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]