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Order of calculations

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« on: September 01, 2012, 18:03:25 PM »

This has been floating around on Facebook:

Thousands of comments, all with different answers. :-)

I get 7, using the BODMAS rule. But I note some people refer to the PEMDAS rule. Never heard of it (I assume the last four letters stand for multiply, divide, add, subtract, but what does P and E stand for?), and using it some people get 5, while others get 6 or 7. Does the order in which one multiplies and divides really not matter? It seems not to matter in this particular problem, but I recall having seen cases where it matters a great deal, and you get two completely different answers depending on whether you first divide and then multiply, or first multiply and then divide.

Is the BODMAS rule simply a convention, or are there other reasons why it must be followed?

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In solidarity with rwenzori: Κοπρος φανεται

« Reply #1 on: September 01, 2012, 18:49:54 PM »

Multiplication and division are hierarchically equal, as are addition and subtraction.  However, multiplication/division takes precedence over addition/subtraction.  Therefore,

6 – 1 × 0 + 2 ÷ 2
= 6 – (1 × 0) + (2 ÷ 2)
= 6 – 0 + 1
= 7

There is no other valid answer.  Any other answer reveals a misunderstanding of BODMAS/BEDMAS/BIDMAS/PEMDAS.

Remember that multiplication/division and addition/subtraction are binary operations, i.e. they take two operands.

The BODMAS rules are a convention and they derive mostly from the way we write algebraic expressions such as polynomials, e.g. y = 3x2 – 4x3.  Without the BODMAS rules, such expressions would be a lot more cumbersome to write down.

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