The document discusses order of operations and how to correctly evaluate mathematical expressions. It provides examples of evaluating expressions involving multiplication, division, addition, subtraction, exponents, and grouping symbols. The order of operations is: 1) operations within grouping symbols from innermost to outermost, 2) multiplication and division from left to right, 3) addition and subtraction from left to right. Examples are worked through step-by-step to demonstrate applying the order of operations rules.

1. Order of Operations

2. If we have two $5-bill and two $10-bills,
Order of Operations

3. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars.
Order of Operations

4. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars. To get the correct answer 30,
we multiply the 2 and the 5 and multiply the 2 and the10 first,
Order of Operations

5. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars. To get the correct answer 30,
we multiply the 2 and the 5 and multiply the 2 and the10 first,
then we add the products 10 and 20.
Order of Operations

6. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars. To get the correct answer 30,
we multiply the 2 and the 5 and multiply the 2 and the10 first,
then we add the products 10 and 20.
If I have three $10-bills and you have four $10-bills,
Order of Operations

7. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars. To get the correct answer 30,
we multiply the 2 and the 5 and multiply the 2 and the10 first,
then we add the products 10 and 20.
If I have three $10-bills and you have four $10-bills, we have
3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $.
Order of Operations

8. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars. To get the correct answer 30,
we multiply the 2 and the 5 and multiply the 2 and the10 first,
then we add the products 10 and 20.
If I have three $10-bills and you have four $10-bills, we have
3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $.
In this case, we group the 3 + 4 in the “( )” to indicate that we
are to add them first,
Order of Operations

9. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars. To get the correct answer 30,
we multiply the 2 and the 5 and multiply the 2 and the10 first,
then we add the products 10 and 20.
If I have three $10-bills and you have four $10-bills, we have
3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $.
In this case, we group the 3 + 4 in the “( )” to indicate that we
are to add them first, then multiply the sum to 10.
Order of Operations

10. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars. To get the correct answer 30,
we multiply the 2 and the 5 and multiply the 2 and the10 first,
then we add the products 10 and 20.
If I have three $10-bills and you have four $10-bills, we have
3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $.
In this case, we group the 3 + 4 in the “( )” to indicate that we
are to add them first, then multiply the sum to 10.
Order of Operations
This motivates us to set the rules for the order of operations.

11. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars. To get the correct answer 30,
we multiply the 2 and the 5 and multiply the 2 and the10 first,
then we add the products 10 and 20.
If I have three $10-bills and you have four $10-bills, we have
3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $.
In this case, we group the 3 + 4 in the “( )” to indicate that we
are to add them first, then multiply the sum to 10.
Order of Operations
Order of Operations (excluding raising power)
This motivates us to set the rules for the order of operations.

12. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars. To get the correct answer 30,
we multiply the 2 and the 5 and multiply the 2 and the10 first,
then we add the products 10 and 20.
If I have three $10-bills and you have four $10-bills, we have
3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $.
In this case, we group the 3 + 4 in the “( )” to indicate that we
are to add them first, then multiply the sum to 10.
Order of Operations
Order of Operations (excluding raising power)
Given an arithmetic expression, we perform the operations in
the following order .
This motivates us to set the rules for the order of operations.

13. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars. To get the correct answer 30,
we multiply the 2 and the 5 and multiply the 2 and the10 first,
then we add the products 10 and 20.
If I have three $10-bills and you have four $10-bills, we have
3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $.
In this case, we group the 3 + 4 in the “( )” to indicate that we
are to add them first, then multiply the sum to 10.
Order of Operations
Order of Operations (excluding raising power)
Given an arithmetic expression, we perform the operations in
the following order .
1st . Do the operations within grouping symbols, starting with
the innermost grouping symbol.
This motivates us to set the rules for the order of operations.

14. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars. To get the correct answer 30,
we multiply the 2 and the 5 and multiply the 2 and the10 first,
then we add the products 10 and 20.
If I have three $10-bills and you have four $10-bills, we have
3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $.
In this case, we group the 3 + 4 in the “( )” to indicate that we
are to add them first, then multiply the sum to 10.
Order of Operations
Order of Operations (excluding raising power)
Given an arithmetic expression, we perform the operations in
the following order .
1st . Do the operations within grouping symbols, starting with
the innermost grouping symbol.
2nd. Do multiplications and divisions (from left to right).
This motivates us to set the rules for the order of operations.

15. If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars. To get the correct answer 30,
we multiply the 2 and the 5 and multiply the 2 and the10 first,
then we add the products 10 and 20.
If I have three $10-bills and you have four $10-bills, we have
3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $.
In this case, we group the 3 + 4 in the “( )” to indicate that we
are to add them first, then multiply the sum to 10.
Order of Operations
Order of Operations (excluding raising power)
Given an arithmetic expression, we perform the operations in
the following order .
1st . Do the operations within grouping symbols, starting with
the innermost grouping symbol.
2nd. Do multiplications and divisions (from left to right).
3rd. Do additions and subtractions (from left to right).
This motivates us to set the rules for the order of operations.

16. Example A.
a. 4(–8) + 3(5)
Order of Operations

17. Example A.
a. 4(–8) + 3(5)
Order of Operations

18. Example A.
a. 4(–8) + 3(5)
= –32 + 15
Order of Operations

19. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
Order of Operations

20. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
Order of Operations
b. 4 + 3(5 + 2)

21. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
Order of Operations
b. 4 + 3(5 + 2)

22. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)

23. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21

24. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25

25. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25

26. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25

27. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25

28. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25

29. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
= 9 – 2[7 – 21]
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25

30. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
= 9 – 2[7 – 21]
= 9 – 2[ –14 ]
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25

31. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
= 9 – 2[7 – 21]
= 9 – 2[ –14 ]
= 9 + 28
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25

32. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
= 9 – 2[7 – 21]
= 9 – 2[ –14 ]
= 9 + 28
= 37
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25

33. Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
= 9 – 2[7 – 21]
= 9 – 2[ –14 ]
= 9 + 28
= 37
(Don’t perform “4 + 3” or “9 – 2” in the above problems!!)
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25

34. Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations

35. Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15

36. Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself.

37. Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power

38. Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.

39. Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
The base is the quantity immediately beneath the exponent,

40. Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
The base is the quantity immediately beneath the exponent,
hence 2b3 means 2*b3

41. Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
The base is the quantity immediately beneath the exponent,
hence 2b3 means 2*b3 = 2*b*b*b.

42. Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
The base is the quantity immediately beneath the exponent,
hence 2b3 means 2*b3 = 2*b*b*b.
If we want multiply 2b to itself three times, i.e. 2b to the third
power,

43. Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
The base is the quantity immediately beneath the exponent,
hence 2b3 means 2*b3 = 2*b*b*b.
If we want multiply 2b to itself three times, i.e. 2b to the third
power, we write it as (2b)3

44. Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
The base is the quantity immediately beneath the exponent,
hence 2b3 means 2*b3 = 2*b*b*b.
If we want multiply 2b to itself three times, i.e. 2b to the third
power, we write it as (2b)3 which is (2b)*(2b)*(2b) =8b3.

45. Order of Operations
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.

46. Order of Operations
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).

47. Order of Operations
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3)

48. Order of Operations
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

49. Order of Operations
b. Expand – 32
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

50. Order of Operations
b. Expand – 32
The base of the 2nd power is 3.
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

51. Order of Operations
b. Expand – 32
The base of the 2nd power is 3.
Hence – 32 means – (3*3)
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

52. Order of Operations
b. Expand – 32
The base of the 2nd power is 3.
Hence – 32 means – (3*3) = – 9
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

53. c. Expand (3*2)2 and simplify the answer.
Order of Operations
b. Expand – 32
The base of the 2nd power is 3.
Hence – 32 means – (3*3) = – 9
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

54. c. Expand (3*2)2 and simplify the answer.
The base for the 2nd power is (3*2).
Order of Operations
b. Expand – 32
The base of the 2nd power is 3.
Hence – 32 means – (3*3) = – 9
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

55. c. Expand (3*2)2 and simplify the answer.
The base for the 2nd power is (3*2).
Hence(3*2)2 is (3*2)(3*2)
Order of Operations
b. Expand – 32
The base of the 2nd power is 3.
Hence – 32 means – (3*3) = – 9
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

56. c. Expand (3*2)2 and simplify the answer.
The base for the 2nd power is (3*2).
Hence(3*2)2 is (3*2)(3*2) = (6)(6) = 36
Order of Operations
b. Expand – 32
The base of the 2nd power is 3.
Hence – 32 means – (3*3) = – 9
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

57. c. Expand (3*2)2 and simplify the answer.
The base for the 2nd power is (3*2).
Hence(3*2)2 is (3*2)(3*2) = (6)(6) = 36
d. Expand 3*22 and simplify the answer.
Order of Operations
b. Expand – 32
The base of the 2nd power is 3.
Hence – 32 means – (3*3) = – 9
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

58. c. Expand (3*2)2 and simplify the answer.
The base for the 2nd power is (3*2).
Hence(3*2)2 is (3*2)(3*2) = (6)(6) = 36
d. Expand 3*22 and simplify the answer.
The base for the 2nd power is 2.
Order of Operations
b. Expand – 32
The base of the 2nd power is 3.
Hence – 32 means – (3*3) = – 9
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

59. c. Expand (3*2)2 and simplify the answer.
The base for the 2nd power is (3*2).
Hence(3*2)2 is (3*2)(3*2) = (6)(6) = 36
d. Expand 3*22 and simplify the answer.
The base for the 2nd power is 2.
Hence 3*22 means 3*2*2
Order of Operations
b. Expand – 32
The base of the 2nd power is 3.
Hence – 32 means – (3*3) = – 9
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

60. c. Expand (3*2)2 and simplify the answer.
The base for the 2nd power is (3*2).
Hence(3*2)2 is (3*2)(3*2) = (6)(6) = 36
d. Expand 3*22 and simplify the answer.
The base for the 2nd power is 2.
Hence 3*22 means 3*2*2 = 12
Order of Operations
b. Expand – 32
The base of the 2nd power is 3.
Hence – 32 means – (3*3) = – 9
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
Hence (–3)2 is (–3)(–3) = 9

61. Order of Operations
e. Expand (–3y)3 and simplify the answer.

62. Order of Operations
e. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y)

63. Order of Operations
e. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y) (the product of three negatives number is negative)

64. Order of Operations
e. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y) (the product of three negatives number is negative)
= –(3)(3)(3)(y)(y)(y)

65. Order of Operations
e. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y) (the product of three negatives number is negative)
= –(3)(3)(3)(y)(y)(y)
= –27y3

66. Order of Operations
e. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y) (the product of three negatives number is negative)
= –(3)(3)(3)(y)(y)(y)
= –27y3
From part b above, we see that the power is to be carried out
before multiplication.

67. Order of Operations
e. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y) (the product of three negatives number is negative)
= –(3)(3)(3)(y)(y)(y)
= –27y3
From part b above, we see that the power is to be carried out
before multiplication. Below is the complete rules of order of
operations.

68. Order of Operations
e. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y) (the product of three negatives number is negative)
= –(3)(3)(3)(y)(y)(y)
= –27y3
Order of Operations (PEMDAS)
From part b above, we see that the power is to be carried out
before multiplication. Below is the complete rules of order of
operations.

69. Order of Operations
e. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y) (the product of three negatives number is negative)
= –(3)(3)(3)(y)(y)(y)
= –27y3
Order of Operations (PEMDAS)
1st. (Parenthesis) Do the operations within grouping symbols,
starting with the innermost one.
From part b above, we see that the power is to be carried out
before multiplication. Below is the complete rules of order of
operations.

70. Order of Operations
e. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y) (the product of three negatives number is negative)
= –(3)(3)(3)(y)(y)(y)
= –27y3
Order of Operations (PEMDAS)
1st. (Parenthesis) Do the operations within grouping symbols,
starting with the innermost one.
2nd. (Exponents) Do the exponentiation
From part b above, we see that the power is to be carried out
before multiplication. Below is the complete rules of order of
operations.

71. Order of Operations
e. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y) (the product of three negatives number is negative)
= –(3)(3)(3)(y)(y)(y)
= –27y3
Order of Operations (PEMDAS)
1st. (Parenthesis) Do the operations within grouping symbols,
starting with the innermost one.
2nd. (Exponents) Do the exponentiation
3rd. (Multiplication and Division) Do multiplications and
divisions in order from left to right.
From part b above, we see that the power is to be carried out
before multiplication. Below is the complete rules of order of
operations.

72. Order of Operations
e. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y) (the product of three negatives number is negative)
= –(3)(3)(3)(y)(y)(y)
= –27y3
Order of Operations (PEMDAS)
1st. (Parenthesis) Do the operations within grouping symbols,
starting with the innermost one.
2nd. (Exponents) Do the exponentiation
3rd. (Multiplication and Division) Do multiplications and
divisions in order from left to right.
4th. (Addition and Subtraction) Do additions and
subtractions in order from left to right.
From part b above, we see that the power is to be carried out
before multiplication. Below is the complete rules of order of
operations.

73. Example C. Order of Operations
a. 52 – 32
Order of Operations

74. Example C. Order of Operations
a. 52 – 32
= 25 – 9
Order of Operations

75. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
Order of Operations

76. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
Order of Operations

77. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
Order of Operations

78. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
= – 4
Order of Operations

79. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
= – 4
c. –2*32 + (2*3)2
Order of Operations

80. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
= – 4
c. –2*32 + (2*3)2
= –2*9 + (6)2
Order of Operations

81. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
= – 4
c. –2*32 + (2*3)2
= –2*9 + (6)2
= –18 + 36
Order of Operations

82. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
= – 4
c. –2*32 + (2*3)2
= –2*9 + (6)2
= –18 + 36
= 18
Order of Operations

83. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
= – 4
c. –2*32 + (2*3)2
= –2*9 + (6)2
= –18 + 36
= 18
d. –32 – 5(3 – 6)2
Order of Operations

84. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
= – 4
c. –2*32 + (2*3)2
= –2*9 + (6)2
= –18 + 36
= 18
d. –32 – 5(3 – 6)2
= –9 – 5(–3)2
Order of Operations

85. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
= – 4
c. –2*32 + (2*3)2
= –2*9 + (6)2
= –18 + 36
= 18
d. –32 – 5(3 – 6)2
= –9 – 5(–3)2
= –9 – 5(9)
Order of Operations

86. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
= – 4
c. –2*32 + (2*3)2
= –2*9 + (6)2
= –18 + 36
= 18
d. –32 – 5(3 – 6)2
= –9 – 5(–3)2
= –9 – 5(9)
= –9 – 45
Order of Operations

87. Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
= – 4
c. –2*32 + (2*3)2
= –2*9 + (6)2
= –18 + 36
= 18
d. –32 – 5(3 – 6)2
= –9 – 5(–3)2
= –9 – 5(9)
= –9 – 45 = –54
Order of Operations

88. Make sure that you interpret the operations correctly.
Exercise A. Calculate the following expressions.
Order of Operations
7. 1 + 2(3) 8. 4 – 5(6) 9. 7 – 8(–9)
1. 3(–3) 2. (3) – 3 3. 3 – 3(3) 4. 3(–3) + 3
5. +3(–3)(+3) 6. 3 + (–3)(+3)
B.Make sure that you don’t do the ± too early.
10. 1 + 2(3 – 4) 11. 5 – 6(7 – 8) 12. (4 – 3)2 + 1
13. [1 – 2(3 – 4)] – 2 14. 6 + [5 + 6(7 – 8)](+5)
15. 1 + 2[1 – 2(3 + 4)] 16. 5 – 6[5 – 6(7 – 8)]
17. 1 – 2[1 – 2(3 – 4)] 18. 5 + 6[5 + 6(7 – 8)]
19. (1 + 2)[1 – 2(3 + 4)] 20. (5 – 6)[5 – 6(7 – 8)]
C.Make sure that you apply the powers to the correct bases.
23. (–2)2 and –22 24 (–2)3 and –23 25. (–2)4 and –24
26. (–2)5 and –25 27. 2*32 28. (2*3)2
21. 1 – 2(–3)(–4) 22. (–5)(–6) – (–7)(–8)

89. Order of Operations
D.Make sure that you apply the powers to the correct bases.
29. (2)2 – 3(2) + 1 30. 3(–2)2 + 4(–2) – 1
31. –2(3)2 + 3(3) – 5 32. –3(–1)2 + 4(–1) – 4
33. 3(–2)3 – 4(–2)2 – 1 34. (2)3 – 3(2)2 + 4(2) – 1
35. 2(–1)3 – 3(–1)2 + 4(–1) – 1 36. –3(–2)3 – 4(–2)2 – 4(–2) – 3
37. (6 + 3)2 38. 62 + 32 39. (–4 + 2)3 40. (–4)3 + (2)3
E. Calculate.
41. 72 – 42 42. (7 + 4)(7 – 4 )
43. (– 5)2 – 32 44. (–5 + 3)(–5 – 3 )
45. 53 – 33 46. (5 – 3) (52 + 5*3 + 32)
47. 43 + 23 48. (4 + 2)(42 – 4*2 + 22)
7 – (–5)
5 – 353.
8 – 2
–6 – (–2)
54.
49. (3)2 – 4(2)(3) 50. (3)2 – 4(1)(– 4)
51. (–3)2 – 4(–2)(3) 52. (–2)2 – 4(–1)(– 4)
(–4) – (–8)
(–5) – 3
55.
(–7) – (–2)
(–3) – (–6)
56.