Positive and Negative Number Theory

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

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

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

Plot 7 Start at the origin Positive to the right

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

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 = -2 - 7 x = -2 + - 7 x = -9

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 = -2 - -7 x = -2 + 7 x = 5

Adding and Subtracting Addition does not change the sign of a number Example: 2 + 3 = x -2 + 3 = x 5 = x 1 = x Subtraction is the addition of the opposite sign Example: 2 – 3 = x -2 - -3 = x 2 - -3 = x -2 + +3 = x -1 = x 1 = x

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. + * - = - - * + = -

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

Example Solve for x. Subtraction sign Negative sign x = 18 – (–16) – 3 – (–5) + 2      = 18 + 16 – 3 + 5 + 2      = 18 + 16 + (–3) + 5 + 2      = 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