Download Beg. Alg. 01 Addition and Subtraction of Signed Numbers

HFCC Math Lab
Beginning Algebra - 1
ADDITION AND SUBTRACTION OF SIGNED NUMBERS
PART I:
Addition of Signed Numbers
Rules for Addition of Signed Numbers: (These rules must be memorized.)
Rule 1: To add two numbers with the same sign, add their absolute values and
use the common sign for the result.
Rule 2: To add two numbers with different signs, subtract the smaller absolute
value from the larger absolute value. Then assign the sign of the number
having the larger absolute value to the result.
We can state the Addition Rules in another equivalent way:
 Positive + Positive = Positive 
Rule 1: 
 Add absolute values
 Negative + Negative = Negative 
 Positive + Negative = Sign of the number with larger absolute value 
Rule 2: 
 Subtract absolute values
 Negative + Positive = Sign of the number with larger absolute value 
Examples: (Rule 1)
1.
(+3) + (+4) = +7 = 7
The absolute values are 3 and 4. Their sum is 7. The common
sign is "+". Note that +7 = 7.
2.
(−3) + (−4) = −7
The absolute values are 3 and 4. Their sum is 7. The
common sign is “ − “
3.
(−8) + (−5)+ (−12)
Add from left to right. The first 2 numbers have absloute
⇓
(−13) + (−12)
values of 8 and 5. Their sum is 13. The common sign is " − ".
⇓
− 25
The two numbers have absolute values of 13 and 12.
Their sum is 25. The common sign is " − ".
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Revised 02/09
4. (−5) + (−9)+ (−2) + (−20)
Use Rule 1 three times in succession, from left to right.
⇓
(−14) + (−2)+ (−20)
⇓
(−16) + (−20)
⇓
− 36
Examples: (Rule 2)
(+18) + (−6)
+ 12 = 12
The absolute values are 18 and 6. The difference is 12.
The sign of the larger absolute value is "+".
2. (−18) + (+6)
− 12
The absolute values are 18 and 6. The difference is 12.
The sign of the larger absolute value is " − ".
3. (−15) + (+15)
The absolute values are 15 and 15. The difference is 0.
1.
0
The answer is 0.
Examples: (Both Rules):
1.
(−6) + (+3)+ (−8)
Rule 2
⇓
(−3) + (−8)
Rule 1
⇓
− 11
2. (−12) + (−18)+ (+42)
Rule 1
⇓
(−30) + (+42)
Rule 2
⇓
+ 12 = 12
3.
(−15) + (+18)+ (−12) + (−14)
Rule 2
⇓
(+3) + (−12)+ (−14)
Rule 2
⇓
(−9) + (−14)
Rule 1
⇓
− 23
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Revised 02/09
Part II:
Subtraction of Signed Numbers
Rules for Subtraction of Signed Numbers: (These rules must be memorized.)
1. a − b = a + (−b)
2. a − (−b) = a + b
Therefore, to perform a subtraction:
a. Leave the first number the same.
b. Change the subtraction to addition of the opposite.
c. Use the Rules for Addition to complete the problem.
Examples:
1. 10 − 8
10 + (−8)
2
10 remains the same. Convert to addition.
The opposite of 8 is − 8.
Addition Rule 2
2. 15 − 20
15 + (−20)
−5
15 remains the same. Convert to addition.
The opposite of 20 is − 20.
Addition Rule 2
3.
(−14) − (−3)
− 14 + (+3)
− 11
−14 remains the same. Convert to addition.
The opposite of (−3) is (+3)
Addition Rule 2
Note: The first number in an addition or subtraction problem is not normally encased in
parentheses. So problem 3 above would be written: −14 − (−3) and would be done exactly
the same way. From here to the end of the handout, the first number will not be encased in
parentheses.
4. 19 − (−5)
19 + (+5)
24
19 remains the same. Convert to addition.
The opposite of (−5) is (+5).
Addition Rule 1
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Revised 02/09
Sometimes the problem involves both addition and subtraction. It is usually best in this case to
convert all subtractions to addition of the opposite before beginning the problem.
Examples:
1.
− 16 + (−5) − (−3)
Convert the subtraction to addition of the opposite.
⇓
−16 + (−5)+ (+3)
Addition Rule 1
⇓
−21 + (+3)
Addition Rule 2
⇓
− 18
2.
18 − 5− (−3) + (−8) + (−25)
Convert the first subtraction to addition of the opposite.
⇓
18 + (−5) − (−3)+ (−8) + (−25)
Convert the second subtraction to addition of the opposite.
⇓
18 + (−5)+ (+3) + (−8) + (−25)
Addition Rule 2
⇓
13 + (+3)+ (−8) + (−25)
Addition Rule 1
⇓
16 + (−8)+ (−25)
Addition Rule 2
⇓
8 + (−25)
Addition Rule 2
⇓
− 17
3.
−8 − 5+ 4 − 3 − 10
Convert all subtractions to addition of the opposite, one at a time.
⇓
− 8 + (−5) + 4 − 3 − 10
⇓
− 8 + (−5) + 4 + (−3) − 10
⇓
−8 + (−5) + 4 + (−3) + (−10)
Addition Rule 1
⇓
−13 + 4+ (−3) + (−10)
Addition Rule 2
⇓
−9 + (−3)+ (−10)
Addition Rule 1
⇓
−12 + (−10)
Addition Rule 1
⇓
− 22
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Revised 02/09
Exercises: Perform the following additions and subtractions:
1.
15 − 17
2.
−18 − 22
3.
13 + 14
4.
−18 + 24
5.
−32 − (−35)
6.
−18 − (−14) + (−3)
7.
12 + (−2) − (−3) − 8
8.
−13 + 13
9.
−12 + (−12)
10.
−18 − (−18)
11.
12 − 10 − (−3) + (−4) − 5
12.
15 + (−2) + (−12) − 5 − 4 + 2
13.
6 − 5 + 4 − 20 − 9
14.
−2 + 5 − 8 + 12 − 5
15.
−5 − 8 − 2 − 9 − 3
16.
−9 − 3 − 10
17.
12 − (+4) − (+8) − (+13)
18.
4 + (−6) + (−3) + (−9) + (−10)
19.
−2 − (−6) − (+4) + (−3) − (−9)
20.
14 − (−2) + (−5) − (+5) − 8
21.
3 − 3 − (−3) − 3 + (−3) − (+3)
22.
−1 + (−2) + (−3) + (−4) + (−5)
23.
−3 − (−4) − (−5) − (−6) − (−7)
24.
4 + (−5) − (−5) + 5 + (−8)
25.
10 − 20 − (−30) + (−25) − (−15) − 20
Answers to all problems and solutions to most odd numbered problems:
1. 15 − 17
15 + (−17)
−2
2.
− 40
3.
27
4.
6
5.
− 32 − (−35)
− 32 + (+35)
3
6.
−7
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Revised 02/09
7. 12 + (−2) − (−3) − 8
12 + (−2) + (+3) + (−8)
10 + (+3) + (−8)
13 + (−8)
5
9.
8. 0
− 24
11. 12 − 10 − (−3) + (−4) − 5
12 + (−10) + (+3) + (−4) + (−5)
2 + (+3) + (−4) + (−5)
5 + (−4) + (−5)
1 + (−5)
−4
10.
0
12.
−6
13.
6 − 5 + 4 − 20 − 9
6 + (−5) + 4 + (−20) + (−9)
1 + 4 + (−20) + (−9)
5 + (−20) + (−9)
− 15 + (−9)
− 24
14.
2
15.
− 5−8 − 2 − 9 −3
− 5 + (−8) + (−2) + (−9) + (−3)
− 13 + (−2) + ( −9) + (−3)
− 15 + (−9) + (−3)
− 24 + (−3)
− 27
16.
− 22
18.
− 24
17. 12 − (+4) − (+8) − (+13)
12 + (−4) + (−8) + (−13)
8 + (−8) + (−13)
0 + (−13)
− 13
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Revised 02/09
− 2 − (−6) − (+4) + (−3) − (−9)
− 2 + (+6) + (−4) + (−3) + (+9)
4 + (−4) + (−3) + (+9)
0 + (−3) + (+9)
− 3 + (+9)
6
20.
−2
21. 3 − 3 − (−3) − 3 + (−3) − (+3)
3 + (−3) + (+3) + (−3) + (−3) + (−3)
0 + (+3) + (−3) + (−3) + (−3)
+ 3 + ( −3) + (−3) + (−3)
0 + (−3) + (−3)
− 3 + (−3)
−6
22.
− 15
19.
23.
− 3 − (−4) − (−5) − (−6) − (−7)
− 3 + (+4) + (+5) + (+6) + (+7)
+ 1 + (+5) + (+6) + (+7)
+ 6 + (+6) + (+7)
+ 12 + (+7)
19
24. 1
25. 10 − 20 − (−30) + (−25) − (−15) − 20
10 + (−20) + (+30) + (−25) + (+15) + (−20)
− 10 + (+30) + (−25) + (+15) + (−20)
+ 20 + (−25) + (+15) + (−20)
− 5 + (+15) + (−20)
+ 10 + (−20)
− 10
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Revised 02/09
NOTE: You can get additional instruction and practice by going to the following
websites:
http://www.themathpage.com/alg/add-subtract-signed-numbers.htm#rules
This website gives rules for adding and subtracting signed numbers along with
many interactive examples.
http://www.mathsteacher.com.au/year8/ch03_integers/03_addsub/integers.h
tm This website shows how to add and subtract numbers using the number line.
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Revised 02/09