1. Adding Integers

2. Adding Integers
Objectives:
Add integers.
Identify properties of addition.

3. Adding Integers
EXAMPLE Using a Number Line to Add Integers
Use a number line to find –3 + –2.
Think of the number line as a thermometer. Let’s say the temperature is currently 0 degrees Fahrenheit.
0º F
3º F ↓
On our first observation, the temperature has fallen by 3 degrees.
–3º F
2º F ↓
–5º F
On our second observation, it has fallen by an additional 2 degrees.
The total decline in temperature is 5 degrees.

4. Adding Integers
Adding Two Integers with the Same Sign
Step 1: Add the absolute values of the numbers.
Step 2: Use the common sign as the sign of the sum.
(If both numbers are positive, the sum is positive.)
(If bothnumbers are negative, the sum is negative.)

5. Adding Integers
EXAMPLE Adding Two Integers with the Same Sign
Add.
(a) –6 + –15
Step 1 : Add the absolute values.
| –6 | = 6 and | –15 | = 15
Add to get 21.
Step 2: Use the common sign as the sign of the sum. Both numbers are negative, so the sum is negative.
–6 + –15 = –21

6. Adding Integers
EXAMPLE Adding Two Integers with the Same Sign
Add.
(b)
In Step 1, when both numbers are positive, their absolute values are also positive, so we only need to show Step 2.
= 31
Both positive
Sum is positive

7. Adding Integers
Adding Two Integers with the Unlike Signs
Step 1 : Subtract the smaller absolute value from the larger absolute value.
Step 2: Use the sign of the number with the larger absolute value as the sign of the sum.

8. Adding Integers
EXAMPLE Adding Two Integers with Unlike Signs
Add.
(a) –
Step | –12 | = and | 8 | = 8
Subtract 12 – 8 to get 4.
Step –12 has the larger absolute value and is negative, so the sum is also negative.
– = –4

9. –9 + 27 = +18 or 18 Adding Integers
EXAMPLE 3 Adding Two Integers with the Unlike Signs
Add.
(b) –
Step | –9 | = and | 27 | = 27
Subtract 27 – 9 to get 18.
Step has the larger absolute value and is positive, so the sum is also positive.
– = or

10. –2 + 5 + –1 + –3 + 4 –1 + 4 Adding Integers
EXAMPLE Adding Several Integers
Jernice is a competitive golfer. She lost 2 matches her first week, won 5 matches the second week, lost 1 match the third week, lost 3 matches the fourth week, and won 4 matches the fifth week. What can be said about Jernice’s wins and losses?
– –1 + –
–1 + – – –
Since the result is positive, Jernice won 3 more matches than she lost. 3

11. Adding Integers
EXAMPLE Adding Several Integers (Another Method)
Jernice is a competitive golfer. She lost 2 matches her first week, won 5 matches the second week, lost 1 match the third week, lost 3 matches the fourth week, and won 4 matches the fifth week. What can be said about Jernice’s wins and losses?
Total Losses: Total Wins: 9
– = 3
Using either method, we can see that Jernice won 3 more matches than she lost. or
9 + –6 = 3

12. Adding Integers
Addition Property of 0
Adding 0 to any number leaves the number unchanged.
Some examples are shown below.
= 9
– = –75
18, = 18,345

13. Adding Integers
Commutative Property of Addition
Changing the order of two addends does not change the sum.
Here are some examples.
= Both sums are 40.
– = –24 Both sums are –16.

14. –15 + 12 = 12 + –15 –3 = –3 Adding Integers
EXAMPLE Using the Commutative Property of Addition
Rewrite each sum using the commutative property of addition. Check that the sum is unchanged.
(a) –24
–24 = – =
(b) –
– = –15
– = –3

15. –10 + 5 –1 + –4 –5 –5 Adding Integers Associative Property of Addition
Changing the grouping of addends does not change the sum.
Here are some examples.
( ) = 3 + ( )
(–1 + –9) = –1 + (– ) = – =
– –4 13 = 13 –5 = –5

16. Using the Associate Property of Addition
Adding Integers
Using the Associate Property of Addition
NOTE
When using the associative property to make the addition of a group of numbers easier:
Look for two numbers whose sum is 0.
Look for two numbers whose sum is a multiple of 10 (the sum ends in 0, such as 10, 20, 30, or –100, –200, etc.).

17. Adding Integers
EXAMPLE Using the Associative Property of Addition
In each addition problem, pick out the two addends that would be easiest to add. Write parentheses around those addends. Then find the sum.
(a) –
Group – because the sum is 0.
7 + (– ) 7

18. Adding Integers
EXAMPLE Using the Associative Property of Addition
In each addition problem, pick out the two addends that would be easiest to add. Write parentheses around those addends. Then find the sum.
(b) –6 + –
Group –6 + –34 because the sum is –40, which is a multiple of 10.
(–6 + –34) + 4 –
–36