Order of Operations is WRONG

[MiTT3NZ]

Okay, so just had a mammoth Facebook debate about this. Basically, what do you think the answer to this equation is?:

40 + 40 x 0 + 1

It's 41, apparently. I say 1. Here's why...

Order of Operations (commonly taught as BODMAS, or other variations apparently, depending on where you live) basically state that you must follow these steps:

1) Moving from left to right in the equation, calculate what's inside brackets.
2) Moving from left to right in the equation, calculate the square roots
3) Moving from left to right in the equation, multiply and/or divide any multiplication/divisional instances.
4) Moving from left to right in the equation, add and/or subtract any addition/subtractional instances.

So, using this method, this is how we work out this equation...

40 + 40 x 0 + 1
= 40 + 0 +1
= 40 + 1
= 41

This shouldn't be the case though. Whilst I agree with the first two steps of the order of operations, the resulting equation should be calculated from left to right, regardless of whether it's from step 3 or 4.

That would mean that we calculate it this way:

40 + 40 x 0 + 1
= 80 x 0 + 1
= 0 + 1
= 1

Yes, the answer should be 1. Here's why:

Brackets are there for a reason, and it isn't to keep pupils/students on their toes. Basically, let's say I want to add together what I've got in my savings jar and what's in my wallet. I've got a £2 coin and a £1 coin in my savings jar, and a £10 note and £5 note in my wallet. So

(2+1) + (10+5) = 3 + 15 = 18.

That is proper useage of brackets in a mathematic formula, because you need to know the sum inside of the brackets in order to proceed. Order of Operations, on the other hand, essentially assumes where brackets should be. Let's go back to the original equation.

40 + 40 x 0 + 1

With Order of Operations, this is how it sees the above equation:

40 + (40 x 0) + 1

But, why? Why see something that isn't there? Why assume? I'll be honest, I haven't a fucking clue. I mean, why does it not see it like these two instead?

(40 + 40) x 0 + 1
40 + 40 x (0 + 1)

I know, I know, it's because Multiplication and Division are a step before Addition and Subtraction, but saying it is so does not justify it. I can justify my reasons against it though.

First off, it is not a law of mathematics. 40 x 2 is definitely 80 because there are two lots of that number, this is fact. That is a mathematical law, and you cannot escape that fact at all. Ever.

What the Order of Operations does is scans the equation for brackets. If it cannot find them, it will leech onto the nearest multiplication or divisional problem. It is essentially one of the earliest forms of auto correct. It isn't asked for, and isn't needed.

If an equation is supposed to be:

40 + (40 x 0) + 1

Then it will be written so.

Order of operations puts words in your mouth. After brackets and square roots, equations should be tackled bit by bit from left to right. This is how and why:

Let's look at it this way in nursery terms...

Greg gets a shipment of apples every day. Within a day, those apples go bad, so he has to throw them away. Greg gets paid a flat rate of £1 every two days, and an extra £1 for every apple he has sold. He is trying to calculate how much money he will make on payday.

On Monday he got a shipment of 40 apples.
On Tuesday he got a shipment of another 40 apples.
He sold no apples.
However, he still gets £1 for every two days.
So therefore:

40 + 40 x 0 + 1
= 80 x 0 + 1
= 0 + 1
= 1

That is left to right calculating. Order of Operations states that, unless you put 40 + 40 in brackets, it will create invisible brackets around 40 x 0, which makes as much sense as trying to fly to work using my toothbrush encapsulated in ice.

Again, Order of Operations is not fact, it is not a mathematical law, however much mathematicians may try to bill it as this. At best, it is the way in which equations are read. It reminds me of comedy films where someone tries to speak another language, only for the resulting speech to be completely absurd.

Order of Operations is not fact, whichever way you look at it. Mathematics can still continue to function correctly if steps 3 & 4 are ignored. If brackets are needed, they are used.

Order of Operations is like Clippy from old skool MS Office auto-correcting everything you say and mostly getting it wrong, yet when it gets it right, it still has that squiggly green line underneath that always reappears despite how many times you click ignore.



Mittens has disproven a so-called mathematical "fact". Bow your heads in awe.

[Bluecast]

[youtube]http://www.youtube.com/watch?v=2QamU4-8NUw[/youtube]

[Kenny]

That's basically it. The brackets dictate everything.

Without them, we follow the equation with whatever group of numbers come immediately after the next.

[south carmain]

^ so the answer is 1? 40+40=80 80x0=0 0+1=1

[Kenny]

Exactly. That's pretty much the whole argument.

[south carmain]

cool, I'll probably never multiply something by 0 in my life but good to know

[MiTT3NZ]

It pisses me off though, because the Order of Operation is seen as fact and essentially a law in maths, the multiplication and division would be done first, meaning the answer would be 41, and that's wrong. The fact that mathematicians back this up just irritates me.

Order of Operation should only ever apply when brackets are involved, or just drop steps 3 & 4, otherwise it makes no sense whatsoever.

[wude]

40 + 40 x 0 + 1 is always 41 and it's different from the other equations you posted

[Spokane]

cool, I'll probably never multiply something by 0 in my life but good to know

Your a blasphemer in the eyes of math teachers and math curriculum. They throw multiply by 0 and divide by 0 in just for shits and giggles sometimes.

[Bluecast]

0. If you multiply that by 0 then divide by 0 then + 0 you get how much I understand math and was my worst subject. However that's still the same number of fucks I give.

[MiTT3NZ]

40 + 40 x 0 + 1 is always 41 and it's different from the other equations you posted

The point is that it shouldn't be. Going back to the nursery school example...

Greg gets a shipment of apples every day. Within a day, those apples go bad, so he has to throw them away. Greg gets paid a flat rate of £1 every two days, and an extra £1 for every apple he has sold. He is trying to calculate how much money he will make on payday.

On Monday he got a shipment of 40 apples.
On Tuesday he got a shipment of another 40 apples.
He sold no apples.
However, he still gets £1 for every two days.
So therefore:

40 + 40 x 0 + 1
= 80 x 0 + 1
= 0 + 1
= 1


Whilst I agree that 40 + (40 x 0) + 1 = 41, the Order of Operations would assume those brackets were there regardless of whether they were or not.

This is totally flawed logic, as mathematics is set in stone, whereas this rule is man-made. Maths doesn't actually need it, it's just a way of interpreting an equation without confusing people, which in turn does the exact opposite.

Therefore, it may be widely accepted, but that doesn't mean that it is right, so to call it outright fact is wrong.

A much simpler and more logical rule would be for Order of Operations to be:

- Brackets first from left to right.
- All other equations calculated in sequential order from left to right.

That is the only way it should be, as you need to know the calculations within brackets in order to proceed, everything else is just a way of doing it, the calculations can be made regardless of whether or not this rule is in place.

[south carmain]

cool, I'll probably never multiply something by 0 in my life but good to know

Your a blasphemer in the eyes of math teachers and math curriculum. They throw multiply by 0 and divide by 0 in just for shits and giggles sometimes.

my maths teacher was a bitch anyway, pretty dumb as well, she was a 50 year old fat spiteful cat lady

[wude]

40 + 40 x 0 + 1
= 80 x 0 + 1
= 0 + 1
= 1

that's wrong because there are no brackets

On Monday he got a shipment of 40 apples.
On Tuesday he got a shipment of another 40 apples.
He sold no apples.
However, he still gets £1 for every two days.
So therefore:

40x0+40x0+1
0+1
1

or

(40+40)x0+1
80x0+1
1

[MiTT3NZ]

Yes, but the point is that Order of Operations assumes that there are invisible brackets in the equation.

My way isn't wrong, it just doesn't follow the Order of Operations. The Order of Operations is not a mathematical law, it is a way that people interpret equations.

The very fact that there is no logic in it means that it should not be set in stone.

The whole idea behind it is to make an equation less ambiguous, yet if you take my rule and apply it (Brackets left to right, then everything else left to right in sequential order), it works, and it is much more simplified.

So why then must the "Order of Operations" be consider the way and the only way to calculate an equation?

I haven't done extensive research or owt, but even the slightest bit of digging revealed that it was introduced between 1200AD - 1500AD.

That means that it isn't a mathematical law, it is a man-made way of reading certain equations, so for it to be considered the way is wrong.

[wude]

Yes, i understand your point, and you're right , but stuff will get confusing without the "invisible brackets"