Integers include all whole numbers and their opposites, and zero. The key rules for operations with integers are: 1) Adding integers of the same sign yields a positive sum, while those of opposite signs subtracts and uses the sign of the larger number. 2) Multiplying and dividing integers follows sign rules - same signs yield a positive result, different signs a negative one. 3) To subtract integers, change the operation to addition by changing the subtraction sign to addition and changing the sign of the number being subtracted.

1. Operations with Integers
1/30/13

2. What are Integers?
• Integers include all of the positive and
negative whole numbers, and zero.
Integers NOT Integers
3 -1.652
-4 ¾
12 2.5
0 0.7

3. Adding Integers
• On a number line:
1. Find the first number.
2. Move the distance of the second number.
a) Positive (+) numbers, move RIGHT
b) Negative (-) numbers, move LEFT
3. Where you land is the answer!
Example: 5 + 8

4. Examples:
• -4 + 1 =
• 7 + -9 =
• -8 + -4 =

5. Adding Integers Rules
• Use if you don’t have a number line.
• When the integers are:
▫ Both Positive: add the numbers
 Ex: 4 + 6 =
▫ Both Negative: add the numbers and
make it negative
 Ex: -2 + -5 =
▫ One Positive and One Negative: Subtract
and use the sign of the bigger number.
 Ex: -7 + 4 =

6. You Try!
• Add the integers.
• 12 + -4 =
• -8 + -9 =
• 2 + 13 =
• -11 + 5 =

7. Subtracting Integers 1/31/13
• Change the minus to a plus, and change the
sign of the number you are subtracting.
• Then add!
• Ex: -14 – 6 =
• Subtracting a Negative is the same as Adding!
• Ex: 12 – (-3) =

8. You Try!
• Subtract the integers.
• 17 – 4 =
• -8 – (-5) =
• 2 – 11 =
• -4 – 12 =

9. Multiplying Integers 2/1/13
• Sign Rules:
• Same signs -> Positive answer!
+ ∙ + = + and – ∙ – = +
• Ex: 2 ∙ 3 = 6 and -2 ∙ -3 = 6
• Different signs -> Negative answer!
+ ∙ – = – and – ∙ + = –
• Ex: 2 ∙ -3 = -6 and -2 ∙ 3 = -6

10. Examples:
• (5)(-12) =
• -14 x -8 =
• -23 ∙ 7 =

11. You Try!
• -9 x 17 =
• (-20)(-16) =
• 14 ∙ -5 =

12. Dividing Integers
• Sign rules are the same as multiplying!
• Examples:
• -16 ÷ -8 =
• =

13. You Try!
• -90 ÷ 6 =
•
• -57 ÷ 19 =