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Order of Operation (Part 1)

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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.

1,244 x 2 ÷ (64 ÷ 8) =
1,244 x 2 = 2,488
2,488 ÷ 64 = 38.88
38.88 ÷ 8 = 4.86
64 ÷ 8 = 8
2 ÷ 8 = .25
1,244 x .25 = 311
64 ÷ 8 = 8
1,244 x 2 = 2,488
2,488 ÷ 8 = 311
1,244 x 2 = 2,488
64 ÷ 8 = 8
2,488 ÷ 8 = 311
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
2.
Find the answer that shows the correct Order of Operation and the correct answer.

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
3 + 46 + 4 = 53 - 14 = 39
8 x 39 = 312
3 + 46 + 4 = 53 - 14 = 39
4 x 39 = 156
2 + 2 + 156 = 160
4 x 3 = 12
12 + 46 = 58
58 + 4 = 62
62 - 14 = 48
2 + 2 + 4 = 8
8 x 48 = 384
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
3.
Find the answer that shows the correct Order of Operation and the correct answer.

83 - 19 + (31 + 17) ÷ 6 =
31 + 17 = 48
48 ÷ 6 = 8
83 - 19 = 64
64 + 8 = 72
83 - 19 = 64
31 + 17= 48
48 ÷ 6 = 8
64 + 8 = 72
31 + 17 = 48
83 - 19 = 64
64 + 48 = 112
112 ÷ 6 = 18.67
31 + 17 = 48
48 + 83 = 131
131 + 19 = 150
150 ÷ 6 = 25
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 =
6 + 4 = 10
10 ÷ 2 = 5
55 - 7 = 48
48 x 3 = 144
144 + 5 = 149
7 x 3 = 21
6 + 4 = 10
10 ÷ 2 = 5
55 - 21 = 34 + 5 = 39
6 + 4 = 10
55 - 7 = 48
48 x 3 = 144
144 + 10 = 154
154 ÷ 2 = 77
6 + 4 = 10
7 x 3 = 21
10 ÷ 2 = 5
55 - 21 = 34 + 5 = 39
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 = 12
4 + 8 = 12
12 x 12 = 144
9 x 2 = 18
144 - 18 = 126
6 x 6 = 36
126 - 36 = 90
5 + 7 = 12
12 x 4 = 48
48 + 8 = 56
56 - 9 = 47
47 x 2 = 94
94 - 6 = 88
88 x 6 = 528
5 + 4 = 9
7 + 8 = 15
9 x 15 = 135
9 x 6 = 54
2 x 6 = 12
54 - 12 = 42
135 - 42 = 93
5 + 7 = 12
4 + 8 = 12
9 x 2 = 18
6 x 6 = 36
12 x 12 = 144
144 - 18 = 126
126 - 36 = 90
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.

90 ÷ 10 + 5 x (14 + 6) =
14 + 6 = 20
5 x 20 = 100
90 ÷ 10 = 9
9 + 100 = 109
90 ÷ 10 = 9
9 + 5 = 14
14 + 6 = 20
14 x 20 = 280
14 + 6 = 20
90 ÷ 10 = 9
5 x 20 = 100
9 + 100 = 109
10 + 5 = 15
90 ÷ 15 = 6
14 + 6 = 20
5 x 20 = 100
6 + 100 = 106
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
7.
Find the answer that shows the correct Order of Operation and the correct answer.

7 x 4 + (43 - 20) + 5 x (21 ÷ 3) =
28 + 23 = 51
5 x 7 = 35
51 + 35 = 86
28 + 35 = 63
43 - 20 = 23
63 + 23 = 86
43 - 20 = 23
7 x 4 = 28
23 + 28 = 51
21 ÷ 3 = 7
5 x 7 = 35
51 + 35 = 86
43 - 20 = 23
21 ÷ 3 = 7
7 x 4 = 28
5 x 7 = 35
28 + 23 + 35 = 86
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
8.
Find the answer that shows the correct Order of Operation and the correct answer.

112 - (56 - 22) + 23 + (14 - 10) =
56 - 22 = 34
112 - 34 = 78
78 + 23 = 101
14 - 10 = 4
101 + 4 = 105
56 - 22 = 34
14 - 10 = 4
112 - 34 = 78
78 + 23 + 4 = 105
112 - 56 = 56
56 - 22 = 34
34 + 23 = 57
57 + 14 = 71
71 - 10 = 61
56 - 22 = 34
34 + 23 = 78
112 - 78 = 34
14 - 10 = 4
34 + 4 = 38
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
9.
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 = 57
9 x 13 = 117 - 4 = 113
6 x 3 = 18
57 + 113 + 18 = 188
9 x 13 = 117
6 x 3 = 18
12 + 45 + 117 - 4 + 18 = 188
9 x 13 = 117
4 + 18 = 22
12 + 45 = 57
57 + 117 - 22 = 152
9 x 13 = 117
6 x 3 = 18
117 + 18 = 135
12 + 45 = 57
57 + 117 + 18 - 4 = 188
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
10.
Find the answer that shows the correct Order of Operation and the correct answer.

1 + (100 ÷ 5) - (7 x 3) =
100 ÷ 5 = 20
7 x 3 = 21
1 + 20 = 21
21 - 21 = 0
1 + 100 = 101
101 ÷ 5 = 20.2
7x 3 = 21
20.2 - 21 = -0.8
100 ÷ 5 = 20
7 x 3 = 21
20 - 21 = -1
1 + -1 = 0
7 x 3 = 21
100 ÷ 5 = 20
1 + 20 = 21
21 - 21 = 0
The Order of Operation requires us to work the math within parentheses first. Therefore, the first part would need to be 100 ÷ 5 = 20, then 7 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 get 1 + 20 = 21. Finally we have 21 - 21 = 0. Answer (a) shows the correct Order of Operation
Author:  Christine G. Broome

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