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Why PEMDAS is created the confusions?

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Order of Operation and PEMDAS

In some areas of the world people use different order of operation (such as BODMAS or BEDMAS or BIDMAS, but in USA people used to solve by PEMDAS (Please Excuse My Dear Aunt Sally).
P: Parenthesis first
E: Exponents next
MD: Multiplication and Division next
AS: Addition and Subtraction last
Notice that the M and D are grouped together, as are the A and S. This is because Multiplication and Division are at the same priority level, and should be done in left to right order. Likewise, Addition and Subtraction are at the same priority level, and should be done in left to right order.
Technically BODMAS or BEDMAS or BIDMAS as well as PEMDAS are same because they give same result.

Confusions in PEMDAS

Unfortunately, many teachers don’t realize this, and teach that all multiplication is done before all division, and all addition is done before all subtraction. Actually Multiplication and Division are at the same priority level, as are Addition and Subtraction. But problem is still because most of the people try to do multiplication before division. Actually they do multiplication and division in the order. It seems they want to always do multiplication first because multiplication is before the division in PEMDAS. They follow the PEMDAS rule by LETTER P-E-M-D-A-S. Because of this they get wrong answer. This is because people not study the PEDMAS or many teachers not clear this concept. Let us see some examples that how people makes mistakes in PEDMAS.

Example 1 : 81 / 3 × 9
1. When doing division first (by BODMAS), we get 
    81 / 3 × 9 

    = 27 × 9 

    = 243

2. When doing multiplication and division 
   from left to right (by PEMDAS), we get 
    81 / 3 × 9 

    = 27 × 9 

    = 243

3. but when doing multiplication first, we get 
    81 / 3 × 9 

    = 81/27 

    = 3
    (This is WRONG)

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The above example show that when we are doing division before multiplication (by BODMAS) or when we solve multiplication and division from left to right (by PEMDAS) both results are same. But when people try to do multiplication before division they get wrong answer. Let us see some more examples so that we understand it more bitterly.

Example 2 : 125 ÷ 5 × 5 ÷ 5
1. When doing division first (by BODMAS), we get 
    125 ÷ 5 × 5 ÷ 5 

    = 25 × 1 

    = 25

2. When doing multiplication and division from left to right (by PEMDAS), we get 
    125 ÷ 5 × 5 ÷ 5 

    = 25 × 5 ÷ 5 

    = 125 ÷ 5 

    = 25

3. But when doing multiplication first, we get
    125 ÷ 5 × 5 ÷ 5 

    = 125 ÷ 5 × 5  ÷ 5 

    = 125 ÷ 25 ÷ 5 
    
    = 5 ÷ 5 

    = 1
    (This is WRONG)

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Example 3 : 8 ÷ 4 × 4 ÷ 2 × 4 
1. When doing division first (by BODMAS), we get 
    8 ÷ 4 × 4 ÷ 2 × 4 

    = 2 × 2 × 4 

    = 16
    
2. When doing multiplication and division from left to right (by PEMDAS), we get         
    8 ÷ 4 × 4 ÷ 2 × 4 

    = 2 × 4 ÷ 2 × 4 

    = 8 ÷ 2 × 4 

    = 4 × 4 

    = 16

3. but when doing multiplication first, we get 
    8 ÷ 4 × 4 ÷ 2 × 4 

    = 8 ÷ 16 ÷ 8

           1     1
    = 8 × --- × --- 
           16    8

    = 1/16
    (Which is wrong)

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Example 4 : 9 ÷ 3 × 3 ÷ 9  
1. When doing division first (by BODMAS), we get 
    9 ÷ 3 × 3 ÷ 9

    = 3 × 1 ÷ 3

           1 
    = 3 × ---
           3

    = 1

2. When doing multiplication and division from left to right (by PEMDAS), we get         
    9 ÷ 3 × 3 ÷ 9

    = 3 × 3 ÷ 9

    = 9 ÷ 9 

    = 1

3. but when doing multiplication first, we get 
    9 ÷ 3 × 3 ÷ 9

    = 9 ÷ 9 ÷ 9

    = 1 ÷ 9

    = 1/9
    (Which is wrong)

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Example 5 : 2 ÷ 2 ÷ 2 × 2
1. When doing division first (by BODMAS), we get 
    2 ÷ 2 ÷ 2 × 2

           1      1    
    = 2 × --- ×  --- × 2
           2      2    

    = 1

2. When doing multiplication and division from left to right (by PEMDAS), we get         
    2 ÷ 2 ÷ 2 × 2

    = 1 ÷ 2 × 2


       1
    = --- × 2
       2

    = 1

3. but when doing multiplication first, we get 
    2 ÷ 2 ÷ 2 × 2

    = 2 ÷ 2 ÷ 4

           1      1
    = 2 × ---  × --- 
           2      4

    = 1/4
    (Which is wrong)

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Why BODMAS is better then PEMDAS?

After study all above examples we have understand that people should be careful when using PEMDAS. Always keep in mind that solve multiplication and division from left to right similarly solve addition and subtraction from left to right.

Other wise use BODMAS by LETTER B-O-D-M-A-S in such case no need any solution from left to right just do division before multiplication and addition before subtraction. Because BODMAS and PEMDAS are same there will be no different in final result (answers).

Why PEMDAS is awful? (It takes much time) 

There is also one more thing that if we have we have a large number for addition and subtraction i.e.

11 -10 + 9 + 8 – 7 – 6 + 5 + 4 – 3 + 2 – 1

Or have a large number for multiplication and division i.e.

3125 ÷ 125 × 625 ÷ 5 × 25 ÷ 81 × 27 × 9 ÷ 3 ÷ 8 × 4 × 4

Solving these kinds of question from left to right is very awful and time taking. We have tricky solution for these kind of problems which will be discuss in any next article.

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ORDER OF OPERATION ([{(-)}], ()^2 √ , ÷, ×, +, -)

  • What is the correct answer of 6/2(2+1)=? (1 or 9)NEW
  • How MATHEMATICIANS explain answer of 6/2(2+1)=? (1 or 9)NEW
  • Why the answer of 6/2(2+1) should be 9NEW
  • What is the denominator in 6/2(2+1)=? (2, (2+1), 2(2+1), Any other)NEW


  • What is BODMAS? Why we use it?NEW
  • What is PEMDAS? What is different between PEMDAS and BODMAS?NEW
  • What is difference between BODMAS, BEDMAS, BIDMAS, PEDMAS and PEMDAS?NEW

  • Who invented the BODMAS? When BODMAS was introduced?NEW
  • Where we should solve the factorial(!) in BODMAS ? NEW
  • When percentage(%), logarithms and trigonometric involve in BODAMS. How we solve it? NEW

  • Why PEMDAS create confusions?NEW
  • BODMAS Short Questions

  • What is BODMAS?
  • ______________________

  • What is order of operation?
  • ______________________

  • Who invented BODMAS?
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  • Solve 3 - 3 × 2 ÷ 6 = ?
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    BODMAS Questions

  • What is square root of 25?
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  • Solve 10 ÷ 4 of 5 =...?
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  • Solve 2 / 2 - 2 + 2 × 2 =...?
  • ______________________

  • Solve 10-4×0+3÷3 =..?
  • ______________________

  • Solve 7+7÷7+7×7-7 =...?
  • ______________________

  • Solve 3 + 5% =...?
  • ______________________

  • Solve 2e × 100% =...?
  • ______________________

  • If √(0.04)(0.4)a = (0.4)(0.04)√b then a/b ... ?
  • ______________________



  • Solve 5 × (1/5) ÷ (1/5) ÷ (1/5) × 5 =...?
  • ______________________



  • 3 ÷ (5 ÷ 7) = (3 ÷ 5) ÷ 7
  • ______________________

  • Solve 4 - 2 ÷ (1/2) + 3 =...?
  • ______________________

  • Solve 2 - 2 × 2 - 2 ÷ 2 =...?
  • ______________________

  • Solve 3 - 3 × 3 - 3 ÷ 3 =...?
  • ______________________

  • Solve 4 + 4 × 4 - 4 ÷ 4 =...?
  • ______________________

  • Solve -1 + 2 × 0! =...?
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  • Solve -2 + 3! - 1 =...?
  • ______________________

  • Which step is wrong?
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