"I Love College"

**W. Rabbit** · Posted On: 11/09/2012 2:22am

Originally Posted by goodlun

The original problem didn't have the extra set of parenthesis, adding them changes the problem and the answer at that point is 1. There is no special way of using the notation, the notation is what it is. This didn't come from a word problem. Its a typical here are some numbers put down in an order solve them sorts of thing. When you follow the PE MD AS rules the answer comes out to 9.

No. Trust me you'll understand if you keep at it.

This will help.

This problem was presented on Facebook, and I found it rather interesting that the vote for the answer was nearly split 50-50 for each answer, garnering over a million votes in the process. I did some research on both sides, and found validity for each answer to be correct.

The only people who are incorrect, actually, are those who think that you must multiply before you divide because the letter "M" comes before the letter "D" in the acronym PEMDAS.

***Tranquil Suit*** · Posted On: 11/09/2012 2:34am

google "order of operations"

first 3 results:

http://en.wikipedia.org/wiki/Order_of_operations
http://www.mathgoodies.com/lessons/v...perations.html
http://www.purplemath.com/modules/orderops.htm

Basically, they all say:

A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first.

So I remain convinced that this has been the universal rule since... a while. If there is a contradicting source (that's not about calculators), please tell me.

What pisses me off the most here is what Rabbit quoted: A bunch of IT doucheboys decided to make calculators and tried to be clever by tweaking the rules. "Oh ho ho how clever, now we won't have to to write those parentheses so often". Except that now, there is uncertainty whether a given calculator model follows the rules if you know about this bullshit or worse, easily made errors by relying on a calculator for basic calculations if you don't know about this.

Okay, so final question, giving implicit multiplication a higher priority than explicit multiplication, is that a calculator thing?

**goodlun** · Posted On: 11/09/2012 2:41am

Originally Posted by Tranquil Suit

google "order of operations"

http://www.purplemath.com/modules/orderops.htm

Actually Purple Math page 2
http://www.purplemath.com/modules/orderops2.htm

This next example displays an issue that almost never arises but, when it does, there seems to be no end to the arguing.

Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1.
- 16 ÷ 2[8 – 3(4 – 2)] + 1
  = 16 ÷ 2[8 – 3(2)] + 1
  = 16 ÷ 2[8 – 6] + 1
  = 16 ÷ 2[2] + 1 (**) = 16 ÷ 4 + 1
  = 4 + 1
  = 5

The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Typesetting the entire problem in a graphing calculator verifies this hierarchy:

Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!

**W. Rabbit** · Posted On: 11/09/2012 2:42am

Aha I knew you'd find it Good. This is a classic computer science problem in algorithms.

Originally Posted by Tranquil Suit

So I remain convinced that this has been the universal rule since... a while. If there is a contradicting source (that's not about calculators), please tell me.

The issue is the use of juxtaposition in writing formula and it's a very old problem.

It's not so much a calculator thing as a computer algorithm thing....how do you make a computer do exactly what you meant?

Answer: parenthesis.

http://math.stackexchange.com/questi...-juxtaposition

And the answer is, DON'T WRITE a/bc, because it will only cause confusion. Some people/software/whatever will make one interpretation, some will make the other, neither one has been endorsed by the Dalai Lama or any other great leader. Put in enough parentheses to make your writing foolproof.

**Dr. Sleepless** · Posted On: 11/09/2012 2:45am

God damn it you faggots.

It's neither. The answer is, "Take this back and write it more clearly and stop being a lazy piece of ****."

You don't purposefully create confusion in a math problem unless you're TRYING to set someone up to fail. Math is about writing the language that the universe is understood by. You don't do that by purposefully miscommunicating problems. That just creates new sets of problems and then nobody gets anything done.

***Tranquil Suit*** · Posted On: 11/09/2012 2:47am

Originally Posted by Dr. Sleepless

God damn it you faggots.

It's neither. The answer is, "Take this back and write it more clearly and stop being a lazy piece of ****."

You don't purposefully create confusion in a math problem unless you're TRYING to set someone up to fail. Math is about writing the language that the universe is understood by. You don't do that by purposefully miscommunicating problems. That just creates new sets of problems and then nobody gets anything done.

Captain Obvious to the rescue.

I'm gonna go outside and cut down a tree... with my teeth.