Four Rules of Math

The concepts of addition, subtraction, multiplication and division are complex abstract ideas which are interrelated.

1. Addition Rules:

positive + positive = (add) positive

Example: 2 + 1 = 3

negative + negative = (add) negative

Example: −3+ (−5) = −8

negative + positive = (subtract)

Example: 2 + (−10) = −8

Take sign of number with largest absolute value

Example: −14 + 16 = 2

Note: −(−7) means take the opposite of (−7) = 7

2. Subtraction Rules:

Change all subtraction to addition and take the opposite sign of the following number then follow the addition rules.

Example: −7 −(9)

means −7 +(−9) = -16

Example: −3 −(−10)

−3 + (10) = 7

Example:

−8 + (−9) −(−1)−2 (change all subtraction signs)

−8 + (−9)+ (1) + (−2) (do addition and subtraction from left to right)

−17 +(1)+ (−2)

−16 +(−2) = −18

3 and 4. Multiplication / Division Rules:

The rules for multiplication and division are the same.

positive (✗ or ÷) positive = positive

Example: 10 ÷ 2 = 5

negative (✗ or ÷) negative = positive

Example: −4 ✗(−3) = 12

negative (✗ or ÷) positive = negative

Example: 18 ÷ (−2) −9