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Section 7.2
Addition with Real Numbers
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Objectives
o Add real numbers.
o Add real numbers in a vertical format.
o Determine if a given real number is a solution to an
equation.
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Addition with Real Numbers
Rules for Addition with Real Numbers
1. To add two real numbers with like signs,
a. add their absolute values, and
b. use the common sign.
2. To add two real numbers with unlike signs,
a. subtract their absolute values (the smaller from
the larger), and
b. use the sign of the number with the larger
absolute value.
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Example 1: Addition with Like Signs
a.  +10 +  +3 = +  +10 + +3  = + 10 + 3 = 13
b.  10 +  3 =   10 + 3  =  10 + 3 = 13
c.  1.4  +  2.5 =   1.4 + 2.5  =  1.4 + 2.5 = 3.9
 3
1
 3 1
 3  1
d.  +  +  +  = +  + + +  = +  + 
 4 3
 4   3
 4
3
 3 3 1 4
 9 4  13
= +  +   = + +  =
 4 3 3 4
 12 12  12
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Example 2: Addition with Unlike Signs
a.  10 +  +3 =   10  +3  =  10  3 = 7
b.  +10 +  3 = +  +10  3  = + 10  3 = 7
c.  9.5 +  8.7 =   9.5  8.7  =   9.5  8.7 = 0.8
 5 1
5 1
 5 1
d.  + =      =    
 8 2
 8 2
8 2
1
 5 4
 5 1 4
=     =    = 
 8 8
 8 2 4
8
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Example 3: Adding More Than Two Real
Numbers
One technique to add more than two real numbers
is to add the numbers from left to right.
a.  3+ 2 +  5 = 1+  5 = 6
b. 6.0 +  4.3 +  1.5 = 1.7 +  1.5 = 0.2
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Addition in a Vertical Format
Notes
The positive sign ( + ) may be omitted when writing
positive numbers, but the negative sign ( − ) must
always be written for negative numbers. Thus, if there
is no sign in front of a real number, the real number is
understood to be positive.
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Example 4: Addition on a Vertical Format
Find each sum.
a. 10
+ 7
3
b.  4.5
9.1
13.6
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Example 5: Addition in a Vertical Format
Find each sum.
a. 20 Solution
7 One technique for adding several real numbers
is to mentally add the positive and negative real
30
numbers separately and then add these results.
(We are, in effect, using the commutative and
associative properties of addition.)
20 or 50
7
7
30
43
43
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Example 5: Addition in a Vertical Format (cont.)
b. 42
10
 3
Solution
42 or
42
10
 13
 3
29
29
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Example 6: Determining Possible Solutions
Determine whether or not the given real number is a
solution to the given equation by substituting for the
variable and adding.
a. x + 5 = 2 given that x = −7
Solution
 7 + 5 = 2 is true, so −7 is a solution.
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Example 6: Determining Possible Solutions
(cont.)
b. 1.8 + z = −3.9 given that z = 2.1
Solution
1.8 + 2.1 = −3.9 is false since 1.8 + 2.1 = +3.9
So 2.1 is not a solution.
c. |x| + (−7) = −3 given that x = −4
Solution
|−4| + (−7) = 4 + (−7) = −3 is true, so −4 is a solution.
HAWKES LEARNING SYSTEMS
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Example 6: Determining Possible Solutions
(cont.)
1
1
1

d. x +  =  given that x = 
 5
20
4
Solution
1  1 4
 1   1
   +    =  +    
20
5 4
20
5
1
1  4
5
=  +  =  = 
20  20 
4
20
1
is true, so  is a solution.
20
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Practice Problems
Find each sum. Add from left to right if there are more
than two numbers.
1. +16 + (−10)
2. −12 + (8)
3.  1 +   2 
6  3
3  1 
5.  +   
10  15 
4. −1.3 + (1.3)
6. +6 + (−7) + (−1)
7. +100 +(−100) + (+10)
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Practice Problems (cont.)
Find the indicated sum.
8. 42
+ 9
9.
16
10
4
10. Determine whether or not x = −3 is a solution to the
equation
x +  6 = 9.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
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Systems/Quant Systems, Inc.
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Practice Problem Answers
1. 6
2. −4
5
3. 
6
4. 0
11
5. 
30
6. −2
7. 10
8. −33
9. 2
10. yes
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
All rights reserved.