1. Positive and Negative
Number Theory

2. y x Rise on the y Positive up Run on the x Negative to the left
Positive to the right
Negative down

3. Only the sign moves the number on the number line.
Mathematicians are Lazy. We only write the signs of negative numbers.
Subtraction is the addition of the opposite sign
Addition combines numbers

4. Plot -3
Start at the origin
Negative moves to the left

5. Plot 7
Start at the origin
Positive to the right

6. x = -3 + 7 x = 4 Solve for x Start at the origin
Negative moves to the left
Positive moved to the right
x =
x = 4

7. x = -2 - 7 x = -2 + - 7 x = -9 Solve for x Start at the origin
Negative moves to the left
Positive moved to the right
x =
x =
x = -9

8. x = -2 - -7 x = -2 + 7 x = 5 Solve for x Start at the origin
Subtraction is the addition of the opposite sign
Negative to the left
Positive to the right
x =
x =
x = 5

9. Adding and Subtracting
Addition does not change the sign of a number
Example: = x = x
5 = x = x
Subtraction is the addition of the opposite sign
Example: – 3 = x = x
= x = x
-1 = x 1 = x

10. Multiply and Divide If the signs are the same
(both positive or both negative),
the answer will be positive.
+ * + = * - = +
If the signs are different
(one positive and one negative),
the answer will be negative.
+ * - = * + = -

11. Multiply and Divide
Two like signs make a positive sign. Two unlike signs make a negative sign.

12. Example
Solve for x.
Subtraction sign
Negative sign
x = 18 – (–16) – 3 – (–5) + 2      = –      = (–3)      = 41 + (–3) [I added all the positive numbers.]      = 41 – 3 [The addition of a negative is the same as the subtraction of a positive.]      = 38