6÷2(2+1)

Saturn · 2012-12-16 05:17:10

Is it 1 or 9?

DYRE · 2012-12-16 05:18:44

9. You do things in parentheses before other operations, but just putting a number next to parentheses is the same as if you wrote a multiplication sign in between, like 6÷2×(2+1).

Saturn · 2012-12-16 05:29:55

Right so it would be

6 / 2 x 3

You do the division first right?

Then I guess some calculators are wrong?

Nova · 2012-12-16 05:39:05

I don't see how you'd get 1 anyway...

Saturn · 2012-12-16 05:50:37

6 divided by 2 times 3 could equal 1.

Nova · 2012-12-16 06:12:53

But... even without knowing to do things in brackets first, you should know that you do division before addition. Right?

Saturn · 2012-12-16 07:01:19

Do you do division before multiplication?

Whale · 2012-12-16 07:25:16

It would be 9 IIRC

Eelektross · 2012-12-16 07:31:02

^^ trick question

some people say that multiplication would come before division because of the american (PEMDAS) system

others say that division would come before multiplication because of the british (BIDMAS) system

however, both PEMDAS and BIDMAS stand for, respectively:

Parentheses Exponents Multiplication OR Division Addition OR Subtraction

Brackets Indices Division OR Multiplication Addition OR subraction

Whether you do division or multiplication first depends on which cums first on a left-to-right scale.

So the answer would be

6/2 x 3 = 3 x 3= 9 beacause 6/2 comes before 2x3

glennmagusharvey · 2012-12-16 07:46:13

Multiplication and division are on the same "level" so you just do those left to right as long as there are no parentheses.

It's like how addition and subtraction are also on the same "level".

So for 6 / 2 x 3, you have to do the 6/2 first, to get 3, and 3x3 is 9.

You can't do the 2x3 first; that would be like taking 6 - 2 + 3 and saying you do the 2+3 first.

Some calculators will account for order of operations as they do stuff. Some don't, however. So you can't trust calculators to figure out order of operations for you. They just do operations between two numbers, one operation at a time.

Not sure if the following bit is useful but it's how I like to think of it:

Spoiler:

One way that might help to think of this is to think of addition and subtraction as opposed forces operating on the same plane, and similarly for multiplication and division. So 6 - 2 + 3 basically means you are up six, down two, and up three, so no matter how you do it that "two" is still "down two". Similarly, 6 / 2 x 3 is like expanded by six times, contracted by two times, and expanded by three times--a bit more messy to picture, but it works the same way. Perhaps an easier way of picturing the latter is to use the idea of division as a fraction: now you get to say six above, two below, and three above, and you have

6 x 3

2

Which is also clearer.

See, as long as you keep the sign or status of something the same, within either the realm of add/sub (this really is called the negative or positive sign) or the realm of mult/div (whether it's place is above or below), you actually CAN move stuff around...but you just can't switch numbers around without their attached "direction". (You also can't switch numbers around between the two realms.)

Eelektross · 2012-12-16 07:52:09

thats what i said though

Saturn · 2012-12-16 08:16:34

Wow. For the longest time, no one ever told me that Multiplication was on the same level as Division and Addition was on the same level as Subtraction.

Stormtroper · 2012-12-16 08:35:27

The order of operands/factors doesn't alter the result. Since subtracting a positive number is the same as adding a negative number (and vice versa) and dividing is the same as multiplying the inverse of a number, it follows that it doesn't matter the order they're in. Or:

a - b = a + (-b) = (-b) + a = - b + a

(a x b)/c = a x b x 1/c = (1/c) x a x b = (a/c) x b

Nyktos · 2012-12-16 08:55:04

This is why you don't use division signs.

Naas_Human · 2012-12-16 09:40:41

Google's online calculator gives me 9. So does this Casio thing I have.

glennmagusharvey · 2012-12-16 09:45:55

I think it's usually the "four-bangers" (the basic four-function calculators) that don't do order of operations if you just type the thing this thread's title into it.

Raydere · 2012-12-16 10:07:35

The idea is that division is basically just multiplying by the reciprocal of the divisor. Likewise subtraction is just changing one of the two terms' +/- sign and then adding the two terms.

That is to say, 15 / 5 is just 15 * (1/5) and 4 - 2 is just 4 + (-2).

Bee · 2012-12-17 01:59:56

Multiplication/division are on the same priority because they're exactly the same operation, just with opposite arguments. Same for addition/subtraction.

6÷2(2+1) is written objectionably, but not ambiguously. It's 9.

Fuschlatz · 2012-12-17 02:05:22

I'd actually say that the answer is 1, since I was taught to always give implied multiplication higher priority than division (i.e. I basically treat the equation as 6 / [2 * (2 + 1)]).

Bee · 2012-12-17 02:17:05

It's an occasional contention and you'll see a straggler like Wolfram Alpha get through every once in a while, but not often at all -- and when it does happen, they'll almost always clarify their formatting or it will be immediately obvious from the steps they took to get to that expression.

Looking back through my college math and physics texts I can't find a single one that doesn't sidestep the issue altogether with horizontal bar typeset or explicit parentheses. If the expression is longer than 5-6 characters and contains division, they'll usually go ahead and just format the whole thing.

Nova · 2012-12-17 02:23:53

That's pretty silly. Division even comes ahead of multiplication in BODMAS.

Saturn · 2012-12-17 02:30:37

Well it does say it. D is before the M.

glennmagusharvey · 2012-12-17 02:33:58

@Fuschlatz: That looks like more of a programming convention than a math thing.

Fuschlatz · 2012-12-17 02:38:18

I guess my HSC-level maths textbooks were all written by programmers, then?

Bee · 2012-12-17 02:39:11

It is for Wolfram anyway. In pretty much every other case it's quicker and considerably less complicated to back up your parser a space and call multiplication on the bracket if you see one with no operator token than to make an entire extra pass looking for implied multiplication.

Or course, REAL men do Reverse Polish notation.

6 2 / 2 1 + *

Super Lazuli · 2012-12-17 02:39:40

which cums first

whoa

we are not ready for that kind of material in this forum sir

Fuschlatz · 2012-12-17 02:41:10

Haha, I was waiting for someone to point that out...

Or course, REAL men do Reverse Polish notation.

6 2 / 2 1 + *

I can kind of understand that because I have the context, but it still looks confusing as shit so I can't see myself using that unironically any time soon. Just because calculators read math in that way does not mean organic beings have to.

Bee · 2012-12-17 02:52:31

Yeah, it's main use is as a programming exercise to understand stacks. Hewlett-Packard had a massive hardon for it in the 60's, but that was back when everything was so cumbersome that bypassing order of operations was actually a pretty big simplifying step.

glennmagusharvey · 2012-12-17 02:54:27

<3 Rocket Girls

DYRE · 2012-12-17 05:08:54

That's pretty silly. Division even comes ahead of multiplication in BODMAS.

But it comes after in PEMDAS.

In any case, you're supposed to just do them in order from left to right. Same for addition and subtraction.

And in practice it never ever matters because you never actually see anything written using a division sign.

Nova · 2012-12-17 05:12:47

But it comes after in PEMDAS.

But Fuschlatz is Australian, and thus would be taught BODMAS.

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