I went to a book sale. Books were $2 each. I picked 5 books. The person counted the books then said she had problems adding the total. I said there are 5 books at $2. That’s 5*2=10. She was a college volunteer.
I did it! At 64, I haven't used math other than budgeting and bills in years. Some old dogs do remember tricks. Loved it. Thanks for the brain massage.
I remember reading somewhere that while both the division symbol and slash are acceptable in situations which require you to write the equation in one line, it's far better and less ambiguous to write division as a fraction so visually all of the dividend is on top (numerator) and the divisor is on the bottom (denominator).
Back in the 70s, I learned that multiplication and division were both *dot* operations (e.g. 5 *•* 2 = 5 *÷* 0.5) and addition and subtraction were line operations (e.g. 1 *+* 2 = 4 *-* 1) with dot operations having higher ranking over line operations and each were done left to right; the way we read. Therefore I got it right from the thumbnail 😊
I’m a 69 yr old retired man and haven’t had a math class in nearly 50 years. I came up with 29 without a calculator or watching and selecting the answer from the multiple choices. I’ve never forgotten PEMDAS. It’s always the fundamentals.
@@marcorizzo3854Not all Americans are bad at this though I’m only 15 born in 2008 and I also got this correct just by looking at the thumbnail. I was taught PEMDAS and you go left to right. I’m a gen x and didn’t have issues doing this problem I think it depends on what school you went to and what the teachers taught you. I’m also from the only state that partially adopted common core standards. We only adopted the English standards and made our own math standards so I learned it differently from most states. We’re also in the top 10 states that score the highest on national math tests to see where schools and states are.
For anyone who doesn't want to watch the full length video, the answer is simply 29. How? 3^3+4(8-5) / 6 is equivalent to 27+4x3/6 then 4x3=12, 12/6=2 now it's 27+2=29
It's interesting that 3 of the incorrect answers stem not from an error in the order of operations, but either a misunderstanding of the function or a typo when working through it. Curiously, those wrong answers otherwise demonstrate a proper use of the order of operations. So what does that demonstrate about what/how students have learned?
And those are mistakes most often due to rushing through the problem, as students would do on a timed test. While a youtube poll gives you all the time you need.
@@micaelstarfire8639 also, the viewerbase for this channel will likely be people who have an interest in maths, so skewed even more in favour of the poll. I got the correct answer, but i did do a couple of things in the incorrect order, so even i learned something.
I disagree with both his and your interpretation. Some people would have guessed. Any answer which receives less than its equal proportion of the answers, or perhaps it's equal proportion when the most common answer is removed, shouldn't be read into too far.
@@hainsay people who know the answer do not guess. People who have am interest in maths/this channel are therefore less likely to guess as they know the answer. You proved my point whilst disagreeing with it. I don't know the statistics on who guessed and who just worked their way through the wrong answer... and neither do you, so using that as the foundation for your argument against the other commenter makes no sense. This is a problem with multiple choice questions in general. Could argue that 25% guess right (for this question) but there are plenty of others that are really a 50/50 and others where the correct answer is counter-intuitive (i.e. the people guessing the answer are unlikely to get the correct one).
Having done a lot of mathematical modeling of physical systems in FORTRAN, learned the 'operator precedence' of the language. Many a bug were made by folks by not applying parenthesis correctly. Our mantra became, "When in doubt, put parenthesis around it!" Nice the way you walk through the solution, makes it very clear.
As a fellow programmer, I almost always just use parenthesis with both mathematical and boolean operations. It makes it so I make fewer mistakes, and it's way more clear when I or someone else come to read it later.
In C++, the operators &, ^, and | are lower in precedence than == and !=. This makes no sense. &, ^, and | return a number, which one often wants to compare with something. Therefore, one must always put parentheses around expressions using &, ^, and | and around their operands if they have operators in them.
@@DavideCanton LOL More like, 'clarity of purpose' over 'obscure gotcha'. Reminds me of the young twit that said in a job interview, "I don't need to put in comments because my code is always right the first time." (P.S. We pointed out that we have teams of programmers and a loner such as himself probably wouldn't fit in, have a nice day)
Knowing the correct precedence is useful, but even more useful is knowing when confusion will result and then using parentheses to preclude any confusion.
I see these types of questions on Twitter all the time. (by World of Engineering) and almost on all occasions the right order gets about 45-48% correct answers. Many are of the opinion that PEMDAS and BODMAS have different rules. Your channel is likely followed people who actually like math :)
A lot of the disputed ones on social media use the ambigous writing of e.g. 6(7-4) instead of 6*(7-4). While technically both are the same, a lot of people learned that you only write 6(7-4) if the 6 belongs to the paranthesis. So you only omit multiplication symbols for grouped expressions This causes confusion when promted with e.g.: 4 + 10 / 6(7-4) If you learned that the multiplication is only omitted if it belongs to the paranthesis this would read like 4 + 10 / (6*(7-4)) for everyone else. Now I know, people will say that is an incorrect way to learn it, but if I prompted you with 4 + 10 / 6x you most likely would also assume 4 + 10 / (6x) instead of 4 + 10 / 6 * x
@@NanoNaps 6x notation is known as implied multiplication, it is treated as if it is written as you did '(6x)'. However 6(7-4) is not ambiguous. iirc according to the rules you should get the correct answer?
I actually wound up doing this question both ways, without a calculator, expecting this to be a case of "in the past textbooks sometimes used the division sign to save space" before watching the video or reading the description.
I had a brain fart and initially came up with 11 because I focused all my attention on doing the right side of the equation properly then only tack on the easy 3^3 at the end but carelessly did it as 3^2. Realized this mistake almost instantly and revised to 29, but if I were in a rush to submit an answer I would have been capable of submitting 11, albeit not due to a shortfall in order of operations but just pure carelessness😄
@@smart_lizard_3149 Where I come from if someone's flatulence is noticeably audible another person will criticize the perpetrator by saying "Take a pill!" I guess all of our problem is that there is no medication out there for brain farts.
I ended up getting the right answer, but I was confused at first because my math homework always uses a fraction bar for division. I was a little unsure of my answer, but it turns out that dogmatically following the order of operations does, in fact, work out. 😂
I think this is what confuses some people, they think ÷ means everything on the left divided by everything on the right, which it isn't. If someone wanted that, they would put brackets around everything on the left, and brackets around everything on the right.
That's really how it should be written in the real world to avoid any possible misinterpretation. An expression would never be written like this except in a math problem trying to test your knowledge of order of operations.
I would take serious issue with the recommendations in the document issued by the Australian government. In my opinion, NO serious mathematician should ever use the divide symbol. Ever. It's for kiddies and should be jettisoned before school kids reach the age of 13.
When my sister (5 years younger than me) was in High School, she was at the bottom of her maths class. She had not been taught BODMAS. Once I taught her BODMAS she went to nearly the top of the class. It is a simple and essential thing to know and yet it was not being specifically taught.
Thank you for not only giving an interesting problem, but also explaining where the wrong answers came from. It's good to understand what happened when people made mistakes.
I'm from Germany, and the mnemonic we learned at school for the order of operations was POKLAPS, an abbreviation of POtenz (exponent), KLAmmer (brackets), Punkt (dot; for multiplication (⋅) and division (:) ) and Strich (line; for + and - ) But if you say Poklaps as one word, it means butt-slap, so it's easy to remember XD
that's exactly how I learned it (except with the popo klaps mnemonic) although I was taught that in Latinamerica... through a European private school 😁
I don't remember learning any mnemonic trick, but I've never had a problem with the order of operations... They are introduced gradually during the different school years, so you have all the time to learn the correct order, without even trying, before you end middle school! At least in my country...
The only thing more important than being right, is recognizing how and where you make a mistake. "'We learn wisdom from failure much more than from success" - Samuel Smiles.
being a 13 year old who is familiar with these type of questions, I can say people tend to forget pemdas or aren't able to apply it properly as they reach higher classes
Yup: you have it correct. As far as I know it's taught during a short spurt in one year of math. If you miss that week, or just don't understand it through not having brain space for it (too much stuff going on, not enough coffee, no breakfast) you're forever at a loss. And can go through adult hood getting it wrong. That's why some of us are astrophysicists and some of us write novels.
when you made the poll, I originally put 11, because even though it says 3 cubed, and I saw the three, I processed it as 3 squared. it wasn't until I read the comments, someone saying they did the same thing that I realized my mistake.
I've developed the habit of breaking problems into units (terms) separated by addition or subtraction and working through the most complicated first to aid the mental process. I completed the second term, stepped back to make confirm the first term was 3^2=9 and had a moment of surprise when I saw a three up there. Of course that also made me forget the second term and I had to recalculate it, but maybe the problem really was about misreading the exponent instead of multiplying by it.
@@johnno4127 See, my problem was, I'm pretty sure when I was reading the equation for the first time before solving it, I even read it as "3 cubed" or "3 to the power of 3" or whatever, but, even though I read it correctly, I processed the information incorrectly... I think because before it, I had just got done reading (and thus following along and doing) a bunch of simple equations involving squares and square roots, so I just saw an exponent and habitually did a square.
I still like to think of the order of operations in terms of complexity, solving from more complex to least complex: addition is the simplest binary operation (includes subtraction since A - B = A + (-B)), multiplication is repeated addition (includes division since A/B = A × 1/B), and exponentiation is just repeated multiplication (includes radicals since x√A = A^(1/x)). Grouping with parentheses is pretty much common sense as are unary operations like log, sin, tan, etc. The only unary operator that might get confusing in some cases is the additive inverse, especially when combined with exponents.
The one thing I'd add to this is that, at least in some circles, implied operations (such as the implied multiplication in the problem) take precedence over ones that are explicit. In this case, it doesn't matter as the implied multiplication appears first in left to right order. However, it's best to check with the instructor or the style guides of any journal you happen to be writing for to see if they give precedence to implied multiplication. If you're one of those people who actually read the instruction manuals that come with calculators, sometimes you'll find a section that addresses implied operations.
In most instances implied operations like you said would always take precedence. It's just a short form and if written out longhand the equations would have additional brackets around the multiplication and the addition in the shown brackets
Agreed. That's always been the case as I've run into it. However, I will point out that some calculators don't do this and a few Internet math teachers have insisted that implied multiplication is just multiplication and left to right takes precedence (thus the warning to check with style guides and instructors).
I've been teaching since 2004 and have dealt with this problem at the college level. In my book: Taking Fear Out of Math, I make a point of teaching order of operations in a simple, straight forward manner parents and students can easily grasp.
If you write an equation that makes people interpret order-of-operation, you're doing it wrong. As a lead engineer, if one of my guys had put on a document that I was reviewing, my red pen would be all over it with a terse note to try again.
Agree as programmer. Just because I know that the compiler is going to evaluate an expression in a certain order, doesn't mean I shouldn't make the code more readable to others by using brackets and linebreaks anyway.
In german we have the "KlaPuStri - Klammer Punkt Strich" which means Brackets, Dots, Lines...although this does neglect the exponential operations it helped quiet well over all these years.
ISO standard says that "division sign" should not be used You can use / or : in example like you have. So by ISO standard you didn't have a division sign you had an undefined sign making your problem undefined.
Interesting point. I am not used to the division sign, and it threw me off doing this in my head. When he wrote it out, I instantly realized my mistake. Not sure that this is a "math" problem at all. Thanks for your comment.
but i know you because i like watching you. We are not the same. isn’t that 29? That was easy you didn’t even get the chance you read the answer and i didnt know it was a multiple choice lol
The only issue I ever faced was that here in India, implied multiplication still exists. I.e. 4(3) would take precedence over any regular multiplication or division. This twists things up when I became a computer programmer and an android app was failing because we forgot about it.
I always assumed it was the same thing here in the US. That the a(b) was an extension of the parentheses. With the sole exception of a(b)^c which I would perform as a((b)^c)
@@chengshengway The inside of the parentheses take precedence, but the multiplication of the evaluation of the parentheses expression is the same as any other multiplication
You can do it both ways, but the author should state what rule (I don't remember the name) they're using. Interestingly, it's often multiplied with a variable first: 8÷2x, but less commonly with parentheses: 8÷2(6).
That’s an interesting video. Two things stand out for me, firstly the number of correct/incorrect answers in the original test. But secondly the importance of clarity when you set or present a problem. The number of correct answers would rise significantly with better use of parentheses - but that’s the point of the original problem, I guess. Thanks for posting.
Not sure how much "better" you can use parentheses in this example problem. Yeah, you can add more, but you run into cluttering the problem and potentially confusing people even more. Understanding PEMDAS better would be more useful.
When I write C code (or any language), I often put parentheses in for every term to show the order of operations explicitly. It is more typing for me, but I find that when others read my code, they interpret it better with explicit parentheses. The code comes out the same if I just followed the order default of operations which the complier follows (the same as math in general), it just takes the complier a few milliseconds more to work the explicit parentheses as it would in the normal order of operations. The code runs just as fast either way. I often "go vertical" in code to help others see the nesting of operations more clearly (very close to "pretty print" like my TI-82+ calculator displays): Default order of operations: x = pow(3, 3) + 4 * (8 - 5) / 6; // x = 29 With explicit parentheses: x = (pow(3, 3) + ((4 * (8 - 5)) / 6)); // x = 29 My explicit parentheses pretty print notation: x = ( pow(3, 3) + ( (4 * (8 - 5)) / 6 ) ); // x = 29 All 3 styles result in the EXACT code and result. Now, this is a just small example. Try it all on one line with, say 10, parentheses levels deep. Then break it out to multiple lines using whitespace (pretty print) to make it more readable.
@@georgeandrews1394 True, but I often (not always) encapsulate the entire equation just to show the order of operations is the equation first and the equals is evaluated last. Yes, not needed just a bit more explicit. I teach Summer STEM. When my students have trouble getting parentheses to match up or they get lost in interpreting an equation from a single line, I tell them to do what I taught them and "go vertical" ... they find their problems quickly every time. We are engineers not mathematicians, so we are not normally writing down pages and pages of equations to solve somthing, so it's OK to type a little more in formal code, let the complier do the work and ignore the parentheses that are there just for we humans. When they can't figure out why their code won't complie or they get run-time errors, I tell them "Remember, white space and alignment is your friend)... they are amazed on how quickly they find bugs when they space things out and line things up. Code typing is two dimentional... use both! I have known a couple of accomplished engineers that try to cram all they can on one or two screens for a function. Their code is hard to read (except for themselves as the authors)... apparently, they are teaching this philosophy in schools that cramming all the code together is easier to read just because you can see it all without a bit of scrolling. No... white space is free, so what if it takes a few milliseconds more for the complier's parser to filter out the whitespace. As for cramming it tightly: Imagine writing a book with no double spaces after sentences, no paragraph indents and seperations, and all one chapter. It's a crude example but it hits the message home. My students are like sponges!
@@georgeandrews1394 Oh, I never realized it before, I guess I encapsulate the whole equation (especially when going vertical) is to separate the semicolon which is there only for the language syntax, not the math. This way, as you work an equation to include/simplify terms, you don't have to worry about that pesky semicolon at the end and you can focus on the math within the language pairs: ( ... math ... ); I never gig my students for not having the extra set, as long as it is clean and easy to read. I could just put the semicolon on its own line and not use the extraneous parentheses, but a stray semicolon looks out of place. Sometimes I may start the equation on the next line after the equals: x = ( pow(3, 3) + ( (4 * (8 - 5)) / 6 ) ); I teach my students to (when they are putting in debug code or code that is not yet formalized) NOT to indent properly or follow good coding conventions. This way, the "infant" code looks out of place and is easy to find later when formalizing the code for release. If they comment something out or change something temporarily, I tech them to put tags like or in their comments in case they are called away and can't revisit the code for maybe days later. So, when formalizing the code, not finding these is search helps reduce bugs from "spur of the moment" code fragments.
Got it! These are really good practice. May I suggest math problems to solve common everyday problems ie how to figure out how much wood is needed to build a deck or frame a house; how much cement to make a pool; etc. I use math everyday to figure out how much material I need for my art work or for cooking or for fuel consumption on trips. Keep up the good work! Love your videos!
How about this one: You have multiple errands to run. You know the position of each errand and you need to visit all of the places once. Starting at an arbitrary point, what is the ideal order to minimise distance travelled?
4:15 why? how? where have they ever learned that? Feels like a feature in an obscure programming language, like you have two strings and you want them on one string and you type str = str1(str2
I don't remember if this is how I learned things, but I think of solving problems like that by separating them into terms. So I'd have 3^3 and 4(8-5)/6 to solve before any addition. I don't think of addition and subtraction as part of the order of operations, merely as the last step in evaluating things after each term has been solved. I actually had a hard time figuring out how those other answers were even possible.
This video kind of illustrates one of my pet peeves, which is that "PEMDAS" is often presented as if were the be-all and end-all of order of operations. But in fact, it is only a helper tool for beginners. With a little more experience, one learns that it does not need to be followed literally and blindly. For example, it's perfectly valid to do everything on the right side of the "+" sign first, before exponentiating. Or, one can evaluate the three cubed first, before evaluating the expression inside the parentheses.
kind of. Order of Operations does need to be followed, but generally the more complicated a problem is the more attention you need to pay. There are things like doing the rest of the problem first and then performing the exponent to make it easier to do mentally, but only because there is nothing until the + the requires the exponent term
@@goldencloud7527 But that's the whole point. If you first find the lowest order operations, you can chop the issue up into easier to handle individual terms and evaluate those seperately, which reduces the complexity of the problem.
Yea, I don't really know how to explain it but I just solve problems from left to right as normal unless the operation I am trying to do is superseded by another operation which is higher on the list. For instance if you have 2+3*4, you attempt to add the 2, but the term you're trying to add is blocked by a multiplication. So you skip the addition and you go to the next operator, in this case is the multiplication. However if you have something like 2+3*(3/(4+5)), you attempt to add, can't, you try to multiply, can't, you try to divide, can't, and finally you get to the second addition leaving you with 2+3*(3/9). You keep doing passthroughs in this way until nothing is left. However it's possible to do multiple steps at one time when you have something like 10*2+3*(3/(4+5)), your first passthrough of the problem will be 20+3*(3/9).
Using / for division is tricky. I always use extra parentheses to. Avoid any ambiguity. Some programming languages also needs more parentheses to work correctly.
That's the point of problems like these. They're purposefully ambiguous to trick the audience where as anyone truly writing that equation to be straightforward and easy to understand would write it as: 3^3 + (4 * (8 - 5)) / 6 = 29.
If your object is to determine how well people understand operator precedence rules, you have your answer. If your object is to communicate clearly, especially if you are writing a program that must be read and maintained by others, then, especially in light of that answer, USE MORE PARENTHESES!
I originally got B because I misread the first part as 3² (thus equivalent to 3×3), then after I realized it actually said 3³, I got the correct answer of D.
Got it!😁 it’s sad that lots of people misunderstand pemdas…it’s true that maybe they weren’t taught pemdas in the correct way, but I think it’s very underrated and schools should put it as a revision lesson every year..
its largely because there is 2 different ways of writing equations and people confuse the way of solving one way of them being written, with the other.
I calculated 29 in my head but was extremely doubtful of the answer and will admit it did take me like 30 seconds, but when I watched the video and figured out it was right I was so happy.
Can you make a video about how calculators don't follow PEMDAS as intended, resulting in wrong answers? That might have been the culprit here, and I know that has been argued to be the case for some TI models.
Thought the exact same thing. I found that breaking the problem into smaller parts is more accurate than a calculator. I assumed it was because i input the data incorrectly. I.e. the calculator was correct in the calculations based on what was input, but those inputs were not translated properly to the calculator to begin with.
Can confirm, as someone who turned 18 in 1992, that they drilled this order into us in junior high, and most students still consistently got this wrong (usually by going left to right regardless of the operations). ETA: This was before we were permitted to use calculators in math class, not that it would have helped.
No matter how clear the instructions or how many times you have people do it, many will just not bother to learn at all and then get frustrated when they get wrong answers.
I found that using calculators for more complicated problems lead to more incorrect answers than if i broke the problem down step by step. A calculator is a tool, and like any tool, it can require skill to use effectively.
@@turbo8628 most calculators just do left to right, and to fix that you have to use a massive heap of brackets, and trying to deal with nested brackets is a nightmare.
Note that only one of the incorrect answers comes from doing the order of operations wrong: the one where the addition was done before the division. The other three errors were some form of sloppiness, such as misreading 3 cubed as 3 squared. And those three errors still got the order of operations right. So if you look at it that way, 59% got the order of operations right and 40% did not. Which is still not great, but maybe the educators need to focus on being careful as much as on order of operations.
I was taught BODMAS thus getting brackets (3) then divided by 6 = half, then multiplied by 4 giving 2, then add 3 cubed which is 27 then add 2 giving 29.
TBH I calculated 29 instantly on the thumbnail. So I was curious to see where am I missing as the ques can't be this easy. But man, now I feel like a god
I think that the reason so many people have problems with mathematical order is that is not how we are taught. Not that we don't get taught the order eventually, but that we are taught addition and subtraction very early in our lives. Then we are taught multiplication (and the subtopic of multiplying what is in parentheses) and division later on, and exponents later still. This means we are most familiar and most comfortable with adding and subtracting. Thus, when those of us that seldom have to use mathematical orders on a daily basis are suddenly confronted with one, we try to solve it using the most familiar tool we have. There is a reason when asked what math is, the answer is often "You know, add, subtract, multiply and divide.", because that is the order we learned it. I, for one, was not taught PEMDAS until I started taking university courses when I was in my 30's. Ah, I wonder how different my life would have been but for the want of an acronym...
The only time an order-of-operations issue arose in my whole life was on RUclips. I used to get problem books to solve complicated definite integrals for fun, as relaxation from the real stuff.
Funny enough, I actually came up with 11 when I looked at the thumbnail, but I read the exponent as a 2. As soon as I heard Presh say "Three to the power of three", I realized my mistake and came up with 29. Read and re-read! Lesson learned.
I want to ask is it really 12th class program in U.S schools? Because it looks too easy for 12th grade. I have learnt this at 6-7th grade. And in my school we start learn math analysis in 12th grade
Personally, I think this would be a lot more interesting to solve if the question prompted you to explain how someone could have reached each conclusion
29% for grade 12 because they can’t see the percentage so they just pick the one they choose The RUclips poll can see the percentage so they just pick the one with the most percentage
I've overthought things before, as I did with this problem. I've followed PEMDAS to wrong answers before, because that order is sometimes overruled by the left to right rule. I've also found that folks that NEVER make this mistakes on rather simple problems, are not usually adept at much more difficult math. That's not a rule, just an observation.
I gave the wrong answer by going 3x3x3 is 21 in my head xD and was really confused when the answer didn't show 23 as an option, would have been able to spolve correctly if i knew the 1x9 tho
The better term is BODMAS. I can not believe that 71% of Americans could not get the right answer. We learnt this in primary school in Australia. If you can not get questions like this correct then Mathematics, Statistics, Computer Science, Physics and Physical Chemistry will be forever out of your grasp and reach!
I somehow ended up with 15.5, when I saw it wasn't one of the alternatives I tried doing it a different way and ended up with 6.5 but I kinda suspected this was wrong so I tried again and ended up with 15.5 once more lol, I don't remember how to do these at all it seems
You are young then I suppose? In the 'old' days students were drilled so much in arithmetic and algebra that they were like machines, (at least in some school systems). Example I can still do multiplications like 74293 times 49873.
Maybe it is the notation that is bad not the students. If you added more () or you staked the division, I think you could get much closer to 100%. But then people like me watching math videos on youtube would not feel smarter than everybody else and I do not think my fragile ego could handle that.
@@Crisis__ cmon dude ... when in real life do you need to remember this sort of thing? Its like how an ox bow lake is formed or price elasticity of demand. Probably had an unfair advantage though ... not being american. ;o)
'If there are two operations of same precedence then evaluate left to right' this rule is not needed. Even if we go from right to left or do it some other way still it gives the same solution.
You are 100% correct. However, going L to R reduces errors. So it's generally better to teach that variety of the order of operations for that reason alone. Many make the mistake of 10 - 8 + 2 = 10 - 10 = 0 Going R to L or doing A before S incorrectly when it's clearly 10 - 6 = 4 if you go R to L or A before S. Same with M and D. 16/8×2 R to L or M first is 16/4 = 4 R to L or M first done incorrectly is 16/16 = 1. I've seen a lot of people make those errors. With L to R those errors can't happen. Prevention is better than cure.
The plus sign makes this one easy. I had to add something to the 27. Anything after the plus sign had to be treated completely on its own. 12/6 has been 2 for as long as I remember..... So easy ........ Took 3 seconds.
This is relatively easy for these kinds of questions, the problem begins when you must choose an order for multiplication and division as calculating them in different order would then result in different answers. e.g. try 4 ÷ 2(1+1)
If using the "straight across" method proper above (PE[>>>MD][>>>AS]/BO[>>>DM][>>>AS], using the [>>>__] to indicate Left to Right): 4 ÷ 2(1+1) 4 ÷ 2(2) 4 ÷ 2 × 2 2 × 2 4 Using the method I thought was going to be used: 4 "over" 2(1+1) 4 "over" 2(2) 4 "over" 4 1
In my neighborhood, someone on NextDoor posted a similar math problem, which over half of the people got wrong - simply going left to right, ignoring the order of precedence. When 2 or 3 of us pointed out and explained the correct answer, one person claimed that order of precedence for math problems isn't clearly defined because calculators don't know about it. This is akin to claiming that decimal points aren't clearly defined because slide rules don't keep track of them. I informed this person that order of precedence was defined by mathematicians long before calculators were invented and that it's the responsibility of the user to know how his or her calculator works and to present the problem to the calculator in such a way that order of precedence will be followed. At last report, this particular neighbor is doubling down on his claim that calculators are the final arbiters of mathematics rules and I've given up on trying to explain to soneone who's determined not to listen.
Is there a calculator app available that can solve pretty much any problem? The one I use on my iPhone gave me the correct answer for this problem, but some types of problems it won't solve. I figure this is due to 1) my lack of advanced math skills in general, and/or 2) the lack of available functions in my app du jour.
I'm going to assume that most people got 6.5 wrong because of how the calculator calculated it. If the calculator they were using made it 3^3 + 4(8-5) / 6, instead of the division symbol, then perhaps the calculator automatically calculated out everything on the numerator first, and then divided all that by 6.
Great video, but instead of using a RUclips poll to gather info on something like this, try something that’ll only let you choose once. People can change their answer in a RUclips poll.
The real mistake generally is doing the math too quickly. Tests are generally timed, and people don't want to take time on any given post when scrolling social media feeds.
true, but in this example there really isn't much excuse for picking 6.5. it barely takes much time and since the poll is multiple choice you can easily estimate and eliminate (answer must be larger than 3^3 and cannot be .16 leaving only 27.5 and 29 which is obvious). 40% is just absurd.
The most common mistake people make now is with the division sign. Eg. 2/3*6=? If you go left to right it works fine but you don’t have to, you can do it in any order. You just have to realize that the division symbol is attached to the value after it. If I go right to left, I don’t do 3*6, I do ➗3*6, or 1/3*6, or 6/3. This equals 2, so the equation becomes 2*2=4. Going left to right ends up with the same answer.
I can only refer to Wikipedia: The division sign (÷) is a symbol consisting of a short horizontal line with a dot above and another dot below, used in Anglophone countries to indicate mathematical division. However, this usage, though widespread in some countries, is not universal; it is used for other purposes in other countries and its use to denote division is not recommended in the ISO 80000-2 standard for mathematical notation.[1]
Love the fact that the right answer of 29 was obtained by 29% of students. So collectively the students were right, right?
29 likes
Yaayyyy
i also got 29... howd they fail?
ironic that 29% got the right answer of 29
@@gmp39 same 29 here
It feels great when you get the problem right only lookin at the thumbnail, I wish every problem was as easy as this one
Agreed 😂
Yeah i wish so, but it every quest cant be so ez like that one.
sadge
I went to a book sale. Books were $2 each. I picked 5 books. The person counted the books then said she had problems adding the total. I said there are 5 books at $2. That’s 5*2=10. She was a college volunteer.
You are right
I calculated 29 without using calculator, but I thought the answer must surprise me so I watched the video, but then I saw 29 is the correct answer 😀
me to
Is very Easy, i think many people who passed 9th grade can with this
@@QuicklyMan 💀 9th grade bruh even a 3rd grader can do this no cap
@@QuicklyMan I'm a 6th grader, this is easy
@@QuicklyMan I am a 9th grader and I did it in my mind within a min lol
I did it! At 64, I haven't used math other than budgeting and bills in years. Some old dogs do remember tricks. Loved it. Thanks for the brain massage.
39 years old... Got the answer right in my head in less than 10 seconds
Same here, and I am 74 years old :-)
Same here and I’m 75, it seemed pretty easy.
Thats great... yet in an exam you would have had to show your working to get the marks unfortunately
Same here and I am 1,000,000 years , and it took me less than 1 milliseconds
me too at 62 y/o.
Whoops, I was one who chose 3x3, not 3^3, that’s how I got 11. Good stuff!
I made that oopsie while doing it faaast. But the next second I realised that the 3x3 is an oopsie.
Oopsie, me too
I'm so ashamed, did that as well!
same
Oops, me too!
Personally I've never struggled with the order of operations, but it was still interesting to see that most people get this wrong!
ikr
its 29 right
It was in the US, what do you expect 😂
@@elite6804 I mean yeah
Can’t prove you wrong
jeez thats a lot of likes on a comment. also i think this is the only comment of mine to get a like lol
I remember reading somewhere that while both the division symbol and slash are acceptable in situations which require you to write the equation in one line, it's far better and less ambiguous to write division as a fraction so visually all of the dividend is on top (numerator) and the divisor is on the bottom (denominator).
I agree, we should abolish both the slash and the ÷ symbol. If it's absolutely necessary to write on one line, parentheses must be used no matter what
@@ThomasTheThermonuclearBomb I feel the exception is putting explicit parentheses
So if you're in one line then (3-2)/4 is fine
division is just reverse multiplication so you can think of it as multiplying by the reciprocal of the divisor
Back in the 70s, I learned that multiplication and division were both *dot* operations (e.g. 5 *•* 2 = 5 *÷* 0.5) and addition and subtraction were line operations (e.g. 1 *+* 2 = 4 *-* 1) with dot operations having higher ranking over line operations and each were done left to right; the way we read.
Therefore I got it right from the thumbnail 😊
@@RobiBue Did you have a different mnemonic for the order of operations then? I never learned a mnemonic, but I can see how useful one would be.
I’m a 69 yr old retired man and haven’t had a math class in nearly 50 years. I came up with 29 without a calculator or watching and selecting the answer from the multiple choices. I’ve never forgotten PEMDAS. It’s always the fundamentals.
I am fourteen and I came up with 29 from looking at the thumbnail!
Please Excuse My Dear Aunt Sally
I'm in my father's nutsack and I came up with 29. Truly incredible how the young generations are able to get this one problem wrong!
@@uwatrkoda9131 the american young generation*, i am european and i got the right answer in less than 5 seconds. I'm 17
@@marcorizzo3854Not all Americans are bad at this though I’m only 15 born in 2008 and I also got this correct just by looking at the thumbnail. I was taught PEMDAS and you go left to right. I’m a gen x and didn’t have issues doing this problem I think it depends on what school you went to and what the teachers taught you. I’m also from the only state that partially adopted common core standards. We only adopted the English standards and made our own math standards so I learned it differently from most states. We’re also in the top 10 states that score the highest on national math tests to see where schools and states are.
For anyone who doesn't want to watch the full length video, the answer is simply 29. How? 3^3+4(8-5) / 6 is equivalent to 27+4x3/6 then 4x3=12, 12/6=2 now it's 27+2=29
It's interesting that 3 of the incorrect answers stem not from an error in the order of operations, but either a misunderstanding of the function or a typo when working through it. Curiously, those wrong answers otherwise demonstrate a proper use of the order of operations. So what does that demonstrate about what/how students have learned?
And those are mistakes most often due to rushing through the problem, as students would do on a timed test. While a youtube poll gives you all the time you need.
@@micaelstarfire8639 also, the viewerbase for this channel will likely be people who have an interest in maths, so skewed even more in favour of the poll.
I got the correct answer, but i did do a couple of things in the incorrect order, so even i learned something.
I disagree with both his and your interpretation. Some people would have guessed. Any answer which receives less than its equal proportion of the answers, or perhaps it's equal proportion when the most common answer is removed, shouldn't be read into too far.
@@hainsay people who know the answer do not guess. People who have am interest in maths/this channel are therefore less likely to guess as they know the answer.
You proved my point whilst disagreeing with it.
I don't know the statistics on who guessed and who just worked their way through the wrong answer... and neither do you, so using that as the foundation for your argument against the other commenter makes no sense. This is a problem with multiple choice questions in general. Could argue that 25% guess right (for this question) but there are plenty of others that are really a 50/50 and others where the correct answer is counter-intuitive (i.e. the people guessing the answer are unlikely to get the correct one).
None of the “answers” are “correct.”
Having done a lot of mathematical modeling of physical systems in FORTRAN, learned the 'operator precedence' of the language. Many a bug were made by folks by not applying parenthesis correctly. Our mantra became, "When in doubt, put parenthesis around it!" Nice the way you walk through the solution, makes it very clear.
As a fellow programmer, I almost always just use parenthesis with both mathematical and boolean operations. It makes it so I make fewer mistakes, and it's way more clear when I or someone else come to read it later.
In C++, the operators &, ^, and | are lower in precedence than == and !=. This makes no sense. &, ^, and | return a number, which one often wants to compare with something. Therefore, one must always put parentheses around expressions using &, ^, and | and around their operands if they have operators in them.
o7 that's a good mantra
So the mantra became "put parenthesis instead of learning precedence of operators"? Hope I'll never work with you then.
@@DavideCanton LOL More like, 'clarity of purpose' over 'obscure gotcha'. Reminds me of the young twit that said in a job interview, "I don't need to put in comments because my code is always right the first time." (P.S. We pointed out that we have teams of programmers and a loner such as himself probably wouldn't fit in, have a nice day)
Knowing the correct precedence is useful, but even more useful is knowing when confusion will result and then using parentheses to preclude any confusion.
I see these types of questions on Twitter all the time. (by World of Engineering) and almost on all occasions the right order gets about 45-48% correct answers. Many are of the opinion that PEMDAS and BODMAS have different rules.
Your channel is likely followed people who actually like math :)
A lot of the disputed ones on social media use the ambigous writing of e.g. 6(7-4) instead of 6*(7-4). While technically both are the same, a lot of people learned that you only write 6(7-4) if the 6 belongs to the paranthesis. So you only omit multiplication symbols for grouped expressions
This causes confusion when promted with e.g.: 4 + 10 / 6(7-4)
If you learned that the multiplication is only omitted if it belongs to the paranthesis this would read like 4 + 10 / (6*(7-4)) for everyone else.
Now I know, people will say that is an incorrect way to learn it, but if I prompted you with 4 + 10 / 6x you most likely would also assume 4 + 10 / (6x) instead of 4 + 10 / 6 * x
@@NanoNaps 6x notation is known as implied multiplication, it is treated as if it is written as you did '(6x)'. However 6(7-4) is not ambiguous. iirc according to the rules you should get the correct answer?
Love math
I actually wound up doing this question both ways, without a calculator, expecting this to be a case of "in the past textbooks sometimes used the division sign to save space" before watching the video or reading the description.
I had a brain fart and initially came up with 11 because I focused all my attention on doing the right side of the equation properly then only tack on the easy 3^3 at the end but carelessly did it as 3^2. Realized this mistake almost instantly and revised to 29, but if I were in a rush to submit an answer I would have been capable of submitting 11, albeit not due to a shortfall in order of operations but just pure carelessness😄
Lol same
Brain fart? Take a pill....
@@HeavensDemon966 what is your problem?
@@HeavensDemon966 lol weird take
@@smart_lizard_3149 Where I come from if someone's flatulence is noticeably audible another person will criticize the perpetrator by saying "Take a pill!" I guess all of our problem is that there is no medication out there for brain farts.
I ended up getting the right answer, but I was confused at first because my math homework always uses a fraction bar for division. I was a little unsure of my answer, but it turns out that dogmatically following the order of operations does, in fact, work out. 😂
I think this is what confuses some people, they think ÷ means everything on the left divided by everything on the right, which it isn't. If someone wanted that, they would put brackets around everything on the left, and brackets around everything on the right.
That's really how it should be written in the real world to avoid any possible misinterpretation. An expression would never be written like this except in a math problem trying to test your knowledge of order of operations.
I would take serious issue with the recommendations in the document issued by the Australian government. In my opinion, NO serious mathematician should ever use the divide symbol. Ever. It's for kiddies and should be jettisoned before school kids reach the age of 13.
@@HiltonBenchley ÷: I am your worst enemy
When my sister (5 years younger than me) was in High School, she was at the bottom of her maths class. She had not been taught BODMAS. Once I taught her BODMAS she went to nearly the top of the class. It is a simple and essential thing to know and yet it was not being specifically taught.
What kind of education doesn't teach BODMAS by high school? What? That stuff is taught when you're like 10
it one of those things that everyone thinks everyone else knows it, when not alot do.
What's BODMAS? I remember PEMDAS.
@@terryschilling5320 Same thing using different words." Brackets, Of, Division, Multiplication, Addition, Subtraction".
@@terryschilling5320 He explained it in the video. 1:28
Thank you for not only giving an interesting problem, but also explaining where the wrong answers came from. It's good to understand what happened when people made mistakes.
got it right from the thumbnail. I learned how you explained it-order from left to right (for multiplication/division and addition/subtraction)
to eliminate the possibility the division sign affects either part or all of the equation, it is best to show it as a fraction
Yep! ISO standards...
you know what, screw division just multiply by a fraction
@@LineOfThy a fraction is division.
@@A.Martin I meant the symbol
I'm from Germany, and the mnemonic we learned at school for the order of operations was POKLAPS, an abbreviation of POtenz (exponent), KLAmmer (brackets), Punkt (dot; for multiplication (⋅) and division (:) ) and Strich (line; for + and - )
But if you say Poklaps as one word, it means butt-slap, so it's easy to remember XD
Eyy
Clever one there
we never learned any mnemonics for it
that's exactly how I learned it (except with the popo klaps mnemonic) although I was taught that in Latinamerica... through a European private school 😁
wir hatten eigentlich nur punkt vor strich
I don't remember learning any mnemonic trick, but I've never had a problem with the order of operations... They are introduced gradually during the different school years, so you have all the time to learn the correct order, without even trying, before you end middle school! At least in my country...
I almost got it. My mistake was the exponent part. Instead of solving 3 to the power of 3, I did 3x3 instead. Thanks for the video.
The only thing more important than being right, is recognizing how and where you make a mistake.
"'We learn wisdom from failure much more than from success" - Samuel Smiles.
being a 13 year old who is familiar with these type of questions, I can say people tend to forget pemdas or aren't able to apply it properly as they reach higher classes
Yup: you have it correct. As far as I know it's taught during a short spurt in one year of math. If you miss that week, or just don't understand it through not having brain space for it (too much stuff going on, not enough coffee, no breakfast) you're forever at a loss. And can go through adult hood getting it wrong. That's why some of us are astrophysicists and some of us write novels.
I did it in my head and got it right on the first try! Not bad for someone whose last Math class was 12 years ago. I had an excellent Math professor.
when you made the poll, I originally put 11, because even though it says 3 cubed, and I saw the three, I processed it as 3 squared. it wasn't until I read the comments, someone saying they did the same thing that I realized my mistake.
I've developed the habit of breaking problems into units (terms) separated by addition or subtraction and working through the most complicated first to aid the mental process. I completed the second term, stepped back to make confirm the first term was 3^2=9 and had a moment of surprise when I saw a three up there. Of course that also made me forget the second term and I had to recalculate it, but maybe the problem really was about misreading the exponent instead of multiplying by it.
@@johnno4127 See, my problem was, I'm pretty sure when I was reading the equation for the first time before solving it, I even read it as "3 cubed" or "3 to the power of 3" or whatever, but, even though I read it correctly, I processed the information incorrectly... I think because before it, I had just got done reading (and thus following along and doing) a bunch of simple equations involving squares and square roots, so I just saw an exponent and habitually did a square.
I did exactly the same thing!! I very confidently read it as 3 squared and didn’t notice
29. I found the wrong answers really interesting!
I still like to think of the order of operations in terms of complexity, solving from more complex to least complex: addition is the simplest binary operation (includes subtraction since A - B = A + (-B)), multiplication is repeated addition (includes division since A/B = A × 1/B), and exponentiation is just repeated multiplication (includes radicals since x√A = A^(1/x)). Grouping with parentheses is pretty much common sense as are unary operations like log, sin, tan, etc. The only unary operator that might get confusing in some cases is the additive inverse, especially when combined with exponents.
The one thing I'd add to this is that, at least in some circles, implied operations (such as the implied multiplication in the problem) take precedence over ones that are explicit. In this case, it doesn't matter as the implied multiplication appears first in left to right order. However, it's best to check with the instructor or the style guides of any journal you happen to be writing for to see if they give precedence to implied multiplication. If you're one of those people who actually read the instruction manuals that come with calculators, sometimes you'll find a section that addresses implied operations.
In most instances implied operations like you said would always take precedence. It's just a short form and if written out longhand the equations would have additional brackets around the multiplication and the addition in the shown brackets
Agreed. That's always been the case as I've run into it. However, I will point out that some calculators don't do this and a few Internet math teachers have insisted that implied multiplication is just multiplication and left to right takes precedence (thus the warning to check with style guides and instructors).
I've been teaching since 2004 and have dealt with this problem at the college level. In my book: Taking Fear Out of Math, I make a point of teaching order of operations in a simple, straight forward manner parents and students can easily grasp.
S0 what answer would you get for the numerical expression 6 ÷ 2(1 + 2)...
If you write an equation that makes people interpret order-of-operation, you're doing it wrong. As a lead engineer, if one of my guys had put on a document that I was reviewing, my red pen would be all over it with a terse note to try again.
Agree as programmer. Just because I know that the compiler is going to evaluate an expression in a certain order, doesn't mean I shouldn't make the code more readable to others by using brackets and linebreaks anyway.
In german we have the "KlaPuStri - Klammer Punkt Strich" which means Brackets, Dots, Lines...although this does neglect the exponential operations it helped quiet well over all these years.
We have VPMDAS " Veronica, Please Excuse My Dear Aunt Sally "
We also had KlaPuStri but also later learned KlaPoPuStri
So Klammer Potenz(exponent) Punkt Strich
ISO standard says that "division sign" should not be used
You can use / or : in example like you have.
So by ISO standard you didn't have a division sign you had an undefined sign making your problem undefined.
Interesting point. I am not used to the division sign, and it threw me off doing this in my head. When he wrote it out, I instantly realized my mistake. Not sure that this is a "math" problem at all. Thanks for your comment.
Yes, division sign should not be used but fraction. Makes everything clear and less arguments.
@@chengshengway yep, the obelus sign means subtraction in some countries and division in others.
77 years old. Got it right in 1 min with no calculator (absolutely mental arithmetic!). ..WHAT do they OMIT to teach in schools?
How to make a viral math problem
Step 1: ÷
Step 2: Profit
but i know you because i like watching you. We are not the same.
isn’t that 29? That was easy you didn’t even get the chance you read the answer and i didnt know it was a multiple choice lol
The only issue I ever faced was that here in India, implied multiplication still exists. I.e. 4(3) would take precedence over any regular multiplication or division. This twists things up when I became a computer programmer and an android app was failing because we forgot about it.
Exactly where many fail, parenthesis " ( ) " take precedence and should NOT be taken as normal multiplication.
I always assumed it was the same thing here in the US. That the a(b) was an extension of the parentheses. With the sole exception of a(b)^c which I would perform as a((b)^c)
@@chengshengway The inside of the parentheses take precedence, but the multiplication of the evaluation of the parentheses expression is the same as any other multiplication
You can do it both ways, but the author should state what rule (I don't remember the name) they're using. Interestingly, it's often multiplied with a variable first: 8÷2x, but less commonly with parentheses: 8÷2(6).
what i learned it that you would not wirte down 4(3) but make it 4x3. we just removed the "( )" when possible.
That’s an interesting video. Two things stand out for me, firstly the number of correct/incorrect answers in the original test. But secondly the importance of clarity when you set or present a problem.
The number of correct answers would rise significantly with better use of parentheses - but that’s the point of the original problem, I guess.
Thanks for posting.
Not sure how much "better" you can use parentheses in this example problem. Yeah, you can add more, but you run into cluttering the problem and potentially confusing people even more. Understanding PEMDAS better would be more useful.
"Why did 70% of US stusents fail?" The answer is in the question (US).
When I write C code (or any language), I often put parentheses in for every term to show the order of operations explicitly. It is more typing for me, but I find that when others read my code, they interpret it better with explicit parentheses. The code comes out the same if I just followed the order default of operations which the complier follows (the same as math in general), it just takes the complier a few milliseconds more to work the explicit parentheses as it would in the normal order of operations. The code runs just as fast either way. I often "go vertical" in code to help others see the nesting of operations more clearly (very close to "pretty print" like my TI-82+ calculator displays):
Default order of operations:
x = pow(3, 3) + 4 * (8 - 5) / 6;
// x = 29
With explicit parentheses:
x = (pow(3, 3) + ((4 * (8 - 5)) / 6));
// x = 29
My explicit parentheses pretty print notation:
x = (
pow(3, 3) +
(
(4 * (8 - 5))
/
6
)
);
// x = 29
All 3 styles result in the EXACT code and result. Now, this is a just small example. Try it all on one line with, say 10, parentheses levels deep. Then break it out to multiple lines using whitespace (pretty print) to make it more readable.
I see your point. You could make it shorter, though. The outermost set of parentheses isn't doing anything here.
@@georgeandrews1394 True, but I often (not always) encapsulate the entire equation just to show the order of operations is the equation first and the equals is evaluated last. Yes, not needed just a bit more explicit. I teach Summer STEM. When my students have trouble getting parentheses to match up or they get lost in interpreting an equation from a single line, I tell them to do what I taught them and "go vertical" ... they find their problems quickly every time. We are engineers not mathematicians, so we are not normally writing down pages and pages of equations to solve somthing, so it's OK to type a little more in formal code, let the complier do the work and ignore the parentheses that are there just for we humans. When they can't figure out why their code won't complie or they get run-time errors, I tell them "Remember, white space and alignment is your friend)... they are amazed on how quickly they find bugs when they space things out and line things up. Code typing is two dimentional... use both! I have known a couple of accomplished engineers that try to cram all they can on one or two screens for a function. Their code is hard to read (except for themselves as the authors)... apparently, they are teaching this philosophy in schools that cramming all the code together is easier to read just because you can see it all without a bit of scrolling. No... white space is free, so what if it takes a few milliseconds more for the complier's parser to filter out the whitespace. As for cramming it tightly: Imagine writing a book with no double spaces after sentences, no paragraph indents and seperations, and all one chapter. It's a crude example but it hits the message home. My students are like sponges!
@@georgeandrews1394 Oh, I never realized it before, I guess I encapsulate the whole equation (especially when going vertical) is to separate the semicolon which is there only for the language syntax, not the math. This way, as you work an equation to include/simplify terms, you don't have to worry about that pesky semicolon at the end and you can focus on the math within the language pairs: ( ... math ... ); I never gig my students for not having the extra set, as long as it is clean and easy to read. I could just put the semicolon on its own line and not use the extraneous parentheses, but a stray semicolon looks out of place.
Sometimes I may start the equation on the next line after the equals:
x =
(
pow(3, 3)
+
(
(4 * (8 - 5))
/
6
)
);
I teach my students to (when they are putting in debug code or code that is not yet formalized) NOT to indent properly or follow good coding conventions. This way, the "infant" code looks out of place and is easy to find later when formalizing the code for release. If they comment something out or change something temporarily, I tech them to put tags like or in their comments in case they are called away and can't revisit the code for maybe days later. So, when formalizing the code, not finding these is search helps reduce bugs from "spur of the moment" code fragments.
Got it! These are really good practice. May I suggest math problems to solve common everyday problems ie how to figure out how much wood is needed to build a deck or frame a house; how much cement to make a pool; etc. I use math everyday to figure out how much material I need for my art work or for cooking or for fuel consumption on trips. Keep up the good work! Love your videos!
How about this one: You have multiple errands to run. You know the position of each errand and you need to visit all of the places once. Starting at an arbitrary point, what is the ideal order to minimise distance travelled?
As as as
@@regarrzo I see what you did there...
4:15 why? how? where have they ever learned that? Feels like a feature in an obscure programming language, like you have two strings and you want them on one string and you type str = str1(str2
Human brains are pattern seeking machines , plus student goes on autopilot from sheer boredom = weird results. It's the same as seeing Jesus on toasts
I don't remember if this is how I learned things, but I think of solving problems like that by separating them into terms. So I'd have 3^3 and 4(8-5)/6 to solve before any addition. I don't think of addition and subtraction as part of the order of operations, merely as the last step in evaluating things after each term has been solved. I actually had a hard time figuring out how those other answers were even possible.
Same lol
@@BromeoWuggles yea, you basically ignore the addition and subtraction until later, unless it is in brackets.
This video kind of illustrates one of my pet peeves, which is that "PEMDAS" is often presented as if were the be-all and end-all of order of operations. But in fact, it is only a helper tool for beginners. With a little more experience, one learns that it does not need to be followed literally and blindly.
For example, it's perfectly valid to do everything on the right side of the "+" sign first, before exponentiating. Or, one can evaluate the three cubed first, before evaluating the expression inside the parentheses.
kind of. Order of Operations does need to be followed, but generally the more complicated a problem is the more attention you need to pay. There are things like doing the rest of the problem first and then performing the exponent to make it easier to do mentally, but only because there is nothing until the + the requires the exponent term
@@goldencloud7527 But that's the whole point. If you first find the lowest order operations, you can chop the issue up into easier to handle individual terms and evaluate those seperately, which reduces the complexity of the problem.
@@Llortnerof that's what my math teachers always drill into my head: *divide in terms* . it clears up everything
Yea, I don't really know how to explain it but I just solve problems from left to right as normal unless the operation I am trying to do is superseded by another operation which is higher on the list. For instance if you have 2+3*4, you attempt to add the 2, but the term you're trying to add is blocked by a multiplication. So you skip the addition and you go to the next operator, in this case is the multiplication. However if you have something like 2+3*(3/(4+5)), you attempt to add, can't, you try to multiply, can't, you try to divide, can't, and finally you get to the second addition leaving you with 2+3*(3/9). You keep doing passthroughs in this way until nothing is left. However it's possible to do multiple steps at one time when you have something like 10*2+3*(3/(4+5)), your first passthrough of the problem will be 20+3*(3/9).
Using / for division is tricky. I always use extra parentheses to. Avoid any ambiguity. Some programming languages also needs more parentheses to work correctly.
That's the point of problems like these. They're purposefully ambiguous to trick the audience where as anyone truly writing that equation to be straightforward and easy to understand would write it as: 3^3 + (4 * (8 - 5)) / 6 = 29.
@@Ankuhr_1 "They're purposefully ambiguous "
They are not ambiguous.
You either know how to read a math problem or you do not.
If your object is to determine how well people understand operator precedence rules, you have your answer. If your object is to communicate clearly, especially if you are writing a program that must be read and maintained by others, then, especially in light of that answer, USE MORE PARENTHESES!
If you ever had to write this in a line of code wouldn't this be one of the few times a comment is absolutely necessary?
I originally got B because I misread the first part as 3² (thus equivalent to 3×3), then after I realized it actually said 3³, I got the correct answer of D.
I made the same mistake. Too quick a glance at the question, seeing it but not reading it.
same lol the ^ is very small as is the *
Same squared instead of cubed
I did the same. Got 11 off the thumbnail, but corrected it to 29 when I started the video.
Got it!😁 it’s sad that lots of people misunderstand pemdas…it’s true that maybe they weren’t taught pemdas in the correct way, but I think it’s very underrated and schools should put it as a revision lesson every year..
its largely because there is 2 different ways of writing equations and people confuse the way of solving one way of them being written, with the other.
I calculated 29 in my head but was extremely doubtful of the answer and will admit it did take me like 30 seconds, but when I watched the video and figured out it was right I was so happy.
Same
uh am I the only one confused on why people thought this was hard? literally did it in my head without a calculator before even clicking on the video…
Can you make a video about how calculators don't follow PEMDAS as intended, resulting in wrong answers? That might have been the culprit here, and I know that has been argued to be the case for some TI models.
What's the point if you just use a calculator?
Some Calculators follow PEJMDAS :)
I remember this with a calculator app on an old nokia phone!
Thought the exact same thing.
I found that breaking the problem into smaller parts is more accurate than a calculator. I assumed it was because i input the data incorrectly. I.e. the calculator was correct in the calculations based on what was input, but those inputs were not translated properly to the calculator to begin with.
Just use brackets
dang! I muffed it. I got A: 6.5
but then I'm 73 and haven't refreshed my math skills in decades 🙂
I'm 67 and got it right... but I play with math a lot :D
Well sir props to you for following this channel even at your age
Somehow I got 3.5, which wasn’t even on the multiple choice list.
@Maddog7, I think your answer of 6.5 is correct.
Just unsubscribed from this misinformation channel.
@@WeAreAllOneNature why? What is your order of operations for that answer?
Can confirm, as someone who turned 18 in 1992, that they drilled this order into us in junior high, and most students still consistently got this wrong (usually by going left to right regardless of the operations). ETA: This was before we were permitted to use calculators in math class, not that it would have helped.
No matter how clear the instructions or how many times you have people do it, many will just not bother to learn at all and then get frustrated when they get wrong answers.
I found that using calculators for more complicated problems lead to more incorrect answers than if i broke the problem down step by step.
A calculator is a tool, and like any tool, it can require skill to use effectively.
@@turbo8628 most calculators just do left to right, and to fix that you have to use a massive heap of brackets, and trying to deal with nested brackets is a nightmare.
Note that only one of the incorrect answers comes from doing the order of operations wrong: the one where the addition was done before the division.
The other three errors were some form of sloppiness, such as misreading 3 cubed as 3 squared. And those three errors still got the order of operations right.
So if you look at it that way, 59% got the order of operations right and 40% did not. Which is still not great, but maybe the educators need to focus on being careful as much as on order of operations.
I was taught BODMAS thus getting brackets (3) then divided by 6 = half, then multiplied by 4 giving 2, then add 3 cubed which is 27 then add 2 giving 29.
Though the order of operations were wrong
Luckily your answer were right
division and multiplication are equal precedence, should do left to right
TBH I calculated 29 instantly on the thumbnail.
So I was curious to see where am I missing as the ques can't be this easy.
But man, now I feel like a god
Also, late questions on timed tests were probably guessed.
i got the order right but somehow mistook 3^3 as 81 💀
Same but I mistook it for 9 🙁
@@maplenotsyrup9996 ong 💀💀
I think that the reason so many people have problems with mathematical order is that is not how we are taught. Not that we don't get taught the order eventually, but that we are taught addition and subtraction very early in our lives. Then we are taught multiplication (and the subtopic of multiplying what is in parentheses) and division later on, and exponents later still. This means we are most familiar and most comfortable with adding and subtracting. Thus, when those of us that seldom have to use mathematical orders on a daily basis are suddenly confronted with one, we try to solve it using the most familiar tool we have.
There is a reason when asked what math is, the answer is often "You know, add, subtract, multiply and divide.", because that is the order we learned it.
I, for one, was not taught PEMDAS until I started taking university courses when I was in my 30's. Ah, I wonder how different my life would have been but for the want of an acronym...
The only time an order-of-operations issue arose in my whole life was on RUclips. I used to get problem books to solve complicated definite integrals for fun, as relaxation from the real stuff.
I will never understand how people don't understand the order of operations
Literally did this in my head based on the thumbnail, and got 29
I learned this first in 5th grade, I am now in 10th. People in my grade continue to get it wrong and it’s insane
3:25 oh yeah, 29 got 29% what a coincidence
how’d you get 29% 💀
In the UK we use BIDMAS (Brackets, Indices, Multiplication/Division, Addition, Subtraction) for this - another variation that exists 😅
It’s so funny how many different ones there are. In Canada it’s BEDMAS. Brackets, exponents, division/multiplication, addition/subtraction.
I learned it as GEMDAS- Grouping, Exponents, Multiplication/Division, Addition/Subtraction
@@krishnannarayanan8819 Same for my school but it's called GEMA instead of GEMDAS
I am from the UK and we were taught BODMAS back in the 1960s. BIDMAS probably makes a bit more sense.
"please, my dear Aunt Sally" I was taught in 4th grade in the 50s. Never forget those mnemonics!
Funny enough, I actually came up with 11 when I looked at the thumbnail, but I read the exponent as a 2. As soon as I heard Presh say "Three to the power of three", I realized my mistake and came up with 29. Read and re-read! Lesson learned.
Not the brain teasers we need, but brain teasers we deserve 👍
I want to ask is it really 12th class program in U.S schools? Because it looks too easy for 12th grade. I have learnt this at 6-7th grade. And in my school we start learn math analysis in 12th grade
Personally, I think this would be a lot more interesting to solve if the question prompted you to explain how someone could have reached each conclusion
I'm a math tutor, and I can confirm that students do actually get asked questions like that.
29% for grade 12 because they can’t see the percentage so they just pick the one they choose
The RUclips poll can see the percentage so they just pick the one with the most percentage
It’d be interesting to see how many wouldn’t have responded had it said “calculators NOT” allowed
I've overthought things before, as I did with this problem. I've followed PEMDAS to wrong answers before, because that order is sometimes overruled by the left to right rule. I've also found that folks that NEVER make this mistakes on rather simple problems, are not usually adept at much more difficult math. That's not a rule, just an observation.
Some people even confuse 1+2+3+... with -1/12 🤔
Yes, the zeta function of -1 is equal to -1/12, if you Google it
I gave the wrong answer by going 3x3x3 is 21 in my head xD and was really confused when the answer didn't show 23 as an option, would have been able to spolve correctly if i knew the 1x9 tho
Lolllll
Not hard bro 😏 ,we are waiting for hard and challenging questions from this channel, I love you 💙🌹
According to the rules you should get 29. That example should be gotten correct by all students it is hardly ambiguous.
The better term is BODMAS. I can not believe that 71% of Americans could not get the right answer. We learnt this in primary school in Australia. If you can not get questions like this correct then Mathematics, Statistics, Computer Science, Physics and Physical Chemistry will be forever out of your grasp and reach!
Am I the only one who felt like a scientist when I solved it from the first time easily!!!
I somehow ended up with 15.5, when I saw it wasn't one of the alternatives I tried doing it a different way and ended up with 6.5 but I kinda suspected this was wrong so I tried again and ended up with 15.5 once more lol, I don't remember how to do these at all it seems
You are young then I suppose? In the 'old' days students were drilled so much in arithmetic and algebra that they were like machines, (at least in some school systems). Example I can still do multiplications like 74293 times 49873.
bros iq is 2.5
@@dannygjk what's the answer
@@himaririku5289 If you mean the video question the answer is 29.
Maybe it is the notation that is bad not the students. If you added more () or you staked the division, I think you could get much closer to 100%. But then people like me watching math videos on youtube would not feel smarter than everybody else and I do not think my fragile ego could handle that.
wow .... havent been inside a maths class in 41 years and I got it right first time. respect to my teachers from back then. they could teach!
It's really just a simple problem to be honest. You probably did have good teachers though (:
@@Crisis__ cmon dude ... when in real life do you need to remember this sort of thing? Its like how an ox bow lake is formed or price elasticity of demand. Probably had an unfair advantage though ... not being american. ;o)
@@shuggiehamster I see where you are coming from but there are a good amount of jobs that require you to know the basics of Algebra.
I am just 12 years old, still, I got the correct answer with exact same process as yours. Thank you to make me learn my capability ☺
100 % of those 89% must be INDIAN !!! 😂😂😂😂😂😂
or just asian, like sri lankan or Chinese
@@59SONGOKU59 youtube is banned in china ??!!
@@AnitaSharma-oe6tu you can be Chinese but not like in China 😐
'If there are two operations of same precedence then evaluate left to right' this rule is not needed. Even if we go from right to left or do it some other way still it gives the same solution.
You are 100% correct.
However, going L to R reduces errors. So it's generally better to teach that variety of the order of operations for that reason alone.
Many make the mistake of
10 - 8 + 2 = 10 - 10 = 0
Going R to L or doing A before S incorrectly when it's clearly
10 - 6 = 4 if you go R to L or A before S.
Same with M and D.
16/8×2
R to L or M first is
16/4 = 4
R to L or M first done incorrectly is
16/16 = 1.
I've seen a lot of people make those errors. With L to R those errors can't happen.
Prevention is better than cure.
Exponent: 3^3 = 27
Inside 💠 the Brackets: 8 - 5 = 3
4 × 3 = 12
27 + 12 ÷ 6 = 27 + 2 = 29
Multiple and Division ➗ are the same
So Should be 29
29
The plus sign makes this one easy. I had to add something to the 27. Anything after the plus sign had to be treated completely on its own. 12/6 has been 2 for as long as I remember..... So easy ........ Took 3 seconds.
This is relatively easy for these kinds of questions, the problem begins when you must choose an order for multiplication and division as calculating them in different order would then result in different answers.
e.g. try 4 ÷ 2(1+1)
If using the "straight across" method proper above (PE[>>>MD][>>>AS]/BO[>>>DM][>>>AS], using the [>>>__] to indicate Left to Right):
4 ÷ 2(1+1)
4 ÷ 2(2)
4 ÷ 2 × 2
2 × 2
4
Using the method I thought was going to be used:
4 "over" 2(1+1)
4 "over" 2(2)
4 "over" 4
1
Asian : what is this grade 1 lesson
I'm 15 and got it right. Guess my teachers did a great job and I understand it perfectly. 👍
In my neighborhood, someone on NextDoor posted a similar math problem, which over half of the people got wrong - simply going left to right, ignoring the order of precedence. When 2 or 3 of us pointed out and explained the correct answer, one person claimed that order of precedence for math problems isn't clearly defined because calculators don't know about it.
This is akin to claiming that decimal points aren't clearly defined because slide rules don't keep track of them.
I informed this person that order of precedence was defined by mathematicians long before calculators were invented and that it's the responsibility of the user to know how his or her calculator works and to present the problem to the calculator in such a way that order of precedence will be followed. At last report, this particular neighbor is doubling down on his claim that calculators are the final arbiters of mathematics rules and I've given up on trying to explain to soneone who's determined not to listen.
Got it right just by looking at the thumbnail, just use order of operations and every problem you should get right
Is there a calculator app available that can solve pretty much any problem? The one I use on my iPhone gave me the correct answer for this problem, but some types of problems it won't solve. I figure this is due to 1) my lack of advanced math skills in general, and/or 2) the lack of available functions in my app du jour.
I'm going to assume that most people got 6.5 wrong because of how the calculator calculated it. If the calculator they were using made it 3^3 + 4(8-5) / 6, instead of the division symbol, then perhaps the calculator automatically calculated out everything on the numerator first, and then divided all that by 6.
I almost fell for it, but caught myself mid-calculation and adjusted my process. Glad I went for 29.
Great video, but instead of using a RUclips poll to gather info on something like this, try something that’ll only let you choose once. People can change their answer in a RUclips poll.
I'm 62. Took a minute or so to recall the order of operations, but I'm happy to say I did it right
The real mistake generally is doing the math too quickly. Tests are generally timed, and people don't want to take time on any given post when scrolling social media feeds.
true, but in this example there really isn't much excuse for picking 6.5. it barely takes much time and since the poll is multiple choice you can easily estimate and eliminate (answer must be larger than 3^3 and cannot be .16 leaving only 27.5 and 29 which is obvious). 40% is just absurd.
Good reminder how important Order of Operations is for accurate computations.
Remember P.E.M.D.A.S.
ORDER OF OPERATIONS
I learned this in early middle school. I didn't know People were learning this in late high school...
The most common mistake people make now is with the division sign. Eg. 2/3*6=?
If you go left to right it works fine but you don’t have to, you can do it in any order. You just have to realize that the division symbol is attached to the value after it. If I go right to left, I don’t do 3*6, I do ➗3*6, or 1/3*6, or 6/3. This equals 2, so the equation becomes 2*2=4. Going left to right ends up with the same answer.
I was not even the slightest bit confused by this question. I knew the order of operations and came up with 29 immediately.
I can only refer to Wikipedia:
The division sign (÷) is a symbol consisting of a short horizontal line with a dot above and another dot below, used in Anglophone countries to indicate mathematical division. However, this usage, though widespread in some countries, is not universal; it is used for other purposes in other countries and its use to denote division is not recommended in the ISO 80000-2 standard for mathematical notation.[1]
Exactly.
It shouldn't be used anymore.