
12
5
5
2
�� � �� � �� � ��
5
5
5
5
2
� 1 � 1 � �5�
2
� 2 � �5�
2
� 2�5�
Write each improper fraction as a mixed number.
� � � � �
9
�� � �� � �� � �� � �� � ��
2
2
2
2
2
2
�
�
�
�
�
�
�
4
� � �
8
�� � �� � �� � ��
3
3
3
3
�
�
�
�
�
�
13
�� �
5
�
�
�
�
�����
�� �� ��
� � �
�
�
7
�
2
5
7
�� �
2
�
�
�
�
8
� � � �
15
�� � � � � � � � � � � ��
4
4
4
4
4
�
�
�
�
�
�
�
�������
� � �� � � ��
� � � �
�
�
�
15
�� �
8
3
6
11
�� �
3
�
�
�
�
�������
� � � � �� � �
� � � �
�
�
�
9
24
�� �
5
19
�� �
6
Check
Write each improper fraction as a mixed number.
10 25
�� �
8
11 27
12 17
�� �
10
�� �
4
96
Holt McDougal Mathematics
© Houghton Mifflin Harcourt Publishing Company
1
1
99
1
3�2�
1
�
3
�
� ��
1
� �3� � �3� � �3�
�
1
1
2�3� � 1 � 1 � �3�
1
2�3�
2
↓
↓
2
2
2
1
� �2� � �2� � �2� � �2�
↓
1
� 1 � 1 � 1 � �2�
�
�
� ��
�
�
3
� �4� � �4� � �4� � �4�
�
3�4� � 1 � 1 � 1 � �4�
3
3
3�4�
3
Step 2
Use the denominator of the fraction to write equivalent fractions
for the ones.
Write each mixed number as an improper fraction.
Try These
3�2� � 1 � 1 � 1 � �2�
1
Step 1
Write the whole number as a
sum of ones.
Write the mixed number 3�2� as an improper fraction.
1
Write a Mixed Number as a Fraction
© Houghton Mifflin Harcourt Publishing Company
1
3
4
2
4
�
�
� ��
4
� �5� � �5�
�
1
1
7
Go to the next side.
So, the fraction for 3�2� is �2� .
2
1�5� � 1 � �5�
4
1�5�
� �2�
7
2
� �2� � �2� � �2� � �2�
3�2� � 1 � 1 � 1 � �2�
↓ ↓ ↓
1
Step 3
Add the numerators to find the
improper fraction.
Skill 22
Name
Skill
Holt McDougal Mathematics
Name
Skill
Skill 22
Practice on Your Own
Think:
2
Write the whole number as a sum of ones.
Write equivalent fractions for the ones.
Add the numerators to find the fraction.
2
2�5� � 1 � 1 � �5�
5
5
2
� �5� � �5� � �5�
12
� �5�
Write each mixed number as an improper fraction.
2
1
4�2�
1
1
3
4�2� � 1 � 1 � 1 � 1 � �2�
�
�
�
3
2�4�
�
�
1
� �2� � �2� � �2� � �2� � �2�
�
3
� �4� � �4� � �4�
�
�
�
�
� ��
3
3
2�4� � 1 � 1 � �4�
� ��
4
2
3�3�
2
3�5�
2
3�5� �
2
�
�
�
� ��
�
2
3�3� � 1 � 1 � 1 � �3�
�
�
�
�
�
�
�
�
�
�
� ��
�
�
� �� � �� � �� � ��
�
2
� �3� � �3� � �3� � �3�
�
�
� ��
5
6
1
2�8�
1
2�8� �
�
�
�
� ��
�
�
�
�
�
�
5
3�6� �
� ��
�
�
�
�
�
� ��
�
� �� � �� � ��
7
3
5�4� �
5
3�6�
�
�
�
�
�
�
�
�
� ��
�
�
� �� � � � � � � � � �
8
9
4
8�5� �
2
6�3� �
Check
Write each mixed number as an improper fraction.
10
3
5�4� �
11
12
1
6�8� �
100
3
4�5� �
Holt McDougal Mathematics
© Houghton Mifflin Harcourt Publishing Company
1
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5. �
6. �
7. 0.89, 0.91, 3.42
8. 0.03, 0.5, 2.4,
1. 7, 4, no, 37
2. 1, 2, no, 83.1
3. 2, 5, 63
4. 7, 6, 52.488
22 hundredths
PRACTICE
432
56 hundredths
690 and
8. 123 thousand,
© Houghton Mifflin Harcourt Publishing Company
489 and 9 tenths
7. 6 thousand,
CHECK
6. 2,165.5
12. 35.613
11. 47.5
19 hundredths
5. 169.45
10. 62
CHECK
9. 0.812
8. 57.1
7. 2
6. 4, 27.595
434 and
106 thousand,
4. 106,434.19;
3 tenths
3. 890.3; 890 and
68 hundredths
2. 177.68, 177 and
57 hundredths
1. 23.57; 23 and
1.83
13. 0.5, 1.18, 1.38,
2.38, 1.7
12. 2.83, 2.48,
11. �
10. �
CHECK
1.11
9. 1.3, 1.27, 1.18,
2.65
4. �
PRACTICE
sand, 351 and
5. 8, 4.8
3. �
3. 4, 7, yes, 28.535
3 tenths
1. 826.3; 826 and
2. 4,351.22; 4 thou-
PRACTICE
17
K
2. �
S
2. 1, 1, no, 13.1
S
1. �
TRY THESE
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TRY THESE
15
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1. 7, 6, yes, 8
S
K
I
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S
2
5
10. �6�
7
11. �8�
6
12. �1�0
9
9. �9�
3
8. �8�
3
7. �6�
2
6. �3�
5
5. �7�
CHECK
��
3. 1, 2, 1
2
5
4. �8�
1. 1, 4, �4�
3
2. 3, 4, �4�
1
3. 2, 5, �5�
PRACTICE
2
1. 2, 3, �3�
1
2. 1, 4, �4�
TRY THESE
18
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Holt McDougal Mathematics
Answers
L
6. 1
1, 2, 7, 14; 2, 7��
5. 1, 2, 3, 5, 6, 10,
6
1
4. �2�
433
��
11. 1
2
3
1
12. 2�� or 12��
2
10. 5��
CHECK
��
7. 32
3
8. 1�� or 3
3
9. 5��
�� or
1, 3, 5, 15; 3, 56
1
15��
6. 1, 2, 3, 6, 9, 18;
5, 8, 10, 20, 40;
��
10, 43
15, 30; 1, 2, 4,
14. 1
1
13. �2�
12. 0
11. 1
9. 1
1
10. �2�
8. 0
7. 1
5. 0
3. 1
3. 3, 3, 3��, 6��
4. 1, 2, 3, 4, 6, 12;
1
1. �2�
1
2. �2�
3 1
L
CHECK
PRACTICE
1
3. �2�
2. 1
1. 3, 3, 3��, 4��
3 2
2. 3, 3, 3��, 5��
3 3
PRACTICE
I
20
K
TRY THESE
1. 0
S
© Houghton Mifflin Harcourt Publishing Company
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TRY THESE
19
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S
3
CHECK
1
10. 3�8�
7
11. 2�1�0
1
12. 4�4�
9.
8.
7.
6.
5.
4.
3
3 3
��, 3, ��, 3��
4
4 4
5 5 3
3
��, ��, ��, 1, 1, ��, 2,
5 5 5
5
3 3
��, 2��
5 5
2 2 2 1
��, ��, ��, ��, 1, 1, 1,
2 2 2 2
1
1 1
��, 3, ��, 3��
2
2 2
3 3 3 2
��, ��, ��, ��, 1, 1, 1,
3 3 3 3
2
2 2
��, 3, ��, 3��
3
3 3
7
1�8�
4
4�5�
1
3�6�
3. 4, 4, 4, 3, 1, 1, 1,
1
1 1
1, 1, �2�, 4, �2�, 4�2�
2
2. 3, 3, 2, 1, 1, �3�, 2,
2 2
��, 2��
3 3
1. 2, 2, 2, 2, 1, 1, 1,
3. 1, 1, 2�4�
PRACTICE
1
1. 1, 1�2�
2
2. 1, 1�3�
TRY THESE
21
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3 4
1. 3, 3, 3��, 5��
4 1
2. 4, 4, 4��, 3��
2 4
3. 2, 2, 2��, 5��
S
I
I
L
S
15
11
23
12. �5�
49
11. �8�
23
10. �4�
9.
8.
7.
6.
5.
CHECK
5
5
5
2 17
�� � � � � � � � �� , � �
5
5
5
5 5
1
1 � 1 � �8�,
8
8
1 7
�� � �� � �� , 1
��
8
8
8 8
5
1 � 1 � 1 � �6�,
6
6
6
5 3
�� � � � � � � � �� , 2
��
6
6
6
6 6
23
��
4
44
��
5
20
��
3
3. 3, 3, 3, �3�
2
4. 1 � 1 � 1 � �5�,
9
1. 2, 2, 2, 2, �2�
11
2. 4, 4, �4�
PRACTICE
2. 4, 4, 4, �4�
9
3. 5, �5�
1. 3, 3, 7
TRY THESE
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Holt McDougal Mathematics
Answers