signed numbers addition and subtraction

1. Signed Numbers

2. We track the “directions” of measurements by giving them
positive (+) or negative (-) signs.
Signed Numbers

3. Signed Numbers
We track the “directions” of measurements by giving them
positive (+) or negative (-) sign. Signed measurements
represent amounts of increases versus decreases,

4. Signed Numbers
We track the “directions” of measurements by giving them
positive (+) or negative (-) sign. Signed measurements
represent amounts of increases versus decreases, surpluses
versus deficiencies,

5. Signed Numbers
We track the “directions” of measurements by giving them
positive (+) or negative (-) sign. Signed measurements
represent amounts of increases versus decreases, surpluses
versus deficiencies, credits versus debits and so on.

6. Signed Numbers
We track the “directions” of measurements by giving them
positive (+) or negative (-) sign. Signed measurements
represent amounts of increases versus decreases, surpluses
versus deficiencies, credits versus debits and so on. Numbers
with signs are called signed numbers.

7. Signed Numbers
Example A:
a. We deposited $400 into a bank account then withdrew $350
from the account, write the transactions using signed numbers.
How much is left in the account?
We track the “directions” of measurements by giving them
positive (+) or negative (-) sign. Signed measurements
represent amounts of increases versus decreases, surpluses
versus deficiencies, credits versus debits and so on. Numbers
with signs are called signed numbers.

8. We track the “directions” of measurements by giving them
positive (+) or negative (-) sign. Signed measurements
represent amounts of increases versus decreases, surpluses
versus deficiencies, credits versus debits and so on. Numbers
with signs are called signed numbers.
Signed Numbers
Example A:
a. We deposited $400 into a bank account then withdrew $350
from the account, write the transactions using signed numbers.
How much is left in the account?
We use “+” for deposit or having surplus in the account

9. Signed Numbers
Example A:
a. We deposited $400 into a bank account then withdrew $350
from the account, write the transactions using signed numbers.
How much is left in the account?
We use “+” for deposit or having surplus in the account
and “–” for withdraw or debit from the account,
We track the “directions” of measurements by giving them
positive (+) or negative (-) sign. Signed measurements
represent amounts of increases versus decreases, surpluses
versus deficiencies, credits versus debits and so on. Numbers
with signs are called signed numbers.

10. Signed Numbers
Example A:
a. We deposited $400 into a bank account then withdrew $350
from the account, write the transactions using signed numbers.
How much is left in the account?
We use “+” for deposit or having surplus in the account
and “–” for withdraw or debit from the account, then the
transactions may be listed as: +400, –350. (In this section we
will use red color for negative numbers for emphasis.)
We track the “directions” of measurements by giving them
positive (+) or negative (-) sign. Signed measurements
represent amounts of increases versus decreases, surpluses
versus deficiencies, credits versus debits and so on. Numbers
with signs are called signed numbers.

11. Signed Numbers
Example A:
a. We deposited $400 into a bank account then withdrew $350
from the account, write the transactions using signed numbers.
How much is left in the account?
We use “+” for deposit or having surplus in the account
and “–” for withdraw or debit from the account, then the
transactions may be listed as: +400, –350. (In this section we
will use red color for negative numbers for emphasis.)
The amount left in the account is $50.
We track the “directions” of measurements by giving them
positive (+) or negative (-) sign. Signed measurements
represent amounts of increases versus decreases, surpluses
versus deficiencies, credits versus debits and so on. Numbers
with signs are called signed numbers.

12. Signed Numbers
Example A:
a. We deposited $400 into a bank account then withdrew $350
from the account, write the transactions using signed numbers.
How much is left in the account?
We use “+” for deposit or having surplus in the account
and “–” for withdraw or debit from the account, then the
transactions may be listed as: +400, –350. (In this section we
will use red color for negative numbers for emphasis.)
The amount left in the account is $50. This is a surplus so
its +50.
We track the “directions” of measurements by giving them
positive (+) or negative (-) sign. Signed measurements
represent amounts of increases versus decreases, surpluses
versus deficiencies, credits versus debits and so on. Numbers
with signs are called signed numbers.

13. Signed Numbers
Example A:
a. We deposited $400 into a bank account then withdrew $350
from the account, write the transactions using signed numbers.
How much is left in the account?
We use “+” for deposit or having surplus in the account
and “–” for withdraw or debit from the account, then the
transactions may be listed as: +400, –350. (In this section we
will use red color for negative numbers for emphasis.)
The amount left in the account is $50. This is a surplus so
its +50. We write the entire transactions as +400 – 350 = +50.
We track the “directions” of measurements by giving them
positive (+) or negative (-) sign. Signed measurements
represent amounts of increases versus decreases, surpluses
versus deficiencies, credits versus debits and so on. Numbers
with signs are called signed numbers.

14. Signed Numbers
b. We deposited $400 into the account then withdrew $600
from the account, write the transactions using signed numbers.
How much is left in the account?

15. Signed Numbers
b. We deposited $400 into the account then withdrew $600
from the account, write the transactions using signed numbers.
How much is left in the account?
The transactions may be listed as: +400, –600.

16. Signed Numbers
b. We deposited $400 into the account then withdrew $600
from the account, write the transactions using signed numbers.
How much is left in the account?
The transactions may be listed as: +400, –600.
The account is short by $200.

17. Signed Numbers
b. We deposited $400 into the account then withdrew $600
from the account, write the transactions using signed numbers.
How much is left in the account?
The transactions may be listed as: +400, –600.
The account is short by $200. This is a deficiency so its –200.

18. Signed Numbers
b. We deposited $400 into the account then withdrew $600
from the account, write the transactions using signed numbers.
How much is left in the account?
The transactions may be listed as: +400, –600.
The account is short by $200. This is a deficiency so its –200.
We write the entire transactions as +400 – 600 = –200

19. Signed Numbers
b. We deposited $400 into the account then withdrew $600
from the account, write the transactions using signed numbers.
How much is left in the account?
The transactions may be listed as: +400, –600.
The account is short by $200. This is a deficiency so its –200.
We write the entire transactions as +400 – 600 = –200
c. We deposited $400 in a bank account, later deposited
another $200, then withdrew $350, then deposited $250, then
withdrew $600, make a list of the transactions using signed
numbers. How much is left?

20. Signed Numbers
b. We deposited $400 into the account then withdrew $600
from the account, write the transactions using signed numbers.
How much is left in the account?
The transactions may be listed as: +400, –600.
The account is short by $200. This is a deficiency so its –200.
We write the entire transactions as +400 – 600 = –200
c. We deposited $400 in a bank account, later deposited
another $200, then withdrew $350, then deposited $250, then
withdrew $600, make a list of the transactions using signed
numbers. How much is left?
The transactions are listed as +400, +200, –350, +250, –600.

21. Signed Numbers
b. We deposited $400 into the account then withdrew $600
from the account, write the transactions using signed numbers.
How much is left in the account?
The transactions may be listed as: +400, –600.
The account is short by $200. This is a deficiency so its –200.
We write the entire transactions as +400 – 600 = –200
c. We deposited $400 in a bank account, later deposited
another $200, then withdrew $350, then deposited $250, then
withdrew $600, make a list of the transactions using signed
numbers. How much is left?
The transactions are listed as +400, +200, –350, +250, –600.
To find the final balance in the account, we note that the total
of the deposits is +850

22. Signed Numbers
b. We deposited $400 into the account then withdrew $600
from the account, write the transactions using signed numbers.
How much is left in the account?
The transactions may be listed as: +400, –600.
The account is short by $200. This is a deficiency so its –200.
We write the entire transactions as +400 – 600 = –200
c. We deposited $400 in a bank account, later deposited
another $200, then withdrew $350, then deposited $250, then
withdrew $600, make a list of the transactions using signed
numbers. How much is left?
The transactions are listed as +400, +200, –350, +250, –600.
To find the final balance in the account, we note that the total
of the deposits is +850 and the total of the withdrawals is –950,

23. Signed Numbers
b. We deposited $400 into the account then withdrew $600
from the account, write the transactions using signed numbers.
How much is left in the account?
The transactions may be listed as: +400, –600.
The account is short by $200. This is a deficiency so its –200.
We write the entire transactions as +400 – 600 = –200
c. We deposited $400 in a bank account, later deposited
another $200, then withdrew $350, then deposited $250, then
withdrew $600, make a list of the transactions using signed
numbers. How much is left?
The transactions are listed as +400, +200, –350, +250, –600.
To find the final balance in the account, we note that the total
of the deposits is +850 and the total of the withdrawals is –950,
so the account is short of $100, or there is “–100” left in the
account.

24. Signed Numbers
b. We deposited $400 into the account then withdrew $600
from the account, write the transactions using signed numbers.
How much is left in the account?
The transactions may be listed as: +400, –600.
The account is short by $200. This is a deficiency so its –200.
We write the entire transactions as +400 – 600 = –200
c. We deposited $400 in a bank account, later deposited
another $200, then withdrew $350, then deposited $250, then
withdrew $600, make a list of the transactions using signed
numbers. How much is left?
The transactions are listed as +400, +200, –350, +250, –600.
To find the final balance in the account, we note that the total
of the deposits is +850 and the total of the withdrawals is –950,
so the account is short of $100, or there is “–100” left in the
account. We write these transactions as
+400 + 200 – 350 + 250 – 600 = –100.

25. Signed Numbers
The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.

26. Signed Numbers
Example B:
+100 + 200 = +300,
The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.

27. Signed Numbers
Example B:
+100 + 200 = +300, –100 – 200 = –300
The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.

28. Signed Numbers
Example B:
+100 + 200 = +300, –100 – 200 = –300
+500 – 300 = +200,
The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.

29. Signed Numbers
Example B:
+100 + 200 = +300, –100 – 200 = –300
+500 – 300 = +200, –500 + 300 = –200
The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.

30. The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.
Signed Numbers
Example B:
+100 + 200 = +300, –100 – 200 = –300
+500 – 300 = +200, –500 + 300 = –200
A number written without a sign is treated as a positive
number.

31. Signed Numbers
Example B:
+100 + 200 = +300, –100 – 200 = –300
+500 – 300 = +200, –500 + 300 = –200
A number written without a sign is treated as a positive
number. Therefore, 100 + 200 is the same as +100 + 200
and both combined to 300.
The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.

32. Signed Numbers
Example B:
+100 + 200 = +300, –100 – 200 = –300
+500 – 300 = +200, –500 + 300 = –200
A number written without a sign is treated as a positive
number. Therefore, 100 + 200 is the same as +100 + 200
and both combined to 300.
In order to state precisely the rules for combining signed
numbers, we introduce the notion of absolute values.
The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.

33. Signed Numbers
Example B:
+100 + 200 = +300, –100 – 200 = –300
+500 – 300 = +200, –500 + 300 = –200
A number written without a sign is treated as a positive
number. Therefore, 100 + 200 is the same as +100 + 200
and both combined to 300.
In order to state precisely the rules for combining signed
numbers, we introduce the notion of absolute values.
In example A of the bank account, if we are only interested in
the amount of the transactions but not the type of transactions,
this amount is called the absolute value.
The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.

34. Signed Numbers
Example B:
+100 + 200 = +300, –100 – 200 = –300
+500 – 300 = +200, –500 + 300 = –200
A number written without a sign is treated as a positive
number. Therefore, 100 + 200 is the same as +100 + 200
and both combined to 300.
In order to state precisely the rules for combining signed
numbers, we introduce the notion of absolute values.
In example A of the bank account, if we are only interested in
the amount of the transactions but not the type of transactions,
this amount is called the absolute value.
The absolute value of a number x is written as |x|.
The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.

35. Signed Numbers
Example B:
+100 + 200 = +300, –100 – 200 = –300
+500 – 300 = +200, –500 + 300 = –200
A number written without a sign is treated as a positive
number. Therefore, 100 + 200 is the same as +100 + 200
and both combined to 300.
In order to state precisely the rules for combining signed
numbers, we introduce the notion of absolute values.
In example A of the bank account, if we are only interested in
the amount of the transactions but not the type of transactions,
this amount is called the absolute value.
The absolute value of a number x is written as |x|.
Hence, |500| = 500,
The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.

36. Signed Numbers
Example B:
+100 + 200 = +300, –100 – 200 = –300
+500 – 300 = +200, –500 + 300 = –200
A number written without a sign is treated as a positive
number. Therefore, 100 + 200 is the same as +100 + 200
and both combined to 300.
In order to state precisely the rules for combining signed
numbers, we introduce the notion of absolute values.
In example A of the bank account, if we are only interested in
the amount of the transactions but not the type of transactions,
this amount is called the absolute value.
The absolute value of a number x is written as |x|.
Hence, |500| = 500, |-350| = 350,
The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.

37. Signed Numbers
Example B:
+100 + 200 = +300, –100 – 200 = –300
+500 – 300 = +200, –500 + 300 = –200
A number written without a sign is treated as a positive
number. Therefore, 100 + 200 is the same as +100 + 200
and both combined to 300.
In order to state precisely the rules for combining signed
numbers, we introduce the notion of absolute values.
In example A of the bank account, if we are only interested in
the amount of the transactions but not the type of transactions,
this amount is called the absolute value.
The absolute value of a number x is written as |x|.
Hence, |500| = 500, |-350| = 350, |-600| = 600, etc..
The above operation of totaling two or more signed numbers
into a single signed number is called the combining operation.

38. Signed Numbers
Rules for Combining Signed Numbers

39. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign,

40. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.

41. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300,

42. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300

43. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300
II. To combine two numbers of different signs, keep the sign
of the number with larger absolute value,

44. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300
II. To combine two numbers of different signs, keep the sign
of the number with larger absolute value, take the difference
of the absolute values of the numbers.

45. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300
II. To combine two numbers of different signs, keep the sign
of the number with larger absolute value, take the difference
of the absolute values of the numbers.
+500 – 300 = +200,

46. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300
II. To combine two numbers of different signs, keep the sign
of the number with larger absolute value, take the difference
of the absolute values of the numbers.
+500 – 300 = +200, –500 + 300 = –200

47. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300
II. To combine two numbers of different signs, keep the sign
of the number with larger absolute value, take the difference
of the absolute values of the numbers.
+500 – 300 = +200, –500 + 300 = –200
There are different ways to combine multiple signed numbers,
we may combine them from left to right.

48. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300
II. To combine two numbers of different signs, keep the sign
of the number with larger absolute value, take the difference
of the absolute values of the numbers.
+500 – 300 = +200, –500 + 300 = –200
Example C: 8 – 9 + 11
There are different ways to combine multiple signed numbers,
we may combine them from left to right.

49. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300
II. To combine two numbers of different signs, keep the sign
of the number with larger absolute value, take the difference
of the absolute values of the numbers.
+500 – 300 = +200, –500 + 300 = –200
Example C: 8 – 9 + 11 = –1 + 11
There are different ways to combine multiple signed numbers,
we may combine them from left to right.

50. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300
II. To combine two numbers of different signs, keep the sign
of the number with larger absolute value, take the difference
of the absolute values of the numbers.
+500 – 300 = +200, –500 + 300 = –200
Example C: 8 – 9 + 11 = –1 + 11 = 10
There are different ways to combine multiple signed numbers,
we may combine them from left to right.

51. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300
II. To combine two numbers of different signs, keep the sign
of the number with larger absolute value, take the difference
of the absolute values of the numbers.
+500 – 300 = +200, –500 + 300 = –200
Example C: 8 – 9 + 11 = –1 + 11 = 10
To combine many numbers, an alternative way is to do it as in
example A of the bank transactions.
There are different ways to combine multiple signed numbers,
we may combine them from left to right.

52. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300
II. To combine two numbers of different signs, keep the sign
of the number with larger absolute value, take the difference
of the absolute values of the numbers.
+500 – 300 = +200, –500 + 300 = –200
Example C: 8 – 9 + 11 = –1 + 11 = 10
To combine many numbers, an alternative way is to do it as in
example A of the bank transactions. That is, we combined all
the positive ones (deposits) first,
There are different ways to combine multiple signed numbers,
we may combine them from left to right.

53. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300
II. To combine two numbers of different signs, keep the sign
of the number with larger absolute value, take the difference
of the absolute values of the numbers.
+500 – 300 = +200, –500 + 300 = –200
Example C: 8 – 9 + 11 = –1 + 11 = 10
To combine many numbers, an alternative way is to do it as in
example A of the bank transactions. That is, we combined all
the positive ones (deposits) first, then combine all the negative
ones (withdrawals),
There are different ways to combine multiple signed numbers,
we may combine them from left to right.

54. Signed Numbers
Rules for Combining Signed Numbers
I. To combine two or more numbers of the same signs, keep
the sign, take the sum of the absolute values of the numbers.
+100 + 200 = +300, –100 – 200 = –300
II. To combine two numbers of different signs, keep the sign
of the number with larger absolute value, take the difference
of the absolute values of the numbers.
+500 – 300 = +200, –500 + 300 = –200
Example C: 8 – 9 + 11 = –1 + 11 = 10
To combine many numbers, an alternative way is to do it as in
example A of the bank transactions. That is, we combined all
the positive ones (deposits) first, then combine all the negative
ones (withdrawals), then combine the two results.
There are different ways to combine multiple signed numbers,
we may combine them from left to right.

55. * This way is easier if there are many numbers to combine.
Signed Numbers

56. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers

57. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11

58. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front

59. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
= 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11

60. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
= 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11

61. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
= 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11
= 36

62. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
= 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11
= 36 – 61 = –25

63. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
= 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11
= 36 – 61 = –25
Another method for combining many signed numbers is to do
two in groups of two’s.

64. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
= 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11
= 36 – 61 = –25
Another method for combining many signed numbers is to do
two in groups of two’s. Hence
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs

65. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
= 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11
= 36 – 61 = –25
Another method for combining many signed numbers is to do
two in groups of two’s. Hence
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs
= –4

66. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
= 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11
= 36 – 61 = –25
Another method for combining many signed numbers is to do
two in groups of two’s. Hence
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs
= –4 +2

67. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
= 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11
= 36 – 61 = –25
Another method for combining many signed numbers is to do
two in groups of two’s. Hence
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs
= –4 +2 –4 –19

68. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
= 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11
= 36 – 61 = –25
Another method for combining many signed numbers is to do
two in groups of two’s. Hence
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs
= –4 +2 –4 –19 in pairs again

69. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
= 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11
= 36 – 61 = –25
Another method for combining many signed numbers is to do
two in groups of two’s. Hence
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs
= –4 +2 –4 –19 in pairs again
= –2 – 23 = –25

70. * This way is easier if there are many numbers to combine.
* When doing this, it helps to move all the positive ones to the
front and the negative ones to the back.
Signed Numbers
Example D:
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
= 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11
= 36 – 61 = –25
Another method for combining many signed numbers is to do
two in groups of two’s. Hence
7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs
= –4 +2 –4 –19 in pairs again
= –2 – 23 = –25
(Two Method Strategy) Use these two methods to cross check
the + or – of multiple signed numbers.

71. Addition and Subtraction of Signed Numbers

72. Addition of Signed Numbers
Addition and Subtraction of Signed Numbers

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

74. 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

75. 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

76. 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

77. 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)

78. 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

79. 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

80. 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)

81. 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

82. 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

83. 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)

84. 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

85. 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

86. 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)

87. 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

88. 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

89. Addition and Subtraction of Signed Numbers
e. 5  (4) + (–3) + (–8) + 4 – 6

90. Addition and Subtraction of Signed Numbers
e. 5  (4) + (–3) + (–8) + 4 – 6 remove ( )’s
= 5 + 4 – 3 – 8 + 4 – 6

91. 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

92. 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

93. 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

94. 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

95. 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.

96. 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.

97. 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.

98. 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.

99. 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.

100. 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.

101. 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,

102. 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
opposite

103. 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) = a + b
opposite opposite

104. Addition and Subtraction of Signed Numbers
Example B. Remove parentheses then combine.
a. 5 – (+4)

105. Addition and Subtraction of Signed Numbers
Example B. Remove parentheses then combine.
a. 5 – (+4)  remove “( )”, change to opposite
= 5 – 4

106. Addition and Subtraction of Signed Numbers
Example B. Remove parentheses then combine.
a. 5 – (+4)  remove “( )”, change to opposite
= 5 – 4 = 1

107. 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)

108. 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

109. 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

110. 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)

111. 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

112. 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

113. 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:

114. 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

115. 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

116. 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)

117. 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

118. 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

119. 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

120. 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

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

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

123. 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

124. 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

125. 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

126. 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.

127. 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.

128. 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. Each set
encloses calculations that are to be done within the symbol.

129. 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. Each set
encloses calculations that are to be done within the symbol.
Example D.
a. –6 – (8 – 9)

130. 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. Each set
encloses calculations that are to be done within the symbol.
Example D.
a. –6 – (8 – 9) do the calculation inside the “( )”

131. 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. 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)

132. 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. 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

133. 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. 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

134. 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. 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

135. 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. 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

136. 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. 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

137. 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. 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

138. 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.

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

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

141. 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 set of grouping symbol inside another set of
grouping symbol, the inner set is to be calculated first.

142. 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 set of grouping symbol inside another set of
grouping symbol, the inner set is to be calculated first.

143. 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 set of grouping symbol inside another set of
grouping symbol, the inner set is to be calculated first.

144. 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 set of grouping symbol inside another set of
grouping symbol, the inner set is to be calculated first.

145. Exercise A. Combine
1. 2 + 3 2. 10 + 6 3. 34 + 21 + 4 + 17 4. –6 –2
5. –11 – 5 6. –14 –15 7. –26 –15 – 5 –14
8. –3 + 2 9. 5 –11 10. –14 + 15
11. 26 –15 12. 12 – 13 13. –23 +18
B. Combine by moving the positive numbers to the front first.
Combine the positive numbers, the negative numbers
separately then then combine the two results.
14. 23 – 18 +7 –12 15. –6 –2 + 10 + 6
16. –14 + 23 –15 – 3 +12 17. –26 + 15 –5 –14 + 9
18. 19 – 13 – 9 – 3 + 15 19. –6 + 19 – 15 + 5 – 9
20. – 4 + 7 – 23 + 8 + 17 – 8 + 6 + 9 – 22 – 2
21. Try to get the same answer for #20 by combining two
numbers at a time without separating the positive
numbers from the negative numbers.
Signed Numbers