Integers: “Sheriffs Versus Bandits” 3 + (-2) = n

1. Integers: “Sheriffs Versus Bandits” 3 + (-2) = n Now that you have figured out that the equation is “ready for you to solve,” think of the POSITIVE numbers as SHERIFFS and the NEGATIVE numbers as the BANDITS. Imagine that there is a shoot-out and the good guys are fighting the bandits. Each sheriff is forced to shoot a bandit in self-defense because they will not surrender, so the deal is you are trying to see who wins the fight. For example, your “shoot-out” would look like this,… 3 + (-2) = n n = positive 1 because 1 sheriff is left standing and sheriffs are positive because they are the “good guys”. What happens if you see two groups of sheriffs ready to fight? They don’t have a shoot-out, they join together to make a larger group! For example, the “stand-off” would look like this,… 4 + 2 = n n = positive 6because 6 sheriffs have joined together to make a larger group and sheriffs are positive because they are the “good guys”. If you are looking at an addition problem, just think in terms of, “This problem is ready for you to solve”. + = + =

2. What happens if you see two groups of bandits ready to fight? They don’t have a shoot-out either, they join together to make a larger group of bad guys! For example, this “stand-off” would look like this,… (-2) + (-1) = n n = negative 3because 3 bandits have joined together to make a larger group and bandits are negative because they are the “bad guys”. It is as simple as that! Good guys + Bad guys = a shoot-out. Good guys + Good guys = a larger group of Good guys and Bad guys + Bad guys = a larger group of Bad guys Subtraction is a different kind of shoot-out! Any guys to the right of the subtraction sign become traitors and change sides! For example,… 2 – (+2) = n So just like that, 2 – (+2) = n became 2 + (-2) = n and now looks like,… n = 0because 2 sheriffs became bandits and had a shoot-out with the two remaining sheriffs. In other words, everybody shot and killed each other and no good guy or bad guy was left standing. + = All because of this sneaky old subtraction sigh, the guys to the right of the sign turn traitor! That means that the two good guys just became two bad guys! + = 0

3. Now here is another example of some traitors,… (-3) – (-2) = n So, (-3) – (-2) became (-3) + (+2) = n and looked like,… n = negative 1all because 2 bandits “saw the light” and decided to become good guys and then had a nasty shoot-out with the three remaining bad guys. After everybody shot and killed each other, that only left one bad guy. So remember, when you see a subtraction sign in an integer equation, that means that there is some back-stabbing going on and guys to the right of the subtraction sign become traitors and change sides! All you have to do is remember to change the traitors to the other side and treat the “shoot-out” like an addition problem. It is as simple as that! That brings us to multiplication and division wild, wild west,… All you have to do is remember this simple rule: Good guys X Good guys = Good guys or POSITIVE Bad guys X Bad guys = Good guys or POSITIVE Good guys X Bad guys = Bad guys or NEGATIVE Bad guys X Good guys = Bad guys or NEGATIVE Here are some more traitors! See the two bandits hiding to the right of the subtraction sign? They just became good guys! + =