6÷2(1+2) = ?

well said

as a matter of fact wrote:

PE(MD)(AS) wrote:

The thing they're trying to trick you on is that PEMDAS isn't multiplication, then division, then addition, then subtraction. Rather it is multiplication and division, then addition and subtraction, left to right.

If you apply PEMDAS incorrectly, you'll multiply first, then divide. If you use it correctly, you'll go left to right and do 6/2 first, then multiply.

6/2(1+2)

6/2(3)

3(3)

9

That's exactly what I said. Left to right for multiplication OR division. Whichever one you encounter first, you do. The answer is always 9 if you use the order of operations correctly.

CORRECT!

Bad Wigins wrote:

feef wrote:

Transformations for the above trivial cases exist so that only associative operations are necessary, e.g., a%b => a*(1/b), or more generally a*b^(-1)

While I miswrote it as "commutative," it's no mere transformation, it's the very definition of division! It's how it is read.

9/2a? that's 9/2 x a,, i.e. 9a/2, unless you put 2a in parentheses. Absolutely no ambiguity about it at all.

Division is also non-commutative, i.e., a/b != b/a. I was only opining that its non-associativity imparts an even greater burden with respect to composition (one of defining properties of an algebra is the ways in which expressions can be decomposed and recomposed).

I'm ignoring your second point because you seem to be confused and I don't care.

I should walkback this comment slightly.

While I stand by the need for the same convention to have the same interpretation, and the need to understand the one who wrote the equation, or the problem being modeled, it appears I have understated the issue as simply one of "implied multiplication by juxtaposition". Historically there have been other conventions proposed and used:

- the "obelus" division sign (the line with two dots) being performed *after* you evaluate the left and right sides

- the well known PE(MD)(AS) or equivalents

- a strict PEMDAS putting multiplication *before* division

- a strict PEDMAS putting division *before* multiplication

So if you found "1", you could be following the old "obelus" convention, a strict multiplication first PEMDAS convention, or implicit multiplication convention. But if you were taught PE(MD)(AS) is the only rule, you will find "9".

It seems that PE(MD)(AS) is a position highly favored by North American teachers, who lobbied for calculators like Texas Instruments and Cascio to change, but that mathematicians, engineers, physicists, in and out of North America, and teachers outside of North America, generally use a PEJMDAS rule (J = implicit multiplication by juxtaposition). You might think it is because they are too lazy to use parentheses, but it does improve readability, while the context should prevent ambiguity. "9a^2 / 3a " is more readable than "9a^2 / (3a)", and not likely to generate ambiguity.

Even those who proposed PEMDAS in the early 1900's violated this rule in the very same textbooks when it came to "implicit" multiplication by juxtaposition, although all the examples I have seen included variables rather than expressions solely with numbers like 2(1+2) . It makes sense to me to interpret "3x / 2y" as "(3*x) / (2 * y)".

If you found your way to this thread, you have already wasted time. You could do worse things with your time than spend another 17 minutes with this Australian math tutor/physicist, who walks you through the history from the early 1900s to today, and let her have the final word.

The subject line is correct.

6➗2(1+2) does = ?

I got 1 using PEMDAS

The answer is 9

9

The answer is nine.

I think it is 9 but it is not surprising if I am wrong. Guys, admit it, who hated maths at school and college as much as I did? Honestly, I couldn't stand this subject, because it's boring for me. I loved the humanities, where you can reflect, guess, evaluate… And the numbers and formulas just didn't sink in. I always had to take out a calculator and double-check whether I had counted everything correctly. Well, I'm still opening online divisibility calculator, because I get very confused when I count in my mind.

1 is the answer

Easy 9

6÷2(1+2) = ?

I'd do brackets first 2(1+2)

2x1 + 2x2 solving the brackets = 6

6 divided by 6 = 1

It isn't written as 6÷2 x (1+2) = ?

To me 2 is part of the brackets and that takes precedence.

That is just how I would do it.

Multiplication and division are effectively the same operation, just like addition and subtraction, so multiplication has no precedence over division. Technically, the answer should be 9, but the division symbol used in the original equation is ambiguous and there's a reason nobody uses it past like 5th grade. Most people would reasonably interpret it as 6 / (2(1+2)), which yields 1 obviously. But not for the reason you seem to think.

Yours steps are correct as that is the way it is taught in schools. People who claim the answer is 9 are sloppy programmers, and will fail a simple math class. The math should be programmed as, 6÷(2(1+2)). The answer is 1. If your answer is 9 then you will get fired from your programming job.

Yes. The coefficient [2] of the monomial [2(1+2)] is to be treated as part of the parenthesis. Try putting a variable in the monomial [for example, 2(1x+2)] and you'll see how treating a coefficient as just a step of multiplication within PEMDAS is problematic.

To solve this any other way is to follow the conventions of machine coding (excel, calculators including Google, Wolfram Alpha) which exist as a convenience for those programming software and spreadsheets but disregard the more complex nuances of mathematics.

If it's supposed to be written as 6÷(2(1+2)) then they should have written it like that.

Most languages do not support implicit multiplication (i.e. you'd have to write 6/2*(1+2) or 6/(2*(1+2)). So your argument about programming is just preposterous.

Again the answer here is that clarity in communication is key, especially if there are different expectations or standards floating around.

Doesn’t your second paragraph just invalidate the first? Each context has different rules. There is no correct answer. Groups of people (users of a software, a field of math, a high school curriculum) agree on rules and follow it. There is no higher authority or absolute truth here.