addition and subtraction of signed numbers

1. Addition and Subtraction of Signed Numbers

2. Addition of Signed Numbers
Addition and Subtraction of Signed Numbers

3. Addition of Signed Numbers
Adding signed numbers is the same as combining the numbers.
Addition and Subtraction of Signed Numbers

4. 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,
Addition and Subtraction of Signed Numbers

5. 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 ,
Addition and Subtraction of Signed Numbers

6. 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
Addition and Subtraction of Signed Numbers

7. 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
Addition and Subtraction of Signed Numbers
Example A. Remove parentheses then combine.
a. 5  (+4)

8. 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
Addition and Subtraction of Signed Numbers
Example A. Remove parentheses then combine.
a. 5  (+4)  remove “( )”
= 5 + 4

9. 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
Addition and Subtraction of Signed Numbers
Example A. Remove parentheses then combine.
a. 5  (+4)  remove “( )”
= 5 + 4 = 9

10. 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
Addition and Subtraction of Signed Numbers
Example A. Remove parentheses then combine.
a. 5  (+4)  remove “( )”
= 5 + 4 = 9
b. –7  (3)

11. 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
Addition and Subtraction of Signed Numbers
Example A. Remove parentheses then combine.
a. 5  (+4)  remove “( )”
= 5 + 4 = 9
b. –7  (3)  remove “( )”
= –7 + 3

12. 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
Addition and Subtraction of Signed Numbers
Example A. Remove parentheses then combine.
a. 5  (+4)  remove “( )”
= 5 + 4 = 9
b. –7  (3)  remove “( )”
= –7 + 3 = – 4

13. 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
Addition and Subtraction of Signed Numbers
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 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
Addition and Subtraction of Signed Numbers
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 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
Addition and Subtraction of Signed Numbers
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 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
Addition and Subtraction of Signed Numbers
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 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
Addition and Subtraction of Signed Numbers
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 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
Addition and Subtraction of Signed Numbers
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,
a – (+b) = a – b a – (–b) =

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,
a – (+b) = a – b a – (–b) =
opposite

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
a – (+b) = a – b a – (–b) = a + b
opposite

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. b. 2  (–4) – (–8) – (5)  (–9 )
Addition and Subtraction of Signed Numbers

52. b. 2  (–4) – (–8) – (5)  (–9 ) remove ( )’s
= 2 – 4 + 8 – 5 – 9
Addition and Subtraction of Signed Numbers

53. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
Addition and Subtraction of Signed Numbers

54. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
Addition and Subtraction of Signed Numbers

55. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers

56. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers
The ( ), [ ], or { } are grouping symbols.

57. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers
The ( ), [ ], or { } are grouping symbols. Each set of symbol
must contain both the left-hand and right-hand parts.
Example D.
a. –6 – (8 – 9)

58. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers
The ( ), [ ], or { } are grouping symbols. Each set of symbol
must contain both the left-hand and right-hand parts and each
encloses calculations that are to be done within the symbols.
Example D.
a. –6 – (8 – 9)

59. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers
The ( ), [ ], or { } are grouping symbols. Each set of symbol
must contain both the left-hand and right-hand parts and each
encloses calculations that are to be done within the symbols.
Example D.
a. –6 – (8 – 9)

60. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers
The ( ), [ ], or { } are grouping symbols. Each set of symbol
must contain both the left-hand and right-hand parts and each
encloses calculations that are to be done within the symbols.
Example D.
a. –6 – (8 – 9) do the calculation inside the “( )”

61. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers
The ( ), [ ], or { } are grouping symbols. Each set of symbol
must contain both the left-hand and right-hand parts and each
encloses calculations that are to be done within the symbols.
Example D.
a. –6 – (8 – 9) do the calculation inside the “( )”
= – 6 – (– 1)

62. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers
The ( ), [ ], or { } are grouping symbols. Each set of symbol
must contain both the left-hand and right-hand parts and each
encloses calculations that are to be done within the symbols.
Example D.
a. –6 – (8 – 9) do the calculation inside the “( )”
= – 6 – (– 1) remove parentheses
= – 6 + 1

63. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers
The ( ), [ ], or { } are grouping symbols. Each set of symbol
must contain both the left-hand and right-hand parts and each
encloses calculations that are to be done within the symbols.
Example D.
a. –6 – (8 – 9) do the calculation inside the “( )”
= – 6 – (– 1) remove parentheses
= – 6 + 1
= – 5

64. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers
The ( ), [ ], or { } are grouping symbols. Each set of symbol
must contain both the left-hand and right-hand parts and each
encloses calculations that are to be done within the symbols.
Example D.
a. –6 – (8 – 9) do the calculation inside the “( )”
= – 6 – (– 1) remove parentheses
= – 6 + 1
= – 5
b. (–6 – 8) – 9

65. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers
The ( ), [ ], or { } are grouping symbols. Each set of symbol
must contain both the left-hand and right-hand parts and each
encloses calculations that are to be done within the symbols.
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. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers
The ( ), [ ], or { } are grouping symbols. Each set of symbol
must contain both the left-hand and right-hand parts and each
encloses calculations that are to be done within the symbols.
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. b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s
= 2 – 4 + 8 – 5 – 9
= 2 + 8 – 4 – 5 – 9
= 10 – 18
= –8
Addition and Subtraction of Signed Numbers
The ( ), [ ], or { } are grouping symbols. Each set of symbol
must contain both the left-hand and right-hand parts and each
encloses calculations that are to be done within the symbols.
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 pair of grouping symbols inside another a pair of
grouping symbols, the inner set is to be calculated first.

69. Addition and Subtraction of Signed Numbers
Example E.
2 – [–6 – (8 + 9)]
If there is a pair of grouping symbols inside another a pair of
grouping symbols, the inner set is to be calculated first.

70. Addition and Subtraction of Signed Numbers
Example E.
2 – [–6 – (8 + 9)] do the calculation inside the “( )”
= 2 – [–6 – (17)]
If there is a pair of grouping symbols inside another a pair of
grouping symbols, the inner set is to be calculated first.

71. Addition and Subtraction of Signed Numbers
Example E.
2 – [–6 – (8 + 9)] do the calculation inside the “( )”
= 2 – [–6 – (17)] remove parentheses
= 2 – [– 6 – 17]
If there is a pair of grouping symbols inside another a pair of
grouping symbols, the inner set is to be calculated first.

72. Addition and Subtraction of Signed Numbers
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]
If there is a pair of grouping symbols inside another a pair of
grouping symbols, the inner set is to be calculated first.

73. Addition and Subtraction of Signed Numbers
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
If there is a pair of grouping symbols inside another a pair of
grouping symbols, the inner set is to be calculated first.

74. Addition and Subtraction of Signed Numbers
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
If there is a pair of grouping symbols inside another a pair of
grouping symbols, the inner set is to be calculated first.

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
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
10. –8  (–15) – 9 + (– 3)
20. –8 – (–15) –(– 19) – (+42) – 3

76. 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
35. 5 – [–13) – 41] – [(–32) – 18] – (–41)
34. –[17 – (– 23)] – [(–16) – 11]
36. –[8 – (–15)] – [9 + 35] – [7 + (– 25) – 10]
33. –8 + (– 6) – [(–3) – 5]
Addition and Subtraction of Signed Numbers