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When doing more complex math problems, meaning you are not simply adding, subtracting, multiplying or dividing but are doing a combination of these methods, in order to arrive at the correct answer you must follow a certain order. This order is known as the Order of Operation.
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The Order of Operation can easily be remembered by remembering the following letters: PEMDAS. Broken down you get:
P = Parentheses
E = Exponents (Powers and Square Roots)
MD = Multiplication and Division (Left to Right)
AS = Addition and Subtraction (Left to Right)
Now what does this mean? If the problem presented to you has parentheses in it, you always do the math within the parentheses first.
After the math is done inside the parentheses, you then do all the multiplication and divisions operations followed by any addition and subtraction operations.
Let’s look at the following math problem as an example:
(16 + 21) x 4 - 36 ÷ 6 =
We know we must work the numbers inside of the parentheses first so, 16 + 21 = 37.
Next we must do the multiplications and division so, 37 x 4 = 148 and 36 ÷ 6 = 6.
The problem should now look like 148 – 6 and the answer is that it equals 142.
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1.
|
Find the answer that shows the correct Order of Operation and the correct answer.
12 + 45 + (9 x 13) - 4 + (6 x 3) = |
|
[ ] |
12 + 45 = 57
9 x 13 = 117 - 4 = 113
6 x 3 = 18
57 + 113 + 18 = 188 |
[ ] |
9 x 13 = 117
6 x 3 = 18
12 + 45 + 117 - 4 + 18 = 188 |
[ ] |
9 x 13 = 117
4 + 18 = 22
12 + 45 = 57
57 + 117 - 22 = 152 |
[ ] |
9 x 13 = 117
6 x 3 = 18
117 + 18 = 135
12 + 45 = 57
57 + 117 + 18 - 4 = 188 |
|
|
2.
|
Find the answer that shows the correct Order of Operation and the correct answer.
7 x 4 + (43 - 20) + 5 x (21 ÷ 3) = |
|
[ ] |
28 + 23 = 51
5 x 7 = 35
51 + 35 = 86 |
[ ] |
28 + 35 = 63
43 - 20 = 23
63 + 23 = 86 |
[ ] |
43 - 20 = 23
7 x 4 = 28
23 + 28 = 51
21 ÷ 3 = 7
5 x 7 = 35
51 + 35 = 86 |
[ ] |
43 - 20 = 23
21 ÷ 3 = 7
7 x 4 = 28
5 x 7 = 35
28 + 23 + 35 = 86 |
|
|
3.
|
Find the answer that shows the correct Order of Operation and the correct answer.
90 ÷ 10 + 5 x (14 + 6) = |
|
[ ] |
14 + 6 = 20
5 x 20 = 100
90 ÷ 10 = 9
9 + 100 = 109 |
[ ] |
90 ÷ 10 = 9
9 + 5 = 14
14 + 6 = 20
14 x 20 = 280 |
[ ] |
14 + 6 = 20
90 ÷ 10 = 9
5 x 20 = 100
9 + 100 = 109 |
[ ] |
10 + 5 = 15
90 ÷ 15 = 6
14 + 6 = 20
5 x 20 = 100
6 + 100 = 106 |
|
|
4.
|
Find the answer that shows the correct Order of Operation and the correct answer.
83 - 19 + (31 + 17) ÷ 6 = |
|
[ ] |
31 + 17 = 48
48 ÷ 6 = 8
83 - 19 = 64
64 + 8 = 72 |
[ ] |
83 - 19 = 64
31 + 17= 48
48 ÷ 6 = 8
64 + 8 = 72 |
[ ] |
31 + 17 = 48
83 - 19 = 64
64 + 48 = 112
112 ÷ 6 = 18.67 |
[ ] |
31 + 17 = 48
48 + 83 = 131
131 + 19 = 150
150 ÷ 6 = 25 |
|
|
5.
|
Find the answer that shows the correct Order of Operation and the correct answer.
112 - (56 - 22) + 23 + (14 - 10) = |
|
[ ] |
56 - 22 = 34
112 - 34 = 78
78 + 23 = 101
14 - 10 = 4
101 + 4 = 105 |
[ ] |
56 - 22 = 34
14 - 10 = 4
112 - 34 = 78
78 + 23 + 4 = 105 |
[ ] |
112 - 56 = 56
56 - 22 = 34
34 + 23 = 57
57 + 14 = 71
71 - 10 = 61 |
[ ] |
56 - 22 = 34
34 + 23 = 78
112 - 78 = 34
14 - 10 = 4
34 + 4 = 38 |
|
|
6.
|
Find the answer that shows the correct Order of Operation and the correct answer.
1,244 x 2 ÷ (64 ÷ 8) = |
|
[ ] |
1,244 x 2 = 2,488
2,488 ÷ 64 = 38.88
38.88 ÷ 8 = 4.86 |
[ ] |
64 ÷ 8 = 8
2 ÷ 8 = .25
1,244 x .25 = 311 |
[ ] |
64 ÷ 8 = 8
1,244 x 2 = 2,488
2,488 ÷ 8 = 311 |
[ ] |
1,244 x 2 = 2,488
64 ÷ 8 = 8
2,488 ÷ 8 = 311 |
|
|
7.
|
Find the answer that shows the correct Order of Operation and the correct answer.
(5 + 7) x (4 + 8) - (9 x 2) - (6 x 6) = |
|
[ ] |
5 + 7 = 12
4 + 8 = 12
12 x 12 = 144
9 x 2 = 18
144 - 18 = 126
6 x 6 = 36
126 - 36 = 90 |
[ ] |
5 + 7 = 12
12 x 4 = 48
48 + 8 = 56
56 - 9 = 47
47 x 2 = 94
94 - 6 = 88
88 x 6 = 528 |
[ ] |
5 + 4 = 9
7 + 8 = 15
9 x 15 = 135
9 x 6 = 54
2 x 6 = 12
54 - 12 = 42
135 - 42 = 93 |
[ ] |
5 + 7 = 12
4 + 8 = 12
9 x 2 = 18
6 x 6 = 36
12 x 12 = 144
144 - 18 = 126
126 - 36 = 90 |
|
|
8.
|
Find the answer that shows the correct Order of Operation and the correct answer.
1 + (100 ÷ 5) - (7 x 3) = |
|
[ ] |
100 ÷ 5 = 20
7 x 3 = 21
1 + 20 = 21
21 - 21 = 0 |
[ ] |
1 + 100 = 101
101 ÷ 5 = 20.2
7x 3 = 21
20.2 - 21 = -0.8 |
[ ] |
100 ÷ 5 = 20
7 x 3 = 21
20 - 21 = -1
1 + -1 = 0 |
[ ] |
7 x 3 = 21
100 ÷ 5 = 20
1 + 20 = 21
21 - 21 = 0 |
|
|
9.
|
Find the answer that shows the correct Order of Operation and the correct answer.
2 + 2 + 4 x (3 + 46 + 4 - 14) = |
|
[ ] |
3 + 46 + 4 = 53 - 14 = 39
2 + 2 + 4 = 8
8 x 39 = 312 |
[ ] |
2 + 2 + 4 = 8
3 + 46 + 4 = 53 - 14 = 39
8 x 39 = 312 |
[ ] |
3 + 46 + 4 = 53 - 14 = 39
4 x 39 = 156
2 + 2 + 156 = 160 |
[ ] |
4 x 3 = 12
12 + 46 = 58
58 + 4 = 62
62 - 14 = 48
2 + 2 + 4 = 8
8 x 48 = 384 |
|
|
10.
|
Find the answer that shows the correct Order of Operation and the correct answer.
55 - 7 x 3 + (6 + 4) ÷ 2 = |
|
[ ] |
6 + 4 = 10
10 ÷ 2 = 5
55 - 7 = 48
48 x 3 = 144
144 + 5 = 149 |
[ ] |
7 x 3 = 21
6 + 4 = 10
10 ÷ 2 = 5
55 - 21 = 34 + 5 = 39 |
[ ] |
6 + 4 = 10
55 - 7 = 48
48 x 3 = 144
144 + 10 = 154
154 ÷ 2 = 77 |
[ ] |
6 + 4 = 10
7 x 3 = 21
10 ÷ 2 = 5
55 - 21 = 34 + 5 = 39 |
|
|
1.
|
Find the answer that shows the correct Order of Operation and the correct answer.
12 + 45 + (9 x 13) - 4 + (6 x 3) = |
|
[ ] |
12 + 45 = 57
9 x 13 = 117 - 4 = 113
6 x 3 = 18
57 + 113 + 18 = 188 |
[x] |
9 x 13 = 117
6 x 3 = 18
12 + 45 + 117 - 4 + 18 = 188 |
[ ] |
9 x 13 = 117
4 + 18 = 22
12 + 45 = 57
57 + 117 - 22 = 152 |
[ ] |
9 x 13 = 117
6 x 3 = 18
117 + 18 = 135
12 + 45 = 57
57 + 117 + 18 - 4 = 188 |
|
|
2.
|
Find the answer that shows the correct Order of Operation and the correct answer.
7 x 4 + (43 - 20) + 5 x (21 ÷ 3) = |
|
[ ] |
28 + 23 = 51
5 x 7 = 35
51 + 35 = 86 |
[ ] |
28 + 35 = 63
43 - 20 = 23
63 + 23 = 86 |
[ ] |
43 - 20 = 23
7 x 4 = 28
23 + 28 = 51
21 ÷ 3 = 7
5 x 7 = 35
51 + 35 = 86 |
[x] |
43 - 20 = 23
21 ÷ 3 = 7
7 x 4 = 28
5 x 7 = 35
28 + 23 + 35 = 86 |
|
|
3.
|
Find the answer that shows the correct Order of Operation and the correct answer.
90 ÷ 10 + 5 x (14 + 6) = |
|
[ ] |
14 + 6 = 20
5 x 20 = 100
90 ÷ 10 = 9
9 + 100 = 109 |
[ ] |
90 ÷ 10 = 9
9 + 5 = 14
14 + 6 = 20
14 x 20 = 280 |
[x] |
14 + 6 = 20
90 ÷ 10 = 9
5 x 20 = 100
9 + 100 = 109 |
[ ] |
10 + 5 = 15
90 ÷ 15 = 6
14 + 6 = 20
5 x 20 = 100
6 + 100 = 106 |
|
|
4.
|
Find the answer that shows the correct Order of Operation and the correct answer.
83 - 19 + (31 + 17) ÷ 6 = |
|
[x] |
31 + 17 = 48
48 ÷ 6 = 8
83 - 19 = 64
64 + 8 = 72 |
[ ] |
83 - 19 = 64
31 + 17= 48
48 ÷ 6 = 8
64 + 8 = 72 |
[ ] |
31 + 17 = 48
83 - 19 = 64
64 + 48 = 112
112 ÷ 6 = 18.67 |
[ ] |
31 + 17 = 48
48 + 83 = 131
131 + 19 = 150
150 ÷ 6 = 25 |
|
|
5.
|
Find the answer that shows the correct Order of Operation and the correct answer.
112 - (56 - 22) + 23 + (14 - 10) = |
|
[ ] |
56 - 22 = 34
112 - 34 = 78
78 + 23 = 101
14 - 10 = 4
101 + 4 = 105 |
[x] |
56 - 22 = 34
14 - 10 = 4
112 - 34 = 78
78 + 23 + 4 = 105 |
[ ] |
112 - 56 = 56
56 - 22 = 34
34 + 23 = 57
57 + 14 = 71
71 - 10 = 61 |
[ ] |
56 - 22 = 34
34 + 23 = 78
112 - 78 = 34
14 - 10 = 4
34 + 4 = 38 |
|
|
6.
|
Find the answer that shows the correct Order of Operation and the correct answer.
1,244 x 2 ÷ (64 ÷ 8) = |
|
[ ] |
1,244 x 2 = 2,488
2,488 ÷ 64 = 38.88
38.88 ÷ 8 = 4.86 |
[ ] |
64 ÷ 8 = 8
2 ÷ 8 = .25
1,244 x .25 = 311 |
[x] |
64 ÷ 8 = 8
1,244 x 2 = 2,488
2,488 ÷ 8 = 311 |
[ ] |
1,244 x 2 = 2,488
64 ÷ 8 = 8
2,488 ÷ 8 = 311 |
|
|
7.
|
Find the answer that shows the correct Order of Operation and the correct answer.
(5 + 7) x (4 + 8) - (9 x 2) - (6 x 6) = |
|
[ ] |
5 + 7 = 12
4 + 8 = 12
12 x 12 = 144
9 x 2 = 18
144 - 18 = 126
6 x 6 = 36
126 - 36 = 90 |
[ ] |
5 + 7 = 12
12 x 4 = 48
48 + 8 = 56
56 - 9 = 47
47 x 2 = 94
94 - 6 = 88
88 x 6 = 528 |
[ ] |
5 + 4 = 9
7 + 8 = 15
9 x 15 = 135
9 x 6 = 54
2 x 6 = 12
54 - 12 = 42
135 - 42 = 93 |
[x] |
5 + 7 = 12
4 + 8 = 12
9 x 2 = 18
6 x 6 = 36
12 x 12 = 144
144 - 18 = 126
126 - 36 = 90 |
|
|
8.
|
Find the answer that shows the correct Order of Operation and the correct answer.
1 + (100 ÷ 5) - (7 x 3) = |
|
[x] |
100 ÷ 5 = 20
7 x 3 = 21
1 + 20 = 21
21 - 21 = 0 |
[ ] |
1 + 100 = 101
101 ÷ 5 = 20.2
7x 3 = 21
20.2 - 21 = -0.8 |
[ ] |
100 ÷ 5 = 20
7 x 3 = 21
20 - 21 = -1
1 + -1 = 0 |
[ ] |
7 x 3 = 21
100 ÷ 5 = 20
1 + 20 = 21
21 - 21 = 0 |
|
|
9.
|
Find the answer that shows the correct Order of Operation and the correct answer.
2 + 2 + 4 x (3 + 46 + 4 - 14) = |
|
[ ] |
3 + 46 + 4 = 53 - 14 = 39
2 + 2 + 4 = 8
8 x 39 = 312 |
[ ] |
2 + 2 + 4 = 8
3 + 46 + 4 = 53 - 14 = 39
8 x 39 = 312 |
[x] |
3 + 46 + 4 = 53 - 14 = 39
4 x 39 = 156
2 + 2 + 156 = 160 |
[ ] |
4 x 3 = 12
12 + 46 = 58
58 + 4 = 62
62 - 14 = 48
2 + 2 + 4 = 8
8 x 48 = 384 |
|
|
10.
|
Find the answer that shows the correct Order of Operation and the correct answer.
55 - 7 x 3 + (6 + 4) ÷ 2 = |
|
[ ] |
6 + 4 = 10
10 ÷ 2 = 5
55 - 7 = 48
48 x 3 = 144
144 + 5 = 149 |
[ ] |
7 x 3 = 21
6 + 4 = 10
10 ÷ 2 = 5
55 - 21 = 34 + 5 = 39 |
[ ] |
6 + 4 = 10
55 - 7 = 48
48 x 3 = 144
144 + 10 = 154
154 ÷ 2 = 77 |
[x] |
6 + 4 = 10
7 x 3 = 21
10 ÷ 2 = 5
55 - 21 = 34 + 5 = 39 |
|
|