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The Order of Operation can easily be remembered by remembering the following letters: **PEMDAS**. Broken down you get:

1.

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 =

2.

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

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

3.

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

4.

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

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.

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

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.

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

9.

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

10.

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

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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 be6 x 6 x 6 = 6 x 6 = 36 x 6 = 216and the second exponent number will be3 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 us10 + 216 = 226 - 27 = 199 + 30 = 229. Answer (d), therefore, shows the correct Order of Operation