Math question help

[Duke: A Dynasty]

On another thread there is a huge argument going on over the answer to this. Everyone is saying its 2 or 288.



48/2(9+3)

[dukebluelemur]

On another thread there is a huge argument going on over the answer to this. Everyone is saying its 2 or 288.



48/2(9+3)

Parenthesis always come first. Then left to right. Would people be confused if it was written like this? 48 ÷ 2 x (9+3)

So the answer is 288.

The problem is that the slash is somewhat ambiguous. As well as being a division symbol, it is a fraction symbol, so people are seeing it as:

48
2x(9+3)

But as I see it, that's an incorrect understanding.

http://en.wikipedia.org/wiki/Order_of_operations

[Duke: A Dynasty]

I dont have a division sign to use so had to put the /.

But I thought it went like this:

48 / 2(9+3)
Parenthesis comes first so 9 + 3=12
48 / 2(12)
Your parenthesis did not magically disappear so now you got 2x12=24
48 / (24)
then 48/24
2

[InSpades]

I dont have a division sign to use so had to put the /.

But I thought it went like this:

48 / 2(9+3)
Parenthesis comes first so 9 + 3=12
48 / 2(12)
Your parenthesis did not magically disappear so now you got 2x12=24
48 / (24)
then 48/24
2

Only what is *inside* the parenthesis is evaluated 1st. So once you have 12 inside the parenthesis you proceed to the next step in order of operations. Multiplication and division occur at the same time and are performed left to right. So 288 is correct.

[callmecrazy]

PEMDAS
I teach 6th grade math and oder of operations is one of our topics.
parenthesis exponent multiplication division addition subtraction
The multiplication and division are whichever comes first working left to right. Same with addition and subtraction
288

[dukestheheat]

48 divided by 2 times 9 plus 3.

Moving left to right through PEMDAS, we take the parenthesis first.

48 divided by 2 times 12.

Next up would be multiplication, so 2 times 12 is 24.

48/24, then, is 2, I guess, based on the acronym: parenthesis, no exponents, multiply, then divide, no addition or subtraction.

I ain't no math wizard and clearly my strength is English, which you can see.

dth, on a limb but feeling brave in front of the brethren.

[Duke: A Dynasty]

[Duke: A Dynasty]

PEMDAS
I teach 6th grade math and oder of operations is one of our topics.
parenthesis exponent multiplication division addition subtraction
The multiplication and division are whichever comes first working left to right. Same with addition and subtraction
288

Its not that I dont believe you I just find it kind of confusing.

What about distribution?

48/ 2 (9+3)

48/ 18 + 6

48/ 24

2

[darthur]

You could ask this to the 2 greatest mathematicians in the world and get 2 different answers. Which means it isn't a math question, it's a language question. And the correct answer is everybody loses, and you should just never use this notation.

PS: I would read this as 2.

[BCGroup]

TrY wolfram alpha website. Put in question, it gives you nswe. Kids are loving it for homework these days.

[DevilBen02]

Discussion of this problem:
http://knowyourmeme.com/memes/48293

According to this analysis, the big issue here is whether division or multiplication is performed first. It is explained that even though PEMDAS has multiplication listed first, multiplication and division hold equal precedence. As a result, moving from left to right, the answer is 288.

[snowdenscold]

I always thought M and D has same precedence, just like A and S. Otherwise things get realllly strange.

If you some write 11 - 4 + 2, you wouldn't say the answer was 5, you would say it was 9.

The fact that some versions above have whitespace and others don't also adds confusion.

This is probably only an issue in typed posts (which I suppose will be more much common going forward) rather than hand-written, since you would put a ------ for division and it would be clear where factors go.

[94duke]

PEMDAS
I teach 6th grade math and oder of operations is one of our topics.
parenthesis exponent multiplication division addition subtraction
The multiplication and division are whichever comes first working left to right. Same with addition and subtraction
288

callmecrazy is correct. * and / are treated equally, moving left to right

Its not that I dont believe you I just find it kind of confusing.

What about distribution?

48/ 2 (9+3)

48/ 18 + 6

48/ 24

2

Distribution is really just multiplication. You still have to follow order of operations, moving left to right. It would go like this:

48 / 2 (9 + 3)
24 (9 +3)
(216 + 72)
(288)

To get an answer of 2, you would need another set of parentheses. Without them, the rules say you perform 48/2, first. The only way to multiply 2(12) first is to have parentheses force that operation first.
48 / (2(9+3))
48 / (2(12)) or 48 / (18 + 6)
48 / (24)
2

I liked what darthur said bout this being a language question.
It is a language question. You have to understand the language to interpret it correctly and get the correct answer. (which is 288) <wink>

[anon]

Your parenthesis did not magically disappear

This post needs to be brought to a teacher's convention. I guess it's not being emphasized that the reason parentheses are there is to prioritize the evaluation of what is *inside* them. Multiplication outside them is treated no differently however it is expressed, be it with *, ×, ·, or even juxtaposition (the "parentheses" case everyone is referring to).

I liked what darthur said bout this being a language question.
It is a language question. You have to understand the language to interpret it correctly and get the correct answer.

Math *is* language. It's the study of a special kind of language with strict rules. And unlike the rules of the English language, which invariably change as people break them (see the "mute vs. moot" post for a particularly painful example), these rules can't change just because of an Internet argument.

[hurleyfor3]

Real geeks use HP calaulators, not Casio or TI crap.

48 (enter) 2 (divide) 9 (enter) 3 (plus) (times). Answer, 288.

Anyway, does no one remember the invert and multiply rule? 48 times 1/2 times 12. Two-eighty-eight.

[OldPhiKap]

Math *is* language. It's the study of a special kind of language with strict rules. And unlike the rules of the English language, which invariably change as people break them (see the "mute vs. moot" post for a particularly painful example), these rules can't change just because of an Internet argument.

Unless something gets lost in the translation from binary, of course.

[BD80]

Real geeks use HP calaulators, not Casio or TI crap.

48 (enter) 2 (divide) 9 (enter) 3 (plus) (times). Answer, 288.

Anyway, does no one remember the invert and multiply rule? 48 times 1/2 times 12. Two-eighty-eight.

Ah, RPN, a convention only a Duke coach could love.

[snowdenscold]

I was about to bring up reverse polish notation as a 'solution' to OO ambiguity, but it looks like someone beat me to it.

48 2 % 9 3 + * FTW

[Deslok]

Just to toss some fuel on the fire and be amused. What is:

48/2x

when x is equal to 12?

[Jarhead]

You could ask this to the 2 greatest mathematicians in the world and get 2 different answers. Which means it isn't a math question, it's a language question. And the correct answer is everybody loses, and you should just never use this notation.

PS: I would read this as 2.

No matter how hard I try, I cannot see an approach that properly results in 288. Do this calculation on a chalk board or a sheet of paper, without a keyboard, and if you follow the correct procedure or notation, the answer will always be 2. An answer of 288 can only result from bad structure, the kind offered by a keyboard and a line of characters.

Another approach is to start from the slash symbol. (That is the divide symbol on my keyboard.) Everything to the right of the slash is the divisor which must be evaluated separately from the multiplier. Then the correct result can be evaluated. That's the way I've always done it since the fourth grade, and if I ever made an error, it was because of forgetting that rule.

...48
------= 2
2(9+3)