LLEVADA’S ALGEBRA 1
Section 1.2
Order of Operations
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Order of Operations is the sequence of steps that must be taken to reduce a math expression to its simplest
form, or scale down an equation to find an answer. Not following the proper order will result in the
wrong answer. Understanding these rules is the key to success in algebra and beyond.
Example:
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STEPS:
1. First, simplify all expressions inside all parentheses. If there are parentheses inside the parentheses [or
brackets], work from the inside parentheses first, eliminating parentheses as you go along.
2. Next, do exponents and radicals (roots).
3. Then, do multiplication and division from left to right as they occur. Multiplication is noted with an ,
dot  2  3  , or parentheses, like in 3(4) = 12. Division is noted with a slash (/), fraction line (–), or 
4. Lastly, do addition and subtraction.
3 + 4  8 = 35
FIRST multiply 4  8, then add 3
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If you want to add first, place the addition in parenthesis: (3 + 4)  8 = 56
Add 3 and 4, then multiply by 8. Notice the different answers.
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Example:
7 + 2  5 (5 + 62) – 3  4
7 + 2  5 (5 + 36) – 3  4
7 + 2  5 (41) – 3  4
7 + 2  205 – 12
7 + 410 – 12 = 405
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Example:
9 + 48  [2 (4 + 23)] – 15   2
9 + 48  [2 (4 + 8)] – 15   2
9 + 48  [2 (12)] – 15   2
9 + 48  24 – 15   2
9 + 2 – 10 = 1
(exponent)
(parenthesis)
(multiplication)
(multiplication)
(add and subtract)
(exponent)
(parenthesis)
(parenthesis and bracket)
(divide and multiply)
(add and subtract)
Example:
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3[22 + 36  2 (10 – 16 ) + (7 – 22)]
3[22 + 36  2 (10 – 4) + (7 – 4)]
3[22 + 36  2 (6) + 3]
3[22 + 18(6) + 3]
3[22 + 108 + 3]
3[133] = 399
(root and exponent)
(parentheses)
(division)
(multiplication)
(addition)
(multiplication)
1.2 Order of Operations
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LLEVADA’S ALGEBRA 1
Practice:
Evaluate.
1. 7 + 8  2 – 9 + 8  2 – 6 3  1
2. 10 – 9  3 + 12 + 16  4 – 20 4  3
3. 12 (8 – 5)  9 + 11 – (5  4  2 – 3) + 2  8
37. 5 + 18  3 – 7 + 14  2 – 6 2  5
38. 28 – 5  1 + 10 + 18  6 – 10 2  2
39. 6[16 – (8 – 2)  3] + 12 – (6  5  15 – 2) + 5
4. 9 – (16 + 4  12)  [2 + 4 + (8 + 32  2)] + 21
5. 17 + 9  3 – 4 + 12  3 – 12 6  2
40.
41.
42.
43.
7. 20 (9 – 6)  10 + 12 – (6  5  3 – 4) + 3  9
7 + (10 + 6  14)  [4 + 17 + (10 + 22  4)] + 2
15 + 6  0 – 7 + 6  3 – 10 5  3
13 – 12  6 + 15 + 12  4 – 28 7  5
20 (4 – 1)  3 + 8 – (6  1  3 + 5) + 7  2
12.
13.
14.
15.
12 + (9 + 3  5)  [8 + 2 + (– 46 + 42  3)] + 2
17 + 6  0 – 12 + 4  2 + [9 3  3]
14 – 15  3 + 10 + 8  2 – 10 2  3
6 (9 – 3)  3 + 1 – (6  2  1 – 4) + 6  5
16. 5 – (7 + 8  6)  [4 – 19 + (6 + 22  5)] + 14
17. 27 + 9  3 – 2 +
36  1 – 16 4  2
18. 8 – 12  4 + 10 + 27  3 – 14 7  5
19. 5 (18 – 12)  3 + 15 – (7  5  5 – 4) + 6  4
18 – (22 + 3  21)  [7 – 1 + (4 + 52  3)] + 24
6 + 9  3 – 10 + 10  5 – 24 4  2
18 – 15  5 + 22 + 21  7 – 8 2  5
4 (9 – 3)  12 + 9 – (6  10  4 – 2) + 6  10
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20.
21.
22.
23.
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24. 24 – (18 + 6  5)  [3 + 2 + (7 + 62  1)] + 32
25. 9 + 13  3 – 5 + 18  6 – 6 3  21
26. 1 + 11  1 + 14 + 32  16 + 24 2  5
84 + 60 – (2  8  1 – 5)
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27. 8 (12 – 7)  5 +
10 – (12 + 6  9)  [– 76 + (9 + 52  4)] + 12
17 + 6  12 – 10 + 6  2 – 8 2  1
10 – 9  3 + 12 + 16  2 – 6 2  8
14 (9 – 2)  7 + 10 – (7  8  4 – 1) + 7  4
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28.
29.
30.
31.
44. 59 – (12 + 3  6)  [8 + 7 –
2
5  4 ] + 35  7
45. 3 + 5  4 – 7 + 12  6 – 8 4  2
46. 18 – 6  2 + 15 + 12  6 – 24 8  3
47. 15 (9 – 6)  5 + 13 – (6  3  9 + 4) + 6  1
48. 6 – (20 + 8  14)  [5 + 7 + (6 + 22  3)] + 35
49. 14 + 8  6 – 5 + 16  8 – 18 9  3
50. 79 –
25  5 + 17 + 16  8 – 36 12  6
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8.
9.
10.
11.
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64  2 + 11 + 15  3 – 21 3  2
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6. 9 –
7 + (12 + 3  6)  [5 + 6 + (7 + 22  3)] + 36
75 + 9  3 – 5 + 12  4 – 24 6  5
39 – 12  6 + 12 + 21  7 – 28 4  5
7 (8 – 5)  3 + 42 – (10  20  8 – 7) + 6  11
51. 2 (8 – 8)  15 + 16 – (7  6  2 – 5) + 4  7
52.
53.
54.
55.
3 + (12 + 3  8)  [5 + 9 + (6 + 42  1)] + 1 5
22 + 8  5 – 4 + 8  4 – 18 6  8
17 – 32  8 + 14 + 30  5 – 24 8  7
3 (8 – 3)  10 + 6 – (9  2  6 + 3) + 6  4
56.
57.
58.
59.
6 + (1 + 4  6)  [5 + 2 + (6 + 22  3)] + 4
33 + 3  5 – 15 + 18  6 + [12 4  5]
21 – 35  5 + 13 + 9  3 – 16 4  7
8 (8 – 6)  4 + 6 – (7  3  7 + 5) + 2  3
60. 5 + (8 + 8  6)  [7 – 5 + (3 + 12  2)] + 5
61. 26 + 7  4 – 13 +
81  3 – 20 2  3
62. 9 – 15  5 + 12 + 36  4 + 16 2  8
63. 4(40 – 10)  8 + 14 – (4  4  4 – 1) + 7  2
64.
65.
66.
67.
8 + (3 + 4  3)  [7 + 1 + (3 + 42  4)] + 6
6 + 6  2 – 18 + 12  2 – 36 6  1
21 – 42  6 + 28 + 35  5 – 28 14  7
4 (9 – 3)  10 + 7 – (2  12  3 – 1) + 3  4
32. 5 – (12 + 3  22)  [11 + 10 + (9 + 12  9)] + 2
33. 8 + 13  4 – 19 + 14  7 – 9 3  6
34. 16 – 8  4 + 13 + 15  3 + 25 5  11
68. 21 – (18 + 4  3)  [3 + 2 + (1 + 23  3)] + 8
69. 19 + 7  6 – 6 + 21  7 – 8 2  5
70. 3 + 44  4 + 15 + 36  12 + 21 3  7
35. 2 [(9 – 3)  2 + 15] – (14 
71. 9 (13 – 5)  3 +
4  4 + 4) + 7
36. 23 – (12 + 5  3)  [20 + 6 – (12 + 12  5)] + 8
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Chapter 1: Working with Numbers and Variables
57 + 64 – (6  4  2 – 6)
72. 1 + (13 + 7  5)  [– 6 + (9 + 12  3)] + 8