1. Integer Notes 1. positive numbers any whole number greater than zero 2. negative numbers any whole number less than zero 3. opposites numbers that are the same distance from zero but are on opposite sides of zero 4. integers positive and negative whole numbers 5. absolute value = how far a number is from zero on a number line

2. Comparing and Ordering When you compare and order integers you need to know the integers' positions in relation to zero. Then you can determine which integer is the largest. Example: -5 ___ -12 -9 ___ 4 (Pay attention to this one!) -32 ___-5 29 ____ -2 Put these in descending (greatest to least) order: -7, -19, 0, -4, 6, 29 ________________

3. Practice Compare the following: 45 ____ -35 -13 ____ - 54 -2 ____ -7 -5 ____ 12 3 ____ -30 Put these in ascending order: -4 -7 14 9 -32 -1 28

4. RULES for ADDITION: Positive + Positive = Positive Positive + Negative = find the difference and give the sign of the larger number Negative + Positive = find the difference and give the sign of the larger number Negative + Negative = Negative If we were asked to add 4 + 3, you'd start at 4, then move three units to the right to end at 7. Correct?? So 4 + 3 = 7. What if you were asked to add 8 and -2? You would start at 8. Then you'd move two units left from there because negative numbers make us move toward the left side of the number line. We end up at 6. So 8 + -2 = 6. What about -6 + -5? _____What about -13 + 4? _____

5. Practice Problems: 1.17 + 4 = ___ 2. 14 + (-25) = ____ 3. -11 + 5 = ____ 4. - 25 + -9 = ____ 5. 23 + -62 = _____ 6. 9 + -32 = ____ 7. -7 + (-12) = ____

6. RULES FOR SUBTRACTION: 1. Change the subtraction sign into an addition sign. 2. Take the opposite of the number that immediately follows the addition sign. Think: "Add the Opposite" Examples: 3 -4 = ___ change it to 3 + -4 = -1 6 - (-7) = ___change it to 6 + (7) = 13 You try these: (-3) - 7= ____ -12 - -6 = _____ 4 - (-2) = _____

7. Practice Problems: 1.17 - 4 = ___ 2. 145 - (-25) = ____ 3. -19 + 5 = ____ 4. - 25 + -9 = ____ 5. 35 - 64 = _____ 6. 3 + -19 = ____ 7. -87 - (-14) = ____

8. To multiply and divide integers: Multiply or divide just as you do whole numbers, except you must keep track of the signs! STEPS: 1. Multiply or divide the absolute values. 2. Use these rules to determine the sign of the answer When you multiply or divide two integers with the same signs = the answer is always positive!! POSITIVE X POSITIVE = POSITIVE NEGATIVE X NEGATIVE = POSITIVE POSITIVE ÷ POSITIVE = POSITIVE NEGATIVE ÷ NEGATIVE = POSITIVE When you multiply or divide two integers with different signs = the answer is always negative!! POSITIVE X NEGATIVE = NEGATIVE NEGATIVE X POSITIVE = NEGATIVE POSITIVE ÷ NEGATIVE= NEGATIVE NEGATIVE ÷ POSITIVE = NEGATIVE

9. How can you represent these with integers? The Dead Sea is 420 meters below sea level. The average temperature last week was 7 degrees below zero. Sally works in an office 17 floors above Barbara's office. How (using a real life example or a picture) can you prove to me that 3 x 3 = 9? Can you find a real life example that would explain to me how multplying a negative times a positive? -3 x 3 = -9? Think about digging a hole... - 2 x 4 = -8 Try this one on your own...

10. Can you find a real life example that would explain to me how multiplying a negative x negative = positive? -3 x -2 = 6 Jim walked down 3 steps. Then he walked 2 times as many steps in the opposite direction.