1. Positive and Negative Numbers

2. Adding Positive and Negative Numbers
Adding numbers with the same sign, the sign will not change
Ex: = 11
Ex: =
Answer: -11
Examples: = =
(-5) + (-18) + (-3) =
Answer: 20
Answer : -14
Answer: -26

3. Adding Positive and Negative Numbers
Adding Numbers with Different Signs
Take the sign of the number whose absolute value is larger.
Subtract the smaller absolute value from the larger value
| -3 | = 3
| 10 | = 10
10 > 3, so therefore our answer will be positive because 10 is positive.
10 -3 = 7, so therefore
= 7
You may also use a number line

4. Answers: -3 3 1 -4 4 14
Examples:
-7 + 4
3 + -6
6 + -5
|-7 | + -3
| |
-5 + 5

5. Additive Inverse: Example: 5 Example: -19 Opposite
The opposite of a number
A number plus its additive inverse equals zero.
Example: 5
Additive Inverse (opposite) is -5
5 + (-5) = 0
Example:
Additive Inverse (opposite ) is 19
= 0

6. Find the additive inverse of each problem
Examples:
Find the additive inverse of each problem -6
209
| -3 |
- |6 |
- | -9 |
Answers: 6
-209 -3 9

7. Subtracting Positive and Negative Numbers
When we subtract we move to the left on the number line.
Add the opposite of the number being subtracted
10 – 3 = 7
= 7
So therefore,
10 -3 =
Example:
-3 – 7 = = -10
Example: 4 – 10 = =

8. Examples:
2 – 9 =
4 – 10 =
14 – 8 =
-3 – 8 =
-2 – 10 =
-20 – 19 =
| -8 – 3 | =
- | 2 – 13 | =
Answers
-11 -6 6
-12
-39 11

9. Double negative -4 – (-6) = -4 + 6
-4 – (-6) =
Remember the opposite of -6 is 6
Answer = 2
These problems are called double negatives!
Examples:
-3 – (-9)
4 – (-10)
-13 – (-8)
|-13 – (-7) |
3 – (-|2 |)
Answers: 6 14 -5 5

10. Multiplying and Dividing Positive and Negative Numbers
When you multiple/divide any two numbers of the SAME sign, the answer will always be positive!
Example: (5)(9) = 45
Example: (-5)(-9) = 45
Why is (-5)(-9) = 45?
Because of the Multiplication Property of negative one.
Any number multiplied by negative one is its opposite.
Example: (5)(-1) = -5
Example: (-5)(-1) = 5

11. When you multiply or divide two numbers with opposite signs, the answer is always negative!!!!
10 ÷ -2 = -5
-14/7 = -2
Examples:
3 ∙ (-6)(-2)(-9)
10 0 ÷ ÷ -5 ÷ -6
(5)(-3)
-72 / 9
Answers:
-18
-25
-15 -8
-108 1

12. Exponents and Negatives
(-3)³
What is the base? -3
(-3)³ = (-3)(-3)(-3)
= -27
-4² =
4 is the base, not negative 4
-1(4) = -1(4)(4) = -16
Negative with no parentheses – answer will always be negative!
Examples:
(-1)⁹ =
(-2)³ =
-3⁴ =
-5² =
-(-2)⁵ =

13. Zero Property What happens when you multiply by zero??
Your answer will always be zero!
-5(0) = 0
0(9) = 0
Multiplication Property of Zero
Any number multiplied by zero is zero

14. What about dividing with zero?
Any number divided by zero is undefined!
Example: 14 / 0 is undefined.
You cannot divide a number into zero parts!
What about zero divided by a number?
Zero divided by any real number, is always zero.
Example: 0 / 14 = 0
Example: 0 / -2 = 0

15. Multiplicative Inverse
Reciprocal
Same sign as the number
Fraction is flipped
The product is 1
Example: ¾
Reciprocal is 4/3
Example: -⅝
Reciprocal is -8/5
Example: ½
Reciprocal: 2
Example: 4
Remember 4 as a fraction is 4/1
Reciprocal: 1/4

16. Think about it??? What is the reciprocal of zero???
Zero as a fraction is….
Example: 0/9
Reciprocal: 9/0
Can we divide by zero?
NO, so therefore the reciprocal of zero is undefined.