12 divided by 2 times 3 all over 2 =? A BASIC Math problem MANY will get WRONG! 

My pre calculus professor in college told us in the first class "in the absence of brackets you always resolve left to right"...best math advice ever.

In order of execution use BODMAS; Brackets, of, division, multiplication, addition, subtraction. ie 12/2 =6 then 6 x3 = 18 and then 18/2 = 9

I’m a very long time out of school, but I remember this problem being discussed. We were told there is no correct answer. A maths sentence such as that needs parentheses to make it solvable. In the absence of parentheses, we are not given sufficient information to solve the problem. In the unlikely event an error such as that crept into an exam, we were told to go left to right, as you’ve done, but to put a note in the margin saying that was what we’d done. Always show your work! I think we covered that in 3rd class, purely because of the classroom I remember it in. The teacher had deliberately given us the problem in our homework, to illustrate the importance of parentheses and how they work. From memory, most of our group got 9, but quite a few said 1, having struggled with it and consulted a parent. The teacher concluded by giving us a handout full of parentheses problems for homework and told us that omitting them was every bit as bad as omitting any of the operators in the sentence. In my head I thought of it as like omitting capital letters and punctuation from an English sentence, making it impossible to know what the words mean. Thank you for this trip down memory lane. I didn’t know I still had that memory!

This is a prime example of how some instructors not teaching the whole of PEMDOS...you made this so much easier! Thank you for being a great instructor! We were not told that the groups of Multiplication and division were to be done left to right in order of the problem. We were told that we were to always do multiplication, then division, addition and subtraction. This made many problems very confusing! Thank you again! ❤

The answer is C = 9. I think you should move left to right. So 12 divided by 2 = 6. Then 6 times 3 = 18. Then 18 divided by 2 = 9. Let's see ...

It’s been 40 years since I graduated from high school. At first I was thinking the answer was (a)….but I stopped and thought about it for a second and realized it was (c). Geez. It’s amazing how much of what you learned gets rusty when you don’t really use it that often anymore. 😂 Enjoyed your video!

Great explanation good for us who have been away from math for a long time a good refresher. Thanks

You are absolutely right in that there are not enough problems that demonstrate to students that it is either M or D whichever comes first. Usually there is some other component that makes the order relatively easy to figure out, but in this case, it really needs to be stressed because real life, is never like the textbooks!

In the UK we have BODMAS: B - Brackets, O - Order of powers or roots, D - Division, M - Multiplication A - Addition, and S - Subtraction. We didn’t have it in my school life but apparently this is the way it all works now.

I am also 50+ years from high school, and math was not one of my the courses I liked. My mind is being opened at years old. Thanks!

I have basic degrees in both Compsci (Bachelor) AND Mathematics (Minor), and I was inducted into Kappa Mu Epsilon and Phi Beta Kappa in 1984. In other words, LISTEN TO ME ON THIS. 10:23 1) Courtesy of the "all divided by 2" at the end of the problem statement, there is an implied set of brackets around the entire numerator, which disambiguates any confusion regarding the order of resolution, especially since ... 2) Within those implied brackets, equal operations (re: multiplication & division) are resolved LEFT TO RIGHT, IN ORDER OF OCCURENCE. Answer = 9

12 divided by 2 = 6, 6 x 3 = 18, 18 divided by 2 = 9. Three steps and you’re done 😊 I failed at maths in high school, simply because it was explained to me in such a confusing round about way.

I had a math teacher who worked with me after school on multiple days over a month or so where I was able to learn the order and method of solving algebraic equations. We never discussed Pemdas or what ever. Never heard that term until today's video. We just learned the proper sequence by memory. Now in my mid 70's this stuff still serves me for solving problems. Setting up proportions and solving them helps me in so many ways in the course of my days. Even a simple recipe where I want to make less (or more) of the recipe and where some of this stuff is automatic is a regular use.

I love it! Back in 1974, mid term math, I was flunked, less that 50%! B.S. In 1981 I was attending calculus classes at McGill/Sir George campus (Montreal). To my surprised, just looked to my left, who was sitting there!?? WELL turns out my math teacher from '74! What the hell was he doing in my class!? And he flunked me back in '74? I had to laugh! In 1981 he would have been in his early 40's....go figure. And yes PEMDAS is etched in my brain! I freelance electrical and software engineering! Love this work.! Rf engineering (DSP/SDR/ Antenna design) has brought me into Differential Equations, Imaginary math, etc. Fun stuff man! Botttle of wine and a math problem to solve, classical music playing in the background., The problems do end up as being, solutions!!! LOL!

Got it right and I have been out of school several decades. Lol. I would like to take this time to thank all my teachers and the creator of this video. I remember having to show my work doing math problems and hated doing all of that. Now they just use calculators. So different now, but whatever works. This was fun. I’m ready to do another one, a new challenge. 😂

Easy! The answer is 1. PEMDAS is absolute in that multiplication comes before division.

How to turn a 3 second math problem into a 13 minute video 😅

I was only introduced to math problems like the one you had in the video, but it all made sense to me. Now, my older brother was taking calculus in the 8th grade. 1 time he cought the teacher had made a mistake. The teacher put a problem on the backboard then asked if anyone had questions; and my brother asked shouldn't the answer be this instead of what you have? The teacher re-did the problem and said yes John you are correct."

Thank you! Not once during any math class in high school (1980s) was order of operations explained this clearly.

One of the problems with math is training me to set up and use equations to solve problems. Mathematics teaching often concentrates on how to solve issues, rather than how to apply mathematics in obtaining solutions. Case in point: The movie "Hidden Figures" is about how human computers applied these concepts to figure out ballistic trajectories for Mercury Space Capsule atmospheric reentries. While I tried to follow the "gibberish" written on the blackboard I was not trained well enough to make sense of the calculations. Only once did I resolve a real-world problem using mathematics when planning for convoy road lengths utilizing the formulas that the Staff Officer's guide used. I was able to determine that the road could only support x amount of convoys per day.

I am 70 yo, and I watched this because I have forgotten these things. You are a great teacher, and explain things very well. A lot of teachers teach to the smartest person in the class who already knows a lot.

Bodmas brackets of division,multiplication,addition and subtraction 12 divided by 2 =6times3=18 divide by 2 = 9

Pemdas made me see the light of maths as well as the explanation of m and d (do the one that comes first from left to right) and the a and s as well. It was never explained to me in this way, but now I understand it fully. Thank you for this small piece of information, which makes a massage impact in this field.

I love math ! Glad I found your channel . Subscribed ! Of course . Thank you for your time and great explanation . Wish we had more knowledgeable and dedicated math teachers in our educational system… so our kids wouldn’t be so far behind in math from other countries . Math is an important subject in our daily life , pulse it improve our critical thinking which is so important . Thanks to my outstanding math teacher who thought us so well that today I don’t use any calculator for multiply or subtraction.. etc … I know my time table very well .. they never allow us to use calculator in our math class .. force us to use our brain instead of calculator. That improved our ability to think critically ! If your understanding of basic of math is strong , you will find the subject very sweet and easy to learn . Best of luck ! 🌿

Just discovered you, happy days. At 80 years young, I have always been hopeless @ maths and have long planned to conquer that hangup. As the summer approaches, I will again be spending more time on the golf course but am looking forward to getting my brain limbered up too. I would really like to enjoy maths before I pop my clogs. You sound like the guy for me in 2024. Let’s do it! Thanks 😊

I am 71. I have been terrible in math since I was in first grade! This is a great source of embarrassment to me. I will be using these videos to help me learn or relearn some basic math without the pressure of being in a classroom. Thank you for taking the time to provide this helpful instruction.

Exactly Marianna. BTW the o stands for order of powers or roots.

Another way to solve this that I tend to prefer is to convert all the divisions into multiplications, so the divide by 2 could be multiply by 1/2 instead. Then it's all multiplication and you can combine in whatever order you want. This can be easier for some people to remember.

Nice, I am an old person and did my math education in the 1960 and 1970's. Our mnemonic in those days was always "BODMAS" which has stuck in my head for eternity. Basically exactly like your "PEDMAS" - B=Brackets O=Of (Exp etc.) D=Division M=multiplication A=Addition and S=Subtraction. BODMAS gave me the correct answer to your quiz as I expected.

I graduated HS in '85 and wasn't taught the acronym PEMDAS, but instead the initialism PPMDAS, and Pretty Please, My Dear Aunt Sally as the explainers of the letters. I think it was also more accurately taught as PP(MD)(AS), but just to remember the 'pretty please, my dear aunt sally' part as sufficient. The extra parenthesis were there to let you know that they were a group of systems together and were separate from each other. With the understanding that the solving of left to right in the groups MD and AS. (All of which you explained as well.)

Thank you for the session. Please, what App do you use in recording your class?

It's good practice, very useful, I did get it right. At school, we had to do a lot of mental arithmetic and were expected to get the right answer. I'm sure that I'll benefit from your videos. Thank you.

I grew up thinking that because I am a musician, then I would be bad at math. However as an adult I’m not only seeing how math is all wrapped up in music but I see the beauty of math. Numbers thrill me. Thank you for explaining the order of operations that I’m sure I heard in school but now that my ears are un blocked I can understand and embrace math.

When I was young, I experienced classroom humiliation and beatings because I couldn't grasps math concepts which lead me to conclude, it was a painful subject. Subsequently, I developed "Math Anxiety" and avoided the subject. This tutorial was very comprehensive and has revitalized my curiosity and confidence that I can learn this subject.

Division and subtraction aren't commutative so I just convert division to multiplication. divided by 2 is just multiply by 1/2 which avoids order of operations issues. If you do that, the order doesn't matter

Best answer, the expression if flawed if there is a better way to express the problem.

Thank you so much. I have been looking for years for someone with your skill to teach math in such a simple language

When both division and multiplication are involved, the calculation remains linear from left to right regardless of the operator. The last operation to be carried out is reducing the resultant fraction that the operation of the denominators give.

Why don't we use bodmas b for brackets, o for of,d for division ,m for multiplication,a for addition and s for subtraction

At my school we were taught BEDMAS - brackets, exponent, divide, multiply , add, subtract. PEDMAS gives 1, BEDMAS gives9

Move the (division by 2) from over the long line to under the long line, so (12x3)/(2x2)=9.

It should also be made clear that when division is written as a numerator (on top) and a denominator (underneath) with a horizontal line separating them, then both the numerator & denominator formulae (equations) can be understood to be enclosed in parentheses. Thus the above equation could also be written on a single line as (12 / 2 * 3) / (2).

The answer is c) fot once the priorities are from left to right because of thr division. 12 ÷2=6 .3=18/2 =9

I graduated from high school. I took algebra 1 and geometry. I don't remember taking algebra 2 but I must have taken it in summer school. I spent three years in the Army. I went to college majoring in business. Guess what I had to take first year of college. Math 1110,1120 and 1130. Now I was never great in math, but I got through high school with a C average. After laying out of school for 3 years and not being great at math you can imagine how my college math went. To top it off, I had Chinese professors whose first language was you guessed it (Mandarin Chinese). Teaching was out of their wheelhouse, so they just wrote out problems on the chalk board and bored us to death for an hour each day. You guessed it. I failed this crap miserably. I figured okay it was just a fluke that I got a professor who could not speak English and teach. I signed up for the same class again. My luck, I got another Chinese professor. Probably the same one as I cannot differentiate them. I soon realized this was not going to end well so I decided to take refresher algebra 1 and then go back and take math 1110. This would be my last hurrah as you can only take a class three times. As luck would have it, I got an American retired high school principal who was an accomplished high school math teacher. I took his classes and his main requirement is that you do all the math problems assigned and you turned them in daily. Buford Bible was the best math teacher I ever took classes from and he saved my bacon. I went on to get my business degree from the University of Tennessee. I got through the first year. all three classes. Then I got to take statistics and time series analysis. I told the teacher I might be dumber than a rock but that I went through refresher math and got Bs all the way through. He helped me. (Mr. Lassiter) I got Bs through those two statistics courses and three quarters of finance. I guess the real moral of the story is if you find that a math teacher is not helping you get a refresher math class as soon as possible and hopefully you will get a math teacher as good as I did. Thank you Mr. Bible and Mr. Lassiter. I am 74 now and I have not forgotten the help you gave me. I appreciated all that you did for me. To the math teachers out there. Just writing problems on the board and not being able to explain them is a disservice to your students and maybe you should go back to a refresher math class with an accomplished teacher. I got this answer on the first try. Don't forget PEMDAS.

I remember, my dear aunt Sally. (I have a sister named Sally), but the concept of left to right, and which comes first multiplication or division to process first is new to me. Also you multiplied the numerator first even though it was a fraction which symbolizes division. So simplifying the numerator first seems to be a hidden rule also.

To simplify multiply/division on the same level I would write them as multiplication only, so (12 * 1/2 * 3) / 2 and then the order won't matter and I can remove terms that cancel out. Same for plus-minus, write 2 - 3 + 6 -2 as 2 + -3 + 6 + -2 and order does no longer matter, so I can cancel out -2 against +2 pairs, most useful for lots of terms or larger quantities.

Thankyou for the explanation.I learnt a lot,especially PEMDAS.I love maths problem videos.And Im watching your video from SriLanka ,and Im a retired teacher.😊😊

I'm hopeless at maths, but this was simple even for me!! 😊 We were always taught in school maths lessons to work from left to right.

Nice to see I still got the basics. Thank you for the test.

I hate to say how long ago I did my last complex math problem. It's been easily over 30 yrs since I've done these types of fractions. Why? Computers and programs that deal with both formulae and computation. And yet, I was able to do it correctly. And it was a stretch - like pulling mental teeth. And this is from a person who solved algebraic problems in his head in his youth. So the older you get, practice will keep your mind young.

I would venture to say that there are very few good math teachers; probably less than 10%, although I am biased. I seldomly aced math. If I understand the basic rules, I can ace it, as I did in my DeVry algebra test. You are probably one of the good math teachers. Aarre Peltomaa

I really appreciate this explanation. I don't remember being taught order of operations, even though I had good math scores, so it was very helpful .

Haven't done this in a very long time; like 55 years and still worked it out = C. 9

According to math laws you have to do division first then multiplication then addition subtraction

9- multiply and division are the same level so you start at the left on this one.

Strictly speaking there is implied parenthesis. The horizontal line is interpreted as a divide operation so the expression is equivalent to (12÷2×3)÷2. This would be obvious if the 2 under the line were replaced with a more complicated expression requiring at least one extra arithmetic operator, say 6-4. Then the original expression could be written as (12÷2×3)÷(6-4). Typing this into a calculator would produce the correct result =9. The original expression could be entered without parenthesis but the example I gave illustrates a more general case where parentheses are implied.

Thank you so very much for explaining the M. and the D. order. I’m 51 years old, with college education, who has been diagnosed for many years with Dyscalculia. The way you explained this, it just stuck and helped me understand. I know this may sound silly or “slow” to some. Dyscalculia is the math form of dyslexia. Numbers especially in written form seem very confusing, all over the place, freezes our brain, and may become distorted while looking at the math problem.

This was worth listening to for me because I immediately went to 1 because of the M being before D.

Very good idea of lingering a simple answer.

Where were you when I was struggling with math in school? I love your clear, simple explanations.

I'm 71 and I have always been terrible in math, even I followed and understood this video, thanks so much!

I always pretended that the numerator and denominator have their own parentheses ❤ Thanks bud keep it up

12DIVEDES BY 2 =6X3=18 OVER 2 =9

PEMDAS is ambiguous, since multiplication & division are interchangeable operations (as shown here by a focus on left-to-right, vs the stated order of operations). Addition & subtraction are interchangeable as well. PEMDAS can be PEDMAS, PEDMSA, or PEMDSA. That's why most people get confused, so such facts need to be more widely taught.

I definitely forgot a lot of my math as I am 81 . Once you did this basic problem, it all came back. Use of math is also necessary for remembrance! I rarely use math except for bank statements or very basic necessities. Retention is another problem and I think that is due to interest in a subject, or its usefulness to you.

bodmas method using answer is 1 12/2=6/2=3 3/3=1

9. The order of operations is not confused by addition or subtraction.

PEMDAS but MultiplIcation and Division are equal so you must go left to right when you encounter them both. So 12/2=6 then 6x3/2=9

Another way to look at is 12 ÷ 2 × 3 × ½ =9, so you can just go across the board doing multiplication/division

I thought at 1st that the video was long but the length of time was worth it❤

Thank you for putting helpful material on social media. We need more of this. I have one question. I always thought it better to present the correct way and avoid showing all the potential wrong ways? This keeps the flow of information simple and easy for students to follow. A teacher can talk about the risks of the wrong way afterwards, add in some funny anecdotes, etc. This builds a shared experience, that everyone makes mistakes. Again, thank you for your positive content.

BEDMAS is taught in Ontario. Brackets, Exponents, Division, Multiplication, Addition, Subtraction-Order of Operations. Multiplication and Division treated the same left to right, as are Additional and subtraction.

In Germany we learnt "Punktrechnung geht vor Strichrechnung" => Point-before-bar calculation 🙂

Have to use BODMAS; Brackets, of, Division, Multiplications, Addition, Subtraction.

In the USA, we use PEMDAS Method: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction

I am of a slightly older generation and never learned PEMDAS (Please Excuse My Dear Aunty Sally). I learned it as "Order of Operations." The way Order of Operations goes: Parenthesis (or Brackets) Exponents Multiplication/Division (one does not take precedence over the other, the order goes from left to right, so you do whichever comes first in the order) Addition/Subtraction (just like the above, the order is from left to right, one does not take precedence over the other.) According to this method, the answer is 9. Because the order would be: 12/2 = 6, x3 = 18, /2 = 9 *extra note* I was considered a class clown in my school days. Education bored me to tears and I didn't goof off because I wasn't paying attention. I simply grasped the concepts quickly and was tired of hearing it repeated 5 more times and I was ready to move on or get started on my homework so I could get it done before leaving class. Teachers would always try to call me out for not paying attention by shouting out my name and then asking me to repeat what they just said. I would do so verbatim. My middle school math teacher was the first one to catch on. She asked me to stay after class one day. I agreed and she had a lovely conversation with me. She told me that she understood that I knew what was going on, as evidenced by me always getting 100% on all of my tests. She knew I was picking things up quicker than the rest of the kids in the class. She explained to me that not all kids have the ability to do so like I did, so that they needed to perhaps hear it explained again or a different way. She said that normally because of my behavior she wouldn't ask me, but she asked me to be a tutor to some of the kids that didn't quite understand it. She then asked me if I would do them the favor of not distracting the other kids while she tries to teach them. She wasn't angry with me, not yelling at me, or trying to insult me. That had been the approach of all the other teachers and that was what I was expecting. It caught me very off guard and when she was done I smiled very wide and said, "Sorry, I didn't know, and I would be happy to help the other kids." So I was a tutor for Order of Operations and equations. I had a lot of kids coming to me during classwork and asking to see my answers and they would say, "I got something different." I would then ask them how they attacked the problem, and then I would show them the way I did it and explain it.

I always wanted a reason to do th problem like in addition as a kid if you have 4 apples and eat one you have 3 left. I never heard of any reason why more complicated math relates to any thing in the world

2 goes into 12 six times. 6 divided by 2 = 3. Three multiplied by Three = 9 PEMDAS = PARENTHESIS, EXPONENT, MULTIPLICATION, DIVISION, ADDITION, SUBTRACTION

I live in the UK. I was taught B.I.D.M.A.S - Brackets, Indices, Division, Multiplication, Addition, Subtraction. Basically the same. I don't remember the rhyme that went with it but those letters became a word that will forever be imprinted on my maths brain.

I was thought BODMAS 60 years ago. Brackets, Of (power of); Divide; Multiply; Add and finally Subtract. Our teacher had us memories this and it still sticks in my mind.

I'm no mathematician but I immediately got 9, which is the correct answer. I approached it in the simplest way Left to Right, then Top to Bottom. What I don't get, however, how to arrive at 1, 36 or 4. Can someone explain to me why this is considered a confusing problem and how they would get the other choices.

I was not good at Math. Left school in 1971 at 15. I worked in Post offices & lots of jobs that require good ability to count & balance books. But NEVEr had to work out these kind of problems. Why are they used like this? Excuse my ignorance! lol

You can easily clarify order of operations by using parenthesis

I had to watch your video ALL the way through to the end before PEMDAS made sense (I initially got the answer "1") -- thank you for the clarification 🙏

I am 61 and never needed to do any math problems this way that I know of. Maybe I did but I figured it a different way

Any equation that's ambiguous needs parentheses. The equation is written incorrectly.

I was always taught that order of operations is BEDMAS brackets exponents division multiplication addition subtraction.

Always bracket multiples n solve from there first.. 12:(2x3)=12:6=3 3:3=1

Never seen this in school, wish I had this when my kids were struggling.

7:31 key words! "whatever you see first". Whenever this PEMDAS is written there should be a circle around the MD and an explanatory asterisk above it.

I dropped the "÷2" to below the line where it should be to get 12x3 over 2x2. Two 2s cancel out of 12 to leave 3x3.

Answer is a) 1. 2*3=6. So 12:6=2 let's take 2/2=1 so the answer is 1

Ans. 9. Get rid of denominator, then divide and multiply.

I did this problem slightly different than he did, but still got 9 as the correct answer. Cancelling out the 2 on bottom and 12 on top to make the problem simpler: 6/2*3=9.

I never heard that M and D were interchangeable depending on which comes first. Thank you.

12/2x3/2=12/2/2x3=9

Yes the answer is 9, but I prefer BODMAS to PEMDAS, as in Bracket, Off, Division, Multiplication, Addition and Substraction.

PEMDAS (or BODMAS) stands for Parenthesis (or Brackets), Exponents (or Order of powers), Multiplication OR Division, Addition OR Subtraction. Between multiplication and division there is no order of operations because multiplication and division are basically the same thing: dividing something by 2 is the same as multiplying it by 1/2. That's why you do multiplication and division from left to right and there's no order of operations for these two. So 12/2*3=12*1/2*3=18. The same principle applies to addition and subtraction, they are basically the same thing: subtracting 2 is the same as adding -2. And that's why you do addition and subtraction from left to right and there is no order of operation for these two either. So 12-2+6=12+(-2)+6=16. 12/2*3 ----------- can be written as (12/2*3)/2=18/2=9 2

Before listening to this, the answer s/b a) 1. But, I was in school back in the day when MDAS was the rule. I think, it was changed somewhere down stream, so IDK....Back in the day, multiplication was always first.....

With no brackets in sight, the order of operations is simply left to right, top to bottom. THUSLY 12 divided by 2 is 6, multiplied by 3 is 18, divided by 2 is 9.