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).
TabletClass Math Academy - TCMathAcademy.com/
Help with Middle and High School Math
Test Prep for High School Math, College Math, Teacher Certification Math and More!
Popular Math Courses:
Math Foundations
tabletclass-academy.teachable...
Math Skills Rebuilder Course:
tabletclass-academy.teachable...
50% DISCOUNT: 1 Year Course Plans Use Discount Code: KZbin50
Sale Ends: 11/10/23
Pre-Algebra
tabletclass-academy.teachable...
Algebra
tabletclass-academy.teachable...
Geometry
tabletclass-academy.teachable...
Algebra 2
tabletclass-academy.teachable...
Pre-Calculus
tabletclass-academy.teachable...

[@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 do........and YES!! I GOT IT!!!

[@createdandmade2205]

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.

[@neilprocter]

I teach BIPS : brackets, indices, products, sums. Then the issue of whether multiply or divide comes first is resolved when learnt.

[@sottx8268]

The thing you had to remember is (as you say) it's Multiplication or Division grouped together, same with Addition or Subtraction. THEN everything else is evaluated left to right.

[@soulinspiration1]

Thanks for explaining PEMDAS. Got it now!

[@petercondon5344]

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

[@davidmurphy563]

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.

[@afre3398]

The same if you use proper fraction lines

[@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)

[@karlalawatsch9984]

I never heard of either one until recently but it's been 50 years since my HS graduation. It would have been a useful tool to have.

[@mikenorman2525]

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.

[@citizenmilitia1]

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.

[@Dragonedin]

When did the use of Parentheses end?

[@padraicbrown6718]

Mr KZbin Math Guy likes to put up one of these click bait "you're gonna get this wrong and I'm gonna laugh in your face" videos at least once or twice a month. It's always the same thing: an obelus in stead of a vinculum for division which leads to the PEMDAS crowd getting the wrong answer.

[@nicholasragusano2284]

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.

[@marksolum1794]

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?

[@1947SteveC]

I think the language of math and music is universal.

[@susanm1109]

While it would be less confusing if parentheses were used, the point of these exercises is to learn how to correctly solve math problems even when they are written in an ambiguous manner. It’s my understanding that the convention is to perform multiplication and division from left to right regardless of the direction in which the solver reads written material.

[@nfpnone8248]

@@susanm1109 There is no way to write a math problem correctly and ambiguously, that’s why we have the rules for manipulating equations, which you cannot do algebra without!

[@paulfrank8738]

PEMDAS/BODMAS is the convention that defines the left to right rule. It is widely used/accepted. But to your point, it's not the only convention that ever existed, and it may not be the only convention in use. Also to your point, use of parenthesis would frequently avoid the most commonly misunderstood/misinterpreted parts of PEMDAS/BODMAS and would be a good practice when writing real world equations.

[@nfpnone8248]

@@paulfrank8738 PEMDAS AND BODMAS didn’t exist when I went to school! And the P doesn’t just mean what is inside the parentheses, it means what is associated with the parentheses as implied operators. The whole parenthetical statement must be resolved before you can move on, or you will get the wrong answer. By now you should realize I have had way more math than you, and probably more then more than 95% of everyone including some of the teachers. By the way, how you input equations in calculators and spreadsheets matters, and most have operating systems that work differently, so you need to know how to input equations in the specific calculators and spreadsheets to get them to return the right answer. My advice, learn to do it by hand with a pencil, then learn to input it into the calculator or spreadsheet! Again, there is no right to left or left to right priority in mathematics, it must give the same answer no mater where you start and what direction you take. Left to right priority is a fallacy!

[@mitabpraga7487]

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?

[@paulfrank8738]

There's nothing wrong with it when the equation is simple enough. But PEMDAS/BODMAS is a convention that describes part of the mathematical language. To effectively use any language, it's best to understand the "rules" of that language. And, that's what I believe this video is all about, helping people understand a common misinterpretation of the mathematical language.

[@mitabpraga7487]

@@paulfrank8738 Thanks for the explanation. I'm no mathematician, anything more complicated than E=mc^2 makes my eyes bleed and what's left of my brain starts dribbling out of my ears. I've just read an article on Harvard's website which goes into the issue in some detail pointing out the ambiguity in PEMDAS/BODMAS and why it's used. I didn't understand most of that either, tbh, but I think I got the gist. From the linguistic point of view, though, effective communication relies on clarity rather than brevity and that to avoid ambiguity the latter should be sacrificed in favour of the former.

[@paulfrank8738]

@@mitabpraga7487 Glad I helped. Yes, there are some interesting discussions out there. Based on some things I've come across, I suspect there will be some changes in some mathematical conventions to account for the modern problems in much the same way that PEMDAS/BODMAS was created to deal with the problems that were occurring back then.

[@padraicbrown6718]

@@paulfrank8738 --- Except that he's helping people think that the wrong answer is right. This is NOT good pedagogy.

[@paulfrank8738]

@@padraicbrown6718 Thanks for the comment. I see that I may have implied something that wasn't quite what I meant. My primary point is, if you can write an equation in a way that avoids the common difficulties and/or disagreements in the interpretation of PEMDAS, that's probably a good thing to do. My secondary point is PEMDAS is only a convention, if you have your own "shorthand convention" that doesn't break fundamental mathematical principles (i.e. it always leads to the right answer), you can use it. just be aware that it's not that easy to come up with your own convention for anything other than simple problems, and it won't be easy for anyone else to follow your work.

[@mingkee27]

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?

[@user-ri6rn7ti5h]

(12÷2)=6 (6×6)= 36 (x+6x-6)

[@nicholasragusano2284]

You are absolute;y correct. ALWAYS think of it in that manner, and you won't fall into the PEMDAS trap. Maybe the system should read PEDMAS and people would not get mixed up. Can someone come up with a sentence that uses these letters in that order?

[@russelllomando8460]

Got it, thanks

[@basiltomlinson8895]

36

[@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.

[@mariaolaciregui2128]

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.

[@volkerschmoll4731]

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.

[@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.

[@user-ri6rn7ti5h]

(12÷2) = 6 (6×6)= 36 (x+6x-6)

[@thenetsurferboy]

You are right Why does he persist with his grade 2 gibberish?

[@padraicbrown6718]

@@user-ri6rn7ti5h Try 12 / 2 x 6. The obelus gets you guys every time!

[@stpaulmercantile]

PEMDAS does not mean that multiplication precedes division. M and D are at the same level, so if both appear in the same problem, operations are ordered left to right.

[@therighthandmann]

@@thenetsurferboy B/c he learned order of operations back when parens and brackets were used. Was PEMDAS meant to simplify all that for the mentally challenged generations? Or just add some more rules?

[@sherryroberts7716]

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.

[@newstarcadefan]

There's nothing ambiguous about this.

[@thenetsurferboy]

No It is 12/ 6x2 = 1@@newstarcadefan

[@paulfrank8738]

It turns out that math syntax cannot be written without ambiguity without some definitions on how it's interpreted. PEMDAS/BODMAS is a convention that defines how it's interpreted. Without PEMDAS/BODMAS there are no rules for how to fully interpret anything beyond trivial math equations. Having said that, Math teachers definitely come up with contrived examples that could be written in a way that avoids the common PEMDAS/BODMAS misunderstandings. The good ones do it as a teaching aid, and the bad ones do it as a "gotcha"

[@padraicbrown6718]

@@newstarcadefan ---- It's 100% ambiguous. That obelus, the division sign we all learned in second grade, is fine when you've only got two numbers. Once you get out of arithmetic and into algebra and geometry, you're never going to see an obelus again. You're only going to see the division bar, and problems like this will always be written 12 / 2 x 6. Please explain how you get 12 / 12 = 36

[@padraicbrown6718]

@@paulfrank8738 -- There's really nothing "wrong" with PEMDAS, except that it ain't quite right. You still need to explain to kids why it doesn't quite work. This sounds like a disaster waiting to happen. And all these PEMDAS kids are going to have to be reeducated in high school because they can't use PEMDAS to find the area of a triangle.

[@manuelquitevis6794]

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

[@nfpnone8248]

You can’t do the multiplication first because of the division sign which must have a numerator and a denominator , so everything to the left until you reach the. Ext fixed operator goes on top, and everything on the right till you reach a fixed operator goes on the bottom. This has nothing to do with order of operations, nothing to do with PEMPOS, or BODMAS. If the equation contained parentheses and implied operators, then that whole parenthetical statement must go into the numerator or the denominator. For example, your favorite viral problem. 6 / 2(2 + 1) = 1 but it does not equal (6/2)*3 = 9, which requires you to change the implied operator which only operates on the parentheses into a fixed operator. Again, there is no left to right or right to left in mathematics, everything is modular and interchangeable and you better always get the same answer!

[@paulfrank8738]

Mathematics is a language. There are rules and conventions in that language. Most of what you say is in direct conflict with the widely accepted rules and conventions of the language.

[@nfpnone8248]

@@paulfrank8738 That’s total crap. I learned the rules before I had the classes that showed us how to use the rules. I do know exactly what I’m talking about and what I’m saying is in direct compliance with, and dependence on, those rules. If you don’t know how to rewrite and manipulate equations, in most cases you cannot solve them. The two most important concepts in mathematics are adding zero and multiplying by one. I’ll let you figure out what that means!

[@paulfrank8738]

@@nfpnone8248 I'll go with my Electrical Engineering education over your statements. My understanding is in agreement with my Math teachers, my engineering professors, my mathematical text books, my engineering textbooks, the FE exam, and all of my engineering peers.

[@Andrew-it7fb]

In your example, it depends on the convention you are using. Multiplication by juxtaposition having priority is not a consistent rule.

[@nfpnone8248]

@@Andrew-it7fb What you just said is total nonsense! There is no difference in conventions, FOR A REASON, we have agreed on the principles of mathematics!

[@deidrabrey4043]

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.

[@davidhorn6008]

Answer one

[@kolkattaindia]

Ans:1

[@stephenwhite3632]

1

[@user-ri6rn7ti5h]

(12÷2)=6 (6×6)= 36

[@philipmumford7871]

He does go on 😆

[@bullinmd]

36

[@wam7484]

36 is the answer but more important is that the format is vague and would only be so written by someone looking to cause problems -- or incompetent.

[@Mister_Smit_]

What? Already the simplest expression is not correct? 12:2*6=12*6:2=36 12 12*6 ----*6 = ------- =36 2 2 What is incorrect here?

[@padraicbrown6718]

36 is only the answer if you write the problem correctly: (12 / 2) x 6 = 6 x 6 = 36 Keep in mind that division is, apart from primary school arithmetic, always written with a horizontal bar: 12 / 2 x 6. The bar is a grouping symbol which means that you have to resolve the top and bottom separately, then divide. 12 / (2 x 6) = 12 / (12) = 1

[@afre3398]

In a very recent video you advocated for the use of fraction lines. Why do you not follow you own advice. What you so often do is to present a gotcha problem not a math problem. If this had been written with proper fraction lines the problem would have been quite clear. You could have done (12*6) dived by two or (12/2) times 6

[@annettegollon239]

36 is my answer as well.😊😊

[@curtischamblee7542]

= 1

[@user-ri6rn7ti5h]

(12÷2)= 6 (6×6)= 36

[@padraicbrown6718]

@@user-ri6rn7ti5h True, but it's not written that way. The division bar is a grouping symbol that separates the numerator (the stuff on the left) from the denominator (the stuff on the right). 12 is the numerator; (2 x 6) is the denominator. Then do the math!

[@user-ri6rn7ti5h]

Follow the order of operation s

[@terrybrown8902]

Either 36 or 1

[@RodCalidge]

How could anyone possibly get this wrong??

[@danieldennis9831]

People do the "multiplication" first. Even though multiplication and division are the same thing (division is really multiplication of a fraction) , just like addition and subtraction are really the same thing (subtraction is adding a negative).

[@RodCalidge]

@@danieldennis9831 It was a rhetorical question, dude.

[@Aijia_Vance]

You should have written your sarcasm better. Unless you were trolling for a clapback in which case, well done.

[@padraicbrown6718]

@@danieldennis9831 --- You HAVE to do the multiplication first, because it's in the denominator. You have to resolve the denominator first, before doing the division: 12 / (2 x 6)

[@margritkaminsky1470]

Nobody would make this error if you wrore the division as a fraction, a slash. 12/2.

[@thenetsurferboy]

But is 12/ 6 x 2 Answer is 1

[@Andrew-it7fb]

​@thenetsurferboy no, it's not. 🤦‍♂️

[@bobpipes5183]

12÷2×6= 12 -------'×6=36 2

[@bobpipes5183]

​@@thenetsurferboy 12 ----------×6=36 2 Not 12 ---------=1 2×6

[@thenetsurferboy]

Bomdas. Pemdas Multiply is first Back to grade 2 for you@@Andrew-it7fb Left to right is taken care of by the rule, which is not left to right I must go Is morning playtime now

[@kennethshaheenjr.1164]

Using P.E.M.D.A.S. 36

[@kennethdias9988]

36 straight left to right no multiplication first like the old days.

[@padraicbrown6718]

Try this: 12 ------- 2 x 6 aka 12 / 2 x 6 What did you get?

[@slickrick876]

There were no old days. Math was never solved just left to right. PEMDAS has been around longer than you have been alive

[@julijenkins2249]

Worked he comes up with something other than 36 .

[@dianeandrovett1244]

One

[@briancarruthers1738]

Anyone not using parenthesis in equations is just lazy

[@davidlo9203]

Not lazy but crazy as nuts. They don't know what priority is and try to be smarter than others😂...terrible😮

[@amelafram9949]

6×2/12=1

[@rubybackert3612]

I don't feel bad. I got the answer and didn't use PEMDAS

[@amelafram9949]

12/2×6=1

[@mariajenoure7394]

2×6=12 12÷12=1

[@markinnes4264]

Watch the video.

[@argonwheatbelly637]

12÷2×6=12×½×6=36 in five seconds. Sorry it took so long. I'm really tired.

[@rbrtmllr]

Thinking back to high school, the correlation between the students that couldn't get this then, or today, and hard right conspiracy theorists is 1.

[@margaretyocke5348]

I got 1 for my answer.

[@user-ti4bk9xf4w]

6

[@greorbowlfinder7078]

I think of these like a person who wrote a horrible sentence without punctuation. We have parentheses for a reason. Have some standards! Use the parentheses and stop writing gibberish math sentences just for the controversy. Yes I speak math gibberish too. 36. Good grief. This is what happens when people think not having any standards in written language is a math problem. Whoever writes these is actually just being lazy, they're not testing someone's logic ability.

[@vespa2860]

12 divided by 2, times 6

[@trinne]

Using precedence ambiguity as some kind of relevant math thing, is just boring and wrong. Actually precedence of (inline) division and multiplication is taught differently in different countries. ”The usual” way being that division and multiplication is of equal precedence and is done from left to right. However e.g. when I was a kid in Finland, I was taught that multiplication preceeds division. If there is an ambiguity, just add parenthesis or show divisions as fractions.

[@thenetsurferboy]

Answer is 1 Why not write it this way just to show how wrong you are? 12/6 x 2 Divide by 6 as you would Your answer is 4 I learnt 'O'' for 'of' 4/5 of 25

[@Andrew-it7fb]

You're just rewriting it to be a completely different expression.

[@slickrick876]

Nope

[@lmcwill0502]

I had the answer in 3 seconds if that. 36

[@occultustactical6138]

1?

[@user-ri6rn7ti5h]

(12÷2)=6 (6×6)= 36 (x+6x-6)

[@padraicbrown6718]

Correct. 12 / 2x6 = 12 / 12 = 1

[@user-ri6rn7ti5h]

@@padraicbrown6718 you did not follow the order of operation

[@mariajenoure7394]

1 is the answer

[@wayneriley7367]

I have taught this but find it so stupid. The order of operations is an antiquated idea and it is a reason people hate math. The unambiguous way is to use parentheses which is in the order of operations. When speaking if it is unclear then we use punctuation to clarify, using parentheses tells us exactly what to do. I am an old grouch and suggest anyone putting this up to show they know math is just silly.

[@carlomedina5310]

Too much blah,blah complicated is simple 12/2*6 = 1 you confuse everyone solve what I wrote

[@slickrick876]

So simple and you got it wrong

[@nickclopton7986]

That's too easy 36

[@Mister_Smit_]

😂😂😂 12:2*6=12*6:2 from left to right, not from right to left. How difficult it is to understand. 😂😂😂

[@stitcheruk1150]

You are confusing people with PEMDAS. It’s BODMAS - much easier to explain.

[@garyc7766]

Almost 10 minutes to explain what I solved in 3 seconds.

[@l.elizabethb.361]

= 36

[@eldalemery8181]

12÷2×6=6×6=36

[@eldalemery8181]

12÷2=6×6=36

[@billthorburn7476]

36. 😊

[@darnellseward-my9nb]

The answer is 36

[@padraicbrown6718]

F for yet another poorly written math expression! Again: stop using the obelus as that creates confusion among the PEMDAS folks; start using the division bar as that eliminates the confusion. The answer is 1 because 12 / 2 x 6 is UNAMBIGUOUSLY 12 / 12, rather than 6 x 6. You're much better than this rubbish. Please teach kids to just do things in the the right order and without the outdated & confusing symbol.

[@ImternetExplorer]

Why are you doing multiplication first?

[@slickrick876]

Wrong

[@padraicbrown6718]

@@slickrick876 --- And therein lies the problem. Math and especially arithmetical problems should never be written in a way that leads to this kind of dissention. Ultimately, any real mathematician or math teacher is going to realise that clarity of communication relies on clarity of symbol use. If we can take what Mr KZbin Math Man wrote and interpret it two or four different ways, then the problem is not with our interpretations. Rather the fault lies with Mr KZbin Math Man.

[@kennethwright870]

36

[@mariaolaciregui2128]

1

[@letsnottalkmovies8613]

36

[@rodfulford4306]

36

[@LorenIpsum75]

36

[@kimberlyweston8466]

36

[@chrisafd1]

36

[@magdapringle7868]

36

[@moniquecaton3285]

36

[@doreenleeming4630]

1

[@jimbeglinger]

1

[@basiltomlinson8895]

1

[@williemerritt6036]

36

[@user-ok2tw7yl6v]

1

[@Niah_ducky]

36

[@scottslavik6602]

36

[@staceybarnett2811]

36

[@user-rm2rw1nd1y]

36

[@sekharb6651]

36

[@waynephillips2777]

36

[@bravewave2084]

36

[@fredrickabrown6698]

36

[@user-kd9to7ec9o]

36

[@terriewilliams8831]

36

[@krishnannambiar5988]

36

[@ssebers1903]

36

[@elmerares4653]

36

[@Truth845]

36

[@pavanpatel6637]

36

[@user-iq6lp9cv5c]

36

[@Raindragon4]

36

[@ristoaksila5677]

36

[@doreenleeming4630]

36

[@boleklolek2649]

36

[@mikemassey7403]

36