Whether you use BOMDAS or BODMAS the answer is the same

Order of Operations

Apparently there is some discussion on the internet today as to the correct answer to this problem;  8 ÷ 2(2+2) = ?.

It is reported that “Even mathematics experts are wading in – why? Because people are coming out with two different answers: 1 and 16.”

Well, if your accountant or other mathematical expert is telling you the correct answer is 1, it may be time to review whether they are up to the job or not.

There is no conflict in using either BOMDAS or BODMAS as a mnemonic to help remember in which order to carry out the mathematical operations.

BODMAS stands for: Brackets, Orders, Division, Multiplication, Addition, Subtraction. It gives the order of priority in which to carry out operations. Do what’s needed to remove the brackets first. Next in priority is exponents (powers or indices are other names to signify the order of the number), followed by multiplication or division which have equal priority which in turn are followed by addition or subtraction which equally share the lowest priority.

The problem is not with the mnemonics but with some “experts” lack of  understanding of how to use them.  When operators of equal priority are encountered work from left to right across the equation.

Left to right across the equation to be solved is not necessarily the same as left to right across the way the mnemonic happens to be written. BOMDAS is the same as BODMAS. Or PEDMAS is the same as PEMDAS.

8 ÷ 2(2+2) =  8 ÷ 2 x (2+2) 

Brackets first:   8 ÷ 2 x 4

Division and multiplication have equal priority so work left to right on the equation:  in this case division comes first.   4 x 4 =16.

 

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9 Responses to Whether you use BOMDAS or BODMAS the answer is the same

  1. Robert says:

    Since math exists not for the purpose of itself and just to have fun with it, but for us to use it in in every day work and assigment solving, would you please help me sorting out my current question from reality? I have 8 extra chairs, and my friends are comming over. They are two couples from work and two couples from colledge. How do I devide my 8 chairs for them? Can you put that in a single line math problem for me, please? Much appreciated!

  2. Robert says:

    Hello, dear Admin! The question is not for me to get the result for myself, but was directed to the author of this article. To clarify: How many chairs per person will there be left after we devide 8 chairs on 2 couples from work AND 2 couples from college comming over? Please, put it in a single line math problem, it’s a simple math. Thank you alot!

    • Admin says:

      If you have 8 chairs to divide between 2 couples from work and 2 couples from college each person gets one chair.

      Here we have brackets within brackets. Inner brackets are done first.

      8 ÷ [ (2×2 ) + (2×2) ] = 1

      8 ÷ [ (4 ) + (4) ] = 1

      8 ÷ [8 ] = 1

  3. Robert says:

    Thank you again for your answer! But, I still have questions. You say that the math assignment from the article, once you solve the brackets, you solve what is left 8 ÷ 2 x 4) calculating from the left to right. I must say I don’t remember ever hearing that rule. How is calculating math corelated with reading a text sentence, and what if I’m from middle east, reading arabic, from right to left? Keeping in mind that the very word algebra comes from arabic language..

    • Admin says:

      Maths can be considered as a language that deals with numbers. Over time we have developed methods to use it to solve problems. Any correlation with a language like english or arabic is coincidence. If our methods are to apply universially we need to agree a common set of rules as to how they work. Things we use often tend to have shortcuts deveolped to help us remember them or tell us how to use them. BOMDAS is one such shortcut to the recall how to deal with the order of operations. When such shortcuts are used often they in turn often get shortened and more is to be understood as holding true than is specifically stated. Work from left to right for operations of equal priority falls into this understood even if unstated part of the rule.

      • Robert says:

        “Work from left to right for operations of equal priority falls into this understood even if unstated part of the rule.”
        Well, this is exactly the part I was interested in the most, and least explained. Who, when, where.. When was this unstated rule concieved, by who, and when and how was it ever globaly accepted as a rule?

      • Admin says:

        I am afraid that the who, when and where of this rule being conceived is beyond the knowledge I have on the subject.

  4. Angelo-Felisimo-La-Cruz says:

    Robert asks “Who, when, where.. When was this unstated rule concieved, by who, and when and how was it ever globaly accepted as a rule?”

    Greetings Robert,

    I do not have an answer to Your specific question, but maybe the following might help give a mathematical comprehension for this rule.

    Let a, b and c be Real numbers.

    __________________________
    ADDITION AND SUBSTRACTION PERFORMED FROM LEFT TO RIGHT:

    Then a – b + c = a + (-b) + c

    Here (-b) is read as “negative b”.

    From the COMMUTATIVE PROPERTY OF ADDITION We know that

    a + (-b) + c

    Will give the same answer if evaluated from left to right or from right to left.

    But this is not the case for

    a – b + c

    because SUBSTRACTION IS NOT COMMUTATIVE i.e a – b ≠ b – a.
    for a ≠ b.

    Thus

    a – b + c

    or from the COMUTATIVE PEOPERTY OF ADDITION is equal to

    (a – b) + c

    has to be evaluated from left to right.

    __________________________

    MULTIPLICATION AND DIVISION PERFORMED FROM LEFT TO RIGHT:

    LET b ≠ 0

    Then a ÷ b • c = a • (1/b) • c

    Here (1/b) is read as “inverse of b” or “1 over b”.

    From the COMMUTATIVE PROPERTY OF MULTIPLICATION We know that

    a • (1/b) • c

    Will give the same answer if evaluated from left to right or from right to left.

    But this is not the case for

    a ÷ b • c

    because DIVISION IS NOT COMUTATIVE i.e a ÷ b ≠ b ÷ a
    for a ≠ b.

    Thus

    a ÷ b • c

    or from the COMMUTATIVE PROPERTY OF MULTIPLICATION is equal to

    (a ÷ b) • c

    And thus has to be evaluated from left to right.

    _______________________

    I hope this is helpful and that it gives an answer to Your Question from Mathematic Herself.

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