13.5.12: Chapter 1 Review Exercises
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- Aug 13, 2020
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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 13.5.12.1
26,915
- 1
- 2
- 9
- 5
- 6
- Answer
-
- tens
- ten thousands
- hundreds
- ones
- thousands
Exercise 13.5.12.2
359,417
- 9
- 3
- 4
- 7
- 1
Exercise 13.5.12.3
58,129,304
- 5
- 0
- 1
- 8
- 2
- Answer
-
- ten millions
- tens
- hundred thousands
- millions
- ten thousands
Exercise 13.5.12.4
9,430,286,157
- 6
- 4
- 9
- 0
- 5
In the following exercises, name each number.
Exercise 13.5.12.5
6,104
- Answer
-
six thousand, one hundred four
Exercise 13.5.12.6
493,068
Exercise 13.5.12.7
3,975,284
- Answer
-
three million, nine hundred seventy-five thousand, two hundred eighty-four
Exercise 13.5.12.8
85,620,435
In the following exercises, write each number as a whole number using digits.
Exercise 13.5.12.9
three hundred fifteen
- Answer
-
315
Exercise 13.5.12.10
sixty-five thousand, nine hundred twelve
Exercise 13.5.12.11
ninety million, four hundred twenty-five thousand, sixteen
- Answer
-
90,425,016
Exercise 13.5.12.12
one billion, forty-three million, nine hundred twenty-two thousand, three hundred eleven
In the following exercises, round to the indicated place value.
Exercise 13.5.12.13
Round to the nearest ten.
- 407
- 8,564
- Answer
-
- 410
- 8,560
Exercise 13.5.12.14
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 13.5.12.15
864,951
- Answer
-
- 865,000865,000
- 865,000865,000
- 860,000
Exercise 13.5.12.16
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 13.5.12.17
168
- Answer
-
by 2,3,6
Exercise 13.5.12.18
264
Exercise 13.5.12.19
375
- Answer
-
by 3,5
Exercise 13.5.12.20
750
Exercise 13.5.12.21
1430
- Answer
-
by 2,5,10
Exercise 13.5.12.22
1080
Find Prime Factorizations and Least Common Multiples
In the following exercises, find the prime factorization.
Exercise 13.5.12.23
420
- Answer
-
2⋅2⋅3⋅5⋅7
Exercise 13.5.12.24
115
Exercise 13.5.12.25
225
- Answer
-
3⋅3⋅5⋅5
Exercise 13.5.12.26
2475
Exercise 13.5.12.27
1560
- Answer
-
2⋅2⋅2⋅3⋅5⋅13
Exercise 13.5.12.28
56
Exercise 13.5.12.29
72
- Answer
-
2⋅2⋅2⋅3⋅3
Exercise 13.5.12.30
168
Exercise 13.5.12.31
252
- Answer
-
2⋅2⋅3⋅3⋅7
Exercise 13.5.12.32
391
In the following exercises, find the least common multiple of the following numbers using the multiples method.
Exercise 13.5.12.33
6,15
- Answer
-
30
Exercise 13.5.12.34
60, 75
In the following exercises, find the least common multiple of the following numbers using the prime factors method.
Exercise 13.5.12.35
24, 30
- Answer
-
120
Exercise 13.5.12.36
70, 84
Use the Language of Algebra
Use Variables and Algebraic Symbols
In the following exercises, translate the following from algebra to English.
Exercise 13.5.12.37
25−7
- Answer
-
25 minus 7, the difference of twenty-five and seven
Exercise 13.5.12.38
5⋅6
Exercise 13.5.12.39
45÷5
- Answer
-
45 divided by 5, the quotient of forty-five and five
Exercise 13.5.12.40
x+8
Exercise 13.5.12.41
42≥27
- Answer
-
forty-two is greater than or equal to twenty-seven
Exercise 13.5.12.42
3n=24
Exercise 13.5.12.43
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 13.5.12.44
a≠7⋅4
In the following exercises, determine if each is an expression or an equation.
Exercise 13.5.12.45
6⋅3+5
- Answer
-
expression
Exercise 13.5.12.46
y−8=32
Simplify Expressions Using the Order of Operations
In the following exercises, simplify each expression.
Exercise 13.5.12.47
35
- Answer
-
243
Exercise 13.5.12.48
108
In the following exercises, simplify
Exercise 13.5.12.49
6+10/2+2
- Answer
-
13
Exercise 13.5.12.50
9+12/3+4
Exercise 13.5.12.51
20÷(4+6)⋅5
- Answer
-
10
Exercise 13.5.12.52
33÷(3+8)⋅2
Exercise 13.5.12.53
42+52
- Answer
-
41
Exercise 13.5.12.54
(4+5)2
Evaluate an Expression
In the following exercises, evaluate the following expressions.
Exercise 13.5.12.55
9x+7 when x=3
- Answer
-
34
Exercise 13.5.12.56
5x−4 when x=6
Exercise 13.5.12.57
x4 when x=3
- Answer
-
81
Exercise 13.5.12.58
3x when x=3
Exercise 13.5.12.59
x2+5x−8 when x=6
- Answer
-
58
Exercise 13.5.12.60
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 13.5.12.61
12n
- Answer
-
12
Exercise 13.5.12.62
9x2
In the following exercises, identify the like terms.
Exercise 13.5.12.63
3n,n2,12,12p2,3,3n2
- Answer
-
12 and 3,n2 and 3n2
Exercise 13.5.12.64
5,18r2,9s,9r,5r2,5s
In the following exercises, identify the terms in each expression.
Exercise 13.5.12.65
11x2+3x+6
- Answer
-
11x2,3x,6
Exercise 13.5.12.66
22y3+y+15
In the following exercises, simplify the following expressions by combining like terms.
Exercise 13.5.12.67
17a+9a
- Answer
-
26a
Exercise 13.5.12.68
18z+9z
Exercise 13.5.12.69
9x+3x+8
- Answer
-
12x+8
Exercise 13.5.12.70
8a+5a+9
Exercise 13.5.12.71
7p+6+5p−4
- Answer
-
12p+2
Exercise 13.5.12.72
8x+7+4x−5
Translate an English Phrase to an Algebraic Expression
In the following exercises, translate the following phrases into algebraic expressions.
Exercise 13.5.12.73
the sum of 8 and 12
- Answer
-
8+12
Exercise 13.5.12.74
the sum of 9 and 1
Exercise 13.5.12.75
the difference of x and 4
- Answer
-
x−4
Exercise 13.5.12.76
the difference of x and 3
Exercise 13.5.12.77
the product of 6 and y
- Answer
-
6y
Exercise 13.5.12.78
the product of 9 and y
Exercise 13.5.12.79
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 13.5.12.80
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 13.5.12.81
- 6___2
- −7___4
- −9___−1
- 9___−3
- Answer
-
- >
- <
- <
- >
Exercise 13.5.12.82
- −5___1
- −4___−9
- 6___10
- 3___−8
In the following exercises,, find the opposite of each number.
Exercise 13.5.12.83
- −8
- 1
- Answer
-
- 8
- −1
Exercise 13.5.12.84
- −2
- 6
In the following exercises, simplify.
Exercise 13.5.12.85
−(−19)
- Answer
-
19
Exercise 13.5.12.86
−(−53)
In the following exercises, simplify.
Exercise 13.5.12.87
−m when
- m=3
- m=−3
- Answer
-
- −3
- 3
Exercise 13.5.12.88
−p when
- p=6
- p=−6
Simplify Expressions with Absolute Value
In the following exercises,, simplify.
Exercise 13.5.12.89
- |7|
- |−25|
- |0|
- Answer
-
- 7
- 25
- 0
Exercise 13.5.12.90
- |5|
- |0|
- |−19|
In the following exercises, fill in <, >, or = for each of the following pairs of numbers.
Exercise 13.5.12.91
- −8___|−8|
- −|−2|___−2
- Answer
-
- <
- =
Exercise 13.5.12.92
- |−3|___−|−3|
- 4___−|−4|
In the following exercises, simplify.
Exercise 13.5.12.93
|8−4|
- Answer
-
4
Exercise 13.5.12.94
|9−6|
Exercise 13.5.12.95
8(14−2|−2|)
- Answer
-
80
Exercise 13.5.12.96
6(13−4|−2|)
In the following exercises, evaluate.
Exercise 13.5.12.97
1. |x| when x=−28
- Answer
-
- 28
- 15
Exercise 13.5.12.98
- ∣y∣ when y=−37
- |−z| when z=−24
Add Integers
In the following exercises, simplify each expression.
Exercise 13.5.12.99
−200+65
- Answer
-
−135
Exercise 13.5.12.100
−150+45
Exercise 13.5.12.101
2+(−8)+6
- Answer
-
0
Exercise 13.5.12.102
4+(−9)+7
Exercise 13.5.12.103
140+(−75)+67
- Answer
-
132
Exercise 13.5.12.104
−32+24+(−6)+10
Subtract Integers
In the following exercises, simplify.
Exercise 13.5.12.105
9−3
- Answer
-
6
Exercise 13.5.12.106
−5−(−1)
Exercise 13.5.12.107
- 15−6
- 15+(−6)
- Answer
-
- 9
- 9
Exercise 13.5.12.108
- 12−9
- 12+(−9)
Exercise 13.5.12.109
- 8−(−9)
- 8+9
- Answer
-
- 17
- 17
Exercise 13.5.12.110
- 4−(−4)
- 4+4
In the following exercises, simplify each expression.
Exercise 13.5.12.111
10−(−19)
- Answer
-
29
Exercise 13.5.12.112
11−(−18)
Exercise 13.5.12.113
31−79
- Answer
-
−48
Exercise 13.5.12.114
39−81
Exercise 13.5.12.115
−31−11
- Answer
-
−42
Exercise 13.5.12.116
−32−18
Exercise 13.5.12.117
−15−(−28)+5
- Answer
-
18
Exercise 13.5.12.118
71+(−10)−8
Exercise 13.5.12.119
−16−(−4+1)−7
- Answer
-
-20
Exercise 13.5.12.120
−15−(−6+4)−3
Multiply Integers
In the following exercises, multiply.
Exercise 13.5.12.121
−5(7)
- Answer
-
−35
Exercise 13.5.12.122
−8(6)
Exercise 13.5.12.123
−18(−2)
- Answer
-
36
Exercise 13.5.12.124
−10(−6)
Divide Integers
In the following exercises, divide.
Exercise 13.5.12.125
−28÷7
- Answer
-
-4
Exercise 13.5.12.126
56÷(−7)
Exercise 13.5.12.127
−120÷(−20)
- Answer
-
6
Exercise 13.5.12.128
−200÷25
Simplify Expressions with Integers
In the following exercises, simplify each expression.
Exercise 13.5.12.129
−8(−2)−3(−9)
- Answer
-
43
Exercise 13.5.12.130
−7(−4)−5(−3)
Exercise 13.5.12.131
(−5)3
- Answer
-
−125
Exercise 13.5.12.132
(−4)3
Exercise 13.5.12.133
−4⋅2⋅11
- Answer
-
−88
Exercise 13.5.12.134
−5⋅3⋅10
Exercise 13.5.12.135
−10(−4)÷(−8)
- Answer
-
-5
Exercise 13.5.12.136
−8(−6)÷(−4)
Exercise 13.5.12.137
31−4(3−9)
- Answer
-
55
Exercise 13.5.12.138
24−3(2−10)
Evaluate Variable Expressions with Integers
In the following exercises, evaluate each expression.
Exercise 13.5.12.139
x+8 when
- x=−26
- x=−95
- Answer
-
- −18
- −87
Exercise 13.5.12.140
y+9 when
- y=−29
- y=−84
Exercise 13.5.12.141
When b=−11, evaluate:
- b+6
- −b+6
- Answer
-
- −5
- 17
Exercise 13.5.12.142
When c=−9, evaluate:
- c+(−4)c+(−4)
- −c+(−4)
Exercise 13.5.12.143
p2−5p+2 when
p=−1
- Answer
-
8
Exercise 13.5.12.144
q2−2q+9 when q=−2
Exercise 13.5.12.145
6x−5y+15 when x=3 and y=−1
- Answer
-
38
Exercise 13.5.12.146
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 13.5.12.147
the sum of −4 and −17, increased by 32
- Answer
-
(−4+(−17))+32;11
Exercise 13.5.12.148
- the difference of 15 and −7
- subtract 15 from −7
Exercise 13.5.12.149
the quotient of −45 and −9
- Answer
-
−45−9;5
Exercise 13.5.12.150
the product of −12 and the difference of c and d
Use Integers in Applications
In the following exercises, solve.
Exercise 13.5.12.151
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 13.5.12.152
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 13.5.12.153
14
- Answer
-
28,312,416 answers may vary
Exercise 13.5.12.154
13
Exercise 13.5.12.155
56
- Answer
-
1012,1518,2024 answers may vary
Exercise 13.5.12.156
27
Simplify Fractions
In the following exercises, simplify.
Exercise 13.5.12.157
721
- Answer
-
13
Exercise 13.5.12.158
824
Exercise 13.5.12.159
1520
- Answer
-
34
Exercise 13.5.12.160
1218
Exercise 13.5.12.161
−168192
- Answer
-
−78
Exercise 13.5.12.162
−140224
Exercise 13.5.12.163
11x11y
- Answer
-
xy
Exercise 13.5.12.164
15a15b
Multiply Fractions
In the following exercises, multiply.
Exercise 13.5.12.165
25⋅13
- Answer
-
215
Exercise 13.5.12.166
12⋅38
Exercise 13.5.12.167
712(−821)
- Answer
-
−29
Exercise 13.5.12.168
512(−815)
Exercise 13.5.12.169
−28p(−14)
- Answer
-
7p
Exercise 13.5.12.170
−51q(−13)
Exercise 13.5.12.172
145(−15)
- Answer
-
−42
Exercise 13.5.12.173
−1(−38)
Divide Fractions
In the following exercises, divide
Exercise 13.5.12.174
12÷14
- Answer
-
2
Exercise 13.5.12.175
12÷18
Exercise 13.5.12.176
−45÷47
- Answer
-
−75
Exercise 13.5.12.177
−34÷35
Exercise 13.5.12.178
58÷a10
- Answer
-
254a
Exercise 13.5.12.179
56÷c15
Exercise 13.5.12.180
7p12÷21p8
- Answer
-
29
Exercise 13.5.12.181
5q12÷15q8
Exercise 13.5.12.182
25÷(−10)
- Answer
-
−125
Exercise 13.5.12.183
−18÷−(92)
In the following exercises, simplify.
Exercise 13.5.12.184
2389
- Answer
-
34
Exercise 13.5.12.185
45815
Exercise 13.5.12.186
−9103
- Answer
-
−310
Exercise 13.5.12.187
258
Exercise 13.5.12.188
r5s3
- Answer
-
3r5s
Exercise 13.5.12.189
−x6−89
Simplify Expressions Written with a Fraction Bar
In the following exercises, simplify.
Exercise 13.5.12.190
4+118
- Answer
-
158
Exercise 13.5.12.191
9+37
Exercise 13.5.12.192
307−12
- Answer
-
-6
Exercise 13.5.12.193
154−9
Exercise 13.5.12.194
22−1419−13
- Answer
-
43
Exercise 13.5.12.195
15+918+12
Exercise 13.5.12.196
5⋅8−10
- Answer
-
-4
Exercise 13.5.12.197
3⋅4−24
Exercise 13.5.12.198
15⋅5−522⋅10
- Answer
-
52
Exercise 13.5.12.199
12⋅9−323⋅18
Exercise 13.5.12.200
2+4(3)−3−22
- Answer
-
-2
Exercise 13.5.12.201
7+3(5)−2−32
Translate Phrases to Expressions with Fractions
In the following exercises, translate each English phrase into an algebraic expression.
Exercise 13.5.12.202
the quotient of c and the sum of d and 9.
- Answer
-
cd+9
Exercise 13.5.12.203
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 13.5.12.204
49+19
- Answer
-
59
Exercise 13.5.12.205
29+59
Exercise 13.5.12.206
y3+23
- Answer
-
y+23
Exercise 13.5.12.207
7p+9p
Exercise 13.5.12.208
−18+(−38)
- Answer
-
−12
Exercise 13.5.12.209
−18+(−58)
In the following exercises, subtract.
Exercise 13.5.12.210
45−15
- Answer
-
35
Exercise 13.5.12.211
45−35
Exercise 13.5.12.212
y17−917
- Answer
-
y−917
Exercise 13.5.12.213
x19−819
Exercise 13.5.12.214
−8d−3d
- Answer
-
−11d
Exercise 13.5.12.215
−7c−7c
Add or Subtract Fractions with Different Denominators
In the following exercises, add or subtract.
Exercise 13.5.12.216
13+15
- Answer
-
815
Exercise 13.5.12.217
14+15
Exercise 13.5.12.218
15−(−110)
- Answer
-
310
Exercise 13.5.12.219
12−(−16)
Exercise 13.5.12.220
23+34
- Answer
-
1712
Exercise 13.5.12.221
34+25
Exercise 13.5.12.222
1112−38
- Answer
-
1324
Exercise 13.5.12.223
58−712
Exercise 13.5.12.224
−916−(−45)
- Answer
-
1980
Exercise 13.5.12.225
−720−(−58)
Exercise 13.5.12.226
1+56
- Answer
-
116
Exercise 13.5.12.227
1−59
Use the Order of Operations to Simplify Complex Fractions
In the following exercises, simplify.
Exercise 13.5.12.228
(15)22+32
- Answer
-
1275
Exercise 13.5.12.229
(13)25+22
Exercise 13.5.12.230
23+1234−23
- Answer
-
14
Exercise 13.5.12.231
34+1256−23
Evaluate Variable Expressions with Fractions
In the following exercises, evaluate.
Exercise 13.5.12.232
x+12 when
- x=−18
- x=−12
- Answer
-
- 38
- 0
Exercise 13.5.12.233
x+23 when
- x=−16
- x=−53
Exercise 13.5.12.234
4p2q when p=−12 and q=59
- Answer
-
59
Exercise 13.5.12.235
5m2n when m=−25 and n=13
Exercise 13.5.12.236
u+vw when
u=−4,v=−8,w=2
- Answer
-
-6
Exercise 13.5.12.237
m+np when
m=−6,n=−2,p=4
Decimals
Name and Write Decimals
In the following exercises, write as a decimal.
Exercise 13.5.12.238
Eight and three hundredths
- Answer
-
8.03
Exercise 13.5.12.239
Nine and seven hundredths
Exercise 13.5.12.240
One thousandth
- Answer
-
0.001
Exercise 13.5.12.241
Nine thousandths
In the following exercises, name each decimal.
Exercise 13.5.12.242
7.8
- Answer
-
seven and eight tenths
Exercise 13.5.12.243
5.01
Exercise 13.5.12.244
0.005
- Answer
-
five thousandths
Exercise 13.5.12.245
0.381
Round Decimals
In the following exercises, round each number to the nearest
- hundredth
- tenth
- whole number.
Exercise 13.5.12.246
5.7932
- Answer
-
- 5.79
- 5.8
- 6
Exercise 13.5.12.247
3.6284
Exercise 13.5.12.248
12.4768
- Answer
-
- 12.48
- 12.5
- 12
Exercise 13.5.12.249
25.8449
Add and Subtract Decimals
In the following exercises, add or subtract.
Exercise 13.5.12.250
18.37+9.36
- Answer
-
27.73
Exercise 13.5.12.251
256.37−85.49
Exercise 13.5.12.252
15.35−20.88
- Answer
-
−5.53
Exercise 13.5.12.253
37.5+12.23
Exercise 13.5.12.254
−4.2+(−9.3)
- Answer
-
−13.5
Exercise 13.5.12.255
−8.6+(−8.6)
Exercise 13.5.12.256
100−64.2
- Answer
-
35.8
Exercise 13.5.12.257
100−65.83
Exercise 13.5.12.258
2.51+40
- Answer
-
42.51
Exercise 13.5.12.259
9.38+60
Multiply and Divide Decimals
In the following exercises, multiply.
Exercise 13.5.12.260
(0.3)(0.4)
- Answer
-
0.12
Exercise 13.5.12.261
(0.6)(0.7)
Exercise 13.5.12.262
(8.52)(3.14)
- Answer
-
26.7528
Exercise 13.5.12.263
(5.32)(4.86)
Exercise 13.5.12.264
(0.09)(24.78)
- Answer
-
2.2302
Exercise 13.5.12.265
(0.04)(36.89)
In the following exercises, divide.
Exercise 13.5.12.266
0.15÷5
- Answer
-
0.03
Exercise 13.5.12.267
0.27÷3
Exercise 13.5.12.268
$8.49÷12
- Answer
-
$0.71
Exercise 13.5.12.269
$16.99÷9
Exercise 13.5.12.270
12÷0.08
- Answer
-
150
Exercise 13.5.12.271
5÷0.04
Convert Decimals, Fractions, and Percents
In the following exercises, write each decimal as a fraction.
Exercise 13.5.12.272
0.08
- Answer
-
225
Exercise 13.5.12.273
0.17
Exercise 13.5.12.274
0.425
- Answer
-
1740
Exercise 13.5.12.275
0.184
Exercise 13.5.12.276
1.75
- Answer
-
74
Exercise 13.5.12.277
0.035
In the following exercises, convert each fraction to a decimal.
Exercise 13.5.12.278
25
- Answer
-
0.4
Exercise 13.5.12.279
45
Exercise 13.5.12.280
−38
- Answer
-
−0.375
Exercise 13.5.12.281
−58
Exercise 13.5.12.282
59
- Answer
-
0.¯5
Exercise 13.5.12.283
29
Exercise 13.5.12.284
12+6.5
- Answer
-
7
Exercise 13.5.12.285
14+10.75
In the following exercises, convert each percent to a decimal.
Exercise 13.5.12.286
5%
- Answer
-
0.05
Exercise 13.5.12.287
9%
Exercise 13.5.12.288
40%
- Answer
-
0.4
Exercise 13.5.12.289
50%
Exercise 13.5.12.290
115%
- Answer
-
1.15
Exercise 13.5.12.291
125%
In the following exercises, convert each decimal to a percent.
Exercise 13.5.12.292
0.18
- Answer
-
18%
Exercise 13.5.12.293
0.15
Exercise 13.5.12.294
0.009
- Answer
-
0.9%
Exercise 13.5.12.295
0.008
Exercise 13.5.12.296
1.5
- Answer
-
150%
Exercise 13.5.12.297
2.2
The Real Numbers
Simplify Expressions with Square Roots
In the following exercises, simplify.
Exercise 13.5.12.298
√64
- Answer
-
8
Exercise 13.5.12.299
√144
Exercise 13.5.12.300
−√25
- Answer
-
-5
Exercise 13.5.12.301
−√81
Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers
In the following exercises, write as the ratio of two integers.
Exercise 13.5.12.302
- 9
- 8.47
- Answer
-
- 91
- 847100
Exercise 13.5.12.303
- −15
- 3.591
In the following exercises, list the
- rational numbers,
- irrational numbers.
Exercise 13.5.12.304
0.84,0.79132…,1.¯3
- Answer
-
- 0.84,1.3
- 0.79132…
Exercise 13.5.12.305
2.3¯8,0.572,4.93814…
In the following exercises, identify whether each number is rational or irrational.
Exercise 13.5.12.306
- √121
- √48
- Answer
-
- rational
- irrational
Exercise 13.5.12.307
- √56
- √16
In the following exercises, identify whether each number is a real number or not a real number.
Exercise 13.5.12.308
- √−9
- −√169
- Answer
-
- not a real number
- real number
Exercise 13.5.12.309
- √−64
- −√81
In the following exercises, list the
- whole numbers,
- integers,
- rational numbers,
- irrational numbers,
- real numbers for each set of numbers.
Exercise 13.5.12.310
−4,0,56,√16,√18,5.2537…
- Answer
-
- 0,√16
- −4,0,√16
- −4,0,56,√16
- √18,5.2537…
- −4,0,56,√16,√18,5.2537…
Exercise 13.5.12.311
−√4,0.¯36,133,6.9152…,√48,1012
Locate Fractions on the Number Line
In the following exercises, locate the numbers on a number line.
Exercise 13.5.12.312
23,54,125
- Answer
-
Exercise 13.5.12.313
13,74,135
Exercise 13.5.12.314
213,−213
- Answer
-
Exercise 13.5.12.315
135,−135
In the following exercises, order each of the following pairs of numbers, using < or >.
Exercise 13.5.12.316
−1___−18
- Answer
-
<
Exercise 13.5.12.317
−314___−4
Exercise 13.5.12.318
−79 ___ 49
- Answer
-
>
Exercise 13.5.12.319
−2 ___ 198
Locate Decimals on the Number Line
In the following exercises, locate on the number line.
Exercise 13.5.12.320
0.3
- Answer
-
Exercise 13.5.12.321
−0.2
Exercise 13.5.12.322
−2.5
- Answer
-
Exercise 13.5.12.323
2.7
In the following exercises, order each of the following pairs of numbers, using < or >.
Exercise 13.5.12.324
0.9___0.6
- Answer
-
>
Exercise 13.5.12.325
0.7___0.8
Exercise 13.5.12.326
−0.6___−0.59
- Answer
-
>
Exercise 13.5.12.327
−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 13.5.12.328
−12(4m)
- Answer
-
−48m
Exercise 13.5.12.329
30(56q)
Exercise 13.5.12.330
(a+16)+31
- Answer
-
a+47
Exercise 13.5.12.331
(c+0.2)+0.7
In the following exercises, simplify.
Exercise 13.5.12.332
6y+37+(−6y)
- Answer
-
37
Exercise 13.5.12.333
14+1115+(−14)
Exercise 13.5.12.334
1411⋅359⋅1411
- Answer
-
359
Exercise 13.5.12.335
−18⋅15⋅29
Exercise 13.5.12.336
(712+45)+15
- Answer
-
1712
Exercise 13.5.12.337
(3.98d+0.75d)+1.25d
Exercise 13.5.12.338
11x+8y+16x+15y
- Answer
-
27x+23y
Exercise 13.5.12.339
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 13.5.12.340
- 13
- 5.1
- −14
- −85
- Answer
-
- −13
- −5.1
- -14
- −85
Exercise 13.5.12.341
- −78
- −0.03
- 17
- 125
In the following exercises, find the multiplicative inverse of each number.
Exercise 13.5.12.342
- 10
- −49
- 0.6
- Answer
-
- 110
- −94
- 53
Exercise 13.5.12.343
- −92
- -7
- 2.1
Use the Properties of Zero
In the following exercises, simplify.
Exercise 13.5.12.344
83⋅0
- Answer
-
0
Exercise 13.5.12.345
09
Exercise 13.5.12.346
50
- Answer
-
undefined
Exercise 13.5.12.347
0÷23
In the following exercises, simplify.
Exercise 13.5.12.348
43+39+(−43)
- Answer
-
39
Exercise 13.5.12.349
(n+6.75)+0.25
Exercise 13.5.12.350
513⋅57⋅135
- Answer
-
57
Exercise 13.5.12.351
16⋅17⋅12
Exercise 13.5.12.352
23⋅28⋅37
- Answer
-
8
Exercise 13.5.12.353
9(6x−11)+15
Simplify Expressions Using the Distributive Property
In the following exercises, simplify using the Distributive Property.
Exercise 13.5.12.354
7(x+9)
- Answer
-
7x+63
Exercise 13.5.12.355
9(u−4)
Exercise 13.5.12.356
−3(6m−1)
- Answer
-
−18m+3
Exercise 13.5.12.357
−8(−7a−12)
Exercise 13.5.12.358
13(15n−6)
- Answer
-
5n−2
Exercise 13.5.12.359
(y+10)⋅p
Exercise 13.5.12.360
(a−4)−(6a+9)
- Answer
-
−5a−13
Exercise 13.5.12.361
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 13.5.12.362
A floral arbor is 7 feet tall. Convert the height to inches.
- Answer
-
84 inches
Exercise 13.5.12.363
A picture frame is 42 inches wide. Convert the width to feet.
Exercise 13.5.12.364
Kelly is 5 feet 4 inches tall. Convert her height to inches.
- Answer
-
64 inches
Exercise 13.5.12.365
A playground is 45 feet wide. Convert the width to yards.
Exercise 13.5.12.366
The height of Mount Shasta is 14,179 feet. Convert the height to miles.
- Answer
-
2.7 miles
Exercise 13.5.12.367
Shamu weights 4.5 tons. Convert the weight to pounds.
Exercise 13.5.12.368
The play lasted 134 hours. Convert the time to minutes.
- Answer
-
105 minutes
Exercise 13.5.12.369
How many tablespoons are in a quart?
Exercise 13.5.12.370
Naomi’s baby weighed 5 pounds 14 ounces at birth. Convert the weight to ounces.
- Answer
-
94 ounces
Exercise 13.5.12.371
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 13.5.12.372
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 13.5.12.373
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 13.5.12.374
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 13.5.12.375
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 13.5.12.376
Donna is 1.7 meters tall. Convert her height to centimeters.
- Answer
-
170 centimeters
Exercise 13.5.12.377
Mount Everest is 8,850 meters tall. Convert the height to kilometers.
Exercise 13.5.12.378
One cup of yogurt contains 488 milligrams of calcium. Convert this to grams.
- Answer
-
0.488 grams
Exercise 13.5.12.379
One cup of yogurt contains 13 grams of protein. Convert this to milligrams.
Exercise 13.5.12.380
Sergio weighed 2.9 kilograms at birth. Convert this to grams.
- Answer
-
2,900 grams
Exercise 13.5.12.381
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 13.5.12.382
Minh is 2 meters tall. His daughter is 88 centimeters tall. How much taller is Minh than his daughter?
- Answer
-
1.12 meter
Exercise 13.5.12.383
Selma had a 1 liter bottle of water. If she drank 145 milliliters, how much water was left in the bottle?
Exercise 13.5.12.384
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 13.5.12.385
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 13.5.12.386
Majid is 69 inches tall. Convert his height to centimeters.
- Answer
-
175.3 centimeters
Exercise 13.5.12.387
A college basketball court is 84 feet long. Convert this length to meters.
Exercise 13.5.12.388
Caroline walked 2.5 kilometers. Convert this length to miles.
- Answer
-
1.6 miles
Exercise 13.5.12.389
Lucas weighs 78 kilograms. Convert his weight to pounds.
Exercise 13.5.12.390
Steve’s car holds 55 liters of gas. Convert this to gallons.
- Answer
-
14.6 gallons
Exercise 13.5.12.391
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 13.5.12.392
95° Fahrenheit
- Answer
-
35° C
Exercise 13.5.12.393
23° Fahrenheit
Exercise 13.5.12.394
20° Fahrenheit
- Answer
-
–6.7° C
Exercise 13.5.12.395
64° Fahrenheit
In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.
Exercise 13.5.12.396
30° Celsius
- Answer
-
86° F
Exercise 13.5.12.397
–5° Celsius
Exercise 13.5.12.398
–12° Celsius
- Answer
-
10.4° F
Exercise 13.5.12.399
24° Celsius
Chapter Practice Test
Exercise 13.5.12.1
Write as a whole number using digits: two hundred five thousand, six hundred seventeen.
- Answer
-
205,617
Exercise 13.5.12.2
Find the prime factorization of 504.
Exercise 13.5.12.3
Find the Least Common Multiple of 18 and 24.
- Answer
-
72
Exercise 13.5.12.4
Combine like terms: 5n+8+2n−1.
In the following exercises, evaluate.
Exercise 13.5.12.5
−|x| when x=−2
- Answer
-
−2
Exercise 13.5.12.6
11−a when a=−3
Exercise 13.5.12.7
Translate to an algebraic expression and simplify: twenty less than negative 7.
- Answer
-
−7−20;−27
Exercise 13.5.12.8
Monique has a balance of −$18 in her checking account. She deposits $152 to the account. What is the new balance?
Exercise 13.5.12.9
Round 677.1348 to the nearest hundredth.
- Answer
-
677.13
Exercise 13.5.12.10
Convert 45 to a decimal.
Exercise 13.5.12.11
Convert 1.85 to a percent.
- Answer
-
185%
Exercise 13.5.12.12
Locate 23,−1.5, and 94 on a number line.
In the following exercises, simplify each expression.
Exercise 13.5.12.13
4+10(3+9)−52
- Answer
-
99
Exercise 13.5.12.14
−85+42
Exercise 13.5.12.15
−19−25
- Answer
-
−44
Exercise 13.5.12.16
(−2)4
Exercise 13.5.12.17
−5(−9)÷15
- Answer
-
3
Exercise 13.5.12.18
38⋅1112
Exercise 13.5.12.19
45÷920
- Answer
-
169
Exercise 13.5.12.20
12+3⋅515−6
Exercise 13.5.12.21
m7+107
- Answer
-
m+107
Exercise 13.5.12.22
712−38
Exercise 13.5.12.23
−5.8+(−4.7)
- Answer
-
−10.5
Exercise 13.5.12.24
100−64.25
Exercise 13.5.12.25
(0.07)(31.95)
- Answer
-
2.2365
Exercise 13.5.12.26
9÷0.05
Exercise 13.5.12.27
−14(57p)
- Answer
-
−10p
Exercise 13.5.12.28
(u+8)−9
Exercise 13.5.12.29
6x+(−4y)+9x+8y
- Answer
-
15x+4y
Exercise 13.5.12.30
023
Exercise 13.5.12.31
750
- Answer
-
undefined
Exercise 13.5.12.32
−2(13q−5)
Exercise 13.5.12.33
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