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Integers

Integers. How We add and Subtract. LIVE. This Photo by Unknown Author is licensed under CC BY-SA-NC. LIVE. What Integers are Rules for adding and subtracting Integers A way to show that a rule is true. What will You Learn. What is an Integer.

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Integers

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  1. Integers How We add and Subtract LIVE A. Gilleran This Photo by Unknown Author is licensed under CC BY-SA-NC

  2. LIVE • What Integers are • Rules for adding and subtracting Integers • A way to show that a rule is true What will You Learn A. Gilleran

  3. What is an Integer Integers include positive and negative whole numbers NEWS A. Gilleran

  4. Positive number – a number greater than zero. 0 1 2 3 4 5 6 Positive Numbers A. Gilleran

  5. Negative number – a number less than 0 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Negative Numbers A. Gilleran

  6. What are negative numbers used for? • Negative numbers are used to measure temperature • Used to measure under sea level • Negative numbers used to show debt Negative Numbers A. Gilleran

  7. Temperature A. Gilleran This Photo by Unknown Author is licensed under CC BY-SA

  8. Sea Level 20 10 0 -10 -20 -30 -40 A. Gilleran

  9. Debt • If you owe your friend €20, you would add in -20 to your budget show that you still owe money. A. Gilleran

  10. Question 5 6 7 8 9 10 11 12 13 If it was -3 Degrees in the morning, but by lunch it was +6 degrees. How much did the temperature go up? Clue: If you do not see a negative or positive sign in front of the number, it is positive A. Gilleran This Photo by Unknown Author is licensed under CC BY-SA

  11. Question 5 6 7 8 9 10 11 12 13 If it was -3 Degrees in the morning, but by lunch it was +6 degrees. How much did the temperature go up? A. Gilleran This Photo by Unknown Author is licensed under CC BY-SA

  12. LIVE • Rule # 1 – Same Signs • If the signs are the same, pretend the signs are not there. • Add the numbers, then put the signs that the number had in front of your answer. • 10 + 5 = 15 • - 10 + - 5 = -15 Integer Addition Rules A. Gilleran

  13. You Try A. Gilleran

  14. (+8) (+13) = ? • 5 • 21 • -5 • +5 A. Gilleran

  15. (-22) + (-11) = ? • +33 • -11 • +11 • -33 A. Gilleran

  16. (-12) + (+6) = ? • +6 • -6 • +18 • -18 A. Gilleran

  17. (-16) + (+5) = ? • 11 • 21 • -21 • -11 A. Gilleran

  18. LIVE • Rule # 2 – Different Signs • If the signs are different, pretend they are not there. • Subtract the smaller from the bigger and put the sign of the bigger number in front of your answer. • 10 + 5 = 15 • - 10 + - 5 = -15 -9 + +5 = Larger . value Answer = - 4 9 - 5 = 4 Integer Addition Rules A. Gilleran

  19. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line When the number is positive, count to the right. When the number is negative, count to the left. - + A. Gilleran

  20. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line +3 + -5 = -2 + - A. Gilleran

  21. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line +6 + -4 = +2 + - A. Gilleran

  22. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line +3 + -7 = -4 + - A. Gilleran

  23. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line -3 + +7 = +4 - + A. Gilleran

  24. Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9! Integer Subtraction Rules A. Gilleran

  25. You Try A. Gilleran

  26. 12 – (-8) 12 + (+8) 12 + 8 = 20 -3 – (-11) -3 + (+11) -3 + 11 = 8 A. Gilleran

  27. Answer Now (+12) – (-8) = ? • 4 • -4 • 20 • -20 A. Gilleran

  28. Answer Now (-3) – (-11) = ? • 14 • -14 • 8 • -8 A. Gilleran

  29. Answer Now (+12) - (+8) = ? • -4 • +4 • 20 • -20 A. Gilleran

  30. Answer Now (-3) – (+11) = ? • 8 • -8 • 11 • +11 A. Gilleran

  31. How can we check “Subtracting a negative number is the same as adding a positive” is true? We can use the same method we use to check our answers when we subtract. A. Gilleran

  32. Suppose you subtract a – b and it equals c: a – b = c 5 – 2 = 3 To check if your answer is correct, add b and c: a = b + c 5 = 2 + 3 A. Gilleran

  33. You Try A. Gilleran

  34. a – b = c a = b + c 9 – 5 = 4 9 = 5 + 4 a – b = c a = b + c 20 – 3 = 17 20 = 3 + 17 A. Gilleran

  35. If the method for checking subtraction works, it should also work for subtracting negative numbers. A. Gilleran

  36. Ifa – b = c,and…. 2 – (-5) is the same as 2 + (+5), which equals7, Then let’s check with the negative numbers to see if it’s true… A. Gilleran

  37. a – b = c a = b + c 2 – (-5) = 7 2 = -5 + 7 It works! a – b = c a = b + c -11 – (-3) = -8 -11 = -3 + -8 YES! A. Gilleran

  38. Check Your Answers 1. Solve: 3 – 10 = 7 Check: 3 = 10 + (-7) 2. Solve: 17 – ( 12) = 29 Check: 17 = -12 + 29 A. Gilleran

  39. Check Your Answers 1. Solve: 20 – ( 5) = 25 Check: 20 = -5 + 25 1. Solve: -7 – ( 2) = -5 Check: -7 = -2 + -5 A. Gilleran

  40. You have learned a lot about adding and subtracting integers • Let’s Review Review A. Gilleran

  41. 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 numbers in front of your answer. 9 + 5 = 14 -9 + -5 = -14 A. Gilleran

  42. Integer Addition Rules • Rule #2 – • If the signs are different pretend the signs aren’t there. • Subtract the smaller from the larger one • Put the sign of the one with the larger value in front of your answer. -9 + +5 = Larger value Answer = - 4 9 - 5 = 4 A. Gilleran

  43. Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9! A. Gilleran

  44. Discuss with a partner ways that you know that this problem is solved correctly. 6 – (-9) = 15 A. Gilleran

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