I just wonder what age you guys are. I'm 67 and did exactly L to R as you did and then wondered why this most basic of calculations should be difficult.
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!
The thing I find a little amusing (?) about these many RUclips videos on the order of operations is that in the real world they are somewhat irrelevant. When you are using math to solve a problem in the real world, say engineering for example, the terms are obvious, and they drive the notation and order of operations. When math is a pure abstraction not actually tied to a need to figure something out, the rules and notation are just conventions of the moment.
I was so "Null" in math when I was a student. I was afraid of all this numbers. Up to today, not really my passion. But (Today I am 57 years old) , I am so happy, that I get it.... sometimes, when it is not too tricky. Thank you! Wished, I had this tools in the past in the 80ties.... ❤ Following you from Germany.
@@dennisbailey-j4g L to R is only a tiny part of the process... order of operations takes precedence over left to right. It's pretty simple. It's often remembered as BEDMAS or some such similar acronym. Note: Trap for beginners: When there is a multiplication, and a division (the DM part) order is L to R. Similarly, when there is an addition and subtract together (AS), order is L to R. The Reason... Multiplication and division have equal precedence. Addition and subtraction have equal precedence. Order of operations means for instance; multiplication and division must be done before addition and subtraction. It also means that anything inside parentheses must be done first. So, it's not just left to right OR just order of operations. People seem to forget parts of it. Example 6 + 3 * 4 = 18 because multiplication has higher precedence than addition. Example (6 + 3) * 4 = 36 because the 6 + 3 is inside () Example 2 * 3 + 5 * 6 = 6 * 30 = 180 because working left to right, multiplication takes precedence over addition. These are all basic rules taught (or should have been) in elementary school. We were taught this stuff at age 10. Hope this helps.
@@robertchiarizia9463 - Order of operators account for the use of brackets then upper/lower, etc. In the absence of brackets or indicators L to R is the mathematical order.
i have always loved math. i am 70 years old and got it within seconds. I am glad you are doing this because it seems the younger generation doesn't understand math as well. i grew up when there were no calculators and you had to learn on paper and in your head.
I just started a new job as an instructor in aviation technology! Part of this is aviation math, and it covers order of operations. I needed this refresher in the worst way! I subscribed!
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! ❤
@@TosinAmupitan BODMAS is the more common non-American way iirc. But BODMAS does the same as PEMDAS. While yes in this problem the division came before the multiplication, division and multiplication switch priority based on which one is first from right to left.
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.
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.
@@MS-ig7ku Indeed The youtube person needs to correct their video. You do not have to do the division first. you need to put parenthesis in to tell you WHICH TO DO FIRST. Other wise either answer is equally valid
In Canada, the mnemonic is BEDMAS: Brackets; Exponents; Division & Multiplication (in order of appearance); and Addition & Subtraction (in order of appearance).
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.
Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this : "use proper parenthesis such that it removes all ambiguities. End of story !!!! That teacher was wasting years of your life. Find his or her and enclose them into pairs of parentheses.
I, too, was raised on BODMAS and the solution to that problem is quite straightforward, with BODMAS. This newfangled PEMDAS screws things up as it comes with one or two qualifications that you didn't have to deal with when applying BODMAS to the problem!
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!
I learned it as PEMA or Please Excuse My Arithmetic. Example: 5 divided by 4 is the same as 5 times one quarter. and 4 minus 5 is the same as -5 + 4. (Read as negative five)
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.
I thought I was terrible at math but I had a terrific teacher in grade 10, at an adult high school who apparently taught math the way I need learn. After that I was getting perfect grades. It’s often the instructor not the student that makes the difference. Mind you, the student needs to be motivated.
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).
@@doodlegassum6959 Interesting. To be clear here, and there could easily be confusion as the two are so similar, I was not referring to a horizontal line that behaves as a vinculum. I was referring to the horizontal line, used above as a division symbol, that certainly has a similarity of effect, but is more contained in its meaning than a vinculum. For clarity of reading by anyone, such as myself, who previously had not knowingly been aware of the terms : % is an obelus; / is a solidus; Vinculum is described as a horizontal bar drawn above & across a (sub-)formula to indicate that part of the overall formula should be calculated first. Thus requiring it be included in the BODMAS acronym as VBODMAS (as it takes higher order-priority even than any form of brackets). Thank you for bringing these to my attention 🙂 As far as I understand, the obelus & solidus are notational & functional equivalents, so are interchangeable. The vinculum is, of course, functionally quite different as it can be used even when division is not involved.
But this still does resolve the problem, you are simply putting the 2 in parenthesis which is not needed. The problem part is 12/2 *3 which still needs one set of parentheses to determine whether that part is 12/(2*3) or (12/2)*3 In general, to any expression of the form a/bc : one needs to insert parentheses to show whether one means (a/b)c or a/(bc).
@@zakelwe I'm sorry to be blunt, but everything you've written is completely wrong. Except maybe the fact that the parentheses around the 2 on its own are unrequired? Required or not, as I wrote earlier, the way it *is* written (below a horizontal division bar) is still equivalent to it being within parentheses.
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.
"When both division and multiplication are involved, the calculation remains linear from left to right regardless of the operator." Show me a link that says this is so ? It's actually false. Additions and subtractions have such a rule, not M and D. When you write a diviision over a multplication like this as in the old days 8 -------- 2 * 4 how does the left to right rule work then ? Left to right you do 8/2 first .... How do you do 12/2/3 ? Left to right again ? Is 2 or 8 the answer ? If you write it over more than one line then it is obvious if you use the old convention of smaller division line is done first 12 --- 2 -------- 3 or 12 -------- 2 --- 3 with 12/2/3 you can only get one answer out of the possible two allowed ... hence why left to right is not done on M and D. PS The reason AS has the left to right rule is because of course they are all written on one line ... 4-3+5 etc etc.
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.
@@TigerDelgado Thank you. I had another conversation later in my college years with a professor who once again, asked me to stay after class. I had grown out of my class clown/acting out phase long before this point. She started to ask me all sorts of questions about my educational history and I thought it was a bit odd and then she said, "This confirms what I thought about you. You are one of the Gifted and Talented, but you slipped through the cracks. They really missed the boat on you." I had only heard about gifted and talented and in my young ignorance, I thought it always referred to special needs children and never gave it another thought. After my conversation with this professor, I did some research, and I started to tear up a bit. What they were explaining to me fit me to a tee. I wasn't goofing off because I wanted to be a jerk. It was because I was simply SO bored. I learned my lesson, I proved I could do it, so what is the point of doing it again and again? There was no purpose to it, and that is a huge problem for people like me. If we don't think it makes sense, we're not interested. There was a lot more information included in the description of gifted and talented students and I was pretty much a classic case of it. Almost everything applied to me. I could have been a straight A student for my entire primary school education. I just didn't see the point of doing homework and just never did it unless I had to in order to pass a class. See, I was coming up through the "no child left behind" nonsense which boiled down means that if a child simply turns in their homework (which is not graded) and gets zeroes on everything else, they will pass the class with a 70% score. Here I was getting 100% on all the tests in every subject. Another middle school teacher, my science teacher had me stay after class. He told me he knew I was a very bright kid, I aced all of his tests, but that he was upset that he couldn't give me an A in his class because I didn't do any of the homework. I asked him why I should do it. He said because it was practice for the tests. I told him, "Well, you already said I am acing all of your tests, so why do I need the practice?" He sat there stunned for a few moments, didn't have an answer, and simply smiled and let me go to my next class. At any rate, I went through college and now have a PHD and a Masters, worked in the medical industry for years, ran a few businesses and am now semi-retired.
@@eduardopena5893 Glad everything turned out right for you in the end, there are too many who keep slipping through the cracks downright to rock bottom.
@@apveening Thank you. It left me feeling pretty empty inside after learning about it. Most of my k-12 education was torture for me. The only thing that made it worthwhile was the best friend I met in 4th grade that I still have in my life today. I never wanted to be there. I looked for reasons not to go. The teachers were hit and miss. I had some really good ones. Some recognized that I wasn't the trouble-maker I seemed to be. Some tied into my humor and focused that into my creativity. Sometimes they would ask me to teach lessons for them and inject my silliness into it. I did very, very well in those classes. I had other teachers that just had no idea what to do with me, so they just ignored me for the most part. And then I had some really bad ones that used to try to pick me apart. I took a great deal of delight whenever they would call on me for an answer or to repeat what they just said, and could answer them correctly and repeat what they said like I was a tape recorder. Their faces would get bright red. I debated a great deal about going to college. I thought it would be more of the same. But, thankfully, I met some great professors there. They took the time to explain why you were learning these things. What applications it would have in your life. It was a great experience. I had one professor I would disagree with numerous times, but instead of getting bent out of shape, he would just ask me questions and to explain my view. We'd have a dialog, and sometimes he would change his mind on something or simply say, "I never really thought about it that way, it is interesting. I will have to think about it some more." Other times it would get him to explain things a bit differently and I would agree with him. It just makes me wonder that if I had gotten into the gifted and talented classes, what would my education have been like? A vast majority of my k-12 education memories are bad. How would I have turned out?
@@apveening I know I tend to post some rambling responses, but this is why I had thought about being a teacher. My experience of not being very well understood and my perspective on things, I felt I could relate to children a bit. I would try to explain things in a way to help them understand rather than simply as something to drill into their heads for a test. To try to help them not be bored. I studied Froebel and felt as if I was learning about a kindred spirit, and I very much connected with his theory. There was a statement he made about the educational system to which I will paraphrase, "They recited their lessons parrot-wise, with seemingly no understanding of what they were saying." He is saying that they didn't LEARN anything. He was a pretty amazing man and if you haven't studied him, and any current teachers and would be teachers, I would emplore you to do so. If I had to break down his lessons as simply as possible, it would be: 1) Do not underestimate the intelligence of the child. They are often more clever than you think and they will ever let on. 2) Pay attention to them and listen to them, especially when they play. That is when they are most likely to show you who they are, their creativity, and imagination. 3) He was a firm believer is that you take a concept a child already understands, and use that as a building block to introduce a new concept. For my term paper on him, I engaged my classmates. I had them participate by holding up some learning aids, reciting some quotes for me. And then I left them with a question. I started with the concept of having a child in a crib with a playtoy that had a steering wheel on it and a horn, which is something I had as a little kid. Then a baby buggy that also had a steering wheel and a horn on it. Then a pedal pusher car. Then I brought in my Playstation and a racing simulator game with my steering wheel and pedal attachments and let a fellow student play it. And then I brought up the driving simulators they had in my high school. My question was, "Do you think this would be an example of Froebel's idea of taking something familiar, building upon it, and ultimately teaching them how to drive a real car?" I saw a lot of smiles in class that day and my professor just looked at me and shook her head.
46 and didn't do any of this since high school and I got it because I'm not stupid. Blows my mind people are this dumb these days. Op you are right and I'm not sure the first comment you got is even English, but like I said I'm not surprised because idiocracy was a documentary.
1 or 9 is the answer these are bullshit made up equations that Equate to nonsense. Yes PEMDAS,BEDMAS and so on are all correct but there is no TRUE answer here except keeping People divided.
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.
@@marablemorgan8292Hello again, interesting, why the yo? That's not normally a slang expression associated with an elder person, I'm 60 and my generation don't use it much either. Just curious about usage of languages, slang and different uses depending on age and cultures. 👋
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.
@@karlwithak. It works just fine for the same level. I highly recommended it. But I do wonder why math teachers don't teach this early on. I like the different methods shown on this channel.
@@MrPimperanto You should look at it as 2 + (-3) + 6 + (-2) and then you may order it any way you want. Plus and Minus are on equal level for calculation.
You are correct, except it's best just to say the order matters. If you introduce exponents, then suddenly the order does matter again in the examples you gave. Thus, it's best just to respect the order for the sake of consistency and accuracy. Getting too creative with this simple process is how people get tripped up.
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.
Wow, revitalized just from one video? Well, congratulations. I'm sorry you had such a dreadful childhood experience. I'm glad you can now enjoy the intelligent, calm explanation of a math process. (You must have learned Something, then - but it sounds VERY unpleasant!)
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.
There is no M and D order so Dyscalculia will not effect the result you get It's a notation issue. Seems like 99% of people on here are suffering from it including the presenter, who is just counting money at the moment He has done this more than once to get views.
I was taught that in algebra division is no different than multiply. And adding is the same as substraction. And I still believe that was right. This stuff...?
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."
We had a geometry teacher who would intentionally do that late into a day's lesson, randomly- she'd put a big flub on the board to see who was still paying attention. It was a great idea, because it made us smart-aleck slackers pay attention and learn, just TRYING to find her errors.
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!
Sorry, but this is the type of nonsense our kids are being taught today. Math is a pure applied science! This means there is an answer, and only ONE answer. Math problems are not open to interpretation! That is why we have Social science. God help us!!
The operators, and the precedence and associativity rules that apply to them, are the punctuation. In this instance, just begin at the beginning. None of the punctuation tells you to do anything different.
Order of operations treats multiplication and division with equal priority, so they are solved as they appear from left to right. Solve above the line first. Therefore 12 divided by two is six. Six times three is nine. At that point, we divide the top number by the bottom number, leaving us with the correct answer of nine. Simple! As long as you are intelligent enough to follow simple instructions (like order of operations).
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.
It’s arbitrary - it is simply defined that division goes before multiplication. If you want multiplication to go first you simply put brackets around it, hence brackets (parentheses) always goes first.
@@gweilospur5877 yes exactly, separating the 2 and 3 in the numerator results in the operation yielding a different answer. which is why the expression is written badly in the first place and wouldn't appear in that form in a math paper (unless deliberate) and even then the student would rewrite it - otherwise the 12 would be divided by 2 = 6 then x 3 = 18 then divided by 2 = 9
Looks like you are lost the PEMDASMDEPEMDSA forests. Don't do math, ask someone else Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this : "use proper parenthesis such that it removes all ambiguities. End of story !!!! That teacher was wasting years of your life. Find his or her and enclose them into pairs of parentheses.
@@countingfloats What I've stated is what has been displayed here. If you disagree with it, then research it & disagree with the math teacher that is teaching it... & the countless others that state it all over the internet. I was taught PEMDAS, period, but here we are...
As a math teacher I find the biggest problem is other teachers teaching pemdas. They cause the misconception that multiplying comes first. Please stop teaching tricks and teach mathematics instead!
@@carolynzaremba5469 I’m sorry that you had an incompetent math teacher. In mathematics we follow left to right, just like we read. It’s been that way for centuries
In Australia we were taught BIDMAS OR BIMDAS. We were always told that Multiplication and Division were equal, then Addition and Subtraction were equal. (Brackets, Indices, Multiplication/Division whichever came first then Addition/Subtraction whichever came first)
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.)
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.
@@jra55417 No, you're mistaken. You cancel out all of factors on the bottom with something with same factor or factors on top, in this case 2 has one factor, 2. 12/2*3 becomes 6/2*3. PEDMAS, remember? 6/2=3, 3*3=9. if you took 2 out of everything on top you'd get 6/1*3=18
It's the same exact concept with the only difference being some parts of the world use brackets instead of parenthesis. I believe some other parts of the world use curly braces as well. Really BEDMAS, PEMDAS, and whatever the other ones are is just a way to teach order of operations, which is entirely universal. EDIT: Their may also be regional differences in the name's of certain operations, such as exponents and roots also commonly being refereed to as indices and orders leading to BIDMAS and BODMAS respectively. So remember the acronym used to teach order of operations does not change the order of operations, that is universal.
@@gg-gn3re Incorrect, there is no left to right or right to left with M and D there is no convention. In general, to any expression of the form a/bc : one needs to insert parentheses to show whether one means (a/b)c or a/(bc). See a page called Order of arithmetic operations; in particular, the 48/2(9+3) question by Gary Bergman at Berkely
@@zakelweDivision is literally an inverted multiplication operation. So, multiplication and division are the same in priority. The example you provided can be re-written simply as 48(0.5)(9+3). There is no ambiguity here. If there were ambiguity, then a program like Microsoft Excel would be calculating unpredictable answers all over the place. With the rules, Excel provides a predictable answer every time.
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.
If you had taken each part as a fraction it still works out to 9. 12/2 divided by 2/2 multiplied by 3/2... becomes 6 divided by 1 multiplied by 1.5 equals 9. It's just easier mentally to resolve the numerator first then apply the denominator.
The numerator was done 1st because the vinculum is also a Grouping symbol (like parentheses) it has a beginning and an end. As far as left to right, you actually started learning that when you started learning to add. The key to the Order is left to right for similar operations .
@@johnl.tiemannjr.2662 left to right is not necessary, it just avoids confusing fractions for some -- you can do × and ÷ in any order. But of course you can't do "2x3", rather if you go right to left it you have to know "÷2" is the same as "×1/2". Just like (for example) 3+4-5+6 you can also go right to left but you cannot start with 6+5, it must be 6+(-5). The "-" or "÷" prefix for EACH TERM changes how you handle it. ...Or the simple way if you don't understand all this, just go left to right does work too.
@@pamelas9Sorry but that is incorrect. It happens to work in that example, but what about (for example) add x8 to the numerator? Your method would be: (12/2)÷(2/2)×(3/2)×(8/2)=36 But the correct answer is: (12÷2×3×8)/2=144/2=72. In fact, since " ÷2" is the same as "×1/2" the whole thing can also be written as: 12 x 1/2 x 3 x 1/2, or also (12x3) / (2x2), both of which resolve to 9. If you include my "x8" you get 12 x 1/2 × 3 × 8 × 1/2, or (12x3×8) / (2x2), Both of which resolve to 72.
Multiplication and division are higher order of operation than addition and subtraction but if the operators are of the same precedence, conventionally they are evaluated from left to right.
It is either 9 or 1 depending on the proper grouping of the numerator. Left to right is BS multiplication and division on a properly written equation can be done in either order and get the same result. This is a purposefully ambiguous equation that could potentially have 1 of 2 answers, but not both
@@gg-gn3re and that's where the education system failed you. If the order of multiplication and division matters in an equation, then the equation itself is wrong and all answers are invalid
@@cyrnus This is incorrect. The line is putting it as a fraction which gets simplified last. This isn't an "order of multiplication and division" issue. It is generally written different but that doesn't make this worse written equation have two answers.
And you get the same result no matter which order you do them in. Hint: 12/2*3 = 12*0.5*3 For that matter, you'd still get the same result if you wrote it as 12/2*3/2 instead of (12/2*3)/2 There is no ambiguity. Just a whole lot of people who don't grasp how the math actually works.
OMG! If only I had learned this when I was young!!! I’m 76. I actually get this in my spreadsheets on the computer. Now I understand what to do. Thank you. ❤ Shirley
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 😊
Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this : "use proper parenthesis such that it removes all ambiguities. End of story !!!! That teacher was wasting years of your life. Find his or her and enclose them into pairs of parentheses.
Wonderful I missed some concepts while I was in school and the teacher would not help me see what I was missing. I love math. Been years trying to find those missing components. Thanks for clarity.
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.....
Note : if the answer is s/b a then you are not designing a 747 Jumbo jet. Otherwise read on : Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this : "use proper parenthesis such that it removes all ambiguities. End of story !!!! That teacher was wasting years of your life. Find his or her and enclose them into pairs of parentheses.
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.
Implied parentheses are a dead end and only might work if there are only a few levels and it is you and your twin are working on the same problems. Otherwise all bets are off. Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this : "use proper parenthesis such that it removes all ambiguities. End of story !!!! That teacher was wasting years of your life. Find his or her and enclose them into pairs of parentheses.
@countingfloats My thoughts exactly! Except the end, which made me LOL. I thought it more of a mind puzzle than a math puzzle. Math problems should be clearly expressed.
You have to be careful with this approach because you can't simply add in parenthesis or brackets where there are none. I was in Advanced Academics since I entered the third grade. In middle school, I was doing supposedly college level work. So my order of operations problems were rarely just this simple. I would see things like: (12 - 2)5 - 5 + (4 + 3)2 - 6 = ? Now, you can't just slip in the parenthesis wherever you like. You will get the complete wrong answer.
@eduardopena5893 ABSOLUTELY! I absolutely reject the thought process of the subject video. One might say it is acceptable for less complicated or lower level of problems. No. The lowest levels should introduce and train for the more complicated problems. Thank you for your important voice on this matter. 🌞
@@ritapearl-im3wv Thank you for the reply. Right, it is a very fundamental thing that you have to get the basics in order first, so that you can build up to the next thing. If you think my example looks complicated, you should see something called matrices. Fortunately for me, as complicated as matrices are, they are very formulaic and logical. There's a process you follow, and so long as you follow it, you'll always be correct. Although I was an ace at them, it was rather unfortunate that I never, ever understood why I needed to learn how to do them or what they would be used for. It was never explained to me. It was like, yeah, I can do them. So what?
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.
Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this : "use proper pairs of parentheses such that it removes all ambiguities. End of story !!!! That teacher was wasting years of your life. Find his or her and enclose them into pairs of parentheses.
You don't need the parentheses though. Order of operations goes left to right. The "multiply/divide" means that you do whichever operation comes first in the equation. Multiply doesn't come "before" division. They are equal. Whichever comes first is what you do first. Like he said, it's M OR D.
The opening phrase "in the USA" IS not that relevant on the internet anymore ! As in ,so yes you have your American system and convention AND as a culture and nation you no longer have that much respect globally. So saying what you said does not carry any example of better way of doing things anymore. You are no longer the light on the hill beacon of better democracy anymore. So mine and I am sure a lot of the rest of the world, democracies included, have shifted to a sounder conventional wisdom of international agreed standards for things like explaining why a world citizen needs the context of consensus of agreements to work together. Doing math is important AND it no longer currently needs to be stylised nationalistically. Like math that understood and works on all the continents rather than giving any precedence or nod to allowing the USA to set the standards for the future. Tell me do you still think the Monroe ~ somewhat jingoistic outlook ~is still relevant and proper way to approach diplomatic affairs still. The blunt point is that PEMDAS method is more universal than being an American thingie, so ... if you give up your American prejudices and biases ( apologizes to the Canadians, Mexicans, Cubans etc) there is strong case and instances international too see, hear and feel this. way 🤣😂🤣😂
@@chrislee882 -- I think the point was that this person was explaining what they were taught, and how widespread it is. The Monroe doctrine is outdated.
I would rewrite the problem as this 2/(12/2x3). Now you have a parenthesis to work first. Solving this step we find (6/1x1.5). Now we are rid of the parenthesis leaving 6/1*1.5. 6/1 is 6 thus we have 6*1.5 which is 9. The answer is 9.
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 🙏
You are correct to watch the whole video and learn how to do order of operations correctly. The answer is 9. Don't worry about the comments below. Multiplication and division do not take precedence over each other and are done from left to right just like addition and subtraction.
Thank you. So many people have responded with superior, snarky attitudes. If they had a better math teacher than some others, that's luck and not some accomplishment of their own.
It's wrong. It's a notational problem rather than any generic teaching aid such as PEMDAS or BODMAS, hence the discussion with this badly written ambiguous equation
@@jladdyost The problem here is that this is very middle grade maths using generic teaching rules. If you go to Berkeley or Harvard with high end mathematicians then they don't agree with the result of the OP
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.
Thought? Or taught? Wasnt there something about My Dear Aunt Sally and parentheses?? It's been many years - and truly, I havent needed it in well over 50!!!!
NOT HARD!! Apply the Order of Operations and voila you get the correct answer, which is 9. 1:10 This will be interesting! Oh good!! You got it right!! However, I'm very strongly against the use of a Mnemonic unless you teach the actual mathematics behind it and the Order of Operations. PEMDAS BODMAS BEDMAS BIDMAA DMAS MDAS GEMS GEMDAS These are all mnemonics and acronyms that are taught around the would. And look at the list, it's long and confusing, especially if the mathematical reasoning isnt taught alongside it. Why are multiplication and division done together whichever comes first from left to right. Why are addition and subtraction similarly related? What the heck does the E for exponents, the I for indices and the O for orders in these mnemonics actually involve? How about roots, radicals, factorials, trig functions and fractions?? What and how are parentheses used in math ( ) ? The P for PEMDAS and the B for brackets are what exactly and how do they work?? I drum basic arithmetic into my students. We look at the relationships between the operations. I teach high school math at a private school in Australia. When my Year 6 students arrive at the Senior Campus and begin the Middle School (12 year olds) they get a bit of a shock. Because I take them way back to basics. Manipulating, visualising and understanding ALL the arithmetic operations. On Day 1 in class I take them back to: basics and they think I'm joking. I am not. I'm my experience, an solid grounding and an excellent understanding of basic arithmetic is vital for success in later years. I spend a good of couple of weeks on just the basics 1+1 Then we look at how addition and subtraction undo each other. How they are opposites or and discuss why multiplication and division are relatesd and they 5+5+5+5+5+5+5+5+5+5=50 5×10 =50 The Order of Operations can be used to solve harder arithmetic like this: 4-8+60÷(16÷2×4)²√36+5! I'm proud of my students success; not just in my maths class, but in every class. Because I teach back to basics, because the basics are often skipped over or not taught in the educational context. You can't teach young primary students the reasoning and relationships behind the order of operations, and it's not revisited or it becomes "assumed knowledge" and isn't actually taught at all. The moral of the story is TEACH THE ORDER OF OPERATIONS AND DON'T BE LAZY AND JUST GIVE STUDENTS AN ACRONYM TO REMEMBER. TEACH THE ACTUAL MATH.
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.
I took calculus 40 years ago as a senior in high school. However, when PEMDAS is the ORDER in which you solve a problem, how does division come before multiplication? 40 years later, is it now PEDMAS???
I don't think that PEMDAS is the best tool to use to learn this concept. Computational precedence is really what's under discussion and I don't have a cute mnemonic - you just need to learn the rules. In most formulations, multiplication and division have equal precedence and when both appear consecutively in the absence of parentheses, the order of evaluation is left to right. That's kinda' hard to encapsulate in an acronym/mnemonic. I say "most formulations" because all of the many computer languages have computational precedence rules in their definitions and you cannot rely on them all using the same rules, which is why many programmers use parentheses liberally in mathematical expressions..
You do not drop it below the line. There is no reason to do so. It is the division operator. People confuse division with fractions. Not quite the same thing. Depends on context.
While recovering from a severe stroke this has helped me with improving cognitive function, thank you so much, I look forward to more problems, thank you 💕
Yep, and good for you, for learning! That's why both BODMAS and PEDMAS acronyms are correct, even though one has DM and the other MD, because without parentheses, left to right for all division and multiplication is correct. Ditto with AS: 5-2+3=3+3=6, go left to right even though the first operation is subtraction.
@@ernesthakey3396 Which means that using an acronym like PEDMAS is kind of pointless because it implies that multiplication is always first by the sheer fact that it is a sequence of letters. By itself, the acronym can't indicate that one specific pair is interchangeable while others are not. Why then wouldn't multiplication and addition be interchangeable? The acronym requires some extraneous knowledge, so it's defective as a mnemonic device. It's really just a convenience for teachers who already know what they're teaching, rather than an actual learning-centered practice.
I just subscribe. Stumbled on this video. It reminded me so much of the troubles I had learning math. He explained so easily to remember. Look forward to watching more videos.
I had a misconception about Mult. having priority over Division...so I got it wrong. ..I ignored Left to Right operation because of that misconception....Common sense of going L->R (regardless of signs), is what solves this problem. Yes, I learned some logic out of this so it was worth getting it wrong.
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 learned BODMAS in Australia where O is for Orders but still the same idea. Multiplication has the same priority as division. The video does not make sense because PEMDAS and BODMAS have division and multiplication reversed. Maths can't change depending on the country you were taught. @@schwarzerritter5724
@@Illawong I assume D stands for division and M for multiplication? D is clearly left of M. If D and M have the same priority, than BIDMAS makes people memorize the wrong rule.
@@schwarzerritter5724BIDMAS is a correct rule. Multiplication and division have the same priority. When multiplication and division (or division and multiplication) are seen in a series, then you calculate left to right. Whichever comes first is calculated first. There is no ambiguity. Microsoft Excel calculates a predictable answer every time.
I was an engineer; no math or engineering text I ever studied printed mathematical operations like this where parentheses and/or brackets are omitted. While it may be interesting for a simple operation, doing this in the real world where calculations can become complicated quickly would introduce an unacceptable risk for computational errors.
An engineering degree in 1972 and had no problems with math, yet never heard of PEMDAS. We used parenthesis, brackets, and braces without confusion. If you want your bridge to stand up or your amplifier to amplify without smoking, play it safe and use these.
@@gg-gn3re Yes I'm saying I'd never heard the term PEMDAS prior to a couple of years ago. America does this...takes something that already exists, renames it, claims it as theirs..it's all about projecting a false sense of adequacy (and it fails every time). I've even seen a website claiming that Americans speak English, and in England they speak "British English".
I got the answer right, although with some degree of uncertainty. The reason being that in the days and place I was taught algebra (in the 1960s in Montreal, algebra manuals from France), the writing of such an equation required that there be paranthses to determne the order of opeartions. So, we would have been required to write the numerator as follows: (12/2)x 3.
It's been 50 years, but I believe it was first covered in Pre-Algebra. We used to have two math tracks. I don't believe the Business track had any Algebra courses
No! There is no ambiguity whatsoever, and never has been. Operators with the same precedence (like division and multiplication) are evalutated left to right. It cannot be much simpler than that.
I am in my 70’s. The use of PEMDAS wasn’t heard of, or at least I was never taught it. Thank you for teaching this. It makes such problems as you present here easy. I am keeping it in mind.
Like my dad used to say ‘back in the day’ we didn’t have any of this.. I used a big algebra book that was as heavy as I was too 😂😂 When my kids were in primary school, my youngest had a lot of trouble understanding the way the teacher was teaching them maths, so I started teaching him the old way and he understood it straight away then it became easier for him to understand maths and he got to understand the teachers way.
And thank you for not saying it's all nonsense as so many people have said. It's what mathematicians agreed upon a long time ago. Most of the people objecting to the video either learned PEMDAS (BOMDAS in the UK) when they were young and think it's totally obvious (which it isn't), or they think you just do all the operations as you find them, from left to right, which is logical but wrong.
Here in England in the 1960s I was taught BODMAS, 'Brackets', 'Of', 'Division', 'Multiplication', 'Addition', 'Subtraction'. By the way, here we do mathS, short for mathematicS, not math! I did get it right and get 9 though.
It's very simple. PEMDAS works. You just have to re-imagine the question. As shown, the equation in single line is (12 / 2 * 3) / 2. So solve the parentheses first, in order.
@@Darryl.M It actually is wrong because there are not enough parenthesis to be able to determine which answer is right. It is called an ambiguous equation. In general, to any expression of the form a/bc : one needs to insert parentheses to show whether one means (a/b)c or a/(bc). See a page called Order of arithmetic operations; in particular, the 48/2(9+3) question by Gary Bergman at Berkely
I like it and relied on my those old days key from elementary school called "BODMAS" to be executed from LT to RT and found to be = 9. Surely appreciable!!
I think there is a hidden understanding of grouping that exist between the operations involve and MD is interchangeable same as AS as long as MD comes first before AS....and the solving is from left to right....
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.
It's been 60 years since I was a wiz at this. I can justify both 1 and 9, so I figure I've forgotten a rule or 2. It won't surprise me if they're both wrong.
Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this : "use twins of proper parenthesis such that it removes all ambiguities. End of story !!!! That teacher was wasting 6 decades of your life. Find his or her and enclose them into pairs of parentheses. @@ferengiprofiteer9145
So glad you appeared! Need a refresher to be able to help my granddaughters. Thx! Oh - and i got the answer right, but it was luck. Never heard of Aunt Sally. PEMDAS will help!
Thank you for explaining the order of operations. I kind of forgot a bunch of basic math just because I never use it. Recently a question like this came up. I tend to do math in my head all the time but I really wasn't sure of the O of O because I couldn't remember which came first, multiplication or division and I swear I remember multiplication coming first. It's been well over 50 years since my last basic math course. I did get the answer right, because I made an educated 'guess' but now I know for sure that I did it correctly and I won't make the mistake again of second guessing my answer.
Following the PEMDAS rule, we should rewrite the expression: 12x1/2x1/2x1/2x3/2=9/4 or 2.25. the answer is not in the list. Your answer is 9 because you calculated the nominator first and then divided it by the denominator, which is 2 and obtained 9 as your answer.
9 is correct..... did it in my head while reading the formula the 1st time. I'm 70 years old. I speak some Japanese, latin and French.... constant reader of historical books. I have no college degree.... served in The Marines.... do I qualify to vote? We are no longer a free country if we disqualify Americans from voting. The only qualification should be that you are a US Citizen. Semper Fi
I got both answers, now I know why one was incorrect! Wished id known the “or” for m, d,a&s i always do “and” never “or”… thank you, ones never too old to learn, 😅
![Lethal Company Music Video 🎵 "Follow The Orders" [VERSION A]](http://i.ytimg.com/vi/QeooZB4Z7RA/mqdefault.jpg)
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 ...
I just wonder what age you guys are. I'm 67 and did exactly L to R as you did and then wondered why this most basic of calculations should be difficult.
Division and multiplication take precedence over addition and subtraction, but not over each other
So just read the sum through
Answer is a.
It would be a) but for the lack of parentheses. The answer is 9
C answer is 9
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!
Wait until you are out of school 60 years. I got it right on first try but did not know why.
I got it in 6 seconds. Very simple.
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
Right.
Thats what i got.
1
@@seahunt6055 2. to that..
The thing I find a little amusing (?) about these many RUclips videos on the order of operations is that in the real world they are somewhat irrelevant. When you are using math to solve a problem in the real world, say engineering for example, the terms are obvious, and they drive the notation and order of operations. When math is a pure abstraction not actually tied to a need to figure something out, the rules and notation are just conventions of the moment.
I was so "Null" in math when I was a student. I was afraid of all this numbers. Up to today, not really my passion. But (Today I am 57 years old) , I am so happy, that I get it.... sometimes, when it is not too tricky. Thank you! Wished, I had this tools in the past in the 80ties.... ❤ Following you from Germany.
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.
Exactly what I remember from school L to R .WTF is order of operations .
Order of operations actually
@@dennisbailey-j4g L to R is only a tiny part of the process... order of operations takes precedence over left to right. It's pretty simple. It's often remembered as BEDMAS or some such similar acronym. Note: Trap for beginners: When there is a multiplication, and a division (the DM part) order is L to R. Similarly, when there is an addition and subtract together (AS), order is L to R. The Reason... Multiplication and division have equal precedence. Addition and subtraction have equal precedence.
Order of operations means for instance; multiplication and division must be done before addition and subtraction. It also means that anything inside parentheses must be done first. So, it's not just left to right OR just order of operations. People seem to forget parts of it.
Example 6 + 3 * 4 = 18 because multiplication has higher precedence than addition.
Example (6 + 3) * 4 = 36 because the 6 + 3 is inside ()
Example 2 * 3 + 5 * 6 = 6 * 30 = 180 because working left to right, multiplication takes precedence over addition.
These are all basic rules taught (or should have been) in elementary school. We were taught this stuff at age 10.
Hope this helps.
@@robertchiarizia9463 - Order of operators account for the use of brackets then upper/lower, etc. In the absence of brackets or indicators L to R is the mathematical order.
Very intuitive, but true. I never needed to be told that to come to that conclusion. Good advice, nontheless.
i have always loved math. i am 70 years old and got it within seconds. I am glad you are doing this because it seems the younger generation doesn't understand math as well. i grew up when there were no calculators and you had to learn on paper and in your head.
Same. I’m 71 and clearly we were taught well back then…
Yes. I am 93 and learned the only way permanently.
I’m 69 and thought this was pretty straight forward 🤷♀️
Agree, at 71, we learnt mental arithmetic at age 11 with huge emphasis on doing mental calculations. Still very good at.
1
12 divided by 2= 6 X 3 equals 18, divided by 2 equals 9
I just started a new job as an instructor in aviation technology! Part of this is aviation math, and it covers order of operations. I needed this refresher in the worst way! I subscribed!
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! ❤
Exactly!
BODMAS.
Division comes before multiplication. That's how I was taught
@@TosinAmupitan Not me.
1
@@TosinAmupitan BODMAS is the more common non-American way iirc. But BODMAS does the same as PEMDAS. While yes in this problem the division came before the multiplication, division and multiplication switch priority based on which one is first from right to left.
How to turn a 3 second math problem into a 13 minute video 😅
which is how math teachers left me in the dust when I was younger.
And in the end get an incorrect calculation. Because the right result is: a) 1
😂😂😂 That could be answered in 3 seconds turns into a complex essay. 👽
@@aleksandermilic8919 See the video and go to school...
@@aleksandermilic8919 nope
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 think they teach it poorly on purpose. 100 years ago people used to do calculus in their head, now young adults can't add 7 plus 9
. . . . .and you still failed today. MDAS is the code!
@@virgeliotudtud3125 They didn't fail. They followed the MDAS process exactly.
OR do it this way: 12 divided by 2 = 6, 2 divided by 2 = 1, 3 divided by 2 = 1.5 *so* 6 divided by 1 = 6 X 1.5 = 9
@@virgeliotudtud3125And perhaps you know math but have no class on how to treat others.
I've always loved math. At 71, I learned which to calculate first. Thank you. I was looking at 1 & 9. Clear as a bell now.
Order of Operations / BODMAS ----BRACKETS OF DIVISION , Multiply , ADD, Subtract
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!
Bodmas brackets of division,multiplication,addition and subtraction 12 divided by 2 =6times3=18 divide by 2 = 9
Bodmas is UK type.
BODMAS.
B=Bracket
O= Objective
D= Division
M= Multiplication
A= Addition
S= Subtraction
In Canada it's
B brackets
E exponents
D division
M multiplication
A addition
S subtraction
DM and AS go left to right.
I like Brackets. If they are used, there is no confusion about the order
There are no brackets here. Start at the left and move to the right! Need a guidebook?@@roykowalski4125
A
Solve from left to right and follow the order of operations method ..PEMDAS
12:2=6x3=18:2= 9 . Answer C=9
Actually the way you posted it is wrong 12:2 is not equal to 6x3 and 6x3 is not equal to 18:2 🤣
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.
Bomdas is a.lso correct though, multiplication and division have no order hence why you need more brackets in this example.
@@zakelwe Yes it should have parentheses for clarity.
@@MS-ig7ku Indeed The youtube person needs to correct their video. You do not have to do the division first. you need to put parenthesis in to tell you WHICH TO DO FIRST. Other wise either answer is equally valid
@@zakelwe Division AND multiplication share priority based on their position (order) L ⇾ R in the equation (just as addition & subtraction does).
In Canada, the mnemonic is BEDMAS: Brackets; Exponents; Division & Multiplication (in order of appearance); and Addition & Subtraction (in order of appearance).
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 agree, that is how i learnt it. BEDMAS. Division then Multiplication. I don't know when this PEMDOS came about.
Same here!!!!!!
Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this
: "use proper parenthesis such that it removes all ambiguities. End of story !!!! That teacher was wasting years of your life. Find his or her and enclose them into pairs of parentheses.
I, too, was raised on BODMAS and the solution to that problem is quite straightforward, with BODMAS. This newfangled PEMDAS screws things up as it comes with one or two qualifications that you didn't have to deal with when applying BODMAS to the problem!
@@countingfloats Exactly or you get more than one answer.
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!
I learned it as PEMA or Please Excuse My Arithmetic.
Example: 5 divided by 4 is the same as 5 times one quarter. and 4 minus 5 is the same as -5 + 4. (Read as negative five)
You can use BODMAS - bracket, of, division,addition then subtraction
9
This is how I do
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.
and you can backup and repeat if necessary... John is good at explaining
But this ain't really 'basic' math, it's more about what one might expect on a math test like on the SAT.
MATH is quite irrelevant in real life, so don't sweat it. It's only important when the electric and gas companies are trying to rip you off.
@@Stuart.Branson. opinions vary
I thought I was terrible at math but I had a terrific teacher in grade 10, at an adult high school who apparently taught math the way I need learn. After that I was getting perfect grades. It’s often the instructor not the student that makes the difference. Mind you, the student needs to be motivated.
9. The order of operations is not confused by addition or subtraction.
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).
Yes.
Obelus, solidus and vinculum.
The difference is rarely mentioned but is vital
@@doodlegassum6959 Interesting. To be clear here, and there could easily be confusion as the two are so similar, I was not referring to a horizontal line that behaves as a vinculum. I was referring to the horizontal line, used above as a division symbol, that certainly has a similarity of effect, but is more contained in its meaning than a vinculum.
For clarity of reading by anyone, such as myself, who previously had not knowingly been aware of the terms :
% is an obelus; / is a solidus; Vinculum is described as a horizontal bar drawn above & across a (sub-)formula to indicate that part of the overall formula should be calculated first. Thus requiring it be included in the BODMAS acronym as VBODMAS (as it takes higher order-priority even than any form of brackets).
Thank you for bringing these to my attention 🙂 As far as I understand, the obelus & solidus are notational & functional equivalents, so are interchangeable. The vinculum is, of course, functionally quite different as it can be used even when division is not involved.
But this still does resolve the problem, you are simply putting the 2 in parenthesis which is not needed. The problem part is 12/2 *3 which still needs one set of parentheses to determine whether that part is 12/(2*3) or (12/2)*3
In general, to any expression of the form a/bc : one needs to insert parentheses to show whether one means (a/b)c or a/(bc).
Honestly that was easy
@@zakelwe I'm sorry to be blunt, but everything you've written is completely wrong. Except maybe the fact that the parentheses around the 2 on its own are unrequired? Required or not, as I wrote earlier, the way it *is* written (below a horizontal division bar) is still equivalent to it being within parentheses.
In school we were taught rule BEDMAS Bracket Exponent Divide Multiply Add Subtract
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.
Yes.
"When both division and multiplication are involved, the calculation remains linear from left to right regardless of the operator."
Show me a link that says this is so ?
It's actually false.
Additions and subtractions have such a rule, not M and D.
When you write a diviision over a multplication like this as in the old days
8
--------
2 * 4
how does the left to right rule work then ?
Left to right you do 8/2 first ....
How do you do
12/2/3 ?
Left to right again ?
Is 2 or 8 the answer ?
If you write it over more than one line then it is obvious if you use the old convention of smaller division line is done first
12
---
2
--------
3
or
12
--------
2
---
3
with 12/2/3 you can only get one answer out of the possible two allowed ... hence why left to right is not done on M and D.
PS The reason AS has the left to right rule is because of course they are all written on one line ... 4-3+5 etc etc.
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.
God bless you.
❤❤❤❤❤❤❤❤
@@TigerDelgado Thank you. I had another conversation later in my college years with a professor who once again, asked me to stay after class. I had grown out of my class clown/acting out phase long before this point.
She started to ask me all sorts of questions about my educational history and I thought it was a bit odd and then she said, "This confirms what I thought about you. You are one of the Gifted and Talented, but you slipped through the cracks. They really missed the boat on you."
I had only heard about gifted and talented and in my young ignorance, I thought it always referred to special needs children and never gave it another thought. After my conversation with this professor, I did some research, and I started to tear up a bit. What they were explaining to me fit me to a tee.
I wasn't goofing off because I wanted to be a jerk. It was because I was simply SO bored. I learned my lesson, I proved I could do it, so what is the point of doing it again and again? There was no purpose to it, and that is a huge problem for people like me. If we don't think it makes sense, we're not interested. There was a lot more information included in the description of gifted and talented students and I was pretty much a classic case of it. Almost everything applied to me.
I could have been a straight A student for my entire primary school education. I just didn't see the point of doing homework and just never did it unless I had to in order to pass a class. See, I was coming up through the "no child left behind" nonsense which boiled down means that if a child simply turns in their homework (which is not graded) and gets zeroes on everything else, they will pass the class with a 70% score. Here I was getting 100% on all the tests in every subject. Another middle school teacher, my science teacher had me stay after class. He told me he knew I was a very bright kid, I aced all of his tests, but that he was upset that he couldn't give me an A in his class because I didn't do any of the homework. I asked him why I should do it. He said because it was practice for the tests. I told him, "Well, you already said I am acing all of your tests, so why do I need the practice?" He sat there stunned for a few moments, didn't have an answer, and simply smiled and let me go to my next class.
At any rate, I went through college and now have a PHD and a Masters, worked in the medical industry for years, ran a few businesses and am now semi-retired.
@@eduardopena5893 Glad everything turned out right for you in the end, there are too many who keep slipping through the cracks downright to rock bottom.
@@apveening Thank you. It left me feeling pretty empty inside after learning about it. Most of my k-12 education was torture for me. The only thing that made it worthwhile was the best friend I met in 4th grade that I still have in my life today. I never wanted to be there. I looked for reasons not to go.
The teachers were hit and miss. I had some really good ones. Some recognized that I wasn't the trouble-maker I seemed to be. Some tied into my humor and focused that into my creativity. Sometimes they would ask me to teach lessons for them and inject my silliness into it. I did very, very well in those classes. I had other teachers that just had no idea what to do with me, so they just ignored me for the most part. And then I had some really bad ones that used to try to pick me apart. I took a great deal of delight whenever they would call on me for an answer or to repeat what they just said, and could answer them correctly and repeat what they said like I was a tape recorder. Their faces would get bright red.
I debated a great deal about going to college. I thought it would be more of the same. But, thankfully, I met some great professors there. They took the time to explain why you were learning these things. What applications it would have in your life. It was a great experience. I had one professor I would disagree with numerous times, but instead of getting bent out of shape, he would just ask me questions and to explain my view. We'd have a dialog, and sometimes he would change his mind on something or simply say, "I never really thought about it that way, it is interesting. I will have to think about it some more." Other times it would get him to explain things a bit differently and I would agree with him.
It just makes me wonder that if I had gotten into the gifted and talented classes, what would my education have been like? A vast majority of my k-12 education memories are bad. How would I have turned out?
@@apveening I know I tend to post some rambling responses, but this is why I had thought about being a teacher. My experience of not being very well understood and my perspective on things, I felt I could relate to children a bit. I would try to explain things in a way to help them understand rather than simply as something to drill into their heads for a test. To try to help them not be bored.
I studied Froebel and felt as if I was learning about a kindred spirit, and I very much connected with his theory. There was a statement he made about the educational system to which I will paraphrase, "They recited their lessons parrot-wise, with seemingly no understanding of what they were saying." He is saying that they didn't LEARN anything.
He was a pretty amazing man and if you haven't studied him, and any current teachers and would be teachers, I would emplore you to do so.
If I had to break down his lessons as simply as possible, it would be:
1) Do not underestimate the intelligence of the child. They are often more clever than you think and they will ever let on.
2) Pay attention to them and listen to them, especially when they play. That is when they are most likely to show you who they are, their creativity, and imagination.
3) He was a firm believer is that you take a concept a child already understands, and use that as a building block to introduce a new concept.
For my term paper on him, I engaged my classmates. I had them participate by holding up some learning aids, reciting some quotes for me. And then I left them with a question. I started with the concept of having a child in a crib with a playtoy that had a steering wheel on it and a horn, which is something I had as a little kid. Then a baby buggy that also had a steering wheel and a horn on it. Then a pedal pusher car. Then I brought in my Playstation and a racing simulator game with my steering wheel and pedal attachments and let a fellow student play it. And then I brought up the driving simulators they had in my high school. My question was, "Do you think this would be an example of Froebel's idea of taking something familiar, building upon it, and ultimately teaching them how to drive a real car?"
I saw a lot of smiles in class that day and my professor just looked at me and shook her head.
Haven't done this in a very long time; like 55 years and still worked it out = C. 9
At 56 I get 1 and we are noth right with this ambiguous equation.
High 5
46 and didn't do any of this since high school and I got it because I'm not stupid. Blows my mind people are this dumb these days. Op you are right and I'm not sure the first comment you got is even English, but like I said I'm not surprised because idiocracy was a documentary.
1 or 9 is the answer these are bullshit made up equations that Equate to nonsense. Yes PEMDAS,BEDMAS and so on are all correct but there is no TRUE answer here except keeping People divided.
Also known as bidmas Brackets, indices division multiplication addition subtraction
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.
Yo? 70 years old? I think not. Lol
I thought the answer was 17. I still think it's 17.
I'm 73 and think so...
@@marablemorgan8292Hello again, interesting, why the yo? That's not normally a slang expression associated with an elder person, I'm 60 and my generation don't use it much either. Just curious about usage of languages, slang and different uses depending on age and cultures. 👋
Actually, it's 9.
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.
@@karlwithak. It works just fine for the same level. I highly recommended it. But I do wonder why math teachers don't teach this early on. I like the different methods shown on this channel.
2+-3+6+-2……. You nuts????? 2+(-3+6)+(-2) you CANT put - and + RIGHT next to each other!!!!!!
@@MrPimperanto You should look at it as 2 + (-3) + 6 + (-2) and then you may order it any way you want. Plus and Minus are on equal level for calculation.
You are correct, except it's best just to say the order matters. If you introduce exponents, then suddenly the order does matter again in the examples you gave. Thus, it's best just to respect the order for the sake of consistency and accuracy. Getting too creative with this simple process is how people get tripped up.
Francamente tengo 78 años y esta operación las resolvíamos con 10 años,al menos en España y sin darle tantas vueltas
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.
Beatings?
I also suffered humiliation and feelings of shame.
Dang. Beatings at school over math ? What kind of nerd geek school was this?
C.
Wow, revitalized just from one video? Well, congratulations. I'm sorry you had such a dreadful childhood experience. I'm glad you can now enjoy the intelligent, calm explanation of a math process. (You must have learned Something, then - but it sounds VERY unpleasant!)
I did this equation two ways, 1st the way you described it, and to check my work, I divided each numerator by the denominator, so 6/1*1.5. 6* 1.5=9
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.
There is no M and D order so Dyscalculia will not effect the result you get
It's a notation issue.
Seems like 99% of people on here are suffering from it including the presenter, who is just counting money at the moment
He has done this more than once to get views.
I was taught that in algebra division is no different than multiply. And adding is the same as substraction. And I still believe that was right. This stuff...?
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."
We had a geometry teacher who would intentionally do that late into a day's lesson, randomly- she'd put a big flub on the board to see who was still paying attention. It was a great idea, because it made us smart-aleck slackers pay attention and learn, just TRYING to find her errors.
The answer is 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!
Sorry, but this is the type of nonsense our kids are being taught today. Math is a pure applied science! This means there is an answer, and only ONE answer. Math problems are not open to interpretation! That is why we have Social science. God help us!!
😂😂😂 No correct answer!
Answer for Woke generation
maths? math!
@lufknuht5960 Depends on whether you speak English or American. I speak English, so for me Maths is the correct abbreviation for mathematics.
The operators, and the precedence and associativity rules that apply to them, are the punctuation.
In this instance, just begin at the beginning. None of the punctuation tells you to do anything different.
Order of operations treats multiplication and division with equal priority, so they are solved as they appear from left to right. Solve above the line first. Therefore 12 divided by two is six. Six times three is nine. At that point, we divide the top number by the bottom number, leaving us with the correct answer of nine. Simple! As long as you are intelligent enough to follow simple instructions (like order of operations).
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.
It’s arbitrary - it is simply defined that division goes before multiplication. If you want multiplication to go first you simply put brackets around it, hence brackets (parentheses) always goes first.
@@gweilospur5877 rules have changed....IDK if they will again, but who knows.
@@gweilospur5877 yes exactly, separating the 2 and 3 in the numerator results in the operation yielding a different answer. which is why the expression is written badly in the first place and wouldn't appear in that form in a math paper (unless deliberate) and even then the student would rewrite it - otherwise the 12 would be divided by 2 = 6 then x 3 = 18 then divided by 2 = 9
Looks like you are lost the PEMDASMDEPEMDSA forests. Don't do math, ask someone else Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this : "use proper parenthesis such that it removes all ambiguities. End of story !!!! That teacher was wasting years of your life. Find his or her and enclose them into pairs of parentheses.
@@countingfloats What I've stated is what has been displayed here. If you disagree with it, then research it & disagree with the math teacher that is teaching it... & the countless others that state it all over the internet. I was taught PEMDAS, period, but here we are...
As a math teacher I find the biggest problem is other teachers teaching pemdas. They cause the misconception that multiplying comes first. Please stop teaching tricks and teach mathematics instead!
This day an age, it is so confusing the way they teach mathematics. I try to help my grandchildren but I’m lost now. 😮
The answer is later B 36
I was taught that multiplication comes first. Therefore: 2 x 3 = 6. 12 divided by 6 is 2. 2 over 2 = 1.
@@carolynzaremba5469 I’m sorry that you had an incompetent math teacher. In mathematics we follow left to right, just like we read. It’s been that way for centuries
In Australia we were taught BIDMAS OR BIMDAS. We were always told that Multiplication and Division were equal, then Addition and Subtraction were equal. (Brackets, Indices, Multiplication/Division whichever came first then Addition/Subtraction whichever came first)
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.)
I am a70 yrs old lady. Maths was not so interested subject in school time. But now i did it in seconds. Answer is 9.
I'm in my 80's. Answer is 9. NO possibility that there are 2 answers.
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.
If you do that you end up with 6/1*(3/2)=9. Cancelling out the 2 means dividing all terms by 2. You can’t just simplify the 12 in isolation
@@jra55417 No, you're mistaken. You cancel out all of factors on the bottom with something with same factor or factors on top, in this case 2 has one factor, 2. 12/2*3 becomes 6/2*3. PEDMAS, remember? 6/2=3, 3*3=9. if you took 2 out of everything on top you'd get 6/1*3=18
@@steveburke1519 yeah. Not sure what I was thinking!
I was always taught that order of operations is BEDMAS brackets exponents division multiplication addition subtraction.
It's the same exact concept with the only difference being some parts of the world use brackets instead of parenthesis. I believe some other parts of the world use curly braces as well. Really BEDMAS, PEMDAS, and whatever the other ones are is just a way to teach order of operations, which is entirely universal.
EDIT: Their may also be regional differences in the name's of certain operations, such as exponents and roots also commonly being refereed to as indices and orders leading to BIDMAS and BODMAS respectively. So remember the acronym used to teach order of operations does not change the order of operations, that is universal.
multi and divide are the same step, as are add and sub.
B, E, DM, AS
You go left to right with them
Pemdas
@@gg-gn3re Incorrect, there is no left to right or right to left with M and D there is no convention.
In general, to any expression of the form a/bc : one needs to insert parentheses to show whether one means (a/b)c or a/(bc).
See a page called Order of arithmetic operations; in particular, the 48/2(9+3) question by Gary Bergman at Berkely
@@zakelweDivision is literally an inverted multiplication operation. So, multiplication and division are the same in priority. The example you provided can be re-written simply as 48(0.5)(9+3).
There is no ambiguity here. If there were ambiguity, then a program like Microsoft Excel would be calculating unpredictable answers all over the place. With the rules, Excel provides a predictable answer every time.
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.
If you had taken each part as a fraction it still works out to 9. 12/2 divided by 2/2 multiplied by 3/2... becomes 6 divided by 1 multiplied by 1.5 equals 9. It's just easier mentally to resolve the numerator first then apply the denominator.
The numerator was done 1st because the vinculum is also a Grouping symbol (like parentheses) it has a beginning and an end.
As far as left to right, you actually started learning that when you started learning to add.
The key to the Order is left to right for similar operations .
@@johnl.tiemannjr.2662 left to right is not necessary, it just avoids confusing fractions for some -- you can do × and ÷ in any order. But of course you can't do "2x3", rather if you go right to left it you have to know "÷2" is the same as "×1/2". Just like (for example) 3+4-5+6 you can also go right to left but you cannot start with 6+5, it must be 6+(-5). The "-" or "÷" prefix for EACH TERM changes how you handle it. ...Or the simple way if you don't understand all this, just go left to right does work too.
@@pamelas9Sorry but that is incorrect. It happens to work in that example, but what about (for example) add x8 to the numerator? Your method would be:
(12/2)÷(2/2)×(3/2)×(8/2)=36
But the correct answer is:
(12÷2×3×8)/2=144/2=72. In fact, since " ÷2" is the same as "×1/2" the whole thing can also be written as:
12 x 1/2 x 3 x 1/2, or also
(12x3) / (2x2), both of which resolve to 9.
If you include my "x8" you get
12 x 1/2 × 3 × 8 × 1/2, or
(12x3×8) / (2x2),
Both of which resolve to 72.
Multiplication and division are higher order of operation than addition and subtraction but if the operators are of the same precedence, conventionally they are evaluated from left to right.
It is either 9 or 1 depending on the proper grouping of the numerator. Left to right is BS multiplication and division on a properly written equation can be done in either order and get the same result.
This is a purposefully ambiguous equation that could potentially have 1 of 2 answers, but not both
wrong, there's no way to get 1 unless you are doing something wrong.
@@gg-gn3re and that's where the education system failed you. If the order of multiplication and division matters in an equation, then the equation itself is wrong and all answers are invalid
@@cyrnus This is incorrect. The line is putting it as a fraction which gets simplified last. This isn't an "order of multiplication and division" issue. It is generally written different but that doesn't make this worse written equation have two answers.
No, with no parenthesis you go left to right on the top. That's how you get the only correct answer, which is 9
And you get the same result no matter which order you do them in. Hint: 12/2*3 = 12*0.5*3
For that matter, you'd still get the same result if you wrote it as 12/2*3/2 instead of (12/2*3)/2
There is no ambiguity. Just a whole lot of people who don't grasp how the math actually works.
OMG! If only I had learned this when I was young!!! I’m 76. I actually get this in my spreadsheets on the computer. Now I understand what to do. Thank you.
❤ Shirley
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 😊
That’s a good idea! I got the equation right but I think it was luck. Taking a math class would be fun. I’m 67
Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this
: "use proper parenthesis such that it removes all ambiguities. End of story !!!! That teacher was wasting years of your life. Find his or her and enclose them into pairs of parentheses.
@@countingfloats where do you need parenthesis here?
The answer is a) 1
@@darrellwilliams1256 Correct and I did it mentally and I'm 87.-
Wonderful I missed some concepts while I was in school and the teacher would not help me see what I was missing. I love math. Been years trying to find those missing components. Thanks for clarity.
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.....
You must be really old, The order of operation came about in the 1600s.
Note : if the answer is s/b a then you are not designing a 747 Jumbo jet. Otherwise read on :
Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this
: "use proper parenthesis such that it removes all ambiguities. End of story !!!! That teacher was wasting years of your life. Find his or her and enclose them into pairs of parentheses.
@@countingfloats There is no need to use parenthesis when no parenthesis is needed. The order of operation is not really a complicated concept.
@@kingsolaa actually the modern order of operation was in about 1908.
I am 70. I learnt BODMAS. Brackets, of (e.g. Half of 6), Division, Multiplication, Addition, Subtraction.
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.
Implied parentheses are a dead end and only might work if there are only a few levels and it is you and your twin are working on the same problems. Otherwise all bets are off.
Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this
: "use proper parenthesis such that it removes all ambiguities. End of story !!!! That teacher was wasting years of your life. Find his or her and enclose them into pairs of parentheses.
@countingfloats My thoughts exactly! Except the end, which made me LOL. I thought it more of a mind puzzle than a math puzzle. Math problems should be clearly expressed.
You have to be careful with this approach because you can't simply add in parenthesis or brackets where there are none. I was in Advanced Academics since I entered the third grade. In middle school, I was doing supposedly college level work. So my order of operations problems were rarely just this simple. I would see things like:
(12 - 2)5 - 5 + (4 + 3)2 - 6 = ?
Now, you can't just slip in the parenthesis wherever you like. You will get the complete wrong answer.
@eduardopena5893 ABSOLUTELY! I absolutely reject the thought process of the subject video. One might say it is acceptable for less complicated or lower level of problems. No. The lowest levels should introduce and train for the more complicated problems.
Thank you for your important voice on this matter. 🌞
@@ritapearl-im3wv Thank you for the reply. Right, it is a very fundamental thing that you have to get the basics in order first, so that you can build up to the next thing. If you think my example looks complicated, you should see something called matrices.
Fortunately for me, as complicated as matrices are, they are very formulaic and logical. There's a process you follow, and so long as you follow it, you'll always be correct. Although I was an ace at them, it was rather unfortunate that I never, ever understood why I needed to learn how to do them or what they would be used for. It was never explained to me. It was like, yeah, I can do them. So what?
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.
1
We were taught B.E.D.M.A.S🇨🇦
Bless My Dear Aunt Sally
Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this
: "use proper pairs of parentheses such that it removes all ambiguities. End of story !!!! That teacher was wasting years of your life. Find his or her and enclose them into pairs of parentheses.
I would say C, 9. You sank my battleship.
1 is the answer, first 2×3 equal to 6 then 12 divided by 6 equal to 2 then 2 on top divided by 2 on bottom equal to 1
I agree!! 1..!!!!
You can easily clarify order of operations by using parenthesis
Exactly. The whole premise is meaningless.
Exactly! What happens if you can't remember the formula?@@cadenorris4009
Yes the correct answer is use parentheses and don't be ambiguous.
You don't need the parentheses though. Order of operations goes left to right. The "multiply/divide" means that you do whichever operation comes first in the equation. Multiply doesn't come "before" division. They are equal. Whichever comes first is what you do first. Like he said, it's M OR D.
@@MS-ig7ku But it is not ambiguous...
In the USA, we use PEMDAS Method: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction
In USA you believe in Moon landing.... but you are not US guy
there is no need for a method you just need to see what is infront of you
Without parentheses, the problem is stated ambiguously.
The opening phrase "in the USA" IS not that relevant on the internet anymore ! As in ,so yes you have your American system and convention AND as a culture and nation you no longer have that much respect globally. So saying what you said does not carry any example of better way of doing things anymore. You are no longer the light on the hill beacon of better democracy anymore. So mine and I am sure a lot of the rest of the world, democracies included, have shifted to a sounder conventional wisdom of international agreed standards for things like explaining why a world citizen needs the context of consensus of agreements to work together. Doing math is important AND it no longer currently needs to be stylised nationalistically. Like math that understood and works on all the continents rather than giving any precedence or nod to allowing the USA to set the standards for the future. Tell me do you still think the Monroe ~ somewhat jingoistic outlook ~is still relevant and proper way to approach diplomatic affairs still. The blunt point is that PEMDAS method is more universal than being an American thingie, so ... if you give up your American prejudices and biases ( apologizes to the Canadians, Mexicans, Cubans etc) there is strong case and instances international too see, hear and feel this. way 🤣😂🤣😂
@@chrislee882 -- I think the point was that this person was explaining what they were taught, and how widespread it is. The Monroe doctrine is outdated.
I would rewrite the problem as this 2/(12/2x3). Now you have a parenthesis to work first. Solving this step we find (6/1x1.5). Now we are rid of the parenthesis leaving 6/1*1.5. 6/1 is 6 thus we have 6*1.5 which is 9. The answer is 9.
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 🙏
With PEMDAS the answer is still 1. M comes before D
I was taught solv x is first, then ÷.
So i got 1.
@@LeeLoo_22 and you are right
@@Ed19601 ☺
You are correct to watch the whole video and learn how to do order of operations correctly. The answer is 9. Don't worry about the comments below. Multiplication and division do not take precedence over each other and are done from left to right just like addition and subtraction.
I'm 71 and I have always been terrible in math, even I followed and understood this video, thanks so much!
Thank you. So many people have responded with superior, snarky attitudes. If they had a better math teacher than some others, that's luck and not some accomplishment of their own.
It's wrong. It's a notational problem rather than any generic teaching aid such as PEMDAS or BODMAS, hence the discussion with this badly written ambiguous equation
@@jladdyost The problem here is that this is very middle grade maths using generic teaching rules. If you go to Berkeley or Harvard with high end mathematicians then they don't agree with the result of the OP
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.
Thought? Or taught? Wasnt there something about My Dear Aunt Sally and parentheses?? It's been many years - and truly, I havent needed it in well over 50!!!!
@@lindickison3055 Thank for the spelling correction.
Same here but we didn't learn acronyms, we just memorized it. I needed this throughout my career in IT, along with the Boolean operators.
Yes India it is bodmas as we say brackets instead of parenthesis
Who taught you how to spell taught?
NOT HARD!!
Apply the Order of Operations and voila you get the correct answer, which is 9. 1:10
This will be interesting!
Oh good!!
You got it right!!
However, I'm very strongly against the use of a Mnemonic unless you teach the actual mathematics behind it and the Order of Operations.
PEMDAS
BODMAS
BEDMAS
BIDMAA
DMAS
MDAS
GEMS
GEMDAS
These are all mnemonics and acronyms that are taught around the would. And look at the list, it's long and confusing, especially if the mathematical reasoning isnt taught alongside it.
Why are multiplication and division done together whichever comes first from left to right.
Why are addition and subtraction similarly related?
What the heck does the E for exponents, the I for indices and the O for orders in these mnemonics actually involve?
How about roots, radicals, factorials, trig functions and fractions??
What and how are parentheses used in math ( ) ?
The P for PEMDAS and the B for brackets are what exactly and how do they work??
I drum basic arithmetic into my students. We look at the relationships between the operations.
I teach high school math at a private school in Australia. When my Year 6 students arrive at the Senior Campus and begin the Middle School (12 year olds) they get a bit of a shock. Because I take them way back to basics. Manipulating, visualising and understanding ALL the arithmetic operations.
On Day 1 in class I take them back to: basics and they think I'm joking. I am not. I'm my experience, an solid grounding and an excellent understanding of basic arithmetic is vital for success in later years. I spend a good of couple of weeks on just the basics
1+1
Then we look at how addition and subtraction undo each other. How they are opposites or and discuss why multiplication and division are relatesd and they
5+5+5+5+5+5+5+5+5+5=50
5×10
=50
The Order of Operations can be used to solve harder arithmetic like this:
4-8+60÷(16÷2×4)²√36+5!
I'm proud of my students success; not just in my maths class, but in every class.
Because I teach back to basics, because the basics are often skipped over or not taught in the educational context.
You can't teach young primary students the reasoning and relationships behind the order of operations, and it's not revisited or it becomes "assumed knowledge" and isn't actually taught at all.
The moral of the story is TEACH THE ORDER OF OPERATIONS AND DON'T BE LAZY AND JUST GIVE STUDENTS AN ACRONYM TO REMEMBER. TEACH THE ACTUAL MATH.
Nice to see I still got the basics. Thank you for the test.
Great explanation good for us who have been away from math for a long time a good refresher. Thanks
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
B. (
O. Cross multimlication
D. Divide
M. Simple multiplication
A Addition
S substraction
I took calculus 40 years ago as a senior in high school. However, when PEMDAS is the ORDER in which you solve a problem, how does division come before multiplication? 40 years later, is it now PEDMAS???
M and D are equal. Division is inverse multiplication. e.g. 3 divided by 2 is the same as 3 multiplied by 1/2
I don't think that PEMDAS is the best tool to use to learn this concept. Computational precedence is really what's under discussion and I don't have a cute mnemonic - you just need to learn the rules. In most formulations, multiplication and division have equal precedence and when both appear consecutively in the absence of parentheses, the order of evaluation is left to right. That's kinda' hard to encapsulate in an acronym/mnemonic. I say "most formulations" because all of the many computer languages have computational precedence rules in their definitions and you cannot rely on them all using the same rules, which is why many programmers use parentheses liberally in mathematical expressions..
This is a 4th grade math problem. What’s the problem?
Another way to write this (12 / 2 * 3) / 2=
@@fuzzyjaxi did not like math, and by 4th grade i was using a slide rule
0:13 Ans is 9
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.
You do not drop it below the line. There is no reason to do so. It is the division operator. People confuse division with fractions. Not quite the same thing. Depends on context.
While recovering from a severe stroke this has helped me with improving cognitive function, thank you so much, I look forward to more problems, thank you 💕
I never heard that M and D were interchangeable depending on which comes first. Thank you.
Yep, and good for you, for learning!
That's why both BODMAS and PEDMAS acronyms are correct, even though one has DM and the other MD, because without parentheses, left to right for all division and multiplication is correct. Ditto with AS: 5-2+3=3+3=6, go left to right even though the first operation is subtraction.
This video is wrong. Don't think him. He is literally confusing people on purpose.
Exhibit A 😭
@@ernesthakey3396 Which means that using an acronym like PEDMAS is kind of pointless because it implies that multiplication is always first by the sheer fact that it is a sequence of letters. By itself, the acronym can't indicate that one specific pair is interchangeable while others are not. Why then wouldn't multiplication and addition be interchangeable? The acronym requires some extraneous knowledge, so it's defective as a mnemonic device. It's really just a convenience for teachers who already know what they're teaching, rather than an actual learning-centered practice.
The answer is a) 1... this guy is changing math history and is wrong multiply divide add subtract
Where were you when I was struggling with math in school? I love your clear, simple explanations.
I sure would've helped you! I hated geometry!
Actually its wrong
Yes it is wrong and he has done it more than once now just to get more clicks and more money ..
SAD
I do the top left to right. I got 18/2=9
you did it correct I got 18/2 = 9 since 12/2 = 6 and 6 x 3 = 18 So you do know ya math.
I just subscribe. Stumbled on this video. It reminded me so much of the troubles I had learning math. He explained so easily to remember. Look forward to watching more videos.
I had a misconception about Mult. having priority over Division...so I got it wrong. ..I ignored Left to Right operation because of that misconception....Common sense of going L->R (regardless of signs), is what solves this problem. Yes, I learned some logic out of this so it was worth getting it wrong.
I agree. Believing you are right and to learn why you are not seems to have a stronger hold on how to do things.
Me to as I did the multiplecation first ..wrong
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.
Division has a higher priority than multiplication in the UK?
I learned BODMAS in Australia where O is for Orders but still the same idea. Multiplication has the same priority as division. The video does not make sense because PEMDAS and BODMAS have division and multiplication reversed. Maths can't change depending on the country you were taught. @@schwarzerritter5724
@@schwarzerritter5724 Division and multiplication have equal priority. It is just easier to teach it one way around but either are correct.
@@Illawong I assume D stands for division and M for multiplication? D is clearly left of M. If D and M have the same priority, than BIDMAS makes people memorize the wrong rule.
@@schwarzerritter5724BIDMAS is a correct rule. Multiplication and division have the same priority. When multiplication and division (or division and multiplication) are seen in a series, then you calculate left to right. Whichever comes first is calculated first. There is no ambiguity. Microsoft Excel calculates a predictable answer every time.
I was an engineer; no math or engineering text I ever studied printed mathematical operations like this where parentheses and/or brackets are omitted. While it may be interesting for a simple operation, doing this in the real world where calculations can become complicated quickly would introduce an unacceptable risk for computational errors.
True, nevertheless you cannot rely on others to use the best math grammar. Gotta know the rules.
Exactly
An engineering degree in 1972 and had no problems with math, yet never heard of PEMDAS. We used parenthesis, brackets, and braces without confusion. If you want your bridge to stand up or your amplifier to amplify without smoking, play it safe and use these.
I got it but you make things too complicated
In the UK we learn BODMAS. If you simplify to 0.5(12 / 2 x 3) = 9 you resolve the bracket then times a half.
The first I ever heard of PEMDAS was a couple of years ago. I'm 57 and was educated in Australia, where we were taught BODMAS (Brackets of...)
They're the same thing and result in the same answer
Can you please tell us the rest of yours? I've never heard of that one. Thanks!
It's brackets, of ,division multiplication, addition and subtraction
@@faddyifyI’m 51, that’s what I was taught, Wales UK
@@gg-gn3re Yes I'm saying I'd never heard the term PEMDAS prior to a couple of years ago. America does this...takes something that already exists, renames it, claims it as theirs..it's all about projecting a false sense of adequacy (and it fails every time).
I've even seen a website claiming that Americans speak English, and in England they speak "British English".
I got the answer right, although with some degree of uncertainty. The reason being that in the days and place I was taught algebra (in the 1960s in Montreal, algebra manuals from France), the writing of such an equation required that there be paranthses to determne the order of opeartions. So, we would have been required to write the numerator as follows: (12/2)x 3.
Right. That's better!
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.
That;s why BODMAS is the best! In any case with PEMDAS one can do the multiplication 1st and still get the same answer!!
@@rascocky6366
Americans like their backward ways. I learnt BODMAS in the sixties.
@@rascocky6366😂
@christopherellis2663 😂
They're still using feet, inches, pounds quarts etc: Why would you expect anything else?@@christopherellis2663
I figured it out once I found out
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 .
It's been 50 years, but I believe it was first covered in Pre-Algebra.
We used to have two math tracks. I don't believe the Business track had any Algebra courses
You need to use brackets to take away the confusion. The left to right rule applies if that is not given.
Correct on the first with brackets, wrong with left to right with M and D, No such thing. Hence the need to use brackets.
You don’t need brackets. You just do it in order.
No! There is no ambiguity whatsoever, and never has been.
Operators with the same precedence (like division and multiplication) are evalutated left to right.
It cannot be much simpler than that.
@@zakelweM and D .solve from left to right
I am in my 70’s. The use of PEMDAS wasn’t heard of, or at least I was never taught it. Thank you for teaching this. It makes such problems as you present here easy. I am keeping it in mind.
Like my dad used to say ‘back in the day’ we didn’t have any of this.. I used a big algebra book that was as heavy as I was too 😂😂
When my kids were in primary school, my youngest had a lot of trouble understanding the way the teacher was teaching them maths, so I started teaching him the old way and he understood it straight away then it became easier for him to understand maths and he got to understand the teachers way.
PEMDAS - Parenthesis Exponents Multiplication Division Addition Subtraction then from Left to Right.
And thank you for not saying it's all nonsense as so many people have said. It's what mathematicians agreed upon a long time ago. Most of the people objecting to the video either learned PEMDAS (BOMDAS in the UK) when they were young and think it's totally obvious (which it isn't), or they think you just do all the operations as you find them, from left to right, which is logical but wrong.
I agree this was not taught to me either. You went with what came first on the paper
If you were never taught this PEMDAS then you don’t stand a chance of getting this right
PEMDAS - with MD ,since it is non-parenthetical, follow the order of execution from left to right. the answer is 9
Here in England in the 1960s I was taught BODMAS, 'Brackets', 'Of', 'Division', 'Multiplication', 'Addition', 'Subtraction'. By the way, here we do mathS, short for mathematicS, not math! I did get it right and get 9 though.
Bodmas and Pemdas are exactly the same, just worded a different way.
It's very simple. PEMDAS works. You just have to re-imagine the question. As shown, the equation in single line is (12 / 2 * 3) / 2. So solve the parentheses first, in order.
Wouldn't that be even easier as (12 / 2) * 3 for the top line, or even (12 / 2)3
Wow, the most complicated and in depth video ever to tell you the basic answer
and still people are arguing that it is wrong.
@@Darryl.M It actually is wrong because there are not enough parenthesis to be able to determine which answer is right. It is called an ambiguous equation.
In general, to any expression of the form a/bc : one needs to insert parentheses to show whether one means (a/b)c or a/(bc).
See a page called Order of arithmetic operations; in particular, the 48/2(9+3) question by Gary Bergman at Berkely
@@zakelweno sorry it's not ambiguous if you use the order of operations correctly.
I like it and relied on my those old days key from elementary school called "BODMAS" to be executed from LT to RT and found to be = 9. Surely appreciable!!
I think there is a hidden understanding of grouping that exist between the operations involve and MD is interchangeable same as AS as long as MD comes first before AS....and the solving is from left to right....
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.
I agree. I'm almost 67 and it was confusing, even though I knew how to do it right.
It's actually wrong
@@zakelwe What does "It.." represent as a pronoun? The video, the math, my comment on the presentation, or something else?
@@zakelwe If you think 9 is wrong, then you should sue Microsoft for Excel Spreadsheet being wrong for decades. (9 is the correct answer.)
@@patchup The solution
I should have been more verbose.
It's been 60 years since I was a wiz at this.
I can justify both 1 and 9, so I figure I've forgotten a rule or 2.
It won't surprise me if they're both wrong.
Ha! Worse than I thought, I can't recall ever hearing of PEMDAS.
(Order of operations rings a bell. [Or is that tinnites😂])
Stop presenting these mindless problems. All of them wrong, including your "solution". The correct answer is this
: "use twins of proper parenthesis such that it removes all ambiguities. End of story !!!! That teacher was wasting 6 decades of your life.
Find his or her and enclose them into pairs of parentheses. @@ferengiprofiteer9145
So glad you appeared! Need a refresher to be able to help my granddaughters. Thx!
Oh - and i got the answer right, but it was luck. Never heard of Aunt Sally. PEMDAS will help!
Thank you for explaining the order of operations. I kind of forgot a bunch of basic math just because I never use it. Recently a question like this came up. I tend to do math in my head all the time but I really wasn't sure of the O of O because I couldn't remember which came first, multiplication or division and I swear I remember multiplication coming first. It's been well over 50 years since my last basic math course. I did get the answer right, because I made an educated 'guess' but now I know for sure that I did it correctly and I won't make the mistake again of second guessing my answer.
1 is the answer 2x3 first equals 6 then 12 divided by 6 equals 2 then 2 on top divided by 2 on the bottom equals 1
It’s not in brackets so it’s not first. It’s 12/2 x3 = 18/ 2=9
Thank you so much. I have been looking for years for someone with your skill to teach math in such a simple language
Following the PEMDAS rule, we should rewrite the expression: 12x1/2x1/2x1/2x3/2=9/4 or 2.25. the answer is not in the list. Your answer is 9 because you calculated the nominator first and then divided it by the denominator, which is 2 and obtained 9 as your answer.
no , he is right you are wrong and I can prove that (12:2*3) /2 = a
12:2*3= 2*a -->18 = 2a ---> a = 9
that's called algebra
PEMDAS SAYS THE ANSWER IS A.) 1
Because "Parentheses" are absent is why "1" for an answer is wrong.
Believe it or not they switch M and D so they get BODMAS. Absolutely mental no wonder they're still on imperial.
9 is correct..... did it in my head while reading the formula the 1st time. I'm 70 years old. I speak some Japanese, latin and French.... constant reader of historical books. I have no college degree.... served in The Marines.... do I qualify to vote? We are no longer a free country if we disqualify Americans from voting. The only qualification should be that you are a US Citizen. Semper Fi
PEMDAS - parentheses, exponents, multiplication, division, addition, subtraction.
I applaud your knowledge and your service, but the answer is 1.
@jtfmfhp7080 what do you mean the answers 1? Back to school for you champ!
Have to use BODMAS; Brackets, of, Division, Multiplications, Addition, Subtraction.
I got both answers, now I know why one was incorrect! Wished id known the “or” for m, d,a&s i always do “and” never “or”… thank you, ones never too old to learn, 😅
Wish I could have had you in high school. You actually explain this so well.