Adding Real Numbers with Different SignsFind each sum.
(a)
First find the absolute values: and.
Because and 11 have differentsigns, subtract their absolute values.
The number has a greater absolute value than 11, so the answer is negative.
- 17 + 11 = - 6
- 17
17 - 11 = 6
- 17
|- 17 |= 17 | 11 |= 11
- 17 + 11
EXAMPLE 2
SECTION 1.2 Operations on Real Numbers 15
(d)
=-
7
6
=-a
5
6
+
2
6
b-
5
6
+ a-
1
3
b =-a
5
6
+
1
3
b Add the absolute values. Both numbers are
negative, so the sum will be negative.The least common denominator is 6;Add numerators.
Keep the same denominator.1 # 2
3 # 2 =2
6NOW TRYNOW TRY
EXERCISE 1
Find each sum.
(a)
(b)
(c)-
2
5
+ a-3
10
b- 7.25+ 1 - 3.57 2
- 4 + 1 - 92
(b)
Subtract the absolute values, 4 and 1. Because 4 has the greater absolute value,
the sum must be positive.
4 + 1 - 12 = 4 - 1 = 3
4 + 1 - 12
(c) or 8
(d) or 3.3
(e)
The absolute values are 16 and 12. Subtract the absolute values.
- 16 + 12 = - 116 - 122 = - 4
- 16 + 12
- 2.3+5.6=5.6-2.3,
- 9 + 17 = 17 - 9,
(f )
= -
2
15
= -a
12
15
-
10
15
b
-
4
5
+
2
3
=-
12
15
+
10
15
The sum is negative
because .|- 17 | 7 | 11 |The sum is positive
because .| 4 | 7 |- 1 |The sum is negative
because .|- 16 | 7 | 12 |Subtract the absolute values. has the
greater absolute value, so the answer will
be negative.
Subtract numerators.
Keep the same denominator.-^1215
NOW TRYOBJECTIVE 2 Subtract real numbers.Recall that the answer to a subtraction
problem is called the difference.Compare the following two statements.
Thus, 6 - 4 = 6 + 1 - 42 .To subtract 4 from 6, we add the additive inverse of 4 to 6.
6 + 1 - 42 = 2
6 - 4 = 2
NOW TRY
EXERCISE 2
Find each sum.
(a)
(b)
(c)-
5
9
+
2
7
4.6+ 1 - 2.8 2
- 15 + 7
NOW TRY ANSWERS
- (a) (b)
(c) - (a)- 8 (b)1.8 (c)-^1763
- 107
- 13 - 10.82
- 107
The least common denominator is 15.-^4
# 3
5 # 3 =-12
15 ;2 # 5
3 # 5 =10
15