 # BEFORE WE START……………. It is best to simplify our “Signs”…. It gets really confusing when we have two signs next to one another. To counter this, we multiply.

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BEFORE WE START……………. It is best to simplify our “Signs”…. It gets really confusing when we have two signs next to one another. To counter this, we multiply the signs together. There are 2 sets: When the signs are the same When the signs are different

* * * * = = = =

3 + 5 -4 - 2 -9 + -1 -2 – (-1) Notice how there is only 1 sign in a row? We can leave it the way it is, and do our arithmetic normally. Although we have two signs, they are not right next to each other. We can leave it how it is. Ouch. We are adding a negative. We have 2 signs next to each other. Since they are DIFFERENT, the negative takes over! - We are subtracting a negative. Since there are 2 signs in a row, we must change it. Since they are the SAME, we replace it with a positive. +

When adding and subtracting integers, there are 2 different methods I like to use. 1) The number line method 2) The “money” method

Number Line Like GEMDAS says, we go from left to right. The number on the left is the “starting point.” The number on the right is WHERE and HOW MANY we go. If it is a negative, it is to the left. If it is a positive, it is to the right.

-4 + 3 Starting at -4 Moving Right 3 Units Planning Phase What do we know?

-4 + 3 Planning Phase What do we know? Where are we starting in relation to 0? Starting left of 0 |-4| = 4 4 units to the left of 0

-4 + 3 Planning Phase What do we know? Since we are 4 to the left of 0, but only moving 3 to the right, We are still on the NEGATIVE side of 0. Therefore, we can expect our answer to be negative.

Doing Phase -4 + 3 Starting Point Now move 3 to the right +1+2+3 We now have moved 3 to the right and are on -1, a negative answer. We made it!

Money! Sometimes, it helps to think about positive and negative integers as forms of money. A positive integer is the amount that you HAVE Example: +3 would refer to HAVING \$3 A negative integer is the amount that you OWE Example: -3 would refer to OWING \$3.

5 - (-3) Starting out with \$5 Subtracting a (–) is Eliminating a debt Don’t worry about that money you owe me man! You were expecting to have 3 less dollars, but now you have 3 more! 5+3 = 8

-20 - 4 Owe \$20Lose \$4 bet You now can add 4 more dollars to the amount you OWE. Add them together to find the total DEBT 20 + 4 = 24 Dollars owed, or -24

-18 + 100 Owe \$18Find \$100 on ground You found more money than you owe, so you know you should HAVE extra Subtract your debt from how much you found to find your earnings 100 – 18 = \$82 had

-100 + 25 Owe \$18Grandma gives you \$25 You OWE more money than you gave. You know you should still owe money. Subtract your findings from how much you owe to find how much you still owe 100 – 25 = \$75 owed = -75

Practice Practice Practice

Classwork: 1.4 Pg. 42-45 #3-54 e.3 1.5 Pg. 46-49 #3-57 e.3 Homework Notes 1.6 & Study Due next class! Make sure you bring your past classwork to class each day! You never know when you’ll have a classwork quiz

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