1. Bellwork
Write an algebraic expression for each verbal expression.
A. The sum of a number x and twenty-one
B. The difference of twice a number x and 8.
C. Five times a number x
D. The quotient of a number x and 15

2. Operations with Integers

3. Can be visualized on a number line:
What is an Integer?
A whole number that is either greater than 0 (positive) or less than 0 (negative)
Can be visualized on a number line:

4. What is a Number Line?
A line with arrows on both ends that show the integers with slash marks
Arrows show the line goes to infinity in both directions ( + and -)
Uses a negative sign (-) with negative numbers but no positive sign (+) with positive numbers
Zero is the origin and is neither negative nor positive

5. What are Opposites?
Two integers the same distance from the origin, but on different sides of zero
Every positive integer has a negative integer an equal distance from the origin
Example: The opposite of 6 is -6
Example: The opposite of -2 is 2

6. What is Absolute Value?
Distance a number is from zero on a number line (always a positive number)
Indicated by two vertical lines | |
Every number has an absolute value
Opposites have the same absolute values since they are the same distance from zero
Example: |-8| = 8 and |8| = 8
Example: |50| = 50 and |-50| = 50

7. What Can We Do to Integers?
Integers are numbers, so we can add, subtract, multiply, and divide them
Each operation has different rules to follow

8. 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

9. 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!)

10. 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

11. 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!)

12. 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

13. 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

14. 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

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

16. 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

17. 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

18. Solve the following problems:
Mixed Practice
Solve the following problems:
7 · -4
(-19)
-35 ÷ -7

19. Review Visit the website below for additional information on integers:
lessons/S1U1L10GL.html