12 divided by 2 times 6 = ? Many don’t get this BASIC Math concept! (Order of Operations)

Order of Operations problem - how to use PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction).

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[survivrs]

36 is my answer and I haven't seen the problem or other's answers, so I think I got the A+, but I appreciate an easier problem although I like challenges that I have the ability to learn eventually. Why I'm wanting to do this in my 60s is beyond me but I just YES!! I GOT IT!!!

[createdandmade]

My teacher taught me PEMDAS with the multiplication and division being grouped, and the addition and subtraction. I am glad I learned it this way, it makes me always be able to know the answer to these types of problems.

[reykcoldej]

What about BODMAS? (Brackets power Of, Division, Multiplication, Addition and Subtraction). I think that's they way I was taught at school (a long time ago now)

[davidmurphy]

You can re-express the division as multiplication: 12 * 0.5 * 6. This is the same sum.

Now the answer is 36 regardless of the order to do it.

[citizenmilitia]

I have a maths degree. What I'll say is that these stupid Facebook questions are always terrible. You should avoid using the divide symbol like this because it causes ambiguity.

Write it as a fraction with 12 as the numerator (top bit) and 2 on the denominator (bottom bit). So now the "x 6" can be inserted into the top or bottom of your fraction. Thus you avoid ambiguity.

BODMAS, PEMDAS, BIDMAS are all useful to an extent but they differ in the order slightly between D and M. They're worth teaching so people know to do Exponents before Multiplication / Division, and before Addition / Subtraction... But they're also often wrongly applied in contrived "teaching examples" such as this.

The most important thing is to recognise that maths is a language. Learning to write and interpret maths with clarity is at the core of the subject. So please, let's avoid doing this. Most importantly, absolutely STOP telling children they're wrong when they fail to interpret your poorly written contrived expression in a different way to what you intended. You kill their love of the subject.

[petercondon]

Not sure how they are teaching math these days but I was in High School in the early 1960’s and was not familiar with PEMDAS and this took me about 10 to 15 seconds to solve. I was a B+ student in general math to include (algebra, trigonometry, physics, chemistry) with no calculator. I think if he could reduce this video to <5 minutes more would listen.

[nicholasragusano]

I've seen this same issue with other examples you have given. Once again, remember that any two numbers separated by a division sign actually are a/b; hence 12/2. That is the first thing to think about. That works even if the multiplication part of the problem came first, i.e., 2 x 12 •/• 6 =. (The •/• is the division sign--keyboards don't work for math sometimes.) ALWAYS think of any number divided by another number in that manner, and you won't fall into the PEMDAS trap.

[marksolum]

Add parenthesis to remove all confusion regardless of which way your language reads. Left to right is not a math law. Do people from countries that read right to left then read equations right to left?

[mikenorman]

Division and subtraction are not "associative" or "commutative" which means the order you do things in makes a difference (hence different people may think 36 and 1 are both valid answers to this "problem"). The trick is to get rid of division by changing the division to a multiplication and replacing the divisor with its multiplicative inverse (i.e. its reciprocal, so one half in the case of 2, 3 in the case of one third etc). So in this case it becomes 12 x 0.5 x 6. and then you can rearrange the order of this any way you like and you will always get the correct answer of 36. Similarly if you have a mix of addition and subtraction, replace all the subtractions by additions and change the number to be subtracted to its additive inverse (i.e. its negative, so -2 in the case of 2, 3 in the case of -3 etc). Thus 9-2+3 is 10 (it's 9 + -2 + 3, the same as 9 + 3 + -2, or -2 + 9 + 3 etc), it is not 4.

[soulinspiration]

Thanks for explaining PEMDAS. Got it now!

[mitabpraga]

Instead of mucking about with PEMDAS (BODMAS for us Brits) what's wrong with just setting out the problem in the order in which it needs to be solved and using brackets (parentheses) if and when necessary?

[TheDerlick]

Division is simply multiplication of the inverse. So, rewritten:

12 • ½ • 6 =

Now, no groupings, evaluate from left to right or right to left, it doesn't matter.

[volkerschmoll]

From left to right: 36. 2x6:12=1, but this another question. It is a concentration question. I guess, sometimes I'm wrong, because bad concentration. OMG.

[mariaolaciregui]

Hello professor, I will like you will place parenthesis, because, as you said 12 divided by 2x6, looks like 12/2×6. I saw first that was 36 , however when I read look like in other way. Sorry. It is possible for me that the way to express in English make me confused. Thank you. I like a lot your math section.

[mingkee]

Make this concept and it's all clear
How about 12/2 * 6/1 (the latter is 6 anyway) >>> 12*6/2*1 >>> 72/2 = 36
Isn't it easy?

[sherryroberts]

Thank you! I am a very old person and I find your channel to be very mind-challenging, which is so important for old farts! LOL

[mesomachines]

Regardless of PEDMAS, I see this as a failure of the field of mathematics. Math syntax can be written without ambiguity (or am I wrong?) If so, we should list problems as unsolvable due to ambiguities rather than relying on PEDMAS which still often results in error.

[manuelquitevis]

12 divided by 2 equals 6.And 6 times 6 equals 36

[deidrabrey]

I got 36 but I think back in the 70s the answer would have been 1.

The thing about order of operations that I do not get is that the left to right rule semes like we're mixing reading and writing with math, two different subject areas entirely. Talk about apples and oranges. What if you are from the Middle East? PEMDAS Order of Operations with left to right primacy seems arbitrary because middle easterners read right to left. Seems like math guys got together and said, "it's left to right!"

I think a better rule would be to introduce a new Order of Operations rule that equations with multiple cases of multiplication and division REQUIRE parentheses to show the true intent of the equation. This would divorce math from English language once and for all.


So in my new word order, 12\2 x 6 = ? would be wrong due to no parentheses.

[therighthandmann]

If we use PEMDAS, the multiplication comes first in this example . That would be the 2x6, and it equals 12. At this point we have simplified the equation to 12 divided by 12, and division is the next operation of the PEMDAS order. So, 12 divided by 12 equals 1. The answer is 1.