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Addition and Subtraction of Signed Numbers
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
Addition of Signed Numbers 
Adding signed numbers is the same as combining the...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s 
= 5 + 4 – 3 – 8 + 4 – 6 
= 5 + ...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
Example B. Remove parentheses then combine. 
a. 5 – (+4)  remove “( )”, chang...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 )
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s 
= 2 – 4 + 8 – 5 – 9 
= 2 + ...
Addition and Subtraction of Signed Numbers 
If there is a set of grouping symbol inside another set of 
grouping symbol, t...
Addition and Subtraction of Signed Numbers 
If there is a set of grouping symbol inside another set of 
grouping symbol, t...
Addition and Subtraction of Signed Numbers 
If there is a set of grouping symbol inside another set of 
grouping symbol, t...
Addition and Subtraction of Signed Numbers 
If there is a set of grouping symbol inside another set of 
grouping symbol, t...
Addition and Subtraction of Signed Numbers 
If there is a set of grouping symbol inside another set of 
grouping symbol, t...
Addition and Subtraction of Signed Numbers 
If there is a set of grouping symbol inside another set of 
grouping symbol, t...
Addition and Subtraction of Signed Numbers 
If there is a set of grouping symbol inside another set of 
grouping symbol, t...
Addition and Subtraction of Signed Numbers 
Exercise A. Drop the parentheses and write the expressions in 
a simpler form,...
Addition and Subtraction of Signed Numbers 
C. Drop the parentheses after the arithmetic operations and 
write the express...
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1 s2 addition and subtraction of signed numbers

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1 s2 addition and subtraction of signed numbers

  1. 1. Addition and Subtraction of Signed Numbers
  2. 2. Addition and Subtraction of Signed Numbers Addition of Signed Numbers
  3. 3. Addition and Subtraction of Signed Numbers Addition of Signed Numbers Adding signed numbers is the same as combining the numbers.
  4. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 19. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6
  20. 20. Addition and Subtraction of Signed Numbers e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s = 5 + 4 – 3 – 8 + 4 – 6
  21. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 34. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)
  35. 35. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4
  36. 36. Addition and Subtraction of Signed Numbers Example B. Remove parentheses then combine. a. 5 – (+4)  remove “( )”, change to opposite = 5 – 4 = 1
  37. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 51. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 )
  52. 52. Addition and Subtraction of Signed Numbers b. 2  (–4) – (–8) – (5)  (–9 ) remove the ( )’s = 2 – 4 + 8 – 5 – 9
  53. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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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