Chapter 1 Review Exercises
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- Jan 6, 2020
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( \newcommand{\kernel}{\mathrm{null}\,}\)
Chapter Review Exercises
Introduction to Whole Numbers
Use Place Value with Whole Number
In the following exercises find the place value of each digit.
Exercise 1
26,915
- 1
- 2
- 9
- 5
- 6
- Answer
-
- tens
- ten thousands
- hundreds
- ones
- thousands
Exercise 2
359,417
- 9
- 3
- 4
- 7
- 1
Exercise 3
58,129,304
- 5
- 0
- 1
- 8
- 2
- Answer
-
- ten millions
- tens
- hundred thousands
- millions
- ten thousands
Exercise 4
9,430,286,157
- 6
- 4
- 9
- 0
- 5
In the following exercises, name each number.
Exercise 5
6,104
- Answer
-
six thousand, one hundred four
Exercise 6
493,068
Exercise 7
3,975,284
- Answer
-
three million, nine hundred seventy-five thousand, two hundred eighty-four
Exercise 8
85,620,435
In the following exercises, write each number as a whole number using digits.
Exercise 9
three hundred fifteen
- Answer
-
315
Exercise 10
sixty-five thousand, nine hundred twelve
Exercise 11
ninety million, four hundred twenty-five thousand, sixteen
- Answer
-
90,425,016
Exercise 12
one billion, forty-three million, nine hundred twenty-two thousand, three hundred eleven
In the following exercises, round to the indicated place value.
Exercise 13
Round to the nearest ten.
- 407
- 8,564
- Answer
-
- 410
- 8,560
Exercise 14
Round to the nearest hundred.
- 25,846
- 25,864
In the following exercises, round each number to the nearest 1. hundred 2. thousand 3. ten thousand.
Exercise 15
864,951
- Answer
-
- 865,000865,000
- 865,000865,000
- 860,000
Exercise 16
3,972,849
Identify Multiples and Factors
In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.
Exercise 17
168
- Answer
-
by 2,3,6
Exercise 18
264
Exercise 19
375
- Answer
-
by 3,5
Exercise 20
750
Exercise 21
1430
- Answer
-
by 2,5,10
Exercise 22
1080
Find Prime Factorizations and Least Common Multiples
In the following exercises, find the prime factorization.
Exercise 23
420
- Answer
-
2⋅2⋅3⋅5⋅7
Exercise 24
115
Exercise 25
225
- Answer
-
3⋅3⋅5⋅5
Exercise 26
2475
Exercise 27
1560
- Answer
-
2⋅2⋅2⋅3⋅5⋅13
Exercise 28
56
Exercise 29
72
- Answer
-
2⋅2⋅2⋅3⋅3
Exercise 30
168
Exercise 31
252
- Answer
-
2⋅2⋅3⋅3⋅7
Exercise 32
391
In the following exercises, find the least common multiple of the following numbers using the multiples method.
Exercise 33
6,15
- Answer
-
30
Exercise 34
60, 75
In the following exercises, find the least common multiple of the following numbers using the prime factors method.
Exercise 35
24, 30
- Answer
-
120
Exercise 36
70, 84
Use the Language of Algebra
Use Variables and Algebraic Symbols
In the following exercises, translate the following from algebra to English.
Exercise 37
25−7
- Answer
-
25 minus 7, the difference of twenty-five and seven
Exercise 38
5⋅6
Exercise 39
45÷5
- Answer
-
45 divided by 5, the quotient of forty-five and five
Exercise 40
x+8
Exercise 41
42≥27
- Answer
-
forty-two is greater than or equal to twenty-seven
Exercise 42
3n=24
Exercise 43
3≤20÷4
- Answer
-
3 is less than or equal to 20 divided by 4, three is less than or equal to the quotient of twenty and four
Exercise 44
a≠7⋅4
In the following exercises, determine if each is an expression or an equation.
Exercise 45
6⋅3+5
- Answer
-
expression
Exercise 46
y−8=32
Simplify Expressions Using the Order of Operations
In the following exercises, simplify each expression.
Exercise 47
35
- Answer
-
243
Exercise 48
108
In the following exercises, simplify
Exercise 49
6+10/2+2
- Answer
-
13
Exercise 50
9+12/3+4
Exercise 51
20÷(4+6)⋅5
- Answer
-
10
Exercise 52
33÷(3+8)⋅2
Exercise 53
42+52
- Answer
-
41
Exercise 54
(4+5)2
Evaluate an Expression
In the following exercises, evaluate the following expressions.
Exercise 55
9x+7 when x=3
- Answer
-
34
Exercise 56
5x−4 when x=6
Exercise 57
x4 when x=3
- Answer
-
81
Exercise 58
3x when x=3
Exercise 59
x2+5x−8 when x=6
- Answer
-
58
Exercise 60
2x+4y−5 when
x=7,y=8
Simplify Expressions by Combining Like Terms
In the following exercises, identify the coefficient of each term.
Exercise 61
12n
- Answer
-
12
Exercise 62
9x2
In the following exercises, identify the like terms.
Exercise 63
3n,n2,12,12p2,3,3n2
- Answer
-
12 and 3,n2 and 3n2
Exercise 64
5,18r2,9s,9r,5r2,5s
In the following exercises, identify the terms in each expression.
Exercise 65
11x2+3x+6
- Answer
-
11x2,3x,6
Exercise 66
22y3+y+15
In the following exercises, simplify the following expressions by combining like terms.
Exercise 67
17a+9a
- Answer
-
26a
Exercise 68
18z+9z
Exercise 69
9x+3x+8
- Answer
-
12x+8
Exercise 70
8a+5a+9
Exercise 71
7p+6+5p−4
- Answer
-
12p+2
Exercise 72
8x+7+4x−5
Translate an English Phrase to an Algebraic Expression
In the following exercises, translate the following phrases into algebraic expressions.
Exercise 73
the sum of 8 and 12
- Answer
-
8+12
Exercise 74
the sum of 9 and 1
Exercise 75
the difference of x and 4
- Answer
-
x−4
Exercise 76
the difference of x and 3
Exercise 77
the product of 6 and y
- Answer
-
6y
Exercise 78
the product of 9 and y
Exercise 79
Adele bought a skirt and a blouse. The skirt cost $15 more than the blouse. Let bb represent the cost of the blouse. Write an expression for the cost of the skirt.
- Answer
-
b+15
Exercise 80
Marcella has 6 fewer boy cousins than girl cousins. Let g represent the number of girl cousins. Write an expression for the number of boy cousins.
Add and Subtract Integers
Use Negatives and Opposites of Integers
In the following exercises, order each of the following pairs of numbers, using < or >.
Exercise 81
- 6___2
- −7___4
- −9___−1
- 9___−3
- Answer
-
- >
- <
- <
- >
Exercise 82
- −5___1
- −4___−9
- 6___10
- 3___−8
In the following exercises,, find the opposite of each number.
Exercise 83
- −8
- 1
- Answer
-
- 8
- −1
Exercise 84
- −2
- 6
In the following exercises, simplify.
Exercise 85
−(−19)
- Answer
-
19
Exercise 86
−(−53)
In the following exercises, simplify.
Exercise 87
−m when
- m=3
- m=−3
- Answer
-
- −3
- 3
Exercise 88
−p when
- p=6
- p=−6
Simplify Expressions with Absolute Value
In the following exercises,, simplify.
Exercise 89
- |7|
- |−25|
- |0|
- Answer
-
- 7
- 25
- 0
Exercise 90
- |5|
- |0|
- |−19|
In the following exercises, fill in <, >, or = for each of the following pairs of numbers.
Exercise 91
- −8___|−8|
- −|−2|___−2
- Answer
-
- <
- =
Exercise 92
- |−3|___−|−3|
- 4___−|−4|
In the following exercises, simplify.
Exercise 93
|8−4|
- Answer
-
4
Exercise 94
|9−6|
Exercise 95
8(14−2|−2|)
- Answer
-
80
Exercise 96
6(13−4|−2|)
In the following exercises, evaluate.
Exercise 97
1. |x| when x=−28
- Answer
-
- 28
- 15
Exercise 98
- ∣y∣ when y=−37
- |−z| when z=−24
Add Integers
In the following exercises, simplify each expression.
Exercise 99
−200+65
- Answer
-
−135
Exercise 100
−150+45
Exercise 101
2+(−8)+6
- Answer
-
0
Exercise 102
4+(−9)+7
Exercise 103
140+(−75)+67
- Answer
-
132
Exercise 104
−32+24+(−6)+10
Subtract Integers
In the following exercises, simplify.
Exercise 105
9−3
- Answer
-
6
Exercise 106
−5−(−1)
Exercise 107
- 15−6
- 15+(−6)
- Answer
-
- 9
- 9
Exercise 108
- 12−9
- 12+(−9)
Exercise 109
- 8−(−9)
- 8+9
- Answer
-
- 17
- 17
Exercise 110
- 4−(−4)
- 4+4
In the following exercises, simplify each expression.
Exercise 111
10−(−19)
- Answer
-
29
Exercise 112
11−(−18)
Exercise 113
31−79
- Answer
-
−48
Exercise 114
39−81
Exercise 115
−31−11
- Answer
-
−42
Exercise 116
−32−18
Exercise 117
−15−(−28)+5
- Answer
-
18
Exercise 118
71+(−10)−8
Exercise 119
−16−(−4+1)−7
- Answer
-
-20
Exercise 120
−15−(−6+4)−3
Multiply Integers
In the following exercises, multiply.
Exercise 121
−5(7)
- Answer
-
−35
Exercise 122
−8(6)
Exercise 123
−18(−2)
- Answer
-
36
Exercise 124
−10(−6)
Divide Integers
In the following exercises, divide.
Exercise 125
−28÷7
- Answer
-
-4
Exercise 126
56÷(−7)
Exercise 127
−120÷(−20)
- Answer
-
6
Exercise 128
−200÷25
Simplify Expressions with Integers
In the following exercises, simplify each expression.
Exercise 129
−8(−2)−3(−9)
- Answer
-
43
Exercise 130
−7(−4)−5(−3)
Exercise 131
(−5)3
- Answer
-
−125
Exercise 132
(−4)3
Exercise 133
−4⋅2⋅11
- Answer
-
−88
Exercise 134
−5⋅3⋅10
Exercise 135
−10(−4)÷(−8)
- Answer
-
-5
Exercise 136
−8(−6)÷(−4)
Exercise 137
31−4(3−9)
- Answer
-
55
Exercise 138
24−3(2−10)
Evaluate Variable Expressions with Integers
In the following exercises, evaluate each expression.
Exercise 139
x+8 when
- x=−26
- x=−95
- Answer
-
- −18
- −87
Exercise 140
y+9 when
- y=−29
- y=−84
Exercise 141
When b=−11, evaluate:
- b+6
- −b+6
- Answer
-
- −5
- 17
Exercise 142
When c=−9, evaluate:
- c+(−4)c+(−4)
- −c+(−4)
Exercise 143
p2−5p+2 when
p=−1
- Answer
-
8
Exercise 144
q2−2q+9 when q=−2
Exercise 145
6x−5y+15 when x=3 and y=−1
- Answer
-
38
Exercise 146
3p−2q+9 when p=8 and q=−2
Translate English Phrases to Algebraic Expressions
In the following exercises, translate to an algebraic expression and simplify if possible.
Exercise 147
the sum of −4 and −17, increased by 32
- Answer
-
(−4+(−17))+32;11
Exercise 148
- the difference of 15 and −7
- subtract 15 from −7
Exercise 149
the quotient of −45 and −9
- Answer
-
−45−9;5
Exercise 150
the product of −12 and the difference of c and d
Use Integers in Applications
In the following exercises, solve.
Exercise 151
Temperature The high temperature one day in Miami Beach, Florida, was 76°. That same day, the high temperature in Buffalo, New York was −8°. What was the difference between the temperature in Miami Beach and the temperature in Buffalo?
- Answer
-
84 degrees
Exercise 152
Checking Account Adrianne has a balance of −$22 in her checking account. She deposits $301 to the account. What is the new balance?
Visualize Fractions
Find Equivalent Fractions
In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.
Exercise 153
14
- Answer
-
28,312,416 answers may vary
Exercise 154
13
Exercise 155
56
- Answer
-
1012,1518,2024 answers may vary
Exercise 156
27
Simplify Fractions
In the following exercises, simplify.
Exercise 157
721
- Answer
-
13
Exercise 158
824
Exercise 159
1520
- Answer
-
34
Exercise 160
1218
Exercise 161
−168192
- Answer
-
−78
Exercise 162
−140224
Exercise 163
11x11y
- Answer
-
xy
Exercise 164
15a15b
Multiply Fractions
In the following exercises, multiply.
Exercise 165
25⋅13
- Answer
-
215
Exercise 166
12⋅38
Exercise 167
712(−821)
- Answer
-
−29
Exercise 168
512(−815)
Exercise 169
−28p(−14)
- Answer
-
7p
Exercise 170
−51q(−13)
Exercise 172
145(−15)
- Answer
-
−42
Exercise 173
−1(−38)
Divide Fractions
In the following exercises, divide
Exercise 174
12÷14
- Answer
-
2
Exercise 175
12÷18
Exercise 176
−45÷47
- Answer
-
−75
Exercise 177
−34÷35
Exercise 178
58÷a10
- Answer
-
254a
Exercise 179
56÷c15
Exercise 180
7p12÷21p8
- Answer
-
29
Exercise 181
5q12÷15q8
Exercise 182
25÷(−10)
- Answer
-
−125
Exercise 183
−18÷−(92)
In the following exercises, simplify.
Exercise 184
2389
- Answer
-
34
Exercise 185
45815
Exercise 186
−9103
- Answer
-
−310
Exercise 187
258
Exercise 188
r5s3
- Answer
-
3r5s
Exercise 189
−x6−89
Simplify Expressions Written with a Fraction Bar
In the following exercises, simplify.
Exercise 190
4+118
- Answer
-
158
Exercise 191
9+37
Exercise 192
307−12
- Answer
-
-6
Exercise 193
154−9
Exercise 194
22−1419−13
- Answer
-
43
Exercise 195
15+918+12
Exercise 196
5⋅8−10
- Answer
-
-4
Exercise 197
3⋅4−24
Exercise 198
15⋅5−522⋅10
- Answer
-
52
Exercise 199
12⋅9−323⋅18
Exercise 200
2+4(3)−3−22
- Answer
-
-2
Exercise 201
7+3(5)−2−32
Translate Phrases to Expressions with Fractions
In the following exercises, translate each English phrase into an algebraic expression.
Exercise 202
the quotient of c and the sum of d and 9.
- Answer
-
cd+9
Exercise 203
the quotient of the difference of h and k, and −5.
Add and Subtract Fractions
Add and Subtract Fractions with a Common Denominator
In the following exercises, add.
Exercise 204
49+19
- Answer
-
59
Exercise 205
29+59
Exercise 206
y3+23
- Answer
-
y+23
Exercise 207
7p+9p
Exercise 208
−18+(−38)
- Answer
-
−12
Exercise 209
−18+(−58)
In the following exercises, subtract.
Exercise 210
45−15
- Answer
-
35
Exercise 211
45−35
Exercise 212
y17−917
- Answer
-
y−917
Exercise 213
x19−819
Exercise 214
−8d−3d
- Answer
-
−11d
Exercise 215
−7c−7c
Add or Subtract Fractions with Different Denominators
In the following exercises, add or subtract.
Exercise 216
13+15
- Answer
-
815
Exercise 217
14+15
Exercise 218
15−(−110)
- Answer
-
310
Exercise 219
12−(−16)
Exercise 220
23+34
- Answer
-
1712
Exercise 221
34+25
Exercise 222
1112−38
- Answer
-
1324
Exercise 223
58−712
Exercise 224
−916−(−45)
- Answer
-
1980
Exercise 225
−720−(−58)
Exercise 226
1+56
- Answer
-
116
Exercise 227
1−59
Use the Order of Operations to Simplify Complex Fractions
In the following exercises, simplify.
Exercise 228
(15)22+32
- Answer
-
1275
Exercise 229
(13)25+22
Exercise 230
23+1234−23
- Answer
-
14
Exercise 231
34+1256−23
Evaluate Variable Expressions with Fractions
In the following exercises, evaluate.
Exercise 232
x+12 when
- x=−18
- x=−12
- Answer
-
- 38
- 0
Exercise 233
x+23 when
- x=−16
- x=−53
Exercise 234
4p2q when p=-\frac{1}{2} and q=\frac{5}{9}
- Answer
-
\frac{5}{9}
Exercise \PageIndex{235}
5m^{2} n when m=-\frac{2}{5} and n=\frac{1}{3}
Exercise \PageIndex{236}
\frac{u+v}{w} when
u=-4, v=-8, w=2
- Answer
-
-6
Exercise \PageIndex{237}
\frac{m+n}{p} when
m=-6, n=-2, p=4
Decimals
Name and Write Decimals
In the following exercises, write as a decimal.
Exercise \PageIndex{238}
Eight and three hundredths
- Answer
-
8.03
Exercise \PageIndex{239}
Nine and seven hundredths
Exercise \PageIndex{240}
One thousandth
- Answer
-
0.001
Exercise \PageIndex{241}
Nine thousandths
In the following exercises, name each decimal.
Exercise \PageIndex{242}
7.8
- Answer
-
seven and eight tenths
Exercise \PageIndex{243}
5.01
Exercise \PageIndex{244}
0.005
- Answer
-
five thousandths
Exercise \PageIndex{245}
0.381
Round Decimals
In the following exercises, round each number to the nearest
- hundredth
- tenth
- whole number.
Exercise \PageIndex{246}
5.7932
- Answer
-
- 5.79
- 5.8
- 6
Exercise \PageIndex{247}
3.6284
Exercise \PageIndex{248}
12.4768
- Answer
-
- 12.48
- 12.5
- 12
Exercise \PageIndex{249}
25.8449
Add and Subtract Decimals
In the following exercises, add or subtract.
Exercise \PageIndex{250}
18.37+9.36
- Answer
-
27.73
Exercise \PageIndex{251}
256.37−85.49
Exercise \PageIndex{252}
15.35−20.88
- Answer
-
−5.53
Exercise \PageIndex{253}
37.5+12.23
Exercise \PageIndex{254}
−4.2+(−9.3)
- Answer
-
−13.5
Exercise \PageIndex{255}
−8.6+(−8.6)
Exercise \PageIndex{256}
100−64.2
- Answer
-
35.8
Exercise \PageIndex{257}
100−65.83
Exercise \PageIndex{258}
2.51+40
- Answer
-
42.51
Exercise \PageIndex{259}
9.38+60
Multiply and Divide Decimals
In the following exercises, multiply.
Exercise \PageIndex{260}
(0.3)(0.4)
- Answer
-
0.12
Exercise \PageIndex{261}
(0.6)(0.7)
Exercise \PageIndex{262}
(8.52)(3.14)
- Answer
-
26.7528
Exercise \PageIndex{263}
(5.32)(4.86)
Exercise \PageIndex{264}
(0.09)(24.78)
- Answer
-
2.2302
Exercise \PageIndex{265}
(0.04)(36.89)
In the following exercises, divide.
Exercise \PageIndex{266}
0.15 \div 5
- Answer
-
0.03
Exercise \PageIndex{267}
0.27 \div 3
Exercise \PageIndex{268}
\$ 8.49 \div 12
- Answer
-
$0.71
Exercise \PageIndex{269}
\$ 16.99 \div 9
Exercise \PageIndex{270}
12 \div 0.08
- Answer
-
150
Exercise \PageIndex{271}
5 \div 0.04
Convert Decimals, Fractions, and Percents
In the following exercises, write each decimal as a fraction.
Exercise \PageIndex{272}
0.08
- Answer
-
\frac{2}{25}
Exercise \PageIndex{273}
0.17
Exercise \PageIndex{274}
0.425
- Answer
-
\frac{17}{40}
Exercise \PageIndex{275}
0.184
Exercise \PageIndex{276}
1.75
- Answer
-
\frac{7}{4}
Exercise \PageIndex{277}
0.035
In the following exercises, convert each fraction to a decimal.
Exercise \PageIndex{278}
\frac{2}{5}
- Answer
-
0.4
Exercise \PageIndex{279}
\frac{4}{5}
Exercise \PageIndex{280}
-\frac{3}{8}
- Answer
-
−0.375
Exercise \PageIndex{281}
-\frac{5}{8}
Exercise \PageIndex{282}
\frac{5}{9}
- Answer
-
0 . \overline{5}
Exercise \PageIndex{283}
\frac{2}{9}
Exercise \PageIndex{284}
\frac{1}{2}+6.5
- Answer
-
7
Exercise \PageIndex{285}
\frac{1}{4}+10.75
In the following exercises, convert each percent to a decimal.
Exercise \PageIndex{286}
5%
- Answer
-
0.05
Exercise \PageIndex{287}
9%
Exercise \PageIndex{288}
40%
- Answer
-
0.4
Exercise \PageIndex{289}
50%
Exercise \PageIndex{290}
115%
- Answer
-
1.15
Exercise \PageIndex{291}
125%
In the following exercises, convert each decimal to a percent.
Exercise \PageIndex{292}
0.18
- Answer
-
18%
Exercise \PageIndex{293}
0.15
Exercise \PageIndex{294}
0.009
- Answer
-
0.9%
Exercise \PageIndex{295}
0.008
Exercise \PageIndex{296}
1.5
- Answer
-
150%
Exercise \PageIndex{297}
2.2
The Real Numbers
Simplify Expressions with Square Roots
In the following exercises, simplify.
Exercise \PageIndex{298}
\sqrt{64}
- Answer
-
8
Exercise \PageIndex{299}
\sqrt{144}
Exercise \PageIndex{300}
-\sqrt{25}
- Answer
-
-5
Exercise \PageIndex{301}
-\sqrt{81}
Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers
In the following exercises, write as the ratio of two integers.
Exercise \PageIndex{302}
- 9
- 8.47
- Answer
-
- \frac{9}{1}
- \frac{847}{100}
Exercise \PageIndex{303}
- −15
- 3.591
In the following exercises, list the
- rational numbers,
- irrational numbers.
Exercise \PageIndex{304}
0.84,0.79132 \ldots, 1 . \overline{3}
- Answer
-
- 0.84,1.3
- 0.79132 \ldots
Exercise \PageIndex{305}
2.3 \overline{8}, 0.572,4.93814 \ldots
In the following exercises, identify whether each number is rational or irrational.
Exercise \PageIndex{306}
- \sqrt{121}
- \sqrt{48}
- Answer
-
- rational
- irrational
Exercise \PageIndex{307}
- \sqrt{56}
- \sqrt{16}
In the following exercises, identify whether each number is a real number or not a real number.
Exercise \PageIndex{308}
- \sqrt{-9}
- -\sqrt{169}
- Answer
-
- not a real number
- real number
Exercise \PageIndex{309}
- \sqrt{-64}
- -\sqrt{81}
In the following exercises, list the
- whole numbers,
- integers,
- rational numbers,
- irrational numbers,
- real numbers for each set of numbers.
Exercise \PageIndex{310}
-4,0, \frac{5}{6}, \sqrt{16}, \sqrt{18}, 5.2537 \ldots
- Answer
-
- 0, \sqrt{16}
- -4,0, \sqrt{16}
- -4,0, \frac{5}{6}, \sqrt{16}
- \sqrt{18}, 5.2537 \ldots
- -4,0, \frac{5}{6}, \sqrt{16}, \sqrt{18}, 5.2537 \ldots
Exercise \PageIndex{311}
-\sqrt{4}, 0 . \overline{36}, \frac{13}{3}, 6.9152 \ldots, \sqrt{48}, 10 \frac{1}{2}
Locate Fractions on the Number Line
In the following exercises, locate the numbers on a number line.
Exercise \PageIndex{312}
\frac{2}{3}, \frac{5}{4}, \frac{12}{5}
- Answer
-
Exercise \PageIndex{313}
\frac{1}{3}, \frac{7}{4}, \frac{13}{5}
Exercise \PageIndex{314}
2 \frac{1}{3},-2 \frac{1}{3}
- Answer
-
Exercise \PageIndex{315}
1 \frac{3}{5},-1 \frac{3}{5}
In the following exercises, order each of the following pairs of numbers, using < or >.
Exercise \PageIndex{316}
−1___-\frac{1}{8}
- Answer
-
<
Exercise \PageIndex{317}
-3 \frac{1}{4}___−4
Exercise \PageIndex{318}
-\frac{7}{9} ___ \frac{4}{9}
- Answer
-
>
Exercise \PageIndex{319}
-2 ___ \frac{19}{8}
Locate Decimals on the Number Line
In the following exercises, locate on the number line.
Exercise \PageIndex{320}
0.3
- Answer
-
Exercise \PageIndex{321}
−0.2
Exercise \PageIndex{322}
−2.5
- Answer
-
Exercise \PageIndex{323}
2.7
In the following exercises, order each of the following pairs of numbers, using < or >.
Exercise \PageIndex{324}
0.9___0.6
- Answer
-
>
Exercise \PageIndex{325}
0.7___0.8
Exercise \PageIndex{326}
−0.6___−0.59
- Answer
-
>
Exercise \PageIndex{327}
−0.27___−0.3
Properties of Real Numbers
Use the Commutative and Associative Properties
In the following exercises, use the Associative Property to simplify.
Exercise \PageIndex{328}
−12(4m)
- Answer
-
−48m
Exercise \PageIndex{329}
30\left(\frac{5}{6} q\right)
Exercise \PageIndex{330}
(a+16)+31
- Answer
-
a+47
Exercise \PageIndex{331}
(c+0.2)+0.7
In the following exercises, simplify.
Exercise \PageIndex{332}
6y+37+(−6y)
- Answer
-
37
Exercise \PageIndex{333}
\frac{1}{4}+\frac{11}{15}+\left(-\frac{1}{4}\right)
Exercise \PageIndex{334}
\frac{14}{11} \cdot \frac{35}{9} \cdot \frac{14}{11}
- Answer
-
\frac{35}{9}
Exercise \PageIndex{335}
-18 \cdot 15 \cdot \frac{2}{9}
Exercise \PageIndex{336}
\left(\frac{7}{12}+\frac{4}{5}\right)+\frac{1}{5}
- Answer
-
1\frac{7}{12}
Exercise \PageIndex{337}
(3.98d+0.75d)+1.25d
Exercise \PageIndex{338}
11x+8y+16x+15y
- Answer
-
27x+23y
Exercise \PageIndex{339}
52m+(−20n)+(−18m)+(−5n)
Use the Identity and Inverse Properties of Addition and Multiplication
In the following exercises, find the additive inverse of each number.
Exercise \PageIndex{340}
- \frac{1}{3}
- 5.1
- -14
- -\frac{8}{5}
- Answer
-
- -\frac{1}{3}
- -5.1
- -14
- -\frac{8}{5}
Exercise \PageIndex{341}
- -\frac{7}{8}
- -0.03
- 17
- \frac{12}{5}
In the following exercises, find the multiplicative inverse of each number.
Exercise \PageIndex{342}
- 10
- -\frac{4}{9}
- 0.6
- Answer
-
- \frac{1}{10}
- -\frac{9}{4}
- \frac{5}{3}
Exercise \PageIndex{343}
- -\frac{9}{2}
- -7
- 2.1
Use the Properties of Zero
In the following exercises, simplify.
Exercise \PageIndex{344}
83\cdot 0
- Answer
-
0
Exercise \PageIndex{345}
\frac{0}{9}
Exercise \PageIndex{346}
\frac{5}{0}
- Answer
-
undefined
Exercise \PageIndex{347}
0 \div \frac{2}{3}
In the following exercises, simplify.
Exercise \PageIndex{348}
43+39+(−43)
- Answer
-
39
Exercise \PageIndex{349}
(n+6.75)+0.25
Exercise \PageIndex{350}
\frac{5}{13} \cdot 57 \cdot \frac{13}{5}
- Answer
-
57
Exercise \PageIndex{351}
\frac{1}{6} \cdot 17 \cdot 12
Exercise \PageIndex{352}
\frac{2}{3} \cdot 28 \cdot \frac{3}{7}
- Answer
-
8
Exercise \PageIndex{353}
9(6 x-11)+15
Simplify Expressions Using the Distributive Property
In the following exercises, simplify using the Distributive Property.
Exercise \PageIndex{354}
7(x+9)
- Answer
-
7x+63
Exercise \PageIndex{355}
9(u−4)
Exercise \PageIndex{356}
−3(6m−1)
- Answer
-
−18m+3
Exercise \PageIndex{357}
−8(−7a−12)
Exercise \PageIndex{358}
\frac{1}{3}(15 n-6)
- Answer
-
5n−2
Exercise \PageIndex{359}
(y+10) \cdot p
Exercise \PageIndex{360}
(a−4)−(6a+9)
- Answer
-
−5a−13
Exercise \PageIndex{361}
4(x+3)−8(x−7)
Systems of Measurement
1.1 Define U.S. Units of Measurement and Convert from One Unit to Another
In the following exercises, convert the units. Round to the nearest tenth.
Exercise \PageIndex{362}
A floral arbor is 7 feet tall. Convert the height to inches.
- Answer
-
84 inches
Exercise \PageIndex{363}
A picture frame is 42 inches wide. Convert the width to feet.
Exercise \PageIndex{364}
Kelly is 5 feet 4 inches tall. Convert her height to inches.
- Answer
-
64 inches
Exercise \PageIndex{365}
A playground is 45 feet wide. Convert the width to yards.
Exercise \PageIndex{366}
The height of Mount Shasta is 14,179 feet. Convert the height to miles.
- Answer
-
2.7 miles
Exercise \PageIndex{367}
Shamu weights 4.5 tons. Convert the weight to pounds.
Exercise \PageIndex{368}
The play lasted 1\frac{3}{4} hours. Convert the time to minutes.
- Answer
-
105 minutes
Exercise \PageIndex{369}
How many tablespoons are in a quart?
Exercise \PageIndex{370}
Naomi’s baby weighed 5 pounds 14 ounces at birth. Convert the weight to ounces.
- Answer
-
94 ounces
Exercise \PageIndex{371}
Trinh needs 30 cups of paint for her class art project. Convert the volume to gallons.
Use Mixed Units of Measurement in the U.S. System.
In the following exercises, solve.
Exercise \PageIndex{372}
John caught 4 lobsters. The weights of the lobsters were 1 pound 9 ounces, 1 pound 12 ounces, 4 pounds 2 ounces, and 2 pounds 15 ounces. What was the total weight of the lobsters?
- Answer
-
10 lbs. 6 oz.
Exercise \PageIndex{373}
Every day last week Pedro recorded the number of minutes he spent reading. The number of minutes were 50, 25, 83, 45, 32, 60, 135. How many hours did Pedro spend reading?
Exercise \PageIndex{374}
Fouad is 6 feet 2 inches tall. If he stands on a rung of a ladder 8 feet 10 inches high, how high off the ground is the top of Fouad’s head?
- Answer
-
15 feet
Exercise \PageIndex{375}
Dalila wants to make throw pillow covers. Each cover takes 30 inches of fabric. How many yards of fabric does she need for 4 covers?
Make Unit Conversions in the Metric System
In the following exercises, convert the units.
Exercise \PageIndex{376}
Donna is 1.7 meters tall. Convert her height to centimeters.
- Answer
-
170 centimeters
Exercise \PageIndex{377}
Mount Everest is 8,850 meters tall. Convert the height to kilometers.
Exercise \PageIndex{378}
One cup of yogurt contains 488 milligrams of calcium. Convert this to grams.
- Answer
-
0.488 grams
Exercise \PageIndex{379}
One cup of yogurt contains 13 grams of protein. Convert this to milligrams.
Exercise \PageIndex{380}
Sergio weighed 2.9 kilograms at birth. Convert this to grams.
- Answer
-
2,900 grams
Exercise \PageIndex{381}
A bottle of water contained 650 milliliters. Convert this to liters.
Use Mixed Units of Measurement in the Metric System
In the following exerices, solve.
Exercise \PageIndex{382}
Minh is 2 meters tall. His daughter is 88 centimeters tall. How much taller is Minh than his daughter?
- Answer
-
1.12 meter
Exercise \PageIndex{383}
Selma had a 1 liter bottle of water. If she drank 145 milliliters, how much water was left in the bottle?
Exercise \PageIndex{384}
One serving of cranberry juice contains 30 grams of sugar. How many kilograms of sugar are in 30 servings of cranberry juice?
- Answer
-
0.9 kilograms
Exercise \PageIndex{385}
One ounce of tofu provided 2 grams of protein. How many milligrams of protein are provided by 5 ounces of tofu?
Convert between the U.S. and the Metric Systems of Measurement
In the following exercises, make the unit conversions. Round to the nearest tenth.
Exercise \PageIndex{386}
Majid is 69 inches tall. Convert his height to centimeters.
- Answer
-
175.3 centimeters
Exercise \PageIndex{387}
A college basketball court is 84 feet long. Convert this length to meters.
Exercise \PageIndex{388}
Caroline walked 2.5 kilometers. Convert this length to miles.
- Answer
-
1.6 miles
Exercise \PageIndex{389}
Lucas weighs 78 kilograms. Convert his weight to pounds.
Exercise \PageIndex{390}
Steve’s car holds 55 liters of gas. Convert this to gallons.
- Answer
-
14.6 gallons
Exercise \PageIndex{391}
A box of books weighs 25 pounds. Convert the weight to kilograms.
Convert between Fahrenheit and Celsius Temperatures
In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.
Exercise \PageIndex{392}
95° Fahrenheit
- Answer
-
35° C
Exercise \PageIndex{393}
23° Fahrenheit
Exercise \PageIndex{394}
20° Fahrenheit
- Answer
-
–6.7° C
Exercise \PageIndex{395}
64° Fahrenheit
In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.
Exercise \PageIndex{396}
30° Celsius
- Answer
-
86° F
Exercise \PageIndex{397}
–5° Celsius
Exercise \PageIndex{398}
–12° Celsius
- Answer
-
10.4° F
Exercise \PageIndex{399}
24° Celsius
Chapter Practice Test
Exercise \PageIndex{1}
Write as a whole number using digits: two hundred five thousand, six hundred seventeen.
- Answer
-
205,617
Exercise \PageIndex{2}
Find the prime factorization of 504.
Exercise \PageIndex{3}
Find the Least Common Multiple of 18 and 24.
- Answer
-
72
Exercise \PageIndex{4}
Combine like terms: 5n+8+2n−1.
In the following exercises, evaluate.
Exercise \PageIndex{5}
-|x| when x=-2
- Answer
-
−2
Exercise \PageIndex{6}
11−a when a=−3
Exercise \PageIndex{7}
Translate to an algebraic expression and simplify: twenty less than negative 7.
- Answer
-
−7−20;−27
Exercise \PageIndex{8}
Monique has a balance of −$18 in her checking account. She deposits $152 to the account. What is the new balance?
Exercise \PageIndex{9}
Round 677.1348 to the nearest hundredth.
- Answer
-
677.13
Exercise \PageIndex{10}
Convert \frac{4}{5} to a decimal.
Exercise \PageIndex{11}
Convert 1.85 to a percent.
- Answer
-
185%
Exercise \PageIndex{12}
Locate \frac{2}{3},-1.5, and \frac{9}{4} on a number line.
In the following exercises, simplify each expression.
Exercise \PageIndex{13}
4+10(3+9)-5^{2}
- Answer
-
99
Exercise \PageIndex{14}
−85+42
Exercise \PageIndex{15}
−19−25
- Answer
-
−44
Exercise \PageIndex{16}
(-2)^{4}
Exercise \PageIndex{17}
-5(-9) \div 15
- Answer
-
3
Exercise \PageIndex{18}
\frac{3}{8} \cdot \frac{11}{12}
Exercise \PageIndex{19}
\frac{4}{5} \div \frac{9}{20}
- Answer
-
\frac{16}{9}
Exercise \PageIndex{20}
\frac{12+3 \cdot 5}{15-6}
Exercise \PageIndex{21}
\frac{m}{7}+\frac{10}{7}
- Answer
-
\frac{m+10}{7}
Exercise \PageIndex{22}
\frac{7}{12}-\frac{3}{8}
Exercise \PageIndex{23}
-5.8+(-4.7)
- Answer
-
−10.5
Exercise \PageIndex{24}
100−64.25
Exercise \PageIndex{25}
(0.07)(31.95)
- Answer
-
2.2365
Exercise \PageIndex{26}
9 \div 0.05
Exercise \PageIndex{27}
-14\left(\frac{5}{7} p\right)
- Answer
-
−10p
Exercise \PageIndex{28}
(u+8)−9
Exercise \PageIndex{29}
6x+(−4y)+9x+8y
- Answer
-
15x+4y
Exercise \PageIndex{30}
\frac{0}{23}
Exercise \PageIndex{31}
\frac{75}{0}
- Answer
-
undefined
Exercise \PageIndex{32}
−2(13q−5)
Exercise \PageIndex{33}
A movie lasted 1\frac{2}{3} hours. How many minutes did it last? ( 1 hour =60 minutes)
- Answer
-
100 minutes
Exercise \PageIndex{34}
Mike’s SUV is 5 feet 11 inches tall. He wants to put a rooftop cargo bag on the the SUV. The cargo bag is 1 foot 6 inches tall. What will the total height be of the SUV with the cargo bag on the roof? (1 foot = 12 inches)
Exercise \PageIndex{35}
Jennifer ran 2.8 miles. Convert this length to kilometers. (1 mile = 1.61 kilometers)
- Answer
-
4.508 km