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Basic Operations with Real Numbers: Exercise Supplement

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

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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".

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

Exercise Supplement

Signed Numbers ((Reference))

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

Exercise 1

27

Solution

−27 −27

Exercise 2

−15 −15

Exercise 3

− 8 9 − 8 9

Solution

8 9 8 9

Exercise 4

−( −3 ) −( −3 )

Exercise 5

k k

Solution

−k −k

Absolute Value ((Reference))

Simplify the following problems.

Exercise 6

| 8 | | 8 |

Exercise 7

| −3 | | −3 |

Solution

3

Exercise 8

−| 16 | −| 16 |

Exercise 9

−( −| 12 | ) −( −| 12 | )

Solution

12

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 )

Solution

−2 −2

Exercise 12

−16+( −18 ) −16+( −18 )

Exercise 13

3−( −14 ) 3−( −14 )

Solution

17

Exercise 14

( −5 )( 2 ) ( −5 )( 2 )

Exercise 15

( −6 )( −3 ) ( −6 )( −3 )

Solution

18

Exercise 16

( −1 )( −4 ) ( −1 )( −4 )

Exercise 17

( 4 )( −3 ) ( 4 )( −3 )

Solution

−12 −12

Exercise 18

−25 5 −25 5

Exercise 19

−100 −10 −100 −10

Solution

10

Exercise 20

16−18+5 16−18+5

Exercise 21

( −2 )( −4 )+10 −5 ( −2 )( −4 )+10 −5

Solution

− 18 5 − 18 5

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

Solution

−7 −7

Exercise 24

−( 2−10 ) −( 2−10 )

Exercise 25

0−6( −4 )( −2 ) 0−6( −4 )( −2 )

Solution

−48 −48

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.

Solution

−1 −1

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

Solution

1 a 1 a

Exercise 30

c −6 c −6

Exercise 31

a 3 b −2 c −5 a 3 b −2 c −5

Solution

a 3 b 2 c 5 a 3 b 2 c 5

Exercise 32

( x+5 ) −2 ( x+5 ) −2

Exercise 33

x 3 y 2 ( x−3 ) −7 x 3 y 2 ( x−3 ) −7

Solution

x 3 y 2 ( x−3 ) 7 x 3 y 2 ( x−3 ) 7

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

Solution

1 2x 1 2x

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

Solution

1 −2 1 −2

Exercise 38

1 x −4 1 x −4

Exercise 39

7x y −3 z −2 7x y −3 z −2

Solution

7x y 3 z 2 7x y 3 z 2

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

Solution

c 2 y 4 z 9 a 5 b 9 x 2 c 2 y 4 z 9 a 5 b 9 x 2

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

Solution

−8 a 2 b 3 −8 a 2 b 3

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

Solution

1 64 1 64

Exercise 46

9 −1 9 −1

Exercise 47

2 −5 2 −5

Solution

1 32 1 32

Exercise 48

( x 3 ) −2 ( x 3 ) −2

Exercise 49

( a 2 b ) −3 ( a 2 b ) −3

Solution

1 a 6 b 3 1 a 6 b 3

Exercise 50

( x −2 ) −4 ( x −2 ) −4

Exercise 51

( c −1 ) −4 ( c −1 ) −4

Solution

c 4 c 4

Exercise 52

( y −1 ) −1 ( y −1 ) −1

Exercise 53

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

Solution

y 24 z 12 x 18 y 24 z 12 x 18

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

Solution

b 28 c 32 y 12 z 4 16 d 16 x 8 b 28 c 32 y 12 z 4 16 d 16 x 8

Scientific Notation ((Reference))

Write the following problems using scientific notation.

Exercise 56

8739

Exercise 57

73567

Solution

7.3567× 10 4 7.3567× 10 4

Exercise 58

21,000

Exercise 59

746,000

Solution

7.46× 10 5 7.46× 10 5

Exercise 60

8866846

Exercise 61

0.0387 0.0387

Solution

3.87× 10 −2 3.87× 10 −2

Exercise 62

0.0097 0.0097

Exercise 63

0.376 0.376

Solution

3.76× 10 −1 3.76× 10 −1

Exercise 64

0.0000024 0.0000024

Exercise 65

0.000000000000537 0.000000000000537

Solution

5.37× 10 −13 5.37× 10 −13

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

Solution

387,000 387,000

Exercise 68

4.145× 10 4 4.145× 10 4

Exercise 69

6.009× 10 7 6.009× 10 7

Solution

60,090,000 60,090,000

Exercise 70

1.80067× 10 6 1.80067× 10 6

Exercise 71

3.88× 10 −5 3.88× 10 −5

Solution

0.0000388 0.0000388

Exercise 72

4.116× 10 −2 4.116× 10 −2

Exercise 73

8.002× 10 −12 8.002× 10 −12

Solution

0.000000000008002 0.000000000008002

Exercise 74

7.36490× 10 −14 7.36490× 10 −14

Exercise 75

2.101× 10 15 2.101× 10 15

Solution

2,101,000,000,000,000 2,101,000,000,000,000

Exercise 76

6.7202× 10 26 6.7202× 10 26

Exercise 77

1× 10 6 1× 10 6

Solution

1,000,000 1,000,000

Exercise 78

1× 10 7 1× 10 7

Exercise 79

1× 10 9 1× 10 9

Solution

1,000,000,000 1,000,000,000

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 )

Solution

2.1× 10 14 2.1× 10 14

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 )

Solution

2.7× 10 78 2.7× 10 78

Exercise 84

(1×104)(1×105)(1×104)(1×105)

Exercise 85

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

Solution

2.4× 10 −8 2.4× 10 −8

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 )

Solution

2.1× 10 1 2.1× 10 1

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 )

Solution

2.9839× 10 −28 2.9839× 10 −28

Exercise 90

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

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