Order of calculations

This has been floating around on Facebook:

Thousands of comments, all with different answers. :slight_smile:

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?

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

6 โ€“ 1 ร— 0 + 2 รท 2
= 6 โ€“ (1 ร— 0) + (2 รท 2)
= 6 โ€“ 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 โ€“ 4x3. Without the BODMAS rules, such expressions would be a lot more cumbersome to write down.