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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: 6^{2}. This also means 6 to the second power. It is also a shorthand used to show 6 x 6. 6 x 6 = 36. 6^{2} also equals 36.

Now let’s look at 2^{4}. 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. 2^{4} equals 16.

1.

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

8 + 27 ÷ 3 - 4 x 2 =

8 + 27 ÷ 3 - 4 x 2 =

8 + 27 = 35

35 ÷ 3 = 11.67

4 x 2 = 8

11.67 - 8 = 3.67

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

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

9 - 8 = 1

8 + 1 = 9

4 x 2 = 8

27 ÷ 3 = 9

8 + 9 = 17 - 8 = 9

27 ÷ 3 = 9

8 + 9 = 17 - 8 = 9

2.

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

4 + 67 + 31 - 15 =

4 + 67 + 31 - 15 =

31 - 15 = 16

4 + 67 = 71

71 + 16 =**87**

4 + 67 = 71

71 + 16 =

67 + 31 = 98

4 + 98 = 102

102 - 15 =**87**

4 + 98 = 102

102 - 15 =

4 + 67 = 71 + 31 = 102 - 15 = **87**

4 + 67 = 71

31 - 15 = 16

71 + 16 =**87**

31 - 15 = 16

71 + 16 =

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

3.

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

5 x (2 x 17) + 3 x (1 x 1) =

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**

1 x 1 = 1

5 x 34 = 170

3 x 1 = 3

170 + 3 =

2 x 17 = 34

5 x 34 = 170

1 x 1 = 1

3 x 1 = 3

170 + 3 =**173**

5 x 34 = 170

1 x 1 = 1

3 x 1 = 3

170 + 3 =

2 x 17 = 34

5 x 34 = 170

170 + 3 = 173

173 x 1 =**173**

5 x 34 = 170

170 + 3 = 173

173 x 1 =

5 x 3 = 15

2 x 17 = 34

1 x 1 = 1

15 + 34 = 49 x 1 =**49**

2 x 17 = 34

1 x 1 = 1

15 + 34 = 49 x 1 =

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

4.

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

100 + 24 ÷ (4 + 4) x 2 =

100 + 24 ÷ (4 + 4) x 2 =

100 + 24 = 124

4 + 4 = 8

124 ÷ 8 = 15.5

15.5 x 2 =**31**

4 + 4 = 8

124 ÷ 8 = 15.5

15.5 x 2 =

4 + 4 = 8

24 ÷ 8 = 3

3 x 2 = 6

100 + 6 =**106**

24 ÷ 8 = 3

3 x 2 = 6

100 + 6 =

4 + 4 = 8

8 x 2 = 16

100 + 24 = 124

124 ÷ 16 =**7.75**

8 x 2 = 16

100 + 24 = 124

124 ÷ 16 =

100 + 24 = 124

4 + 4 = 8

8 x 2 = 16

124 ÷ 16 =**7.75**

4 + 4 = 8

8 x 2 = 16

124 ÷ 16 =

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

5.

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

6 x 40 + (8 - 3) =

6 x 40 + (8 - 3) =

8 - 3 = 5

6 x 40 = 240

240 + 5 =**245**

6 x 40 = 240

240 + 5 =

8 - 3 = 5

40 + 5 = 45

6 x 45 =**270**

40 + 5 = 45

6 x 45 =

6 x 40 = 240

8 - 3= 5

240 + 5 =**245**

8 - 3= 5

240 + 5 =

6 x 40 = 240

240 + 8 = 248

248 - 3 =**245**

240 + 8 = 248

248 - 3 =

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

6.

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

9 x 3 + (8^{2} + 2^{3}) - 14 =

9 x 3 + (8

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**

9 x 3 = 27

27 + 72 = 99 - 14 =

8^{2} + 2^{3} = 10^{5}

9 x 3 = 27

27 + 10^{5} = 37^{5}

10^{5} - 14 = **-4**^{5}

9 x 3 = 27

27 + 10

10

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**

72 - 14 = 58

9 x 3 = 27

27 + 58 =

3 + 8^{2} = 11^{2}

11^{2} + 2^{3} = 13^{5}

9 x 13^{5}= 117^{5}

117^{5} - 14 = **103**^{5}

11

9 x 13

117

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

7.

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

3 + 6 + 9 ÷ 3 x (1 + 4) x 5 =

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**

3 + 6 + 9 = 18

18 ÷ 3 = 6

5 x 5 = 25

6 x 25 =

1 + 4 = 5

9 ÷ 3 = 3

3 x 5 = 15

15 x 5 = 75

3 + 6 + 75 =**84**

9 ÷ 3 = 3

3 x 5 = 15

15 x 5 = 75

3 + 6 + 75 =

3 + 6 + 9 = 18

18 ÷ 3 = 6

1 + 4 = 5

5 x 5 = 25

6 x 25 =**150**

18 ÷ 3 = 6

1 + 4 = 5

5 x 5 = 25

6 x 25 =

1 + 4 = 5

5 x 5 = 25

9 ÷ 3 = 3

3 + 6 = 9

9 + 3 = 12

12 x 25 =**300**

5 x 5 = 25

9 ÷ 3 = 3

3 + 6 = 9

9 + 3 = 12

12 x 25 =

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

8.

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

10 + 6^{3} - 3^{3} + (5 x 6) =

10 + 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**

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 =

10 + 18 = 28

3 x 3 = 9

28 - 9 = 19

5 x 6 = 30

19 + 30 =**49**

3 x 3 = 9

28 - 9 = 19

5 x 6 = 30

19 + 30 =

10 + 216 = 226

27 + 30 = 57

226 - 57 =**169**

27 + 30 = 57

226 - 57 =

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**

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 =

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

9.

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

2^{5} x 3^{2} - 5 + 6 =

2

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

3 x 3 = 9

5 + 6 = 11

32 x 9 = 288

288 - 11 = 277

2^{5} x 3^{2} = 6^{7}

5 + 6 = 11

6^{7} - 11 = -5^{7}

5 + 6 = 11

6

2 x 5 = 10 x 3 x 2 = 6 = 10 x 6 = 60

60 - 5 = 55 + 6 = 61

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

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.

5^{3} + 6^{4} + (3 x 4) =

5

3 x 4 = 12

5 x 3 = 15

6 x 4 = 24

12 + 15 + 24 =**51**

5 x 3 = 15

6 x 4 = 24

12 + 15 + 24 =

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**

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 =

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**

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 =

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**

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 =

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

27 ÷ 3 = 9. Next we have4 x 2 = 8. Now we move to addition and subtraction. This then gives us8 + 9 = 17 - 8 = 9. Answer (b) shows the correct Order of Operation