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Basic Operations with Real Numbers: Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authors

Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples. This module contains the exercise supplement for the chapter "Basic Operations with Real Numbers".

Exercise Supplement

Signed Numbers ((Reference))

For the following problems, find −a −a if a a is

Exercise 1

27

[ Show Solution ]

Exercise 2

−15 −15

Exercise 3

− 8 9 − 8 9

[ Show Solution ]

Exercise 4

−( −3 ) −( −3 )

Exercise 5

k k

[ Show Solution ]

Absolute Value ((Reference))

Simplify the following problems.

Exercise 6

| 8 | | 8 |

Exercise 7

| −3 | | −3 |

[ Show Solution ]

Exercise 8

−| 16 | −| 16 |

Exercise 9

−( −| 12 | ) −( −| 12 | )

[ Show Solution ]

Exercise 10

−| 0 | −| 0 |

AddItion of Signed Numbers ((Reference)) - Multiplication and Division of Signed Numbers ((Reference))

Simplify the following problems.

Exercise 11

4+( −6 ) 4+( −6 )

[ Show Solution ]

Exercise 12

−16+( −18 ) −16+( −18 )

Exercise 13

3−( −14 ) 3−( −14 )

[ Show Solution ]

Exercise 14

( −5 )( 2 ) ( −5 )( 2 )

Exercise 15

( −6 )( −3 ) ( −6 )( −3 )

[ Show Solution ]

Exercise 16

( −1 )( −4 ) ( −1 )( −4 )

Exercise 17

( 4 )( −3 ) ( 4 )( −3 )

[ Show Solution ]

Exercise 18

−25 5 −25 5

Exercise 19

−100 −10 −100 −10

[ Show Solution ]

Exercise 20

16−18+5 16−18+5

Exercise 21

( −2 )( −4 )+10 −5 ( −2 )( −4 )+10 −5

[ Show Solution ]

Exercise 22

−3( −8+4 )−12 4( 3+6 )−2( −8 ) −3( −8+4 )−12 4( 3+6 )−2( −8 )

Exercise 23

−1( −3−2 )−4( −4 ) −13+10 −1( −3−2 )−4( −4 ) −13+10

[ Show Solution ]

Exercise 24

−( 2−10 ) −( 2−10 )

Exercise 25

0−6( −4 )( −2 ) 0−6( −4 )( −2 )

[ Show Solution ]

Multiplication and Division of Signed Numbers ((Reference))

Find the value of each expression for the following problems.

Exercise 26

P=R−CP=R−C. Find PP if R=3000R=3000 and C=3800C=3800.

Exercise 27

z=x−usz=x−us. Find zz if x=22,u=30x=22,u=30, and s=8s=8.

[ Show Solution ]

Exercise 28

P=n(n−1)(n−2) P=n(n−1)(n−2) . Find P P if n=−3 n=−3 .

Negative Exponents ((Reference))

Write the expressions for the following problems using only positive exponents.

Exercise 29

a −1 a −1

[ Show Solution ]

Exercise 30

c −6 c −6

Exercise 31

a 3 b −2 c −5 a 3 b −2 c −5

[ Show Solution ]

Exercise 32

( x+5 ) −2 ( x+5 ) −2

Exercise 33

x 3 y 2 ( x−3 ) −7 x 3 y 2 ( x−3 ) −7

[ Show Solution ]

Exercise 34

4 −2 a −3 b −4 c 5 4 −2 a −3 b −4 c 5

Exercise 35

2 −1 x −1 2 −1 x −1

[ Show Solution ]

Exercise 36

( 2x+9 ) −3 7 x 4 y −5 z −2 ( 3x−1 ) 2 ( 2x+5 ) −1 ( 2x+9 ) −3 7 x 4 y −5 z −2 ( 3x−1 ) 2 ( 2x+5 ) −1

Exercise 37

( −2 ) −1 ( −2 ) −1

[ Show Solution ]

Exercise 38

1 x −4 1 x −4

Exercise 39

7x y −3 z −2 7x y −3 z −2

[ Show Solution ]

Exercise 40

4 c −2 b −6 4 c −2 b −6

Exercise 41

3 −2 a −5 b −9 c 2 x 2 y −4 z −1 3 −2 a −5 b −9 c 2 x 2 y −4 z −1

[ Show Solution ]

Exercise 42

( z−6 ) −2 ( z+6 ) −4 ( z−6 ) −2 ( z+6 ) −4

Exercise 43

16 a 5 b −2 −2 a 3 b −5 16 a 5 b −2 −2 a 3 b −5

[ Show Solution ]

Exercise 44

−44 x 3 y −6 z −8 −11 x −2 y −7 z −8 −44 x 3 y −6 z −8 −11 x −2 y −7 z −8

Exercise 45

8 −2 8 −2

[ Show Solution ]

Exercise 46

9 −1 9 −1

Exercise 47

2 −5 2 −5

[ Show Solution ]

Exercise 48

( x 3 ) −2 ( x 3 ) −2

Exercise 49

( a 2 b ) −3 ( a 2 b ) −3

[ Show Solution ]

Exercise 50

( x −2 ) −4 ( x −2 ) −4

Exercise 51

( c −1 ) −4 ( c −1 ) −4

[ Show Solution ]

Exercise 52

( y −1 ) −1 ( y −1 ) −1

Exercise 53

( x 3 y −4 z −2 ) −6 ( x 3 y −4 z −2 ) −6

[ Show Solution ]

Exercise 54

( x −6 y −2 ) −5 ( x −6 y −2 ) −5

Exercise 55

( 2 b −7 c −8 d 4 x −2 y 3 z ) −4 ( 2 b −7 c −8 d 4 x −2 y 3 z ) −4

[ Show Solution ]

Scientific Notation ((Reference))

Write the following problems using scientific notation.

Exercise 56

8739

Exercise 57

73567

[ Show Solution ]

Exercise 58

21,000

Exercise 59

746,000

[ Show Solution ]

Exercise 60

8866846

Exercise 61

0.0387 0.0387

[ Show Solution ]

Exercise 62

0.0097 0.0097

Exercise 63

0.376 0.376

[ Show Solution ]

Exercise 64

0.0000024 0.0000024

Exercise 65

0.000000000000537 0.000000000000537

[ Show Solution ]

Exercise 66

46,000,000,000,000,000

Convert the following problems from scientific form to standard form.

Exercise 67

3.87× 10 5 3.87× 10 5

[ Show Solution ]

Exercise 68

4.145× 10 4 4.145× 10 4

Exercise 69

6.009× 10 7 6.009× 10 7

[ Show Solution ]

Exercise 70

1.80067× 10 6 1.80067× 10 6

Exercise 71

3.88× 10 −5 3.88× 10 −5

[ Show Solution ]

Exercise 72

4.116× 10 −2 4.116× 10 −2

Exercise 73

8.002× 10 −12 8.002× 10 −12

[ Show Solution ]

Exercise 74

7.36490× 10 −14 7.36490× 10 −14

Exercise 75

2.101× 10 15 2.101× 10 15

[ Show Solution ]

Exercise 76

6.7202× 10 26 6.7202× 10 26

Exercise 77

1× 10 6 1× 10 6

[ Show Solution ]

Exercise 78

1× 10 7 1× 10 7

Exercise 79

1× 10 9 1× 10 9

[ Show Solution ]

Find the product for the following problems. Write the result in scientific notation.

Exercise 80

( 1× 10 5 )( 2× 10 3 ) ( 1× 10 5 )( 2× 10 3 )

Exercise 81

( 3× 10 6 )( 7× 10 7 ) ( 3× 10 6 )( 7× 10 7 )

[ Show Solution ]

Exercise 82

( 2× 10 14 )( 8× 10 19 ) ( 2× 10 14 )( 8× 10 19 )

Exercise 83

( 9× 10 2 )( 3× 10 75 ) ( 9× 10 2 )( 3× 10 75 )

[ Show Solution ]

Exercise 84

(1×104)(1×105)(1×104)(1×105)

Exercise 85

( 8× 10 −3 )( 3× 10 −6 ) ( 8× 10 −3 )( 3× 10 −6 )

[ Show Solution ]

Exercise 86

( 9× 10 −5 )( 2× 10 −1 ) ( 9× 10 −5 )( 2× 10 −1 )

Exercise 87

( 3× 10 −2 )( 7× 10 2 ) ( 3× 10 −2 )( 7× 10 2 )

[ Show Solution ]

Exercise 88

( 7.3× 10 4 )( 2.1× 10 −8 ) ( 7.3× 10 4 )( 2.1× 10 −8 )

Exercise 89

( 1.06× 10 −16 )( 2.815× 10 −12 ) ( 1.06× 10 −16 )( 2.815× 10 −12 )

[ Show Solution ]

Exercise 90

( 9.3806× 10 52 )( 1.009× 10 −31 ) ( 9.3806× 10 52 )( 1.009× 10 −31 )

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