44 CHAPTER 1 The Real Number System
Complete solution available
on the Video Resources on DVD
1.5 EXERCISES
Concept CheckFill in each blank with the correct response.
1.The sum of two negative numbers will always be a number.
(positive/negative)
Give a number-line illustration using the sum
2.The sum of a number and its opposite will always be.
3.When adding a positive number and a negative number, where the negative number has
the greater absolute value, the sum will be a number. Give
(positive/negative)
a number-line illustration using the sum
4.To simplify the expression one should begin by adding
and , according to the rule for order of operations.
5.By the definition of subtraction, in order to perform the subtraction we must
add the opposite of to to get.
6.“The difference between 7 and 12” translates as , while “the difference between
12 and 7” translates as.Concept Check In Exercises 7–10, suppose that x represents a positive number and y rep-
resents a negative number. Determine whether the given expression must represent a positive
number or a negative number.Find each sum. See Examples 1–7.32. 33. 34.
35. 36.
37. 38.
39. 40.
41. 42.
43.
44.
Find each difference. See Examples 1–7.
- 7 - 1 - 22 54. 9 - 1 - 22 55.- 6 - 1 - 22 56.- 7 - 1 - 52
- 7 - 1 - 9 - 4 - 8 - 6 - 9 - 5
4 - 7 8 - 13 5 - 9 6 - 11
3 - 2 + 1 - 1124 + 312 + 1 - 224 + 318 + 1 - 624
3 - 4 + 1 - 624 + 31 - 32 + 1 - 824 + 312 + 1 - 1124
3 - 4 + 1 - 324 + 38 + 1 - 124 3 - 5 + 1 - 924 + 316 + 1 - 2124
3 - 3 + 1 - 424 + 35 + 1 - 624 3 - 8 + 1 - 324 + 3 - 7 + 1 - 624
- 6.1+ 3 3.2+ 1 - 4.8 24 - 9.4+ 3 - 5.8+ 1 - 1.4 24
- 4
3
8
+ 6
1
2
2
1
2
+ a- 31
4
b9
10
+a-3
5
b5
8
+a-17
12
- b
6
25
+
19
20
-
1
6
+
2
3
31 - 92 + 1 - 324 + 12 31 - 82 + 1 - 624 + 14
- 8 + 39 + 1 - 224 - 6 + 36 + 1 - 924 - 3 + 33 + 1 - 824
8 + 3 - 2 + 1 - 124 12 + 3 - 3 + 1 - 424 - 2 + 35 + 1 - 124
- 12.5+21.3 4 + 313 + 1 - 524 6 + 32 + 1 - 1324
4 + 1 - 62 3 + 1 - 72 - 3.5+12.4
- 11 + 1 - 52 6 + 1 - 42 11 + 1 - 82
- 6 + 1 - 22 - 9 + 1 - 22 - 5 + 1 - 72
x-y y-x y-|x| x+|y|- 6 - 1 - 82 ,
8 + 3 - 2 + 1 - 3 + 524 ,
- 4 +2.
- 2 + 1 - 32.
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