Order of Operation (Part 2)

You may have your socks in order, but what about your sums?

Order of Operation (Part 2)

This Math quiz is called 'Order of Operation (Part 2)' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.

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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:

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.

1.
Find the answer that shows the correct Order of Operation and the correct answer.

9 x 3 + (82 + 23) - 14 =
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
The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be 8 x 8 = 64 and then we would do 2 x 2 x 2 = or 2 x 2 = 4 then 4 x 2 = 8. This then gives us (64 + 8 = 72). This shows us that Answers (b) and (d) are not correct. The next step is multiplication and division giving us 9 x 3 = 27. Now we move onto addition and subtraction giving us 27 + 72 = 99 - 14 = 85. Answer (a), therefore, shows the correct Order of Operation
2.
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
The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be 5 x 6 = 30. This shows us that Answers (b) and (c) are not correct. The next step is working out the exponent numbers. As we have two exponent numbers we work from left to right. The first exponent number will then be 6 x 6 x 6 = 6 x 6 = 36 x 6 = 216 and the second exponent number will be 3 x 3 x 3 = 3 x 3 = 9 x 3 = 27. The next step is multiplication and division but since we do not have these, we move on to addition and subtraction, moving left to right. This gives us 10 + 216 = 226 - 27 = 199 + 30 = 229. Answer (d), therefore, shows the correct Order of Operation
3.
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
The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be 3 x 4 = 12. This shows us that Answer (b) is not correct. The next step is working out the exponent numbers. As we have two exponent numbers we work from left to right. The first exponent number will then be 5 x 5 x 5 = 5 x 5 = 25 x 5 = 125. Next we will have 6 x 6 x 6 x 6 = 6 x 6 = 36 x 6 = 216 x 6 = 1,296. The next step is multiplication and division. As we do not have any we move on to addition and subtraction. This gives us 125 + 1,296 + 12 = 1,433. Answer (d), therefore, shows the correct Order of Operation
4.
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
The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be 2 x 17 = 34 and then 1 x 1 = 1. This shows us that Answer (d) is not correct. The next step is working out the exponent numbers. As we do not have any exponents we move on to multiplication and division, always working the problem from left to right. That means that the next step will be 5 x 34 = 170 and then 3 x 1 = 3. Now we move on to addition and subtraction, again working left to right. This gives us 170 + 3 = 173. Answer (a) shows the correct Order of Operation
5.
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
The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be 4 + 4 = 8. This shows us that Answers (a) and (d) are not correct. The next step is working out the exponent numbers. As we do not have any exponents we move on to multiplication and division, always working the problem from left to right. That means that the next step will be 24 ÷ 8 = 3 followed by 3 x 2 = 6. Now we move on to addition and subtraction, again working left to right. This gives us 100 + 6 = 106. Answer (b), therefore, shows the correct Order of Operation
6.
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
4 + 67 = 71 + 31 = 102 - 15 = 87
4 + 67 = 71
31 - 15 = 16
71 + 16 = 87
The Order of Operation requires us to work the math within parentheses first. As we have no parentheses we move to exponents. There are also no exponents so we move to multiplication and division. As there are no multiplications and divisions we move to addition and subtraction. Moving from left to right the problem is solved by 4 + 67 = 71 + 31 = 102 - 15 = 87. Answer (c) shows the correct Order of Operation
7.
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
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
The Order of Operation requires us to work the math within parentheses first. As we have no parentheses we move to exponents. There are also no exponents so we move to multiplication and division. Moving left to right we first get 27 ÷ 3 = 9. Next we have 4 x 2 = 8. Now we move to addition and subtraction. This then gives us 8 + 9 = 17 - 8 = 9. Answer (b) shows the correct Order of Operation
8.
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
The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be 8 - 3 = 5. This shows us that Answers (c) and (d) are not correct. The next step is working out the exponent numbers. As we do not have any exponents we move on to multiplication and division, always working the problem from left to right. That means that the next step will be 6 x 40 = 240. Now we move on to addition and subtraction, again working left to right. This gives us 240 + 5 = 245. Answer (a), therefore, shows the correct Order of Operation
9.
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
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
The Order of Operation requires us to work the math within parentheses first. As we do not have any parentheses we move on to exponents. We have two. Moving left to right we have 2 x 2 x 2 x 2 x 2 = 2 x 2 = 4 x 2 = 8 x 2 = 16 x 2 = 32. The second exponent is 3 x 3 = 9. Next we move to multiplication or division. Again, moving left to right, we now have 32 x 9 = 288. Now we move on to addition and subtraction giving us 288 - 5 = 283 + 6 = 289. Answer (d) shows the correct Order of Operation
10.
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
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
The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be 1 + 4 = 5. This shows us that Answer (c) is not correct. The next step is working out the exponent numbers. As we do not have any exponents we move on to multiplication and division, always working the problem from left to right. That means that the next step will be 9 ÷ 3 = 3. That will be followed by 3 x 5 = 15, followed by 15 x 5 = 75. Now we move on to addition and subtraction, again working left to right. This now gives us 3 + 6 + 75 = 84. Answer (b), therefore, shows the correct Order of Operation
Author:  Christine G. Broome

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