1. COMBINING INTEGERS: Adding & Subtracting Negative & Positive Whole Numbers by S. Bradley

2. Definition Positive number – a number greater than zero. 0123456

3. Definition Negative number – a number less than zero. 0-2-3-4-5-6

4. Definition Opposite Numbers – numbers that are the same distance from zero in the opposite direction on a number line. 0123456-2-3-4-5-6

5. Definition Integers – Integers are all the whole numbers and their opposites. 7 opposite -7

6. Negative Numbers Are Used to Measure Temperature

7. Negative Numbers Are Used to Measure Below Sea Level 0 10 20 30 -10 -20 -30 -40 -50

8. Negative Numbers Are Used to Show Debt Let’s say your parents bought a car but had to get a loan from the bank for $5,000. When counting all their money they add in -$5,000 to show they still owe the bank.

9. Positive & Negative Numbers Working with positive and negative numbers is like driving in traffic. You have to watch the traffic signs and follow the driving rules.

10. Hint If you don’t see a negative or positive sign in front of a number it is positive. 9 = 9 +

11. Integer Addition Rules Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14 (-9) + (-5) = -14

12. Solve the Problems (-3) + (-5) = a 4 + 7 = b (-6) + (-7) = c 5 + 9 = d (-9) + (-9) = f

13. Solutions: a = -8 b = 11 c = -13 d = 14 f = -18

14. Monday’s Problems: 13 + 3 = a (-12) + (-5) = b (-2) + (-3) = c

15. Solutions to Monday’s Problems: 16 -17 -5

16. Integer Addition Rules Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the larger one in front of your answer. -9 + 5 = 9 - 5 = 4 Larger number Answer = - 4

17. Solve These Problems 3 + (-5) = 7 + (-4) = 3 + (-4) = (-6) + 7 = -9 + 5 = (-9) + 9 = -2 5 – 3 = 2 0 -4 1 3 9 – 9 = 0 9 – 5 = 4 7 – 6 = 1 4 – 3 = 1 7 – 4 = 3

18. How do I remember the addition rules? Simple! Let’s apply the rules to a song we all know – “Row, Row, Row Your Boat” Same sign – add & keep! Different signs – subtract, take the sign of the highest number, your answer will be exact!

19. Practice: (-4) + 5 = x (-13) + 3 = y -18 + 5 = z

20. Solutions to Practice: 1 -10 -13

21. Tuesday’s Problems: -5 + (-2) = k 10 + (-4) = j -23 + 7 = n

22. Solutions to Tuesday’s Problems: -7 6 -16

23. One way to add integers is using a number line… 0123456-2-3-4-5-6 When the number is positive, count to the right. When the number is negative, count to the left. +-

24. Here’s an example: 0123456-2-3-4-5-6 + - 3 + (-5) =-2

25. Using Integer Addition Rules or a Number Line – You choose! -150 + (-5) = g 43 + (-20) = f 24 + (-30) = v

26. Solutions to Practice: -155 23 -6

27. Wednesday’s Problem: The Georgia Bulldogs were playing the Auburn Tigers in a playoff game. Auburn’s offense received a penalty which resulted in a loss of 10 yards. If they were at the 25 yard line, what yard line would they be moved to after the penalty? (Write an equation, then solve.)

28. Wednesday’s Solution: -10 + 25 = h h = 15 yard line

29. Subtracting Integers Use the additive inverse. This simply means to change the problem to addition & follow the addition rules. How? Leave the first number “as is”; change subtraction to addition; lastly, change the SECOND number to its opposite…

30. Example: -18 – 5 = n *-18 remains “as is” *subtraction becomes + *change +5 to -5 -18 + (-5) = n *Now, simply follow the addition rules… n = -23

31. Example Problems for Subtraction: -17 – 11 = d -17 + (-11) = -28 25 – 32 = u 25 + (-32) = -7 13 – (-5) = r 13 + 5 = 18

32. You try it! 10 – (-6) = h -19 – 7 = w 9 – 11 = k

33. Solutions to Practice 10 – (-6) = h 10 + 6 = 16 -19 – 7 = w -19 + (-7) = -26 9 – 11 = k 9 + (-11) = -2

34. Thursday’s Problems: 16 – (-5) = t -3 – 8 = p -14 – (-10) = q

35. Thursday’s Solutions: 16 – (-5) = t 16 + 5 = 21 -3 – 8 = p -3 + (-8) = -11 -14 – (-10) = q -14 + 10 = -4

36. Practice for Friday: (Pay attention to the operation given…) -4 + 5 = a -17 – 8 = b -13 – (-7) = c -12 + (-8) = d

37. Solutions for Friday’s Practice: a = 1 b = -25 c = -6 d = -20

38. Monday’s Problems: -11 + (-6) = m -16 – (-57) = c 8 + (-5) = h

39. Monday’s Solutions: m = -17 c = 41 h = 3

40. Tuesday’s Problem: A submarine is 33 feet below sea level. It rises 15 feet. What integer best represents the submarine’s location after its rise? (Write an equation, then solve.)

41. Tuesday’s Solution: -33 + 15 = f f = -18 feet

42. Wednesday’s Problem: You went to the bank and borrowed $200. One week later, you went back to the same bank and borrowed $250 more. How much are you in debt? (Write an equation, then solve.)

43. Wednesday’s Solution: -200 – 250 = d -200 + (-250) = d d = -$450

44. Thursday’s Problems: -3 + (-19) = k 15 – (-7) = j 17 + (-10) = a -8 – 12 = f

45. Thursday’s Solutions: k = -22 j = 22 a = 7 f = -20

46. GOOD LUCK ON FRIDAY’S ASSESSMENT!