6÷2(1+2) = ?

2600 bro wrote:

The point of math notation is to express ideas clearly.

The fact this is interpreted so ambiguously shows it's just written poorly. Use fraction notation...

^ This.

It should be clear from the problem you are modeling whether (1+2) was meant to be in the numerator or denominator.

There is no rule that puts implied multiplication before multiplication/division (although for "6/2x" I would evaluate 2x first).

Parentheses should be used to remove ambiguity in such inline expressions. Or better yet, avoid inline expressions:

6

----- X (1 + 2)

2

if that is what is meant, or

6

------------

2 X (1 + 2)

rekrunner wrote:

There is no rule that puts implied multiplication before multiplication/division

there's no difference between the two, as division is merely multiplication by the -1th power - and exponent comes before either. i.e.

x / y

is an equivalent expression to

xy*-1

avoid inline expressions:

not really possible when programming or doing spreadsheets. Convention has always been to enclose denominator in parentheses

2600 bro wrote:

The point of math notation is to express ideas clearly.

The fact this is interpreted so ambiguously shows it's just written poorly. Use fraction notation...

But following traditional 5th grade algebra and PE(MD)(AS), the answer is 9. Mult/Div and Add/Sub have the same priority and you just move left to right. So this is just 3 * 3 = 9.

It’s not written poorly. You just can’t read. If you put that into a calculator or even excel, it would be read correctly.

Ambiguous would be something like: 6 ÷ 2 * (1+2)

2x is inseparable. They get multiplied or divided together.

Were your parents cousins?

Jeff Albertson wrote:

2600 bro wrote:

The point of math notation is to express ideas clearly.

The fact this is interpreted so ambiguously shows it's just written poorly. Use fraction notation...

But following traditional 5th grade algebra and PE(MD)(AS), the answer is 9. Mult/Div and Add/Sub have the same priority and you just move left to right. So this is just 3 * 3 = 9.

It’s not written poorly. You just can’t read. If you put that into a calculator or even excel, it would be read correctly.

Ambiguous would be something like: 6 ÷ 2 * (1+2)

2x is inseparable. They get multiplied or divided together.

Were your parents cousins?

If you put =6/2(1+2) into Excel it wouldn't give a result. Excel would provide a suggestion to correct it to =6/2*(1+2)

Jeff Albertson wrote:

2600 bro wrote:

The point of math notation is to express ideas clearly.

The fact this is interpreted so ambiguously shows it's just written poorly. Use fraction notation...

But following traditional 5th grade algebra and PE(MD)(AS), the answer is 9. Mult/Div and Add/Sub have the same priority and you just move left to right. So this is just 3 * 3 = 9.

It’s not written poorly. You just can’t read. If you put that into a calculator or even excel, it would be read correctly.

Ambiguous would be something like: 6 ÷ 2 * (1+2)

2x is inseparable. They get multiplied or divided together.

Were your parents cousins?

Obviously you don’t know what inseparable means in mathematics, but that’s neither here nor there.

What is the answer to the thread title problem?

Please don’t get it wrong. Even cheat and plug it into Excel or Wolfram Alpha like you suggested if you have to. If you get it wrong, then we’ll know you weren’t being condescending when you asked if the other poster’s parent were cousins, but rather you were just wondering if their family was like your kinfolk.

PE(MD)(AS) wrote:

as a matter of fact wrote:

PEMDAS. There is only one rule......... You go left to right for multiplication or division after you have solved the parentheses and exponents.....

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.

seriously tho wrote:

as a matter of fact wrote:

PEMDAS. There is only one rule......... You go left to right for multiplication or division after you have solved the parentheses and exponents.....

"As a matter of fact" you're wrong, hence my comment.

Intentionally written to be fairly interpreted in more than one way.

No. You're just dumb, and hence, you didn't learn elementary math in elementary school.

Anyone who thinks this is an issue of mathematics is room temperature. This is a linguistics questions. Be ye daft?

9

We used to call the mnemonic BODMAS for Brackets Orders… instead of PEDMAS like American kids seem to be taught.

grammarian-linguist wrote:

Anyone who thinks this is an issue of mathematics is room temperature. This is a linguistics questions. Be ye daft?

“is room temperature” means dead? Strange interesting phrase if it was intentional.

I calculate it as 9, and wolfram alpha agrees. But it's stupid because it is purposely trying to confuse people as to where the multiplication of the parens is applied.

Rewrite your equation in some sane form. It's garbage like this that makes people think they're bad at math or don't like math. Nobody who actually uses math for anything other than Facebook gotcha posts would ever write this equation like this way it's needlessly unclear.

2600 bro wrote:

The point of math notation is to express ideas clearly.

The fact this is interpreted so ambiguously shows it's just written poorly. Use fraction notation...

But following traditional 5th grade algebra and PE(MD)(AS), the answer is 9. Mult/Div and Add/Sub have the same priority and you just move left to right. So this is just 3 * 3 = 9.

Correct. This thread seems to pivot on whether MDAS is in that order vs M or D then A or S, meaning Mult and div left to right whichever come first. It doesnt mean Multiplication first then division. My Nuns would have said 9.

B0NER wrote:

Jeff Albertson wrote:

It’s not written poorly. You just can’t read. If you put that into a calculator or even excel, it would be read correctly.

Ambiguous would be something like: 6 ÷ 2 * (1+2)

2x is inseparable. They get multiplied or divided together.

Were your parents cousins?

Obviously you don’t know what inseparable means in mathematics, but that’s neither here nor there.

What is the answer to the thread title problem?

Please don’t get it wrong. Even cheat and plug it into Excel or Wolfram Alpha like you suggested if you have to. If you get it wrong, then we’ll know you weren’t being condescending when you asked if the other poster’s parent were cousins, but rather you were just wondering if their family was like your kinfolk.

The truth often lies between. It is not "written poorly". My kids are on this stuff right now and this is exactly how this problem would be written. Sometimes, they write it differently on purpose so as to test your consistent application of order of ops. Its eems to me the ONLY point to this peobem is seeing if people know that MD means mult OR div left to right vs Mult first then div?

seriously tho wrote:

It is technically ambiguous by some rule or some other rule. If you put multiplication before division, its 1. Intentionally written to obfuscate and be ambiguous so it doesnt make someone dumb or wrong to think it's something else.

Very well said.

alpha lobster wrote:

seriously tho wrote:

It is technically ambiguous by some rule or some other rule. If you put multiplication before division, its 1. Intentionally written to obfuscate and be ambiguous so it doesnt make someone dumb or wrong to think it's something else.

Very well said.

There's a reason why the obelus isn't used in any professional mathematical setting.

grammarian-linguist wrote:

Anyone who thinks this is an issue of mathematics is room temperature. This is a linguistics questions. Be ye daft?

Technically you are right. The internets say the answer can be 1 or 9 depending on if you are over 100 years old. All math tests today would want 9, that is the Order of Ops. But, before the advent of the division symbol, you can see how doing it as 2(3) under 6 would be evaluated differently by all of us I suspect. 6/2(3)

Isnt it great that even math isnt certain?

I don't know and I don't care. At a glance I'd say 1, but like others said, it's intentionally ambiguous (which is the whole point of why you see these posted on Facebook and such) unless you rigorously apply some rule.

I'm a engineering professor and do simple arithmetic like this every day, but I haven't used a division symbol in 40 years and have no idea how to do one on the keyboard. The division symbol is shorthand for a fraction, it's a dot over another dot where the things before or after fill in the dots*.

Just use the fraction and use enough parentheses to make it clear if you're typing it in one line. Students still mess it up if I write it in one line even if I have the parentheses correct, so it's much better to use the equation editor and do it right.

*perhaps apocryphal, but it makes sense