1. ADDING INTEGERS (SAME SIGNS)
SAME signs ADD and keep the sign =
4 positives positives = positives

2. ADDING INTEGERS (SAME SIGNS)
SAME signs add and keep the sign
= - 6
4 negatives negatives = 6 negatives

3. ADDING INTEGERS (DIFFERENT SIGNS)
DIFFERENT signs SUBTRACT and keep the sign of the larger number
= 2
4 positives negatives = 2 positives

4. ADDING INTEGERS (DIFFERENT SIGNS)
DIFFERENT signs SUBTRACT and keep the sign of the larger number
= -2
4 negatives positives = 2 negatives

5. SUBTRACTING INTEGERS (KFC & follow Rules for addition)
Problem KFC follow addition rules
K – keep the first number
F – flip the subtraction to an addition sign
C – change the second number to its opposite
****then******
FOLLOW RULES FOR ADDITION!!!!

6. Steps Is it an addition or subtraction problem?
Addition (go to step 2)
Subtraction (go to step 3)
Addition – are the signs the same?
Yes – add and keep the sign
No – subtract and keep the sign of the larger number
Subtraction – KFC –Keep the first number; Flip to an addition problem; Change the last number to its opposite – then go back to step 2

7. MULTIPLYING INTEGERS Multiplying is REPEATED ADDITION
Commutative Property of Multiplication - the order in which numbers are multiplied does not matter a x b = b x a

8. = 8 = 8 MULTIPLYING INTEGERS 4 groups of 2 = 2 groups of 4
4 x = x 4
4 groups of = groups of 4 = 8 = 8 8

9. (HINT: use the commutative property)
4 x -2
4 groups of = - 8
What would
-2 x be?
(HINT: use the commutative property)
- 8

10. -2 x 4
Use the commutative property to turn the problem around to 4 x -2
- 8

11. Use grouping to model these!!
-7 x 2
-14
-12
3 x -4

12. What about a negative times a negative?
-3 x means the opposite of 3
groups of
The OPPOSITE would be

13. So we know that -5 (-6 + 6) equals 0
Another way to look at negative times a negative using the Distributive Property…..
5 ( )
(-5)(-6) + (-5)( 6) ?
= 0
For the problem to equal zero, the negative times a negative must equal a positive!
5 ( )
5 (0)
= 0
So we know that -5 (-6 + 6) equals 0

14. Multiplying Integers Rules
If the signs are the same (+ x + or - x -); multiply and the answer is positive
If the signs are different ( + x – or - x +); multiply and the answer is negative

15. Dividing Integers Division is the inverse operation of multiplication.
4 x 2 = inverse ÷ 2 = 4
4 x (– 2 )= (-8) inverse (-8) ÷ (-2) = 4

16. Dividing Integers ÷ (-5) x 3 =(-15) inverse (-15) 3 = -5

17. Rules for Division Same as Multiplication:
If the signs are the same (+ x + or - x -); multiply and the answer is positive
If the signs are different ( + x – or - x +); multiply and the answer is negative