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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.

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**.

1.

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

1 + (100 ÷ 5) - (7 x 3) =

1 + (100 ÷ 5) - (7 x 3) =

100 ÷ 5 = 20

7 x 3 = 21

1 + 20 = 21

21 - 21 =**0**

7 x 3 = 21

1 + 20 = 21

21 - 21 =

1 + 100 = 101

101 ÷ 5 = 20.2

7x 3 = 21

20.2 - 21 =**-0.8**

101 ÷ 5 = 20.2

7x 3 = 21

20.2 - 21 =

100 ÷ 5 = 20

7 x 3 = 21

20 - 21 = -1

1 + -1 =**0**

7 x 3 = 21

20 - 21 = -1

1 + -1 =

7 x 3 = 21

100 ÷ 5 = 20

1 + 20 = 21

21 - 21 =**0**

100 ÷ 5 = 20

1 + 20 = 21

21 - 21 =

2.

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

1,244 x 2 ÷ (64 ÷ 8) =

1,244 x 2 ÷ (64 ÷ 8) =

1,244 x 2 = 2,488

2,488 ÷ 64 = 38.88

38.88 ÷ 8 =**4.86**

2,488 ÷ 64 = 38.88

38.88 ÷ 8 =

64 ÷ 8 = 8

2 ÷ 8 = .25

1,244 x .25 =**311**

2 ÷ 8 = .25

1,244 x .25 =

64 ÷ 8 = 8

1,244 x 2 = 2,488

2,488 ÷ 8 =**311**

1,244 x 2 = 2,488

2,488 ÷ 8 =

1,244 x 2 = 2,488

64 ÷ 8 = 8

2,488 ÷ 8 =**311**

64 ÷ 8 = 8

2,488 ÷ 8 =

The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be **64 ÷ 8 = 8**. This shows us that Answers (a) and (d) are not correct. As there are no exponents, we move next to multiplication and division. Working left to right we have **1,244 x 2 = 2,488**. Next is **2,488 ÷ 8 = 311**. Answer (c) shows the correct Order of Operation

3.

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

83 - 19 + (31 + 17) ÷ 6 =

83 - 19 + (31 + 17) ÷ 6 =

31 + 17 = 48

48 ÷ 6 = 8

83 - 19 = 64

64 + 8 =**72**

48 ÷ 6 = 8

83 - 19 = 64

64 + 8 =

83 - 19 = 64

31 + 17= 48

48 ÷ 6 = 8

64 + 8 =**72**

31 + 17= 48

48 ÷ 6 = 8

64 + 8 =

31 + 17 = 48

83 - 19 = 64

64 + 48 = 112

112 ÷ 6 =**18.67**

83 - 19 = 64

64 + 48 = 112

112 ÷ 6 =

31 + 17 = 48

48 + 83 = 131

131 + 19 = 150

150 ÷ 6 =**25**

48 + 83 = 131

131 + 19 = 150

150 ÷ 6 =

The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be **31 + 17 = 48**. This shows us that Answer (b) is not correct. As we have no exponents we move on to multiplication and division, working left to right. As we have a division the next step is **48 ÷ 6 = 8**. Next we work left to right giving us **83 - 19 = 64** and then **64 + 8 = 72**. Answer (a) shows the correct Order of Operation

4.

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

55 - 7 x 3 + (6 + 4) ÷ 2 =

55 - 7 x 3 + (6 + 4) ÷ 2 =

6 + 4 = 10

10 ÷ 2 = 5

55 - 7 = 48

48 x 3 = 144

144 + 5 =**149**

10 ÷ 2 = 5

55 - 7 = 48

48 x 3 = 144

144 + 5 =

7 x 3 = 21

6 + 4 = 10

10 ÷ 2 = 5

55 - 21 = 34 + 5 =**39**

6 + 4 = 10

10 ÷ 2 = 5

55 - 21 = 34 + 5 =

6 + 4 = 10

55 - 7 = 48

48 x 3 = 144

144 + 10 = 154

154 ÷ 2 =**77**

55 - 7 = 48

48 x 3 = 144

144 + 10 = 154

154 ÷ 2 =

6 + 4 = 10

7 x 3 = 21

10 ÷ 2 = 5

55 - 21 = 34 + 5 =**39**

7 x 3 = 21

10 ÷ 2 = 5

55 - 21 = 34 + 5 =

The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be **6 + 4 = 10**. This tells us that Answer (b) is not correct. As there are no exponents we move on to multiplication and division. Moving left to right we have **7 x 3 = 21** and then we have **10 ÷ 2 = 5**. Now we move on to addition and subtraction and we have **55 - 21 = 34 + 5 = 39**. Answer (d) shows the correct Order of Operation

5.

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) 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**

4 + 8 = 12

12 x 12 = 144

9 x 2 = 18

144 - 18 = 126

6 x 6 = 36

126 - 36 =

5 + 7 = 12

12 x 4 = 48

48 + 8 = 56

56 - 9 = 47

47 x 2 = 94

94 - 6 = 88

88 x 6 =**528**

12 x 4 = 48

48 + 8 = 56

56 - 9 = 47

47 x 2 = 94

94 - 6 = 88

88 x 6 =

5 + 4 = 9

7 + 8 = 15

9 x 15 = 135

9 x 6 = 54

2 x 6 = 12

54 - 12 = 42

135 - 42 =**93**

7 + 8 = 15

9 x 15 = 135

9 x 6 = 54

2 x 6 = 12

54 - 12 = 42

135 - 42 =

5 + 7 = 12

4 + 8 = 12

9 x 2 = 18

6 x 6 = 36

12 x 12 = 144

144 - 18 = 126

126 - 36 =**90**

4 + 8 = 12

9 x 2 = 18

6 x 6 = 36

12 x 12 = 144

144 - 18 = 126

126 - 36 =

The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be **5 + 7 = 12**, then **4 + 8 = 12**, followed by **9 x 2 = 18** and finally **6 x 6 = 36**. As there are no exponents we move on to multiplication and division. Working left to right we get **12 x 12 = 144**. Next we do addition and subtraction so we then have **144 - 18 = 126** and then **126 - 36 = 90**. Answer (d) shows the correct Order of Operation

6.

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

2 + 2 + 4 x (3 + 46 + 4 - 14) =

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

8 x 39 =

2 + 2 + 4 = 8

3 + 46 + 4 = 53 - 14 = 39

8 x 39 =**312**

3 + 46 + 4 = 53 - 14 = 39

8 x 39 =

3 + 46 + 4 = 53 - 14 = 39

4 x 39 = 156

2 + 2 + 156 =**160**

4 x 39 = 156

2 + 2 + 156 =

4 x 3 = 12

12 + 46 = 58

58 + 4 = 62

62 - 14 = 48

2 + 2 + 4 = 8

8 x 48 =**384**

12 + 46 = 58

58 + 4 = 62

62 - 14 = 48

2 + 2 + 4 = 8

8 x 48 =

The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be **3 + 46 + 4 = 53 – 14 = 39**. This tells us that Answers (b) and (d) are not correct. As there are no exponents we move on to multiplication and division. This then gives us **4 x 39 = 156**. Then we move to addition and subtraction giving us **2 + 2 + 156 = 160**. Answer (c) shows the correct Order of Operation

7.

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 + (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 - 4 = 113

6 x 3 = 18

57 + 113 + 18 =

9 x 13 = 117

6 x 3 = 18

12 + 45 + 117 - 4 + 18 =**188**

6 x 3 = 18

12 + 45 + 117 - 4 + 18 =

9 x 13 = 117

4 + 18 = 22

12 + 45 = 57

57 + 117 - 22 =**152**

4 + 18 = 22

12 + 45 = 57

57 + 117 - 22 =

9 x 13 = 117

6 x 3 = 18

117 + 18 = 135

12 + 45 = 57

57 + 117 + 18 - 4 =**188**

6 x 3 = 18

117 + 18 = 135

12 + 45 = 57

57 + 117 + 18 - 4 =

The answers given in (a), (b), and (d) are all the same and **188** is the correct final answer. Therefore, Answer (c) is not correct. As the Order of Operation requires us to work the math within parentheses first, the first part would need to be **9 x 13 = 117**. We have a second set of numbers in parentheses so that goes next, i.e., **6 x 3 = 18**. The next step in the Order of Operation is to do numbers with exponents, as we do not have any we move on to multiplication and division. As there are no multiplication and divisions to be done, we next do additions and subtractions working from left to right. So next we would have **12 + 45 + 117 - 4 + 18 = 188**. Answer (b) shows the correct Order of Operation

8.

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

90 ÷ 10 + 5 x (14 + 6) =

90 ÷ 10 + 5 x (14 + 6) =

14 + 6 = 20

5 x 20 = 100

90 ÷ 10 = 9

9 + 100 =**109**

5 x 20 = 100

90 ÷ 10 = 9

9 + 100 =

90 ÷ 10 = 9

9 + 5 = 14

14 + 6 = 20

14 x 20 =**280**

9 + 5 = 14

14 + 6 = 20

14 x 20 =

14 + 6 = 20

90 ÷ 10 = 9

5 x 20 = 100

9 + 100 =**109**

90 ÷ 10 = 9

5 x 20 = 100

9 + 100 =

10 + 5 = 15

90 ÷ 15 = 6

14 + 6 = 20

5 x 20 = 100

6 + 100 =**106**

90 ÷ 15 = 6

14 + 6 = 20

5 x 20 = 100

6 + 100 =

The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be **14 + 6 = 20**. This shows us that Answers (b) and (d) are not correct and neither are their final answers. Answers (a) and (c) both have the correct final answer of **109**; however, we must work the problem left to right so step two would then be **90 ÷ 10 = 9**. Answer (c), therefore, shows the correct Order of Operation

9.

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

7 x 4 + (43 - 20) + 5 x (21 ÷ 3) =

7 x 4 + (43 - 20) + 5 x (21 ÷ 3) =

28 + 23 = 51

5 x 7 = 35

51 + 35 =**86**

5 x 7 = 35

51 + 35 =

28 + 35 = 63

43 - 20 = 23

63 + 23 =**86**

43 - 20 = 23

63 + 23 =

43 - 20 = 23

7 x 4 = 28

23 + 28 = 51

21 ÷ 3 = 7

5 x 7 = 35

51 + 35 =**86**

7 x 4 = 28

23 + 28 = 51

21 ÷ 3 = 7

5 x 7 = 35

51 + 35 =

43 - 20 = 23

21 ÷ 3 = 7

7 x 4 = 28

5 x 7 = 35

28 + 23 + 35 =**86**

21 ÷ 3 = 7

7 x 4 = 28

5 x 7 = 35

28 + 23 + 35 =

Each answer shows the final answer as **86** and this is the correct answer. However, the Order of Operation must be followed making the first step to work the math within the parentheses. That would be **43 - 20 = 23** and **21 ÷ 3 = 7**. The next step is to do numbers with exponents. As we do not have any, we move on to multiplication and divisions. Going from left to right, the next step will be **7 x 4 = 28**. Next we have 5 x 7 = 35. Our final step is adding and/or subtracting. In this problem, working left to right, we will have **28 + 23 + 35 = 86**. Answer (d) shows the correct Order of Operation

10.

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

112 - (56 - 22) + 23 + (14 - 10) =

112 - (56 - 22) + 23 + (14 - 10) =

56 - 22 = 34

112 - 34 = 78

78 + 23 = 101

14 - 10 = 4

101 + 4 =**105**

112 - 34 = 78

78 + 23 = 101

14 - 10 = 4

101 + 4 =

56 - 22 = 34

14 - 10 = 4

112 - 34 = 78

78 + 23 + 4 =**105**

14 - 10 = 4

112 - 34 = 78

78 + 23 + 4 =

112 - 56 = 56

56 - 22 = 34

34 + 23 = 57

57 + 14 = 71

71 - 10 =**61**

56 - 22 = 34

34 + 23 = 57

57 + 14 = 71

71 - 10 =

56 - 22 = 34

34 + 23 = 78

112 - 78 = 34

14 - 10 = 4

34 + 4 =**38**

34 + 23 = 78

112 - 78 = 34

14 - 10 = 4

34 + 4 =

The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be **56 - 22 = 34** and then **14 - 10 = 4**. This shows us that Answers (a), (c) and (d) are not correct and/or are not in the correct Order of Operation. Answer (b) shows the correct Order of Operation

100 ÷ 5 = 20, then7 x 3 = 21. As there are no exponents we move on to multiplication and division. There are no more multiplications or divisions so we move to addition and subtraction. Working left to right we get1 + 20 = 21. Finally we have21 - 21 = 0. Answer (a) shows the correct Order of Operation