1. Operations with Integers PowerPoint

2. What is an Integer?
A whole number that is either greater than 0 (positive) or less than 0 (negative)

3. What are Opposites? Example: The opposite of 6 is -6

4. Indicated by two vertical lines | |
What is Absolute Value?
Distance a number is from zero on a number line (always a positive number)
Indicated by two vertical lines | |
Example: |-8| = 8 and |8| = 8
Example: |50| = 50 and |-50| = 50

5. Adding Rules – Same Signs
If the integers have the SAME signs: ADD the numbers & keep the same sign!
Positive + Positive = Positive Answer
Negative + Negative = Negative Answer
Examples: -3 + (-10) = ? ? = -13
6 + (8) = ? ? = 14

6. Adding (Same Signs) - Examples
# (-10)
Step 1: Add the #s
Step 2: Keep same sign (Both #s are negative – Answer is negative!)
# (8)
Step 1: Add the #s
Step 2: Keep same sign (Both #s are positive – Answer is positive!)

7. Adding Rules – Different Signs
If the integers have the DIFFERENT signs: SUBTRACT the numbers & use sign of the BIGGER number!
Bigger # is Positive = Positive Answer
Bigger # is Negative = Negative Answer
Examples: (7) = ? ? = -6
23 + (-8) = ? ? = 15

8. Adding (Different Signs) - Examples
# (7)
Step 1: Subtract the #s
Step 2: Use sign of bigger # (Bigger # is negative - Answer is negative!)
# (-8)
Step 1: Subtract the #s
Step 2: Use sign of bigger # (Bigger # is positive - Answer is positive!)

9. Subtracting Rules Put ( ) around second number & its sign
Change SUBTRACTION sign to an ADDITION sign
Change sign of 2nd number to its opposite
Follow the rules for ADDITION:
-SAME signs: Add & keep the same sign DIFFERENT signs: Subtract & use sign of bigger #
Examples: -5 – -10 = ? ? = 5
= ? ? = -14

10. Subtracting - Examples
#1. -5 – #
Step 1: – (-10) Insert ( ) 9 – (23)
Step 2: (-10) Change – to (23)
Step 3: (10) Change 2nd sign 9 + (-23)
Step 4: Follow adding rules d

11. Multiplying Rules Multiply the numbers like usual
If the integers have the SAME signs: ANSWER will be POSITIVE
If the integers have DIFFERENT signs: ANSWER will be NEGATIVE
Examples: -3 · (-5) = ? ? = 15
-9 · (-10) = ? ? = 90
-7 · 7 = ? ? = -49
6 · -6 = ? ? = -36

12. Multiplying - Examples
# · (-5) #2. -9 · (-10)
15 Multiply the numbers
Same signs = Positive Answer
# · # · -6
Multiply the numbers
Different signs = Negative Answer

13. Dividing Rules Divide the numbers like usual
If the integers have the SAME signs: ANSWER will be POSITIVE
If the integers have DIFFERENT signs: ANSWER will be NEGATIVE
Examples: -33 ÷ (-3) = ? ? = 11
-90 ÷ (-10) = ? ? = 9
-20 ÷ 2 = ? ? = -10
6 ÷ -6 = ? ? = -1

14. Dividing - Examples #1. -33 ÷ (-3) #2. -90 ÷ (-10)
# ÷ (-3) # ÷ (-10)
11 Divide the numbers
Same signs = Positive Answer
# ÷ # ÷ -6
Divide the numbers
Different signs = Negative Answer

15. Solve the following problems:
Mixed Practice
Solve the following problems:
-18
7 · -4
-28
(-19) 9
-35 ÷ -7 5
-10
-32

16. Review Visit the website below for additional information on integers:
lessons/S1U1L10GL.html
Click on the signs below to review the rules for each operation