Mathematics division symbol

[Frane Selak]

I keep seeing these daft equations you have to work out popping up on facebook and I want to tell everyone they are wrong but I know I am in reality but don't think I should be.

Now I know there is an order of doing things, BODMAS/PEDMAS etc and its the accepted way but there are different styles of writing the division sign. ÷ or / or ------ (without the gaps)

So why is 32÷8x3 = 12, 32/8x3=12 but 32 on the top of the line and 8x3 below the line =1.33333

To me the dot in the division sign represents one number or set of numbers and the dot below the line represents the other set and one set should get divided by the other, not done in order.

[Frane Selak]

Ok, why are there loads of posts in the lounge on "my kids maths homework" but this one has been moved to the science forum?

[AndyTR]

That's because in math you work left to right on the first sum and top and bottom working on the second sum. You'd need to rewrite the first sum to be 32÷(8x3) = 1.3333 for them to be the same. HTH.

[smokey mow]

In the absence of brackets defining whether the 3 is above or below the line order of operations goes from left to right so the equation would be 32/8=4 and then 4x3 =12

[Frane Selak]

I know all that but didn't anyone pick up on what I said about the way the symbol is written. Surely when the division symbol was invented they meant it to work like this.



I know it doesn't work like this but can no-one see what I mean.

although I suppose the lower dot could mean just the 8 goes under and not the rest of the equation.

Edited by Frane Selak on Sunday 22 February 09:43

[AndyTR]

I've not heard an obelus described in that way, it's just a short form symbol to indicate division as far as I'm aware. It's the same as /.

[Frankthered]

Frane Selak said:

I know all that but didn't anyone pick up on what I said about the way the symbol is written. Surely when the division symbol was invented they meant it to work like this.



I know it doesn't work like this but can no-one see what I mean.

although I suppose the lower dot could mean just the 8 goes under and not the rest of the equation.

Edited by Frane Selak on Sunday 22 February 09:43

No, I don't think it was. The way I see it, what you are doing is imagining a set of brackets around the (8x3) to say you should do that bit first.

Multiplication and division have "equal" status in the BODMAS / PEDMAS mnemonic (some people write it as PEMDAS), as do addition and subtraction, so it would be BO(DM)(AS).

As an engineer, whenever these things pop up on FB (they are just to cause disagreement IMHO) I always want to know the context so that I can add the brackets as required to make the expression make sense and give me the answer I need.

The fractional representation (the line) is clearer because it is like putting brackets around everything on the top and dividing it by (brackets around) everything on the bottom.

[otolith]

The primary school division symbol is appropriate for primary school arithmetic. The answer to all of those puzzles is “write it out properly like an adult”, and there will be no ambiguity.

[Deviation]

I don’t really understand the problem.

The order of operations is: 32/8, then x3.

If it was 32/(8x3) then you’d be correct, but it isn’t.

[Sporky]

otolith said:

The primary school division symbol is appropriate for primary school arithmetic. The answer to all of those puzzles is write it out properly like an adult , and there will be no ambiguity.

Yup. This is why brackets are first in the order of operations - they absolutely eliminate ambiguity.

[InitialDave]

They're always just designed to promote arguments and get people engaging/posting in the comments.

Fundamentally, if there's ambiguity in how an equation is intended to be understood, it should be reformatted to remove it.