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1 s2 addition and subtraction of signed numbers

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  • 1. Addition and Subtraction of Signed Numbers
  • 2. Addition and Subtraction of Signed Numbers Addition of Signed Numbers
  • 3. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers.
  • 4. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers,
  • 5. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b ,
  • 6. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b
  • 7. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b Example A. Remove parentheses then combine. a. 5  (+4)
  • 8. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b Example A. Remove parentheses then combine. a. 5  (+4)  remove “( )” = 5 + 4
  • 9. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b Example A. Remove parentheses then combine. a. 5  (+4)  remove “( )” = 5 + 4 = 9
  • 10. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b Example A. Remove parentheses then combine. a. 5  (+4)  remove “( )” = 5 + 4 = 9 b. –7  (3)
  • 11. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b Example A. Remove parentheses then combine. a. 5  (+4)  remove “( )” = 5 + 4 = 9 b. –7  (3)  remove “( )” = –7 + 3
  • 12. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b Example A. Remove parentheses then combine. a. 5  (+4)  remove “( )” = 5 + 4 = 9 b. –7  (3)  remove “( )” = –7 + 3 = – 4
  • 13. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b Example A. Remove parentheses then combine. a. 5  (+4)  remove “( )” = 5 + 4 = 9 b. –7  (3)  remove “( )” = –7 + 3 = – 4 c. 2  (–6)
  • 14. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b Example A. Remove parentheses then combine. a. 5  (+4)  remove “( )” = 5 + 4 = 9 b. –7  (3)  remove “( )” = –7 + 3 = – 4 c. 2  (–6)  remove “( )” = 2 – 6
  • 15. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b Example A. Remove parentheses then combine. a. 5  (+4)  remove “( )” = 5 + 4 = 9 b. –7  (3)  remove “( )” = –7 + 3 = – 4 c. 2  (–6)  remove “( )” = 2 – 6 = – 4
  • 16. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b Example A. Remove parentheses then combine. a. 5  (+4)  remove “( )” = 5 + 4 = 9 b. –7  (3)  remove “( )” = –7 + 3 = – 4 c. 2  (–6)  remove “( )” = 2 – 6 = – 4 d. –4  (–8)
  • 17. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b Example A. Remove parentheses then combine. a. 5  (+4)  remove “( )” = 5 + 4 = 9 b. –7  (3)  remove “( )” = –7 + 3 = – 4 c. 2  (–6)  remove “( )” = 2 – 6 = – 4 d. –4  (–8)  remove “( )” = – 4 – 8
  • 18. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers. Rule for Addition of Signed Numbers: To add two signed numbers, remove the parenthesis and combine the numbers, that is, a  (+b) = a + b , a + (–b) = a – b Example A. Remove parentheses then combine. a. 5  (+4)  remove “( )” = 5 + 4 = 9 b. –7  (3)  remove “( )” = –7 + 3 = – 4 c. 2  (–6)  remove “( )” = 2 – 6 = – 4 d. –4  (–8)  remove “( )” = – 4 – 8 = –12
  • 19. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6
  • 20. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6
  • 21. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6
  • 22. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6 = 13 – 17
  • 23. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6 = 13 – 17 = –4
  • 24. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6 = 13 – 17 = –4 Subtraction of Signed Numbers
  • 25. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6 = 13 – 17 = –4 Subtraction of Signed Numbers For subtraction of signed numbers, we need the notion of “opposite” numbers.
  • 26. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6 = 13 – 17 = –4 Subtraction of Signed Numbers For subtraction of signed numbers, we need the notion of “opposite” numbers. The numbers x and –x are said to be the opposite or the negative of each other.
  • 27. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6 = 13 – 17 = –4 Subtraction of Signed Numbers For subtraction of signed numbers, we need the notion of “opposite” numbers. The numbers x and –x are said to be the opposite or the negative of each other. The opposite of x is –x.
  • 28. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6 = 13 – 17 = –4 Subtraction of Signed Numbers For subtraction of signed numbers, we need the notion of “opposite” numbers. The numbers x and –x are said to be the opposite or the negative of each other. The opposite of x is –x. The opposite of –x is –(–x) = x.
  • 29. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6 = 13 – 17 = –4 Subtraction of Signed Numbers For subtraction of signed numbers, we need the notion of “opposite” numbers. The numbers x and –x are said to be the opposite or the negative of each other. The opposite of x is –x. The opposite of –x is –(–x) = x. So the opposite of 6 is –6 , the opposite of –12 is –(–12) = 12.
  • 30. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6 = 13 – 17 = –4 Subtraction of Signed Numbers For subtraction of signed numbers, we need the notion of “opposite” numbers. The numbers x and –x are said to be the opposite or the negative of each other. The opposite of x is –x. The opposite of –x is –(–x) = x. So the opposite of 6 is –6 , the opposite of –12 is –(–12) = 12. Note that the opposite of a negative number is positive.
  • 31. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6 = 13 – 17 = –4 Subtraction of Signed Numbers For subtraction of signed numbers, we need the notion of “opposite” numbers. The numbers x and –x are said to be the opposite or the negative of each other. The opposite of x is –x. The opposite of –x is –(–x) = x. So the opposite of 6 is –6 , the opposite of –12 is –(–12) = 12. Note that the opposite of a negative number is positive. Rule for Subtraction of Signed Numbers: To subtract a signed number x, remove the parenthesis and combine with the opposite of x,
  • 32. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6 = 13 – 17 = –4 Subtraction of Signed Numbers For subtraction of signed numbers, we need the notion of “opposite” numbers. The numbers x and –x are said to be the opposite or the negative of each other. The opposite of x is –x. The opposite of –x is –(–x) = x. So the opposite of 6 is –6 , the opposite of –12 is –(–12) = 12. Note that the opposite of a negative number is positive. Rule for Subtraction of Signed Numbers: To subtract a signed number x, remove the parenthesis and combine with the opposite of x, that is, opposite a – (+b) = a – b
  • 33. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6 = 5 + 4 + 4 – 3 – 8 – 6 = 13 – 17 = –4 Subtraction of Signed Numbers For subtraction of signed numbers, we need the notion of “opposite” numbers. The numbers x and –x are said to be the opposite or the negative of each other. The opposite of x is –x. The opposite of –x is –(–x) = x. So the opposite of 6 is –6 , the opposite of –12 is –(–12) = 12. Note that the opposite of a negative number is positive. Rule for Subtraction of Signed Numbers: To subtract a signed number x, remove the parenthesis and combine with the opposite of x, that is, opposite opposite a – (+b) = a – b a – (–b) = a + b
  • 34. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)
  • 35. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4
  • 36. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1
  • 37. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)
  • 38. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7
  • 39. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7 = 10
  • 40. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7 = 10 c. –12 – (–5)
  • 41. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7 = 10 c. –12 – (–5)  remove “( )”, change to opposite = –12 + 5
  • 42. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7 = 10 c. –12 – (–5)  remove “( )”, change to opposite = –12 + 5 = –7
  • 43. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7 = 10 c. –12 – (–5)  remove “( )”, change to opposite = –12 + 5 = –7 Summary for removing parentheses for addition and subtraction of signed numbers:
  • 44. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7 = 10 c. –12 – (–5)  remove “( )”, change to opposite = –12 + 5 = –7 Summary for removing parentheses for addition and subtraction of signed numbers: For addition: a  (+b) = a + b a + (–b) = a – b
  • 45. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7 = 10 c. –12 – (–5)  remove “( )”, change to opposite = –12 + 5 = –7 Summary for removing parentheses for addition and subtraction of signed numbers: For addition: a  (+b) = a + b a + (–b) = a – b For subtraction: a – (+b) = a – b a – (–b) = a + b
  • 46. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7 = 10 c. –12 – (–5)  remove “( )”, change to opposite = –12 + 5 = –7 Summary for removing parentheses for addition and subtraction of signed numbers: For addition: a  (+b) = a + b a + (–b) = a – b For subtraction: a – (+b) = a – b a – (–b) = a + b Example C. Remove the parentheses, then combine. a. –6 – (–8) – (–2) – (9)
  • 47. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7 = 10 c. –12 – (–5)  remove “( )”, change to opposite = –12 + 5 = –7 Summary for removing parentheses for addition and subtraction of signed numbers: For addition: a  (+b) = a + b a + (–b) = a – b For subtraction: a – (+b) = a – b a – (–b) = a + b Example C. Remove the parentheses, then combine. a. –6 – (–8) – (–2) – (9) remove “( )” = –6 + 8 + 2 – 9
  • 48. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7 = 10 c. –12 – (–5)  remove “( )”, change to opposite = –12 + 5 = –7 Summary for removing parentheses for addition and subtraction of signed numbers: For addition: a  (+b) = a + b a + (–b) = a – b For subtraction: a – (+b) = a – b a – (–b) = a + b Example C. Remove the parentheses, then combine. a. –6 – (–8) – (–2) – (9) remove “( )” = –6 + 8 + 2 – 9 = 8 + 2 – 6 – 9
  • 49. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7 = 10 c. –12 – (–5)  remove “( )”, change to opposite = –12 + 5 = –7 Summary for removing parentheses for addition and subtraction of signed numbers: For addition: a  (+b) = a + b a + (–b) = a – b For subtraction: a – (+b) = a – b a – (–b) = a + b Example C. Remove the parentheses, then combine. a. –6 – (–8) – (–2) – (9) remove “( )” = –6 + 8 + 2 – 9 = 8 + 2 – 6 – 9 = 10 – 15
  • 50. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1 b. 3 – (–7)  remove “( )”, change to opposite = 3 + 7 = 10 c. –12 – (–5)  remove “( )”, change to opposite = –12 + 5 = –7 Summary for removing parentheses for addition and subtraction of signed numbers: For addition: a  (+b) = a + b a + (–b) = a – b For subtraction: a – (+b) = a – b a – (–b) = a + b Example C. Remove the parentheses, then combine. a. –6 – (–8) – (–2) – (9) remove “( )” = –6 + 8 + 2 – 9 = 8 + 2 – 6 – 9 = 10 – 15 = –5
  • 51. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 )
  • 52. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9
  • 53. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9
  • 54. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18
  • 55. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8
  • 56. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8 The ( ), [ ], or { } are grouping symbols.
  • 57. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8 The ( ), [ ], or { } are grouping symbols. Each set of symbol must contain both the left-hand and right-hand parts.
  • 58. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8 The ( ), [ ], or { } are grouping symbols. Each set of symbol must contain both the left-hand and right-hand parts. Each set encloses calculations that are to be done within the symbol.
  • 59. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8 The ( ), [ ], or { } are grouping symbols. Each set of symbol must contain both the left-hand and right-hand parts. Each set encloses calculations that are to be done within the symbol. Example D. a. –6 – (8 – 9)
  • 60. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8 The ( ), [ ], or { } are grouping symbols. Each set of symbol must contain both the left-hand and right-hand parts. Each set encloses calculations that are to be done within the symbol. Example D. a. –6 – (8 – 9) do the calculation inside the “( )”
  • 61. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8 The ( ), [ ], or { } are grouping symbols. Each set of symbol must contain both the left-hand and right-hand parts. Each set encloses calculations that are to be done within the symbol. Example D. a. –6 – (8 – 9) do the calculation inside the “( )” = – 6 – (– 1)
  • 62. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8 The ( ), [ ], or { } are grouping symbols. Each set of symbol must contain both the left-hand and right-hand parts. Each set encloses calculations that are to be done within the symbol. Example D. a. –6 – (8 – 9) do the calculation inside the “( )” = – 6 – (– 1) remove parentheses = – 6 + 1
  • 63. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8 The ( ), [ ], or { } are grouping symbols. Each set of symbol must contain both the left-hand and right-hand parts. Each set encloses calculations that are to be done within the symbol. Example D. a. –6 – (8 – 9) do the calculation inside the “( )” = – 6 – (– 1) remove parentheses = – 6 + 1 = – 5
  • 64. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8 The ( ), [ ], or { } are grouping symbols. Each set of symbol must contain both the left-hand and right-hand parts. Each set encloses calculations that are to be done within the symbol. Example D. a. –6 – (8 – 9) do the calculation inside the “( )” = – 6 – (– 1) remove parentheses = – 6 + 1 = – 5 b. (–6 – 8) – 9
  • 65. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8 The ( ), [ ], or { } are grouping symbols. Each set of symbol must contain both the left-hand and right-hand parts. Each set encloses calculations that are to be done within the symbol. Example D. a. –6 – (8 – 9) do the calculation inside the “( )” = – 6 – (– 1) remove parentheses = – 6 + 1 = – 5 b. (–6 – 8) – 9 do the calculation inside the “( )” = (–14) – 9
  • 66. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8 The ( ), [ ], or { } are grouping symbols. Each set of symbol must contain both the left-hand and right-hand parts. Each set encloses calculations that are to be done within the symbol. Example D. a. –6 – (8 – 9) do the calculation inside the “( )” = – 6 – (– 1) remove parentheses = – 6 + 1 = – 5 b. (–6 – 8) – 9 do the calculation inside the “( )” = (–14) – 9 remove parentheses = – 14 – 9
  • 67. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9 = 2 + 8 – 4 – 5 – 9 = 10 – 18 = –8 The ( ), [ ], or { } are grouping symbols. Each set of symbol must contain both the left-hand and right-hand parts. Each set encloses calculations that are to be done within the symbol. Example D. a. –6 – (8 – 9) do the calculation inside the “( )” = – 6 – (– 1) remove parentheses = – 6 + 1 = – 5 b. (–6 – 8) – 9 do the calculation inside the “( )” = (–14) – 9 remove parentheses = – 14 – 9 = – 23
  • 68. Addition and Subtraction of Signed Numbers If there is a set of grouping symbol inside another set of grouping symbol, the inner set is to be calculated first.
  • 69. Addition and Subtraction of Signed Numbers If there is a set of grouping symbol inside another set of grouping symbol, the inner set is to be calculated first. Example E. 2 – [–6 – (8 + 9)]
  • 70. Addition and Subtraction of Signed Numbers If there is a set of grouping symbol inside another set of grouping symbol, the inner set is to be calculated first. Example E. 2 – [–6 – (8 + 9)] do the calculation inside the “( )” = 2 – [–6 – (17)]
  • 71. Addition and Subtraction of Signed Numbers If there is a set of grouping symbol inside another set of grouping symbol, the inner set is to be calculated first. Example E. 2 – [–6 – (8 + 9)] do the calculation inside the “( )” = 2 – [–6 – (17)] remove parentheses = 2 – [– 6 – 17]
  • 72. Addition and Subtraction of Signed Numbers If there is a set of grouping symbol inside another set of grouping symbol, the inner set is to be calculated first. Example E. 2 – [–6 – (8 + 9)] do the calculation inside the “( )” = 2 – [–6 – (17)] remove parentheses = 2 – [– 6 – 17] do the calculation inside the “[ ]” = 2 – [– 23]
  • 73. Addition and Subtraction of Signed Numbers If there is a set of grouping symbol inside another set of grouping symbol, the inner set is to be calculated first. Example E. 2 – [–6 – (8 + 9)] do the calculation inside the “( )” = 2 – [–6 – (17)] remove parentheses = 2 – [– 6 – 17] do the calculation inside the “[ ]” = 2 – [– 23] = 2 + 23
  • 74. Addition and Subtraction of Signed Numbers If there is a set of grouping symbol inside another set of grouping symbol, the inner set is to be calculated first. Example E. 2 – [–6 – (8 + 9)] do the calculation inside the “( )” = 2 – [–6 – (17)] remove parentheses = 2 – [– 6 – 17] do the calculation inside the “[ ]” = 2 – [– 23] = 2 + 23 = 25
  • 75. Addition and Subtraction of Signed Numbers Exercise A. Drop the parentheses and write the expressions in a simpler form, then combine. 1. 7  (+3) 2. 7  (–3) 3. –7  (3) 4. –7  (– 3) 5. –7  (3) + 4 6. –7  (–3) – 4 7. –17  (– 23) + 24 8. 16  (–31) – 22 9. –8  (–15) – 9 10. –8  (–15) – 9 + (– 3) B. Drop the parentheses after the subtraction (don’t forget to switch the sign) and write the expressions in a simpler form, then combine. 11. 7 – (+3) 12. 7 – (–3) 13. –7 – (3) 14. –7 – (– 3) 15. –7 – (3) + 4 16. –7 – (–3) – 4 17. –17 – (– 23) + 24 18. 16 – (+31) – 22 19. –8 – (–15) – 9 20. –8 – (–15) –(– 19) – (+42) – 3
  • 76. Addition and Subtraction of Signed Numbers C. Drop the parentheses after the arithmetic operations and write the expressions in a simpler form, then combine. 21. 7 – (+3) + (– 3) 22. 7 – (–3) + (3) 23. –7 – (– 3) + (– 5) 24. –8 + (– 6) – (–3) – (5) 25. 17 – (– 6) + 4 – (–12) – 11 27. 5 – (–13) – 41 – (–32) – 18 – (–41) 26. –17 – (– 23) + 4 + (–16) – 11 28. –8 – (–15) – 9 + 35 – 7 + (– 25) – 10 D. Work the problems starting from the inside. Make sure that you copy the ( )’s, [ ]’s correctly. 29. 7 – [+3 + (– 3)] 30. [7 – (–3)] + (3) 31. –7 – [(–3) + (– 5)] 32. –8 + [(– 6) – (–3)] – 5 34. –[17 – (– 23)] – [(–16) – 11] 33. –8 + (– 6) – [(–3) – 5] 35. 5 – [–13) – 41] – [(–32) – 18] – (–41) 36. –[8 – (–15)] – [9 + 35] – [7 + (– 25) – 10]

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