Chapter 3 Summary
Section 3.1
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•
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Converting fractions to mixed numbers
Converting mixed numbers to fractions
Ordering fractions and mixed numbers
Word names and exponential form for decimals
Rounding of decimals
Converting terminating decimals to fractions and mixed numbers
Converting fractions to decimals
Section 3.2
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Fundamental Property of Fractions
Determining if fractions are equivalent
Finding missing numerators and denominators of equivalent fractions
Simplifying fractions using the greatest common factor (GCF)
Simplifying fractions using prime numbers
Determining if the decimal forms of fractions are repeating or terminating
Section 3.3
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Addition and subtraction of fractions and mixed numbers (same denominator)
Addition and subtraction of fractions and mixed numbers (LCM)
Addition and subtraction of decimals
Applications of addition and subtraction of rational numbers
Section 3.4
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Multiplication and division of fractions and mixed numbers
Multiplication and division of decimals
Multiplication and division of decimals by powers of 10
Applications of multiplication and division of rational numbers
240
Section 3.5
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Computing exponents on rational numbers
Computing exponents on multiple fractions
Order of operations with rational numbers
Simplifying complex fractions
Computing the average of rational numbers
Section 3.6
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Ordering rational numbers
Graphing inequalities
Determining if rational numbers are solutions to equations
Finding the next term in an arithmetic or geometric sequence
Solving application problems involving rational numbers
Section 3.7
• Writing numbers in scientific notation
• Writing numbers in standard form
• Significant digits for a number
Chapter 3 Review Exercises
Convert each fraction to mixed form.
1.
3.
61
7
52
!
9
2.
4.
145
13
267
!
15
Convert each mixed number to a fraction.
5.
7.
6
13
8
!9
9
14
241
4
5
6.
15
8.
!14
12
13
Replace the blank with the correct symbol: <, =, or >
25
89
____
4
15
50
64
11. ! ____ !
7
9
31
49
____
5
8
51
66
12. ! ____ !
4
5
9.
10.
Write the (a) word name and (b) expanded form for each decimal.
13. 5.809
15. 5.0038
14. 12.82
16. 23.4581
Round each decimal to the indicated place value.
17. 105.49; ones
19. 15.4998; hundredths
18. 17.651; tenths
20. 8.5944; thousandths
In each case a decimal given has been rounded. Give the accuracy (place-value) of the number.
21. 17.5
23. 26.30
22. 19.08
24. 12.000
Convert each decimal to a fraction or mixed number.
25. 4.9
27. –0.97
26. 0.51
28. –6.517
In each case the expanded form of a decimal is given. Give the decimal it represents.
29. 80 + 6 +
3
9
+
100 1000
30. 50 + 7 +
Convert each fraction or mixed number to a decimal.
31. !
33.
13
25
17
40
11
34.
15
4
36. !12
7
32. !
5
6
35. !26
5
8
242
4
5
+
10 1000
Determine whether the two fractions are equivalent by using the Fundamental Property of
Fractions.
5 60
37. ! , !
6 72
6x 36bx
,
39.
7y 49by
19 456
,!
23 575
7ax 35abx
40. !
,!
10b
50ab
38. !
For each fraction, list three equivalent fractions. Use variables in at least one of your fractions.
41. !
12
17
42.
5a
7b
Find the variable such that the two given fractions are equivalent.
9 !108
=
13
y
13
312
46. ! = !
b
216
6
x
=!
7
84
a 75
=
5 125
43. !
45.
44.
Use the greatest common factor to simplify each fraction.
25
45
15ax
49. !
35bx
60
80
45abx
50.
105axy
48. !
47.
Use prime numbers to simplify each fraction.
111
185
150
53. !
550
45
333
45x 7 y 8
54. !
36x10 y 6
51.
52.
243
Add or subtract the fractions, as indicated. Be sure to simplify all answers.
7
8
+
25 25
1 3 11
57. ! + !
6 8 12
25 19
59. !
+
48 45
7 13
!
36 36
11 17 13
58. !
+
!
30 45 15
13 23
60.
!
36 30
55.
56.
Combine the mixed numbers, as indicated. Be sure to simplify any answers and convert answers
to mixed numbers.
3
7
4
+6 +9
4
10
5
4
5
63. !6 ! 7
5
9
7
5
+ 11
8
12
1
5
64. 5 ! 8
4
6
62. !6
61. 8
Perform the following additions and subtractions.
65. 12.78 + 9.856
67. 6.1 ! 12.231
66. 48 ! 25.632
68. !13.86 ! 27.672
Multiply the given rational numbers. Leave your answers as fractions.
" 75 % " 18 %
70. $ ! ' • $ ! '
# 90 & # 25 &
12xy 15a
•
72.
25ab 16y
15 40
•
32 36
13 " 16 % 45
•$! ' •
71. !
36 # 39 & 20
69. !
Divide the given rational numbers. Leave your answers as fractions.
5 " 10 %
÷ $! '
18 # 21 &
8xy 16xy 2
÷
9a 2b 27ab 2
3
÷9
4
4xy 2 8x 2 y
÷
5a 2b 15ab 2
73. !
74. !
75.
76.
244
Perform the following multiplications and divisions. Write all answers as mixed numbers.
1 " 1%
78. !5 ÷ $ !1 '
3 # 6&
3 " 3%
80. !3 • $ !1 '
4 # 5&
2
1
77. !2 • 4
3
2
3
79. 8 ÷ 15
4
Multiply the following decimals.
82. 5.4 ! ( "10.2 )
84. !0.08 " ( !0.95 )
81. 0.49 ! 2.5
83. !0.000237 " 1000
Divide the following decimals. If a decimal is repeating, be sure to carry enough divisions so that
a pattern is indicated.
86. 8.125 ÷ (!12.5)
88. 4.66 ÷ 0.24
85. 9.15 ÷ 12
87. 12.867 ÷ 100
Compute each of the following whole number divisions using (a) remainders, (b) mixed
numbers, and (c) decimals. If a decimal is repeating, be sure to carry enough divisions so that a
pattern is indicated.
89. 435 ÷ 4
90. 685 ÷ 15
Compute the following exponents.
" 1%
91. $ !3 '
# 2&
2
92. (!1.2)2
2
! 9 $ ! 11 $
93. # & # &
" 22 % " 3 %
2
! 4x $ ! 15y $
94. # & #
&
" 5y % " 16x %
3
2
Compute the following expressions. Express your answers as fractions.
95.
4 5 6
!
•
7 12 7
" 2 5% 4
96. $ ! ' •
# 3 6& 9
2
5 "3
98. ! ! $ !
16 # 4
5 " 3%
!$ '
97.
12 # 4 &
245
5%
'
6&
2
Compute the following expressions. Answer using mixed numbers.
1
1
1
99. 3 ! 2 • 4
4
2
3
1$ 1
! 3
100. # 2 + 3 & • 3
" 5
2%
3
1 1
2
101. 2 • 3 ! 4 • 3
5 2
3
! 2$ ! 3$
102. # 1 & ' # 3 &
" 3% " 4 %
2
2
Simplify the following complex fractions.
2+
103.
3
4
1 3
+
104. 3 4
5
3!
6
2
3
1 +2
4
106. 3
2
3
1 !2
3
4
5
6
1
3
1 !2
4
105. 3
1
5
3 +2
2
6
Find the average of the following sets of numbers.
1 1 5
107. 2 , 3 , 5
3 2 6
109. 2.57, 1.82, 6.8, 8.1
1
3 1
108. !4 , !3 ,1
5
4 2
110. –3.57, 1.18, –8.2, –3.29
Compute the following expressions.
111. 18.21 ! (5.9)(8.2)
113. (6.9)(!7) ! (4 ! 5.3)2
112. 12 ! (6.5)(8.3)
114. (7.1 ! 9.4)2 ! (6 ! 7.3)2
Replace the blank with the correct symbol: <, =, or >
7
14
____
15
29
7
11
117. !6 ____ !6
16
24
21
37
____ !
35
50
8
93
118. !5 ____ !
11
16
116. !
115.
246
Graph the given inequality.
119. x > !6
19
121. x ! "
6
120. x < !2
19
122. x ! "
5
Determine whether or not the given rational number is a solution to the equation.
4
3
2
1
1
3
125. ! x ! 2 = x ! ; x = !
3
3
2
2
1
3
x
x 1
1
126. + 1 = ! + ; x = !
4
3 4
2
123. 3y ! 5 = !1; y = !
124. !2y ! 5 = y ! 4; y = !
Given the sequence, determine whether it is arithmetic or geometric, find the common difference
or common ratio, and find the next term.
3 1 1
127. ! , ! , ! ,...
4 2 4
3
129. 12, !3, ,...
4
128. !1.2, !2.3, !3.4,...
130. 9, !1.8, 0.36,...
Write each number in scientific notation.
131. 507,000
133. –0.00000504
132. –2,450,000
134. 0.0000650
Write each number in standard form.
135. –3.9 ! 10 4
137. 6.002 ! 10 "4
136. 5.08 ! 10 6
138. !3.304 " 10 !6
Determine the amount of significant digits in each number.
139. 290,000
141. 0.00400
140. –5,620,000
142. –0.05000
247
Answer each of the following application questions. Be sure to read the question, interpret the
problem mathematically, solve the problem, then answer the question. You should answer the
question in the form of a sentence.
143. Serpa has $337.24 in her checking account, and writes checks for $35.98, $109.86,
and $89.95. What is her new balance in the account?
144. After depositing two checks for $297.69 and $448.85 in her account, Mulva has
$1469.87 in her savings account. How much was in her account before depositing the
checks?
5
3
145. Kim buys a stock at a price of 102 . During the next day it rises 12 , then it drops
8
4
13
4 the following day. What is the price of the stock after these two days?
16
146. Eunice buys a car for which she makes car payments of $297.68 per month for
5 years. What is the total amount she pays for the car?
147. Alfred pays $4.75 per day for his bus commute in San Francisco. If he budgets
$1353.75 for his bus commuting, how many days does he plan to commute?
3
148. Beatrice leaves
of the value of her property to a nephew. If the nephew inherits a
8
value of $54,375, what is the total value of her property?
1
149. Raul owns 350 shares of a stock which gains $2 per share one day, and 145
4
5
shares of a stock which loses $4
per share that day. Did he have a net gain or loss
16
that day, and how much was it?
150. Martha signs a 20 year loan for her house. The loan requires a $8,650 down payment
and payments of $987.68 per month. What is the total amount she paid for the house?
248