Download Chapter Summary and Summary Exercises

9
Summary
DEFINITION /PROCEDURE
EXAMPLE
REFERENCE
Signed Numbers and Order
Positive Numbers Numbers used to name points to the right
of 0 on the number line.
Negative Numbers Numbers used to name points to the left
of 0 on the number line.
Signed Numbers A set containing both positive and negative
numbers.
Opposites Two numbers are opposites if the points name the
same distance from 0 on the number line, but in opposite
directions.
The opposite of a positive number is negative.
The opposite of a negative number is positive.
0 is its own opposite.
Integers The set consisting of the natural numbers, their
opposites, and 0.
Absolute Value The distance on the number line between the
point named by a number and 0.
The absolute value of a number is always positive or 0.
Section 9.1
Negative
numbers
3 2 1
Positive
numbers
0
1
2
3
Zero is neither
positive nor negative.
5 units
5
5 units
0
5
The opposite of 5 is 5.
3 units
3
3 units
0
3
The opposite of 3 is 3.
The integers are
{. . . , 3, 2, 1, 0, 1, 2, 3, . . .}
The absolute value of a number a
is written a.
7 7
8 8
Adding Signed Numbers
To Add Signed Numbers
1. If two numbers have the same sign, add their absolute
values. Give the sum the sign of the original numbers.
2. If two numbers have different signs, subtract the smaller
absolute value from the larger. Give the result the sign of
the number with the larger absolute value.
Section 9.2
5 8 13
3 (7) 10
5 (3) 2
7 (9) 2
Subtracting Signed Numbers
To Subtract Signed Numbers
To subtract signed numbers, add the first number and the
opposite of the number being subtracted.
© 2001 McGraw-Hill Companies
p. 679
Section 9.3
4 (2) 4 2 6
The opposite of 2.
Multiplying Signed Numbers
To Multiply Signed Numbers
To multiply signed numbers, multiply the absolute values of
the numbers. Then attach a sign to the product according to the
following rules:
pp. 669–672
p. 687
Section 9.4
5 7 35
(4)(6) 24
(8)(7) 56
1. If the numbers have the same sign, the product is positive.
2. If the numbers have different signs, the product is negative.
pp. 693–694
Continued
711
CHAPTER 9
THE REAL NUMBER SYSTEM
DEFINITION /PROCEDURE
EXAMPLE
Dividing Signed Numbers
To Divide Signed Numbers
To divide signed numbers, divide the absolute values of the
numbers. Then attach a sign to the quotient according to the
following rules:
1. If the numbers have the same sign, the quotient is positive.
2. If the numbers have different signs, the quotient is negative.
REFERENCE
Section 9.5
8
4
2
27 (3) 9
16
2
8
p. 703
© 2001 McGraw-Hill Companies
712
Summary Exercises
This supplementary exercise set will give you practice with each of the objectives of the chapter. Each exercise is keyed
to the appropriate chapter section. The answers are provided in the Instructor’s Manual. Your instructor will give you
guidelines on how to best use these exercises in your instructional setting.
[9.1]
Represent the integers on the number line shown.
1. 6, 18, 3, 2, 15, 9
[9.1]
10
0
10
20
Place each of the following sets in ascending order.
2. 4, 3, 6, 7, 0, 1, 2
[9.1]
1
2
2 3
3 5
[9.1]
5. 4, 2, 5, 9, 8, 1, 6
Evaluate.
6. 9
7. 9
8. 9
9. 9
10. 12 8
11. 8 12
12. 8 12
13. 8 12
[9.2]
4 5 7
5 6 10
3. , , , , ,
For each data set, determine the maximum and minimum.
4. 4, 2, 5, 1, 6, 3, 4
© 2001 McGraw-Hill Companies
20
Add.
14. 3 (8)
15. 10 (4)
16. 6 (6)
17. 16 (16)
18. 18 0
19.
20. 5.7 (9.7)
21. 18 7 (3)
[9.3]
11
3
8
8
Subtract.
22. 8 13
23. 7 10
24. 10 (7)
25. 5 (1)
26. 9 (9)
27. 0 (2)
28. 5
17
4
4
29. 7.9 (8.1)
713
714
CHAPTER 9
[9.3]
THE REAL NUMBER SYSTEM
Perform the indicated operations.
30. 4 8
31. 4 8
32. 4 8
33. 4 8
34. 6 (2) 3
35. 5 (5 8)
36. 7 (3 7) 4
37. Subtract 7 from 8.
38. Subtract 9 from the sum of 6 and 2.
[9.4]
Multiply.
39. (10)(7)
40. (8)(5)
41. (3)(15)
42. (1)(15)
43. (0)(8)
44.
32
46.
4(1)
45. (4)
8
3
47. (8)(2)(5)
49.
[9.4]
3
5
48. (4)(3)(2)
5(10)2
2
2
5
50.
3(6)4
4
3
Perform the indicated operations.
51. 2(4 3)
52. (2)(3) (5)(3)
53. (2 8)(2 8)
Divide.
54.
80
16
55.
63
7
56.
81
9
57.
0
5
58.
32
8
59.
7
0
[9.5]
60.
Perform the indicated operations.
8 6
8 (10)
61.
2(3) 1
5 (2)
62.
(5)2 (2)2
5 (2)
© 2001 McGraw-Hill Companies
[9.5]