<< Chapter < Page Chapter >> Page >
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 ( [link] )

For the following problems, find a if a is

27

27

15

8 9

8 9

( 3 )

k

k

Absolute value ( [link] )

Simplify the following problems.

| 8 |

| 3 |

3

| 16 |

( | 12 | )

12

| 0 |

Addition of signed numbers ( [link] ) - multiplication and division of signed numbers ( [link] )

Simplify the following problems.

4 + ( 6 )

2

16 + ( 18 )

3 ( 14 )

17

( 5 ) ( 2 )

( 6 ) ( 3 )

18

( 1 ) ( 4 )

( 4 ) ( 3 )

12

25 5

100 10

10

16 18 + 5

( 2 ) ( 4 ) + 10 5

18 5

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

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

7

( 2 10 )

0 6 ( 4 ) ( 2 )

48

Multiplication and division of signed numbers ( [link] )

Find the value of each expression for the following problems.

P = R C . Find P if R = 3000 and C = 3800 .

z = x u s . Find z if x = 22 , u = 30 , and s = 8 .

1

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

Negative exponents ( [link] )

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

a 1

1 a

c 6

a 3 b 2 c 5

a 3 b 2 c 5

( x + 5 ) 2

x 3 y 2 ( x 3 ) 7

x 3 y 2 ( x 3 ) 7

4 2 a 3 b 4 c 5

2 1 x 1

1 2 x

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

( 2 ) 1

1 2

1 x 4

7 x y 3 z 2

7 x y 3 z 2

4 c 2 b 6

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

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

( z 6 ) 2 ( z + 6 ) 4

16 a 5 b 2 2 a 3 b 5

8 a 2 b 3

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

8 2

1 64

9 1

2 5

1 32

( x 3 ) 2

( a 2 b ) 3

1 a 6 b 3

( x 2 ) 4

( c 1 ) 4

c 4

( y 1 ) 1

( x 3 y 4 z 2 ) 6

y 24 z 12 x 18

( x 6 y 2 ) 5

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

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

Scientific notation ( [link] )

Write the following problems using scientific notation.

8739

73567

7.3567 × 10 4

21,000

746,000

7.46 × 10 5

8866846

0.0387

3.87 × 10 2

0.0097

0.376

3.76 × 10 1

0.0000024

0.000000000000537

5.37 × 10 13

46,000,000,000,000,000

Convert the following problems from scientific form to standard form.

3.87 × 10 5

387 , 000

4.145 × 10 4

6.009 × 10 7

60 , 090 , 000

1.80067 × 10 6

3.88 × 10 5

0.0000388

4.116 × 10 2

8.002 × 10 12

0.000000000008002

7.36490 × 10 14

2.101 × 10 15

2 , 101 , 000 , 000 , 000 , 000

6.7202 × 10 26

1 × 10 6

1 , 000 , 000

1 × 10 7

1 × 10 9

1 , 000 , 000 , 000

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

( 1 × 10 5 ) ( 2 × 10 3 )

( 3 × 10 6 ) ( 7 × 10 7 )

2.1 × 10 14

( 2 × 10 14 ) ( 8 × 10 19 )

( 9 × 10 2 ) ( 3 × 10 75 )

2.7 × 10 78

( 1 × 10 4 ) ( 1 × 10 5 )

( 8 × 10 3 ) ( 3 × 10 6 )

2.4 × 10 8

( 9 × 10 5 ) ( 2 × 10 1 )

( 3 × 10 2 ) ( 7 × 10 2 )

2.1 × 10 1

( 7.3 × 10 4 ) ( 2.1 × 10 8 )

( 1.06 × 10 16 ) ( 2.815 × 10 12 )

2.9839 × 10 28

( 9.3806 × 10 52 ) ( 1.009 × 10 31 )

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Basic mathematics review. OpenStax CNX. Jun 06, 2012 Download for free at http://cnx.org/content/col11427/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Basic mathematics review' conversation and receive update notifications?

Ask