## A Simple Math Problem

May 3, 2011 at 11:05 pm | Posted in General | Comments Off on A Simple Math ProblemSo recently a meme has been running around regarding a relatively simple math problem that confuses people due to a lot of mistaken teaching and mistaken remembering out there. 🙂

Further harming the issue is so-called “learning” sites like Purplemath which have incorrect information on them, and refuse to change in spite of the mistake being contrary to all basic rules of math, and not agreeing with the answers that Google and Wolfram Alpha generate.

Even more, some older graphing calculators are incorrectly programmed, and generate an answer of 1, which many proponents of the 1 answer take as proof that they’re right, even though far more advanced tools as linked above say otherwise. (Not to mention, yet again, the basic rules of mathematics)

The recent problem in question is the following: 6/2(1+2), or 6÷2(1+2), depending on your symbol choice.

The correct answer is 9. Not 1, not 7, not anything else anyone comes up with when they make mistakes.

There are several sources of confusion with this problem – some teachers taught the order of operations incorrectly, while some students simply remember it wrong. Others try to distribute the 2 inside the parentheses, thinking back to algebra, while others assume that implied multiplication is somehow *stronger* than regular multiplication^{1}.

I was taught PEMDAS, which stands for Parentheses, Exponents, Multiplication & Division, Addition & Subtraction. However, some have taught or remember it as Multiplication and THEN Division, and Addition THEN Subtraction, which is wrong. You do the M/D and A/S left to right, whichever comes first.

Wrong way:

6/2(1+2)

6/2*3

6/6

1

The distributing crowd is actually similar to the previous error as well. They try to distribute, but they take only the 2, instead of the entire 6/2, or resulting 3.

Wrong way:

6/2(1+2)

6/(2+4)

6/6

1

The final group start off fine, doing the parentheses first, but then leave it as 2(3), which is the same as 2*3, and assume that somehow makes it stronger, when in fact they are identical.

Wrong way:

6/2(1+2)

6/2(3)

6/6

1

If you fix all these issues, you get only one possible answer, 9.

Right way:

6/2(1+2)

6/2*(1+2) Remember, implied multiplication is still just multiplication!

6/2*3

3*3

9

If you distribute correctly, you can do this:

6/2(1+2)

3(1+2)

3*1 + 3*2

3 + 6

9

No matter how you do it, if you actually follow the rules correctly, you get 9.

Random related images that have come up during discussions of this:

http://i.imgur.com/qiK3V.jpg

http://i.imgur.com/STMJT.jpg

http://i.imgur.com/zrxGL.jpg

http://i.imgur.com/Xvf6s.jpg

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