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Mathematics LibreTexts

13.1.1: Chapter 1

  • Page ID
    117736
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    Try It

    1.1

    yes yes no yes
    no

    1.2

    no yes yes no
    no

    1.3

    2 · 2 · 2 · 2 · 5 2 · 2 · 2 · 2 · 5

    1.4

    2 · 2 · 3 · 5 2 · 2 · 3 · 5

    1.5

    36 36

    1.6

    72 72

    1.7

    16

    1.8

    23

    1.9

    86

    1.10

    1

    1.11

    9 64 40

    1.12

    216 64 185

    1.13

    10 x 2 + 16 x + 17 10 x 2 + 16 x + 17

    1.14

    12 y 2 + 9 y + 7 12 y 2 + 9 y + 7

    1.15

    14x21314x213 12x÷212x÷2
    z+13z+13 8x188x18

    1.16

    17y2+1917y2+19 7y7y
    x+11x+11 11a1411a14

    1.17

    4(p+q)4(p+q) 4p+q4p+q

    1.18

    2x82x8 2(x8)2(x8)

    1.19

    w 7 w 7

    1.20

    l 6 l 6

    1.21

    4 q 8 4 q 8

    1.22

    7 n + 3 7 n + 3

    1.23

    == >> <<
    ==

    1.24

    >> == >>
    <<

    1.25

    16

    1.26

    9

    1.27

    −6−6 2 −2−2

    1.28

    −7−7 3 −3−3

    1.29

    2 −2−2 −10−10 10

    1.30

    3 −3−3 −11−11 11

    1.31

    8,88,8 −18,−18, −18−18
    19,1919,19 −4,−4, −4−4

    1.32

    8,88,8 −22,−22, −22−22
    23,2323,23 3,33,3

    1.33

    3

    1.34

    13

    1.35

    23 60 −63−63 −9−9

    1.36

    39 39 −28 −7

    1.37

    81 −81−81

    1.38

    49 −49−49

    1.39

    4 21

    1.40

    9 6

    1.41

    31

    1.42

    67

    1.43

    ( 9 + ( −16 ) ) + 4 ; 3 ( 9 + ( −16 ) ) + 4 ; 3

    1.44

    ( −8 + ( −12 ) ) + 7 ; 13 ( −8 + ( −12 ) ) + 7 ; 13

    1.45

    The difference in temperatures was 45 degrees.

    1.46

    The difference in temperatures was 9 degrees.

    1.47

    23 40 23 40

    1.48

    5 8 5 8

    1.49

    −33 a −33 a

    1.50

    −26 b −26 b

    1.51

    4 15 4 15

    1.52

    2 3 2 3

    1.53

    3 4 b 3 4 b

    1.54

    4 q 4 q

    1.55

    79 60 79 60

    1.56

    103 60 103 60

    1.57

    27a323627a3236 2a32a3

    1.58

    24k53024k530 2k152k15

    1.59

    4

    1.60

    2

    1.61

    1 90 1 90

    1.62

    272

    1.63

    2

    1.64

    2 7 2 7

    1.65

    1 2 1 2

    1.66

    2 3 2 3

    1.67

    6.586.58 6.66.6 7

    1.68

    15.21815.218 15.2215.22
    15.215.2

    1.69

    −16.49−16.49 −0.42−0.42

    1.70

    −23.593−23.593 −12.58−12.58

    1.71

    −27.4815 −27.4815

    1.72

    −87.6148 −87.6148

    1.73

    25.8 258 2,580

    1.74

    142 1,420 14,200

    1.75

    587.3 587.3

    1.76

    34.25 34.25

    1.77

    117500117500 −0.875−0.875

    1.78

    31253125 −0.375−0.375

    1.79

    0.09, 0.87, 0.039 17%, 175%, 8.25%

    1.80

    0.03, 0.91, 0.083 41%, 225%, 9.25%

    1.81

    6 13 −15−15

    1.82

    4 14 −10−10

    1.83

    4,494,49 −3,4,49−3,4,49
    −3,0.3,95,4,49−3,0.3,95,4,49 22
    −3,2,0.3,95,4,49−3,2,0.3,95,4,49

    1.84

    6,1216,121
    25,−1,6,12125,−1,6,121
    25,38,−1,6,12125,38,−1,6,121
    2.041975...2.041975...
    25,38,−1,6,121,2.041975...25,38,−1,6,121,2.041975...

    1.85
    Figure shows a number line with numbers ranging from minus 4 to 5. Various points on the line are highlighted. From left to right, these are: minus 8 by 3, minus 7 by 4, minus 1, 1 by 3, 6 by 5, 9 by 2 and 5.
    1.86
    Figure shows a number line with numbers ranging from minus 4 to 5. Various points on the line are highlighted. From left to right, these are: minus 7 by 3, minus 2, minus 7 by 4, 2 by 3, 7 by 5, 3 and 7 by 2.
    1.87

    Figure shows a number line with numbers ranging from 0 to 1. 0.6 is highlighted.

    Figure shows a number line with numbers ranging from minus 1.00 to 0.00. Minus 0.74 is highlighted, minus 0.25 is highlighted.
    1.88

    Figure shows a number line with numbers ranging from 0 to 1. 0.9 is highlighted.

    Figure shows a number line with numbers ranging from minus 1.00 to 0.00. Minus 0.74 is highlighted.
    1.89

    32 r + 29 s 32 r + 29 s

    1.90

    41 m + 6 n 41 m + 6 n

    1.91

    1 7 15 1 7 15

    1.92

    1 2 9 1 2 9

    1.93

    −48 a −48 a

    1.94

    −92 x −92 x

    1.95

    5 49 5 49

    1.96

    11 25 11 25

    1.97

    0 undefined

    1.98

    0 undefined

    1.99

    4 x + 8 4 x + 8

    1.100

    6 x + 42 6 x + 42

    1.101

    5 y + 3 5 y + 3

    1.102

    4 n + 9 4 n + 9

    1.103

    70 + 15 p 70 + 15 p

    1.104

    4 + 35 d 4 + 35 d

    1.105

    −10 + 15 a −10 + 15 a

    1.106

    −56 + 105 y −56 + 105 y

    1.107

    z + 11 z + 11

    1.108

    x + 4 x + 4

    1.109

    3 3 x 3 3 x

    1.110

    2 x 20 2 x 20

    1.111

    5 x 66 5 x 66

    1.112

    7 x 13 7 x 13

    Section 1.1 Exercises

    1.

    Divisible by 2, 3, 6

    3.

    Divisible by 2

    5.

    Divisible by 3, 5

    7.

    2 · 43 2 · 43

    9.

    5 · 7 · 13 5 · 7 · 13

    11.

    2 · 2 · 2 · 2 · 3 · 3 · 3 2 · 2 · 2 · 2 · 3 · 3 · 3

    13.

    24

    15.

    280

    17.

    440

    19.

    5

    21.

    58

    23.

    29

    25.

    149

    27.

    50

    29.

    5

    31.

    64 16 7

    33.

    21

    35.

    9

    37.

    10 x + 6 10 x + 6

    39.

    22 a + 1 22 a + 1

    41.

    17 x 2 + 20 x + 16 17 x 2 + 20 x + 16

    43.

    5x26xy5x26xy 6y25x6y25x
    y2+21y2+21 81x26x81x26x

    45.

    4ab2+3a2b4ab2+3a2b 20xy220xy2
    m+15m+15 121x29x121x29x

    47.

    8(y9)8(y9) 8y98y9

    49.

    5(3x+y)5(3x+y) 15x+y15x+y

    51.

    2 c + 14 2 c + 14

    53.

    3 n 7 3 n 7

    55.

    Answers will vary.

    57.

    Answers will vary.

    Section 1.2 Exercises

    59.

    >> >> >> >>

    61.

    == == >> ==

    63.

    0

    65.

    8

    67.

    15

    69.

    1

    71.

    −11−11 −3−3 33

    73.

    32

    75.

    −22 −22

    77.

    29 29

    79.

    6 −6−6 −20−20 2020

    81.

    −59 −59

    83.

    22

    85.

    16 16

    87.

    45 45

    89.

    0

    91.

    4

    93.

    6

    95.

    −32−32 −65−65 −4−4
    1313

    97.

    −4−4 −12−12 −39−39
    1414

    99.

    6464 −64−64

    101.

    −47 −47

    103.

    90 90

    105.

    9 9

    107.

    41 41

    109.

    −9 −9

    111.

    −29 −29

    113.

    1 1

    115.

    −3 −3

    117.

    5 5

    119.

    −47−47 1616

    121.

    121 121

    123.

    −56 −56

    125.

    6 6

    127.

    ( 3 + ( −15 ) ) + 7 ; 5 ( 3 + ( −15 ) ) + 7 ; 5

    129.

    10(−18);2810(−18);28
    −2511;36−2511;36

    131.

    −6 a + b −6 a + b

    133.

    96 ° 96 °

    135.

    21 yards

    137.

    $ 28 $ 28

    139.

    Answers will vary.

    141.

    Answers will vary.

    Section 1.3 Exercises

    143.

    12 7 12 7

    145.

    10 21 10 21

    147.

    2 x 2 3 y 2 x 2 3 y

    149.

    21 a 2 11 b 2 21 a 2 11 b 2

    151.

    1 3 1 3

    153.

    21 50 21 50

    155.

    11 30 11 30

    157.

    9 n 9 n

    159.

    33 4 x 33 4 x

    161.

    4 9 4 9

    163.

    10 u 9 v 10 u 9 v

    165.

    1 16 1 16

    167.

    10 9 10 9

    169.

    2 5 2 5

    171.

    2 m 3 n 2 m 3 n

    173.

    29 24 29 24

    175.

    1 48 1 48

    177.

    17 105 17 105

    179.

    53 40 53 40

    181.

    1 12 1 12

    183.

    4 x + 3 12 4 x + 3 12

    185.

    5656 44

    187.

    25n1625n16 25n163025n1630

    189.

    −8x1518−8x1518 10k2710k27

    191.

    −5(a+1)3−5(a+1)3 aa

    193.

    9 7 9 7

    195.

    −8 −8

    197.

    11 6 11 6

    199.

    5 2 5 2

    201.

    54 54

    203.

    49 25 49 25

    205.

    15 4 15 4

    207.

    5 21 5 21

    209.

    5 4 5 4

    211.

    1 24 1 24

    213.

    −28 15 y 60 −28 15 y 60

    215.

    33 64 33 64

    217.

    7 9 7 9

    219.

    −5 −5

    221.

    23 24 23 24

    223.

    11 5 11 5

    225.

    1 1

    227.

    13 3 13 3

    229.

    1515 6565

    231.

    1 9 1 9

    233.

    5 11 5 11

    235.

    Answers will vary.

    237.

    Answers will vary.

    Section 1.4 Exercises

    239.

    5.78 5.8 6

    241.

    0.30 0.3 0

    243.

    63.48 63.5 63

    245.

    −40.91 −40.91

    247.

    −7.22 −7.22

    249.

    −27.5 −27.5

    251.

    102.212 102.212

    253.

    51.31 51.31

    255.

    −4.89 −4.89

    257.

    −1200.47982 −1200.47982

    259.

    337.8914 337.8914

    261.

    1.305 1.305

    263.

    92.4 92.4

    265.

    2.5

    267.

    55200

    269.

    $ 2.44 $ 2.44

    271.

    −4.8 −4.8

    273.

    2.08 2.08

    275.

    1 25 1 25

    277.

    19 200 19 200

    279.

    0.85 0.85

    281.

    −12.4 −12.4

    283.

    0.71 0.71

    285.

    0.393 0.393

    287.

    156 % 156 %

    289.

    6.25 % 6.25 %

    291.

    8

    293.

    12

    295.

    −10 −10

    297.

    0,36,90,36,9 −8,0,36,9−8,0,36,9 −8,0,125,36,9−8,0,125,36,9 1.95286...,1.95286..., −8,0,1.95286...,125,36,9−8,0,1.95286...,125,36,9

    299.

    none 100,−7,−1100,−7,−1
    100,−7,83,−1,0.77,314100,−7,83,−1,0.77,314
    none
    100,−7,83,−1,0.77,314100,−7,83,−1,0.77,314

    301.
    Figure shows a number line with numbers ranging from 0 to 6. Some values are highlighted. From left to right, these are: 3 by 10, 11 by 6, 7 by 2 and 4.
    303.
    Figure shows a number line with numbers ranging from minus 4 to 4. Some values are highlighted. From left to right, these are: minus 5 by 2, minus 1 and two thirds, minus 3 by 4, 3 by 4, 1 and two thirds, and 5 by 2.
    305.
    Figure shows a number line with numbers ranging from minus 4 to 4. Two values are highlighted. One is between minus 2 and minus 1. The other is between 0 and 1.
    307.
    Figure shows a number line with numbers ranging from minus 4 to 4. Two values are highlighted. One is between minus 2 and minus 1. The other is between 3 and 4.
    309.

    Answers will vary.

    311.

    Answers will vary.

    Section 1.5 Exercises

    313.

    27 m + ( −21 n ) 27 m + ( −21 n )

    315.

    5 4 g + 1 2 h 5 4 g + 1 2 h

    317.

    2.43 p + 8.26 q 2.43 p + 8.26 q

    319.

    −63 −63

    321.

    1 5 6 1 5 6

    323.

    17 17

    325.

    14.88 14.88

    327.

    10 p 10 p

    329.

    44 44

    331.

    7 8 7 8

    333.

    d d

    335.

    49 11 49 11

    337.

    0

    339.

    undefined

    341.

    undefined

    343.

    32 y + 72 32 y + 72

    345.

    6 c 78 6 c 78

    347.

    3 4 q + 3 3 4 q + 3

    349.

    5 y 3 5 y 3

    351.

    3 + 8 r 3 + 8 r

    353.

    36 d + 90 36 d + 90

    355.

    r s 18 r r s 18 r

    357.

    y p + 4 p y p + 4 p

    359.

    −28 p 7 −28 p 7

    361.

    −3 x + 18 −3 x + 18

    363.

    −3 x + 7 −3 x + 7

    365.

    −3 y 8 −3 y 8

    367.

    −33 c + 26 −33 c + 26

    369.

    a + 19 a + 19

    371.

    4 m 10 4 m 10

    373.

    72 x 25 72 x 25

    375.

    22 n + 9 22 n + 9

    377.

    6 c + 34 6 c + 34

    379.

    12 y + 63 12 y + 63

    381.

    Answers will vary.

    383.

    Answers will vary.

    Review Exercises

    385.

    Divisible by 2,3,5,6,102,3,5,6,10

    387.

    120

    389.

    4

    391.

    3

    393.

    6 x 2 x + 5 6 x 2 x + 5

    395.

    11(y2)11(y2) 11y211y2

    397.

    == == >> ==

    399.

    −9 −9

    401.

    8 −8−8 −22−22 22

    403.

    40 40

    405.

    −3−3 −15−15 −56−56 17

    407.

    28

    409.

    −12 −12

    411.

    9

    413.

    ( −4 + ( −9 ) ) + 23 ; 10 ( −4 + ( −9 ) ) + 23 ; 10

    415.

    46 ° 46 °

    417.

    15 x 3 11 y 2 15 x 3 11 y 2

    419.

    8 x 15 y 8 x 15 y

    421.

    31 36 31 36

    423.

    118118 5656

    425.

    1 6 1 6

    427.

    75

    429.

    1 5 1 5

    431.

    6.17 6.17

    433.

    96.978 96.978

    435.

    488.1813

    437.

    56.3 56.3

    439.

    −2.3 −2.3

    441.

    48 5 48 5

    443.

    1. 27 ¯ 1. 27 ¯

    445.

    4.75 % 4.75 %

    447.

    no real number

    449.
    Figure shows a number line with numbers ranging from minus 4 to 4. Some values are highlighted.
    451.

    3 4 x + y 3 4 x + y

    453.

    1 11 15 1 11 15

    455.

    9 17 9 17

    457.

    undefined

    459.

    8 b + 10 8 b + 10

    461.

    x p 5 p x p 5 p

    463.

    −6 x 6 −6 x 6

    465.

    6 y + 16 6 y + 16

    Practice Test

    467.

    7 n + 7 7 n + 7

    469.

    −8 11 ; 19 −8 11 ; 19

    ( −8 ( −3 ) ) + 5 ; 0 ( −8 ( −3 ) ) + 5 ; 0

    471.

    28.1528.15 28.14628.146

    473.
    Figure shows a number line with numbers ranging from minus 4 to 4. Some values are highlighted.
    475.

    1

    477.

    −8 −8

    479.

    15 17 15 17

    481.

    5 3 5 3

    483.

    3 3

    485.

    7 6 7 6

    487.

    −65.4 −65.4

    489.

    −160

    491.

    1 8 13 1 8 13

    493.

    0 undefined

    495.

    13 y 3 13 y 3


    13.1.1: Chapter 1 is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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