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The Order of Operation can easily be remembered by remembering the following letters: PEMDAS. Broken down you get:
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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:
12 - 4 + (7 x 2) x 11 =
We know we must work the numbers inside of the parentheses first so, 7 x 2 = 14.
Next we must do the multiplications and division so, 14 x 11 = 154. Finally we do the addition or subtraction so here we would have 12 - 4 = 8, then 8 + 154 = 162.
Step two of the Order of Operations deals with numbers with exponents. Numbers with exponents have a smaller number placed at the upper right-hand corner of a number. For example: 62. This also means 6 to the second power. It is also a shorthand used to show 6 x 6. 6 x 6 = 36. 62 also equals 36.
Now let’s look at 24. This is the same as writing 2 x 2 x 2 x 2. This gives us 2 x 2 = 4 x 2 = 8 x 2 = 16. 24 equals 16.
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1.
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Find the answer that shows the correct Order of Operation and the correct answer.
3 + 6 + 9 ÷ 3 x (1 + 4) x 5 = |
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[ ] |
1 + 4 = 5
3 + 6 + 9 = 18
18 ÷ 3 = 6
5 x 5 = 25
6 x 25 = 150 |
[ ] |
1 + 4 = 5
9 ÷ 3 = 3
3 x 5 = 15
15 x 5 = 75
3 + 6 + 75 = 84 |
[ ] |
3 + 6 + 9 = 18
18 ÷ 3 = 6
1 + 4 = 5
5 x 5 = 25
6 x 25 = 150 |
[ ] |
1 + 4 = 5
5 x 5 = 25
9 ÷ 3 = 3
3 + 6 = 9
9 + 3 = 12
12 x 25 = 300 |
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2.
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Find the answer that shows the correct Order of Operation and the correct answer.
53 + 64 + (3 x 4) = |
|
[ ] |
3 x 4 = 12
5 x 3 = 15
6 x 4 = 24
12 + 15 + 24 = 51 |
[ ] |
5 x 5 x 5 = 5 x 5 = 25 x 5 = 125
6 x 6 x 6 x 6 = 6 x 6 = 36 x 6 = 216 x 6 = 1,296
3 x 4 = 12
125 + 1,296 + 12 = 1,433 |
[ ] |
3 x 4 = 12
5 + 6 = 11
11 x 11 x 11 x 11 x 11 x 11 x 11 = 11 x 11 = 121 x 11 = 1,331 x 11 = 14,631 x 11 = 161,051 x 11 = 1,771,561 x 11 = 19,487,171
19,487,171 + 12 = 19,487,183 |
[ ] |
3 x 4 = 12
5 x 5 x 5 = 5 x 5 = 25 x 5 = 125
6 x 6 x 6 x 6 = 6 x 6 = 36 x 6 = 216 x 6 = 1,296
125 + 1,296 + 12 = 1,433 |
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3.
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Find the answer that shows the correct Order of Operation and the correct answer.
6 x 40 + (8 - 3) = |
|
[ ] |
8 - 3 = 5
6 x 40 = 240
240 + 5 = 245 |
[ ] |
8 - 3 = 5
40 + 5 = 45
6 x 45 = 270 |
[ ] |
6 x 40 = 240
8 - 3= 5
240 + 5 = 245 |
[ ] |
6 x 40 = 240
240 + 8 = 248
248 - 3 = 245 |
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4.
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Find the answer that shows the correct Order of Operation and the correct answer.
100 + 24 ÷ (4 + 4) x 2 = |
|
[ ] |
100 + 24 = 124
4 + 4 = 8
124 ÷ 8 = 15.5
15.5 x 2 = 31 |
[ ] |
4 + 4 = 8
24 ÷ 8 = 3
3 x 2 = 6
100 + 6 = 106 |
[ ] |
4 + 4 = 8
8 x 2 = 16
100 + 24 = 124
124 ÷ 16 = 7.75 |
[ ] |
100 + 24 = 124
4 + 4 = 8
8 x 2 = 16
124 ÷ 16 = 7.75 |
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5.
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Find the answer that shows the correct Order of Operation and the correct answer.
9 x 3 + (82 + 23) - 14 = |
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[ ] |
8 x 8 = 64 + 2 x 2 x 2 = 2 x 2 = 4 x 2 = 8 = 64 + 8 = 72
9 x 3 = 27
27 + 72 = 99 - 14 = 85 |
[ ] |
82 + 23 = 105
9 x 3 = 27
27 + 105 = 375
105 - 14 = -45 |
[ ] |
8 x 8 = 64 + 2 x 2 x 2 = 2 x 2 = 4 x 2 = 8 = 64 + 8 = 72
72 - 14 = 58
9 x 3 = 27
27 + 58 = 85 |
[ ] |
3 + 82 = 112
112 + 23 = 135
9 x 135= 1175
1175 - 14 = 1035 |
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6.
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Find the answer that shows the correct Order of Operation and the correct answer.
4 + 67 + 31 - 15 = |
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[ ] |
31 - 15 = 16
4 + 67 = 71
71 + 16 = 87 |
[ ] |
67 + 31 = 98
4 + 98 = 102
102 - 15 = 87 |
[ ] |
4 + 67 = 71 + 31 = 102 - 15 = 87 |
[ ] |
4 + 67 = 71
31 - 15 = 16
71 + 16 = 87 |
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7.
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Find the answer that shows the correct Order of Operation and the correct answer.
25 x 32 - 5 + 6 = |
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[ ] |
2 x 2 x 2 x 2 x 2 = 2 x 2 = 4 x 2 = 8 x 2 = 16 x 2 = 32
3 x 3 = 9
5 + 6 = 11
32 x 9 = 288
288 - 11 = 277 |
[ ] |
25 x 32 = 67
5 + 6 = 11
67 - 11 = -57 |
[ ] |
2 x 5 = 10 x 3 x 2 = 6 = 10 x 6 = 60
60 - 5 = 55 + 6 = 61 |
[ ] |
2 x 2 x 2 x 2 x 2 = 2 x 2 = 4 x 2 = 8 x 2 = 16 x 2 = 32
3 x 3 = 9
32 x 9 = 288
288 - 5 = 283 + 6 = 289 |
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8.
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Find the answer that shows the correct Order of Operation and the correct answer.
8 + 27 ÷ 3 - 4 x 2 = |
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[ ] |
8 + 27 = 35
35 ÷ 3 = 11.67
4 x 2 = 8
11.67 - 8 = 3.67 |
[ ] |
27 ÷ 3 = 9
4 x 2 = 8
8 + 9 = 17 - 8 = 9 |
[ ] |
27 ÷ 3 = 9
4 x 2 = 8
9 - 8 = 1
8 + 1 = 9 |
[ ] |
4 x 2 = 8
27 ÷ 3 = 9
8 + 9 = 17 - 8 = 9 |
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9.
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Find the answer that shows the correct Order of Operation and the correct answer.
5 x (2 x 17) + 3 x (1 x 1) = |
|
[ ] |
2 x 17 = 34
1 x 1 = 1
5 x 34 = 170
3 x 1 = 3
170 + 3 = 173 |
[ ] |
2 x 17 = 34
5 x 34 = 170
1 x 1 = 1
3 x 1 = 3
170 + 3 = 173 |
[ ] |
2 x 17 = 34
5 x 34 = 170
170 + 3 = 173
173 x 1 = 173 |
[ ] |
5 x 3 = 15
2 x 17 = 34
1 x 1 = 1
15 + 34 = 49 x 1 = 49 |
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10.
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Find the answer that shows the correct Order of Operation and the correct answer.
10 + 63 - 33 + (5 x 6) = |
|
[ ] |
5 x 6 = 30
6 x 6 x 6 = 6 x 6 = 36 x 6 = 216
3 x 3 x 3 = 3 x 3 = 9 x 3 = 27
216 - 27 = 189
10 + 189 = 199
199 + 30 = 229 |
[ ] |
10 + 18 = 28
3 x 3 = 9
28 - 9 = 19
5 x 6 = 30
19 + 30 = 49 |
[ ] |
10 + 216 = 226
27 + 30 = 57
226 - 57 = 169 |
[ ] |
5 x 6 = 30
6 x 6 x 6 = 6 x 6 = 36 x 6 = 216
3 x 3 x 3 = 3 x 3 = 9 x 3 = 27
10 + 216 = 226
226 - 27 = 199
199 + 30 = 229 |
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1.
|
Find the answer that shows the correct Order of Operation and the correct answer.
3 + 6 + 9 ÷ 3 x (1 + 4) x 5 = |
|
[ ] |
1 + 4 = 5
3 + 6 + 9 = 18
18 ÷ 3 = 6
5 x 5 = 25
6 x 25 = 150 |
[x] |
1 + 4 = 5
9 ÷ 3 = 3
3 x 5 = 15
15 x 5 = 75
3 + 6 + 75 = 84 |
[ ] |
3 + 6 + 9 = 18
18 ÷ 3 = 6
1 + 4 = 5
5 x 5 = 25
6 x 25 = 150 |
[ ] |
1 + 4 = 5
5 x 5 = 25
9 ÷ 3 = 3
3 + 6 = 9
9 + 3 = 12
12 x 25 = 300 |
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2.
|
Find the answer that shows the correct Order of Operation and the correct answer.
53 + 64 + (3 x 4) = |
|
[ ] |
3 x 4 = 12
5 x 3 = 15
6 x 4 = 24
12 + 15 + 24 = 51 |
[ ] |
5 x 5 x 5 = 5 x 5 = 25 x 5 = 125
6 x 6 x 6 x 6 = 6 x 6 = 36 x 6 = 216 x 6 = 1,296
3 x 4 = 12
125 + 1,296 + 12 = 1,433 |
[ ] |
3 x 4 = 12
5 + 6 = 11
11 x 11 x 11 x 11 x 11 x 11 x 11 = 11 x 11 = 121 x 11 = 1,331 x 11 = 14,631 x 11 = 161,051 x 11 = 1,771,561 x 11 = 19,487,171
19,487,171 + 12 = 19,487,183 |
[x] |
3 x 4 = 12
5 x 5 x 5 = 5 x 5 = 25 x 5 = 125
6 x 6 x 6 x 6 = 6 x 6 = 36 x 6 = 216 x 6 = 1,296
125 + 1,296 + 12 = 1,433 |
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3.
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Find the answer that shows the correct Order of Operation and the correct answer.
6 x 40 + (8 - 3) = |
|
[x] |
8 - 3 = 5
6 x 40 = 240
240 + 5 = 245 |
[ ] |
8 - 3 = 5
40 + 5 = 45
6 x 45 = 270 |
[ ] |
6 x 40 = 240
8 - 3= 5
240 + 5 = 245 |
[ ] |
6 x 40 = 240
240 + 8 = 248
248 - 3 = 245 |
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4.
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Find the answer that shows the correct Order of Operation and the correct answer.
100 + 24 ÷ (4 + 4) x 2 = |
|
[ ] |
100 + 24 = 124
4 + 4 = 8
124 ÷ 8 = 15.5
15.5 x 2 = 31 |
[x] |
4 + 4 = 8
24 ÷ 8 = 3
3 x 2 = 6
100 + 6 = 106 |
[ ] |
4 + 4 = 8
8 x 2 = 16
100 + 24 = 124
124 ÷ 16 = 7.75 |
[ ] |
100 + 24 = 124
4 + 4 = 8
8 x 2 = 16
124 ÷ 16 = 7.75 |
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5.
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Find the answer that shows the correct Order of Operation and the correct answer.
9 x 3 + (82 + 23) - 14 = |
|
[x] |
8 x 8 = 64 + 2 x 2 x 2 = 2 x 2 = 4 x 2 = 8 = 64 + 8 = 72
9 x 3 = 27
27 + 72 = 99 - 14 = 85 |
[ ] |
82 + 23 = 105
9 x 3 = 27
27 + 105 = 375
105 - 14 = -45 |
[ ] |
8 x 8 = 64 + 2 x 2 x 2 = 2 x 2 = 4 x 2 = 8 = 64 + 8 = 72
72 - 14 = 58
9 x 3 = 27
27 + 58 = 85 |
[ ] |
3 + 82 = 112
112 + 23 = 135
9 x 135= 1175
1175 - 14 = 1035 |
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6.
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Find the answer that shows the correct Order of Operation and the correct answer.
4 + 67 + 31 - 15 = |
|
[ ] |
31 - 15 = 16
4 + 67 = 71
71 + 16 = 87 |
[ ] |
67 + 31 = 98
4 + 98 = 102
102 - 15 = 87 |
[x] |
4 + 67 = 71 + 31 = 102 - 15 = 87 |
[ ] |
4 + 67 = 71
31 - 15 = 16
71 + 16 = 87 |
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7.
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Find the answer that shows the correct Order of Operation and the correct answer.
25 x 32 - 5 + 6 = |
|
[ ] |
2 x 2 x 2 x 2 x 2 = 2 x 2 = 4 x 2 = 8 x 2 = 16 x 2 = 32
3 x 3 = 9
5 + 6 = 11
32 x 9 = 288
288 - 11 = 277 |
[ ] |
25 x 32 = 67
5 + 6 = 11
67 - 11 = -57 |
[ ] |
2 x 5 = 10 x 3 x 2 = 6 = 10 x 6 = 60
60 - 5 = 55 + 6 = 61 |
[x] |
2 x 2 x 2 x 2 x 2 = 2 x 2 = 4 x 2 = 8 x 2 = 16 x 2 = 32
3 x 3 = 9
32 x 9 = 288
288 - 5 = 283 + 6 = 289 |
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8.
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Find the answer that shows the correct Order of Operation and the correct answer.
8 + 27 ÷ 3 - 4 x 2 = |
|
[ ] |
8 + 27 = 35
35 ÷ 3 = 11.67
4 x 2 = 8
11.67 - 8 = 3.67 |
[x] |
27 ÷ 3 = 9
4 x 2 = 8
8 + 9 = 17 - 8 = 9 |
[ ] |
27 ÷ 3 = 9
4 x 2 = 8
9 - 8 = 1
8 + 1 = 9 |
[ ] |
4 x 2 = 8
27 ÷ 3 = 9
8 + 9 = 17 - 8 = 9 |
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9.
|
Find the answer that shows the correct Order of Operation and the correct answer.
5 x (2 x 17) + 3 x (1 x 1) = |
|
[x] |
2 x 17 = 34
1 x 1 = 1
5 x 34 = 170
3 x 1 = 3
170 + 3 = 173 |
[ ] |
2 x 17 = 34
5 x 34 = 170
1 x 1 = 1
3 x 1 = 3
170 + 3 = 173 |
[ ] |
2 x 17 = 34
5 x 34 = 170
170 + 3 = 173
173 x 1 = 173 |
[ ] |
5 x 3 = 15
2 x 17 = 34
1 x 1 = 1
15 + 34 = 49 x 1 = 49 |
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10.
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Find the answer that shows the correct Order of Operation and the correct answer.
10 + 63 - 33 + (5 x 6) = |
|
[ ] |
5 x 6 = 30
6 x 6 x 6 = 6 x 6 = 36 x 6 = 216
3 x 3 x 3 = 3 x 3 = 9 x 3 = 27
216 - 27 = 189
10 + 189 = 199
199 + 30 = 229 |
[ ] |
10 + 18 = 28
3 x 3 = 9
28 - 9 = 19
5 x 6 = 30
19 + 30 = 49 |
[ ] |
10 + 216 = 226
27 + 30 = 57
226 - 57 = 169 |
[x] |
5 x 6 = 30
6 x 6 x 6 = 6 x 6 = 36 x 6 = 216
3 x 3 x 3 = 3 x 3 = 9 x 3 = 27
10 + 216 = 226
226 - 27 = 199
199 + 30 = 229 |
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