6÷2(1+2) (A math topic)

I was taught "BIDMAS" (the "I" was for "indices"), but as I remember it, that's supposed to mean brackets, then indices, then division and/or multiplication, then addition and/or subtraction.

By the associative property, division and multiplication should have equal priority since they're essential the same operation. Since they don't, the syntax must be flawed.

http://www.mathgoodies.com/lessons/vol7/operations_exponents.html

See example 3, step 3.

Again, coefficients are implicit grouping.

5/2Y = 5/(2*Y), not (5/2)*Y. (Not that it will mate any difference in this specific example.)

edited 30th Apr '11 3:56:19 PM by BlackHumor

You'll note a distinct lack of variables in OP's expression.

What if you use the distributive property?

6/2(1+2) = 6/(2+4) = 6/6 = 1

Can someone explain why that doesn't apply here?

@Lich: A coefficient of parens is still a coefficient. It's the syntax that's important, not the terms.

@Yami: Because, if it was 9, it would mean ((6/2)*(1+2)).

Basically: 2(1+2) is distinct from 2*(1+2)?

Yep.

Alternatively, we write it as a fraction. Six-over-two-(one-plus-two). Problem solved!

edited 30th Apr '11 4:27:51 PM by AllanAssiduity

Can I get a citation on that.

No. No citations. First, you have to explain how this is important to anything at all. Did a context-free grammar kill a relative? Was your grammar school's math teacher abusive? Please let it out.

edited 30th Apr '11 4:30:45 PM by Tzetze

There is a relevant web comic for this.

http://xkcd.com/169/

The answer is 9. Why?

6÷2(1+2) = 6÷2*3 = 3*3 = 9

In order to be 1 the initial equation would have to be 6÷(2(1+2)). Once what is inside the brackets is simplified, the remaining operations work from left to right. Check any calculator or Google if you don't believe me.

My first thought:

6/2(1+2) = 6/2(3) = 6/6 = 1

Though I now see I did this in the wrong order, as I evaluated the multiplication before the division instead of working left to right.

edited 30th Apr '11 5:05:48 PM by CentralAvenue

It's 9. If you want it to be one, you have to write your notation differently, there's a significant difference between the / symbol and the ÷ symbol.

This.

It's 9.

To those who said 1, your math teachers suck because they should have taught you that Multiplication and Division are weighted equally and they are done from left to right. Same goes for Addition and Subtraction.

"To those who said 1, your math teachers suck because they should have taught you that Multiplication and Division are weighted equally and they are done from left to right. Same goes for Addition and Subtraction."

Your math teachers suck for telling you to capitalize operations.

Your math teachers suck for making you care about this!

6/2(1+2)

2(1+2) = 2(1)+2(2) = 2 + 4

6/2 + 4 = 3 + 4 = 7

There.

edited 30th Apr '11 6:03:18 PM by GreatLich

Your suck teachers suck for making you suck sucks!

I guessed nine, but I was never any good at maths.

^ ...

edited 30th Apr '11 6:03:58 PM by BobbyG

@Lich: COEFFICIENTS HAVE IMPLICIT GROUPING! *glares*

edited 30th Apr '11 6:10:18 PM by BlackHumor

I'm with kashchei and BH.

X/Y(Z) always evaluates equal to X/(Y*Z), because Z is directly associated with Y, not an independent term. operator precedence doesn't even have any relevance for this equation — you just divide the left term by the right one. 1. *

^{FWIW, I'm only interested in practical maths anyway -> programming, in which * usually is evaluated before / anyway — C = http://www.difranco.net/cop2220/op-prec.htm; Python = http://docs.python.org/reference/expressions.html#summary}

I love you Lich

But really. Why do you need to repeat what you think the answer is, and whatever thought you used to get there? It doesn't matter. If someone wrote you the sentence «Alex went to the pet store. The dog the boy they sent owned ran around in circles.», you wouldn't talk about singular they, you'd tell them to write like a goddamn human being!

Order of operations is completely arbitrary. A system where, say, addition takes precedence over division, which takes precedence over exponentiation, which takes precedence over the gamma function etc. is completely possible. It's notation. It doesn't matter. It's just a convenience to express mathematical statements. If the notation is ambiguous, you are doing it wrong, and this must be corrected. Whether the answer is nine or one or seven or aleph null is completely orthogonal to anything even resembling an important fact.