John, Long story but I love your courses I just discovered and subscribed too. Here I am, a 67 year year young, Nana. I struggled so much in Algebra in 9th and 10th grade grade. That was back when 7th -9th were jr. high and 10th - 12th was high school. I barely passed. I felt “Less than” and trapped in an algebra world of not even understanding where to start with an equation. A veil of confusion closed before my eyes. I could have taken a basic math class in high school and took algebra again being determined to “Get it”. I had a very good career and am married to an electronics systems engineer who accepted me even with my weakness in algebra.😊 I came upon your courses because I met a young woman who has been married for less than 20 years with no high school diploma and no GED does not work away from home and nothing they own is in her name…. hope to point her in the direction of getting an education. I googled the Order of Operations and see that it was developed in the 1600,s. I was in 9th grade in 1969… I do not remember being taught PEMDAS or Order of Operation but they must have… I was not a talker in class, in fact pretty quiet, I was worried about being called on. My 50th class reunion is next year. I want you to know, you are making a difference in how I feel about my Algebra abilities. I no longer feel “Less Than” . Thank you! ❤ I will keep watching and giving you a 👍🏻.
I found your site by accident. I am reviewing my math skills to help my 6th grader. I made the SAME common mistake you mentioned. I did NOT follow the order of operations concerning the left to right process for multiplication and division. I didn't realize how much I had forgotten. My old mind is waking up...thanks to your video. Now....if I could get my 6th grader to watch and REALLY listen. Within 10 seconds of the video I saw the "distant tuning out" gaze in her eyes.
I finally understand PEMDAS, I would always multiply first then divide or add first then subtract. I was doing what the teacher said so I thought. MD or AS. Left to right what ever comes first Multiply or Divide, Left to right what ever comes first Add or subtract. Grown adult and now I finally understand. My teachers understood how to do math but didn't know how to teach math. How a student in middle school or high school doesn't get at least a B+ in their classes with all the tools they have like the internet at their fingertips is puzzling. My goodness if I had the internet when I was a kid I believe I would have been an honor student. The internet is like your personal tutor. Thank you for making this video.
Just found your channel and love it. I am a 71 year old grandma and I am following your channel in order to keep my brain working . Thanks so much. I do not remember PEDMAS . Maybe if I had I would have done better in Math in highschool!!!! 🙂
I love math. It’s been 40+ years since I had a class. Last year my daughter went back to college and came to me for help with math. I had to refresh my brain. And it reminded me of how much I love math.
i remember how i struggled so bad with this in 7th grade, then i finally got it..here i am 25 years later going back to college and this is the first course i have to take. i will be following for the break down of different math problems. thank you
Thankyou --now I understand(74 yrs old )---never used square or box brackets in African colonial high schools-(1965) still --I am a hopeless mathematician --but I never give up!--sometimes I get lucky !
I really just watched this video thinking I was gonna have some epiphanic out body experience because I missed ONE little crucial detail in school. Nope, watched the whole video and confirmed that, yes, I know the order of operations. All hail the almighty algorithm for bringing is learning opportunity to my feed. Keep up the good fight, teach.
He is so right about the notes. Learn the math, really learn it. Sure, it'll be good for college acceptance. I went a different way and struggled later. Went to work with crew building a new auto manufacturing plant. Believe me, wished I was more proficient at math while I was there. One hobby I have is Hotrods and building the engines. My point, one was welding and turning wrenches for a living,one is just something I like doing when not at work. Good math skills is important in both circumstances by making both easier, profitable, engaging and efficient. So in closing, Learn the math, Really learn it. I wish I had...
I'm 52 years young... I'm watching your videos for... well, just for the sake of it (Just like I'm reading a book on the History of the United States for my health). Actually I started with some of the calculus stuff because I face the (daunting) task of Business Calculus and never had a calculus class before. That said, I DO NOT EVER (even in College Algebra) remember an instructor telling me that you basically "Group" MD and AS to the point that you can do one before the other. Wow. I learned something today. Thanks, John.
Excellent discussion, as usual. Your discussions are always worth their weight in gold. Some Instructors/Professors rush through the Math fundamentals. You have a great gift to be able to explain any Mathematics problem. I am reviewing your RUclips presentations because it really increases my knowledge. I have learned a lot from your presentations. Keep up the good work. America needs a guy who can explain complex Algebra/Geometry/ concepts. Well done, John. Thanks, Rick Starr
Thank you, your videos are informative and refreshing. You explain OoO in a way that’s easy to understand. Respectively, your like the bob ross of mathematics. Great content!
Woow now I will never be scared of oder of operations I'm 52yrs trying to assist my nephew you are really good instructor you know what you are doing thank you with this vhanel
Thank you for this. It's been a LOOONNNNGGG time since I've been in high school. So good to review this. The first set of brackets in the numerator messed me up. It was so much easier when we were younger. Used to love mathematics. Now I have to worry about bills and mortgages. PEDMAS helps. Left to right even more. :)
I love math but I have to practice them more I am 63 years old it is never to late to learn math is like a therapist for my brain I appreciate you for reminding me of something that I had forgotten thank you.
For all who are asking about the exponent being on the outside instead of the inside, it could be placed on the inside like this: 3(2^2) and you would still arrive at 12. For those who see this 3(2)^2 as resulting in 36, please note that the exponent is associated with the base 2 ONLY, not the 3. Therefore, 3(2)^2 becomes 3(4) = 12. Also, as a caution you don't want to be tempted to multiply the 3 with the 2 first, before raising to the power of 2. That would violate the Order of Operations. If you wanted to write a problem that includes the 3 in on the exponent, you would have to write it something like this: [3(2)]^2. Now, EVERYTHING on the inside gets raised to the power of 2, and you have (6)^2 = 36. I hope that helps. The instructor in the video knows his stuff and is very good at teaching. Bless him! We can always use good math teachers.
...well actually in the case of 3(2)^2 its equal to 3(2^1)^2 wich is equal to 3(2^2)^1 by exponent rules, therfor in this case it doesent matter... and 3(2^2) is also therfor equal to (3/2)(2^3)^1 a(b^c) = (a/b)(b^(c+1))^1 [a and a/b are operands to the following parenthesis]
Hi John this was quite straightforward, I am glad I did in my head fairly quickly considering I am 77. It’s obvious brackets first then from left to right times or divide whichever is first.
Iam not well educated in math but I love this problem. I followed your approach and then copied your problem and thenworked it out following your example step by step.
That was me who said the 2-5=3. I could not understand the negative thing until I went back to college about 7/8 years ago - the oldest student in class, but my teacher was rooting for me, patience but didn't give me any breaks. I had to work for it!!! I thought I had it down packed, but here we are again. I had to draw the negative/positive ruler. Order of Operations were challenging but intrigued me for some reason, so I liked doing them. Thanks for sharing your take on it. PEMDAS (the phrase) ... didn't learn until my years at Baker College - the whole class said it / I looked around like WHAT!!!
Rochelle, it might help to rewrite (2 - 5) as (2 + -5). You can do this because Subtraction is merely "Adding the Opposite". In the case of (2 + -5), consider that any positive number represents a deposit and any negative number represents a withdrawal from your checking account. Now, let's say that you deposit $2 in your checking account and that is your current balance. Then you later withdraw $5. Where are you? You are $3 overdrawn. Therefore, your answer is -3. Another way to look at (2 + -5) is to think of a tug-of-war challenge. The positive team has 2 men pulling toward that direction; the negative team has 5 men pulling in the other direction. Now ask yourself, "Which team will win?" The negative team will win because it dominates (has more men on its team). How many more men does it have......3! So the negative team will win by 3 and your answer is -3.
I can’t believe that I actually got it right. But I thought I got it wrong because of the -3/4. I never had any confidence in my math skills because English being my second language there was always a lot that was lost by not understanding English. But apparently I was paying attention. Anyway I wish I has a teacher like you when I was growing up. Also I am learning a lot and refreshing my memory. Thank you
This has been interesting I am from across the pond. Over here we used B.O.D.M.A.S until recently now its B.I.D.M.A.S both the same thing. B is brackets, O is order I is indices like you said just means power, D is division, M is multiplication, A is addition and S is subtraction. Just thought I would put this here incase this helps someone.
50years ago, we had a math inspirational presenter (he didn't teach or instruct, he inspired us by his methods of exposing our class to the principles of mathematics). He had several methods of grading our tests, by answer, how we arrived at that answer, and if we had made mistakes we could take the test back, we had the night to find out what we did wrong, show him the correct answer and solution at next class and he would give us a half point more for each wrong answer that was righted. He believed that correcting your own mistakes will dramatically advance your skills. each m
You did have to verbally explain your process to your teacher the next day for your additional half-point, correct? Nowadays, I just feel kids would go home, get help from their parents with the problem, still not fully understand, and (based on how I read your post) get a half-point more on their grade simply by turning in a paper showing that “2 + 2 = 4” where the student had accidentally written “2 + 2 = 5” the class before.
I thought I could knock this off no problem-wrong. I didn't't finish division before multiplication in the denominator and got -3! Thanks for correcting my "Aunt Sally."
BTW, the explanation was spot on and the answer was absolutely correct... just need to HELP your students by NOT supporting misleading visuals right off the bat. Make the rules clear visually from the start. TEACH them how to visually recall proper orders. In reference to the guy that called you 'the Bob Ross of math'... present a proper 'Happy Little Tree' to your students 😊... not an elm that you then call a pine. Help them remember the pine!
I appreciate that you show it slowly step by step and, yes, I multiplied 6x6 and got 36 which was incorrect. Comprehension doesn't happen in the wink of an eye.
Just one edit (and it may be my brain causing the issue): When you went to “3(2)^2 / 6 - 5” you went straight to E by saying there was no more parentheses. However, there was still a “2” in parentheses. So while doing 2^2 was correct, I think you should have asked: “Is there anything left in parentheses ( ) or brackets [ ] that needs to be simplified? No, there is not. But there is a 2 in parenthesis so 3(2)^2 means we only raise the 2 to the power of 2 because “2” is the only number in parentheses “P” and the power “E” of 2 only deals with the “P” in this instance because of PEMDAS.” A little long winded but TLDR: There still was a parentheses to deal with after you simplified 3(2)^2 / [ 3 x 2 ] - 5 into “3(2)^2 / 6 - 5 “.
If there is nothing in the parentheses then there is nothing to solve, so they can be ignored. It could have been simplified to 2^2 from the start but then you'd need to write 3x2^2/[3x2]-5 but this was a test on the use of parentheses with powers as well.
Thank you. I'm getting better the more I watch. Previously my eyes would be crossing, and I'd be so immediately frustrated, feel panicky, and throw my hands- up.
Love the explanation! One suggestion: the reason we can do the numerator and denominator independently is that both represent IMPLIED parentheses! So many students used to enter expressions like this into calculators incorrectly that calculator manufacturers starting making “stacked fractions” to help eliminate grouping mistakes! So technically, the stuff in the numerator is in a parentheses and the denominator too!
@@andrewm6424 if I asked, “What is 10 divided by the sum of 2 and 3?” Lots of students would mistakenly enter this into their calculator like this 10/2+3 without using parentheses and get 8. But the correct answer is 2 and should have been entered as 10/(2+3). So many students forget to use parentheses in examples like this that calculator manufacturers started providing “stacked fractions” indicated by one box on top divided by one box on the bottom to help students. In our example, a student would enter 10 in the top box and then arrow down to the bottom box to enter 2+3. Basically whatever is in the top box would be divided by what’s in the bottom box, but most importantly it ELIMINATES students having to enter parentheses. I hope this answers your question.
@@ti84satact12 You stated the problem incoprrectly. You SHOULD have asked. "What is 10 divided by the quantity 2+3?". "by the qunantity", expressly means contained within paranthesis. The way you stated the problem, is NOT 10/(2+3)., but 10/2 + 3 = 5 + 3 = 8. Dont blame the student, when you mistated the problem.
Since you mentioned top 5 mistakes in solving problems, What are the Top 5 areas of mistakes? I'm guessing Order of Operations as you said is one & suspect signs positive/negative are a 2nd. BTW, I am old school like you mention frequently but more math teachers should watch your videos to help them present math to students! Thanks for helping me catch up in mathematical areas I either missed or was never taught!
Thank you! At 55+ years old, this always stumped me in school! Appreciate the simple basic break down. BTW, i noticed most of us commenting, are 50+ , do they still teach this in todays schools?, Is it still part of testing? Just wondering?
Exponents & roots are same 'level' & are derived from Divide & multiply which are same 'level', which are from + & - The orders do exponent, mult, add follow the order of complexity & Same level operations are done like reading a word, left to right. Parenthesis are grouped by the symbol so do them first, then in decreasin order of complexity (exp & roots are most complicated, followed by * /, which is from + -) This is a little more confusing than an acronym but you'll never forget it, never have to remember the acronym either, as it has internal logic. Good luck!
I love your comment that "it has internal logic". I think that is what individuals who do well in math realize. Math MUST make sense and it does not break its own rules. You can trust it. If you learn math from a perspective of, "Why is the rule, the rule?" then you can derive a deeper understanding, and it all becomes intuitive. I have never quite understood why so many find math to be difficult. I believe that all it takes is to "live with it" for a while and you are bound to become more familiar with it on an intimate level. That is when you make discoveries and become more creative at solving math problems. You can then throw many of the rules away and proceed with pure logic. If people can learn how to operate the features on their smartphones, they can learn fractions.
Thanks for explaining this. I was always a C or C- student in math class...I just didn't get it. But after you explained PEMDAS....I came up with the correct answer...-3/4. BTW...it has been 39 years since I graduated. My biggest math lesson in life has come with owning my own company. If I made a mistake with math now...it costs me $$$...huge motivator.
As an adult, I discovered that I enjoy learning math. When I was in junior high and high school I thought I had a block against math but actually, I never heard a word my teacher said. I was more interested in who was sitting next to me, what they looked like, what I looked like, etc. etc. I would make much better use of those math classes now!
Well explained....even that my son's teacher taught them the order of operation, she was not clear about doing the operation from left to right on each group of operation ....liked and subs....thanks a lot.
The big fraction bar at the beginning messed me up. Thanks for teaching that we should simplify its numerator and its denominator separately! Great video, sir!!!
The big fraction bar implies PARENTHESES for the numerator and denominator. Calculator manufacturers started offering the “stacked fractions” to eliminate confusion when students were trying to enter an expression!
I got the correct answer so I guess I haven't forgotten everything (I'm 74) I spent many years as a computer programmer in different languages. It has always intrigued me how different the problem looks when you write it in one line of code. Easy enough to duplicate the hand written version until you get to the need to add a grouping so the computer knows to treat the numerator and denominator as two separate terms. Do you have a video that discusses what changes need to be made to this problem for a computer to understand?
I was a compiler writer and used many languages. Frankly I can't remember the order of operations as it changes from language to language. I always explicitly use parenthesis to force the order of operations that I want. I like APL order of operations, which is strictly left to right honoring parenthesis. (Cobol, RPG, Fortran, C, C++, Java, SmallTalk, PL/1, Rexx, APL...). I wonder how many programmers know that floating point is not necessarily associative ie A + (B+C) is not necessarily the same as (A+B) + C.
@@bobshenix Math is indeed math, but order of operations is not inherent to math itself but instead is just a set of conventions for achieving a shared understanding of the meaning of written formulas. Wikipedia has a very nice article on the topic, which covers numerous differences in the implementation of certain aspects of order of operations among various widely used programming languages, calculator brands (and models), spreadsheets, etc. One important and not widely known area of inconsistency is sequential exponentiation such as 2^3^2, which is evaluated as (2^3)^2 = 64 or 2^(3^2) = 512 depending on the platform. Fortunately, one can (and should) use parentheses to resolve or avoid this and any other ambiguities or inconsistencies.
The expression 3(2)^2 is ambiguous. Does it refer to the product of 3 and 2 being squared or does it refer to the 2 being squared? If it refers to the 2 being squared it should be written as 3(2^2).
Thanks for the explanation. Somehow, I cannot recall being taught that in middle school (1968 - 1970). We used parenthesis for every part of the calculation in order "compartmentalize" each operation. I am aware that the order of operation was developed long before my middle school years, but I imagine it was not universally taught back then.
You are not alone. Math teachers, insisting that math is logical, write the problems on the board from left to right. Then, because math isn't really logical and they all seem to have taken an oath not to reveal the truth, they hatched this out of order nonsense and call it "order of operations." The catch, of course, is that math is not done in the same order written.
I went to college in the 70s and it was taught then, but it appears someone is trying is trying to trick people into a new order of operations. Math is precise and they're is not two answer for this problem. the answer is -3
I was one of those "mistakes" you speak about with the first operation of the numerator. It was at this point in school I got lost, and no one was able to rerail me. My question to this day is still: if 3(2)sq MEANS just the 2 is squared, why in the name of the universe is it not written: 3(2sq)???? And please don't say 1) because it just is, OR 2) those are the rules - because it (still) doesn't make sense.
I think you have to think of any non-grouping parentheses as multiplication operators (x or *). If you replace the (2) with 3 x 2 and keep the exponent with the 2, it makes more sense to interpret it as 3 X 4. It's confusing because of the P in PEMDAS being "translated" as "parentheses" when it doesn't necessarily mean that.
This is the first thing that I had problems with. Does some kind of rule take care of the 3(4)² squared part? I take it that the parens around the 4 means only the 4 is to be squared, in other words any numbers occurring inside the parens would be squared first? Is that it? And then we multiply that with 3, as in 12? How exactly do we know it isn't instead 3 times 4 squared? Squaring the whole thing, which would be 144? If it was 3 times 4 squared, I take it, it would be written like this: (3 x 4)² ? Is that right?
Hi, I am a UK viewer of this video. I have always loved maths, and as an 83 year old man, would like to keep my old brain a bit more active. I wish to revise what in the UK is 'A'level maths, I don't know what the American equivalent is. Do you offer something which I could use? I find most Maths Textbooks a little daunting at my age, so I need something simple, which it appears your courses might provide. If so, what would you suggest, how much would it cost, and would it be possible to view some of the content before purchase. Many thanks. Terry Davis
When I taught it I always stressed that when dealing with the M & D or A & S, it can be done in any order as long as the "sign of operation" stays with the term (number). For example: A&S > 6-5 (or +6-5) equals -5+6 M&D > 8/4x2 is equal to 8x2/4 with answer of 4. Note: There is no bracket around the "/4x2" because the question would be written 8/(4x2) which is wrong.
@@Tata-dj6xo PEMDAS doesn't mean multiplication first and then division comes after. It means multiplication and division (as they occur) from left to right
Hahahaha, i made that mistake with the Denominator, and got zero. Then realised left to right, and got the correct answer. Thanks for a great channel. Secrets i never learnt at school. Well, the other kids did, but i missed out on that CRUCIAL week due to flu. 😔
PEDMAS (not PEMDAS) will give you the correct answer every time, without needing to remember the left-to-right rule. In other words, doing division before multiplication always works.
If our math teachers in the Phils had taught us in college just like the way you do then most of us students could have got perfect score in the quizzes. On the contrary, our teachers- engineers tried to make it difficult for the students to understand the lessons by not explaining the concept first but go directly to the problem without letting us know what kind of animal is that or what or when to use that formula or method. In sum, our teachers don’t know applied concept of teaching thats made students confused let alone frustrated of not knowing the lessons which left us students to research and learn on our own making the teacher useless to us.
I can't believe that I have not done equations since school 50 years ago ago and I can remember please excuse my aunt Sally, wow what a blast from the past.And of course always read a equation from left to right.
Thank you for the clear explanation here although, to be honest, the only bit I wasn't sure about was the 3 (2) squared bit. Is that 3 x 4 = 12 or 6 squared = 36 The rest I knew.
John,
Long story but I love your courses I just discovered and subscribed too.
Here I am, a 67 year year young, Nana.
I struggled so much in Algebra in 9th and 10th grade grade. That was back when 7th -9th were jr. high and 10th - 12th was high school.
I barely passed. I felt “Less than” and trapped in an algebra world of not even understanding where to start with an equation. A veil of confusion closed before my eyes. I could have taken a basic math class in high school and took algebra again being determined to “Get it”.
I had a very good career and am married to an electronics systems engineer who accepted me even with my weakness in algebra.😊
I came upon your courses because I met a young woman who has been married for less than 20 years with no high school diploma and no GED does not work away from home and nothing they own is in her name…. hope to point her in the direction of getting an education.
I googled the Order of Operations and see that it was developed in the 1600,s.
I was in 9th grade in 1969… I do not remember being taught PEMDAS or Order of Operation but they must have… I was not a talker in class, in fact pretty quiet, I was worried about being called on. My 50th class reunion is next year.
I want you to know, you are making a difference in how I feel about my Algebra abilities. I no longer feel “Less Than” . Thank you! ❤ I will keep watching and giving you a 👍🏻.
I'll 😅😅😊
Excellent - I am 60 years old and never too old to learn!
I am 76 and I'm learning over again myself.
Same here!
Loved it! ♥️
congratulations darcy ur on the right direction knowledge is freedom
Ditto - me too!
I found your site by accident. I am reviewing my math skills to help my 6th grader. I made the SAME common mistake you mentioned. I did NOT follow the order of operations concerning the left to right process for multiplication and division. I didn't realize how much I had forgotten. My old mind is waking up...thanks to your video. Now....if I could get my 6th grader to watch and REALLY listen. Within 10 seconds of the video I saw the "distant tuning out" gaze in her eyes.
I finally understand PEMDAS, I would always multiply first then divide or add first then subtract. I was doing what the teacher said so I thought. MD or AS. Left to right what ever comes first Multiply or Divide, Left to right what ever comes first Add or subtract. Grown adult and now I finally understand. My teachers understood how to do math but didn't know how to teach math. How a student in middle school or high school doesn't get at least a B+ in their classes with all the tools they have like the internet at their fingertips is puzzling. My goodness if I had the internet when I was a kid I believe I would have been an honor student. The internet is like your personal tutor. Thank you for making this video.
John this is my 3rd week listening to you. I learned more in 2 weeks than I did my entire senior year in high school. Thanks
I wish I had a math teacher like you in school. Thank you!!
Just found your channel and love it. I am a 71 year old grandma and I am following your channel in order to keep my brain working . Thanks so much. I do not remember PEDMAS . Maybe if I had I would have done better in Math in highschool!!!! 🙂
I love math. It’s been 40+ years since I had a class. Last year my daughter went back to college and came to me for help with math. I had to refresh my brain. And it reminded me of how much I love math.
It feels like "coming home" at times.
I’m a 70 year old refreshing my math knowledge. I nearly fell asleep waiting for the answer, but it did remind me of my basics. Thank you n
i remember how i struggled so bad with this in 7th grade, then i finally got it..here i am 25 years later going back to college and this is the first course i have to take. i will be following for the break down of different math problems. thank you
I am 63 years old I am ready to take a math algebraic course and I really love the way you make me understand it. Thank you very much
Thankyou --now I understand(74 yrs old )---never used square or box brackets in African colonial high schools-(1965)
still --I am a hopeless mathematician --but I never give up!--sometimes I get lucky !
Your demeanor is superb. I majored in math years ago. It's a hobby now. Solving various problems are relaxing. Thanks for your service.
Why is the exponent not in the. Brackets?
I wish we had this kind of access when I was learning this stuff 45 years ago
MR. TabletClass Math, thanks for explaining and analyzing PEMDAS with an excellent example.
I really just watched this video thinking I was gonna have some epiphanic out body experience because I missed ONE little crucial detail in school. Nope, watched the whole video and confirmed that, yes, I know the order of operations. All hail the almighty algorithm for bringing is learning opportunity to my feed. Keep up the good fight, teach.
He is so right about the notes. Learn the math, really learn it. Sure, it'll be good for college acceptance. I went a different way and struggled later. Went to work with crew building a new auto manufacturing plant. Believe me, wished I was more proficient at math while I was there. One hobby I have is Hotrods and building the engines. My point, one was welding and turning wrenches for a living,one is just something I like doing when not at work. Good math skills is important in both circumstances by making both easier, profitable, engaging and efficient. So in closing, Learn the math, Really learn it. I wish I had...
I'm 52 years young... I'm watching your videos for... well, just for the sake of it (Just like I'm reading a book on the History of the United States for my health). Actually I started with some of the calculus stuff because I face the (daunting) task of Business Calculus and never had a calculus class before.
That said, I DO NOT EVER (even in College Algebra) remember an instructor telling me that you basically "Group" MD and AS to the point that you can do one before the other. Wow.
I learned something today. Thanks, John.
Excellent discussion, as usual. Your discussions are always worth their weight in gold. Some Instructors/Professors rush through the Math fundamentals. You have a
great gift to be able to explain any Mathematics problem. I am reviewing your RUclips presentations because it really increases my knowledge. I have learned a lot from your
presentations. Keep up the good work. America needs a guy who can explain complex Algebra/Geometry/ concepts. Well done, John. Thanks, Rick Starr
Thank you, your videos are informative and refreshing. You explain OoO in a way that’s easy to understand. Respectively, your like the bob ross of mathematics. Great content!
Woow now I will never be scared of oder of operations I'm 52yrs trying to assist my nephew you are really good instructor you know what you are doing thank you with this vhanel
Thank you for this. It's been a LOOONNNNGGG time since I've been in high school. So good to review this. The first set of brackets in the numerator messed me up. It was so much easier when we were younger. Used to love mathematics. Now I have to worry about bills and mortgages. PEDMAS helps. Left to right even more. :)
I love math but I have to practice them more I am 63 years old it is never to late to learn math is like a therapist for my brain I appreciate you for reminding me of something that I had forgotten thank you.
No one has explained it like you! I wish you were around when my kids went to school! Thank you for sharing your knowledge!
For all who are asking about the exponent being on the outside instead of the inside, it could be placed on the inside like this: 3(2^2) and you would still arrive at 12. For those who see this 3(2)^2 as resulting in 36, please note that the exponent is associated with the base 2 ONLY, not the 3. Therefore, 3(2)^2 becomes 3(4) = 12. Also, as a caution you don't want to be tempted to multiply the 3 with the 2 first, before raising to the power of 2. That would violate the Order of Operations.
If you wanted to write a problem that includes the 3 in on the exponent, you would have to write it something like this: [3(2)]^2. Now, EVERYTHING on the inside gets raised to the power of 2, and you have (6)^2 = 36. I hope that helps. The instructor in the video knows his stuff and is very good at teaching. Bless him! We can always use good math teachers.
...well actually
in the case of 3(2)^2 its equal to 3(2^1)^2 wich is equal to 3(2^2)^1 by exponent rules, therfor in this case it doesent matter... and 3(2^2) is also therfor equal to (3/2)(2^3)^1
a(b^c) = (a/b)(b^(c+1))^1 [a and a/b are operands to the following parenthesis]
I'm 63 and I'm so glad this is still very easy for me ! thank you. Love your videos
Hi John this was quite straightforward, I am glad I did in my head fairly quickly considering I am 77. It’s obvious brackets first then from left to right times or divide whichever is first.
Iam not well educated in math but I love this problem. I followed your approach and then copied your problem and thenworked it out following your example step by step.
That was me who said the 2-5=3. I could not understand the negative thing until I went back to college about 7/8 years ago - the oldest student in class, but my teacher was rooting for me, patience but didn't give me any breaks. I had to work for it!!! I thought I had it down packed, but here we are again. I had to draw the negative/positive ruler. Order of Operations were challenging but intrigued me for some reason, so I liked doing them. Thanks for sharing your take on it. PEMDAS (the phrase) ... didn't learn until my years at Baker College - the whole class said it / I looked around like WHAT!!!
Rochelle, it might help to rewrite (2 - 5) as (2 + -5). You can do this because Subtraction is merely "Adding the Opposite". In the case of (2 + -5), consider that any positive number represents a deposit and any negative number represents a withdrawal from your checking account.
Now, let's say that you deposit $2 in your checking account and that is your current balance. Then you later withdraw $5. Where are you? You are $3 overdrawn. Therefore, your answer is -3.
Another way to look at (2 + -5) is to think of a tug-of-war challenge. The positive team has 2 men pulling toward that direction; the negative team has 5 men pulling in the other direction. Now ask yourself, "Which team will win?"
The negative team will win because it dominates (has more men on its team). How many more men does it have......3! So the negative team will win by 3 and your answer is -3.
Thank you, sir. I learned a tremendous amount from my first session with you. Thank you.
I have to relearn math to take the ASVAB. I am grateful to your videos! Thank you so much for this!!!!!
Thank you tremendously for helping me on my journey to pass the Math portion on the GED..
I am "old school" and was limited to BODMAS years ago as against PEMDAS. Thank you for your thoughtful way of explanations.
What was the order of operations for BODMAS?
@@joyebriggs bracket orders of,division,multiplication,addition and subtraction
What is wrong with Bodmas should stick to that
BOMDAS and PEMDAS are the exact same thing :/
Thanks for the clear explanation.I am also a senior citizen. I learnt through BODMAS and calculated also using PEMDAS.Both are correct.Thank you.
They are just different words for the same things, so yes .. the answer will be the same :/
Where were you when I was in school 🤣 I never did understand this stuff, I’m 60 years old and now I get it, thank you 👍
I can’t believe that I actually got it right. But I thought I got it wrong because of the -3/4. I never had any confidence in my math skills because English being my second language there was always a lot that was lost by not understanding English. But apparently I was paying attention. Anyway I wish I has a teacher like you when I was growing up. Also I am learning a lot and refreshing my memory. Thank you
The correct answer is -3
This has been interesting I am from across the pond. Over here we used B.O.D.M.A.S until recently now its B.I.D.M.A.S both the same thing. B is brackets, O is order I is indices like you said just means power, D is division, M is multiplication, A is addition and S is subtraction. Just thought I would put this here incase this helps someone.
50years ago, we had a math inspirational presenter (he didn't teach or instruct, he inspired us by his methods of exposing our class to the principles of mathematics). He had several methods of grading our tests, by answer, how we arrived at that answer, and if we had made mistakes we could take the test back, we had the night to find out what we did wrong, show him the correct answer and solution at next class and he would give us a half point more for each wrong answer that was righted. He believed that correcting your own mistakes will dramatically advance your skills.
each m
You did have to verbally explain your process to your teacher the next day for your additional half-point, correct? Nowadays, I just feel kids would go home, get help from their parents with the problem, still not fully understand, and (based on how I read your post) get a half-point more on their grade simply by turning in a paper showing that “2 + 2 = 4” where the student had accidentally written “2 + 2 = 5” the class before.
@@andrewm6424 This person that was our 1st year marine engineer math instructor.
I was wondering what notepad you use during your class lectures? It look real easy to use.
@@Cedarsea I believe we called it our text book.
I thought I could knock this off no problem-wrong. I didn't't finish division before multiplication in the denominator and got -3! Thanks for correcting my "Aunt Sally."
Most calming to observe the order of operations. Thankyou .
BTW, the explanation was spot on and the answer was absolutely correct... just need to HELP your students by NOT supporting misleading visuals right off the bat. Make the rules clear visually from the start. TEACH them how to visually recall proper orders. In reference to the guy that called you 'the Bob Ross of math'... present a proper 'Happy Little Tree' to your students 😊... not an elm that you then call a pine. Help them remember the pine!
I appreciate that you show it slowly step by step and, yes, I multiplied 6x6 and got 36 which was incorrect. Comprehension doesn't happen in the wink of an eye.
Don't think there's ever been a math teacher better than this dude on the planet. Bro CLEARS khan academy
Just one edit (and it may be my brain causing the issue): When you went to “3(2)^2 / 6 - 5” you went straight to E by saying there was no more parentheses. However, there was still a “2” in parentheses. So while doing 2^2 was correct, I think you should have asked: “Is there anything left in parentheses ( ) or brackets [ ] that needs to be simplified? No, there is not. But there is a 2 in parenthesis so 3(2)^2 means we only raise the 2 to the power of 2 because “2” is the only number in parentheses “P” and the power “E” of 2 only deals with the “P” in this instance because of PEMDAS.”
A little long winded but TLDR: There still was a parentheses to deal with after you simplified 3(2)^2 / [ 3 x 2 ] - 5 into “3(2)^2 / 6 - 5 “.
There was the Paren (2) with Exp. Juxtaposition? 3(2)^2. Couldn’t that be 3(2^2) ? Or 3 • 2^2 ? Grrr??? Link?
If there is nothing in the parentheses then there is nothing to solve, so they can be ignored. It could have been simplified to 2^2 from the start but then you'd need to write 3x2^2/[3x2]-5 but this was a test on the use of parentheses with powers as well.
I’m 75 and as one person had mentioned in your comment
box, that you are never to old to learn, thanks.
Also, can you upload more math word problems?
Thank you. I'm getting better the more I watch. Previously my eyes would be crossing, and I'd be so immediately frustrated, feel panicky, and throw my hands- up.
Love the explanation! One suggestion: the reason we can do the numerator and denominator independently is that both represent IMPLIED parentheses! So many students used to enter expressions like this into calculators incorrectly that calculator manufacturers starting making “stacked fractions” to help eliminate grouping mistakes! So technically, the stuff in the numerator is in a parentheses and the denominator too!
Stacked fractions?
Thanks, did not know.
@@andrewm6424 if I asked, “What is 10 divided by the sum of 2 and 3?” Lots of students would mistakenly enter this into their calculator like this 10/2+3 without using parentheses and get 8. But the correct answer is 2 and should have been entered as 10/(2+3). So many students forget to use parentheses in examples like this that calculator manufacturers started providing “stacked fractions” indicated by one box on top divided by one box on the bottom to help students. In our example, a student would enter 10 in the top box and then arrow down to the bottom box to enter 2+3. Basically whatever is in the top box would be divided by what’s in the bottom box, but most importantly it ELIMINATES students having to enter parentheses. I hope this answers your question.
there is no such thing as implied paranthesis. That misnomer, contributes to a VAST nr of math errors.
@@ti84satact12 You stated the problem incoprrectly. You SHOULD have asked. "What is 10 divided by the quantity 2+3?". "by the qunantity", expressly means contained within paranthesis. The way you stated the problem, is NOT 10/(2+3)., but 10/2 + 3 = 5 + 3 = 8. Dont blame the student, when you mistated the problem.
Since you mentioned top 5 mistakes in solving problems, What are the Top 5 areas of mistakes? I'm guessing Order of Operations as you said is one & suspect signs positive/negative are a 2nd. BTW, I am old school like you mention frequently but more math teachers should watch your videos to help them present math to students! Thanks for helping me catch up in mathematical areas I either missed or was never taught!
77yo granny hier in France. I enjoy these maths lessons. Learn english and maths at the same time.
Excellent example and explanation of this problem!
thank you for helping me remember pemdas, now I am confident that I can do well in my SAT
This is so 👍...now I knw how to solve it. What ever comes first from L-R. Ur the best. Very well explained...ty😊😊😊
Thank you! At 55+ years old, this always stumped me in school! Appreciate the simple basic break down. BTW, i noticed most of us commenting, are 50+ , do they still teach this in todays schools?, Is it still part of testing? Just wondering?
Exponents & roots are same 'level' & are derived from Divide & multiply which are same 'level', which are from + & -
The orders do exponent, mult, add follow the order of complexity & Same level operations are done like reading a word, left to right.
Parenthesis are grouped by the symbol so do them first, then in decreasin order of complexity (exp & roots are most complicated, followed by * /, which is from + -)
This is a little more confusing than an acronym but you'll never forget it, never have to remember the acronym either, as it has internal logic.
Good luck!
I love your comment that "it has internal logic". I think that is what individuals who do well in math realize. Math MUST make sense and it does not break its own rules. You can trust it. If you learn math from a perspective of, "Why is the rule, the rule?" then you can derive a deeper understanding, and it all becomes intuitive.
I have never quite understood why so many find math to be difficult. I believe that all it takes is to "live with it" for a while and you are bound to become more familiar with it on an intimate level. That is when you make discoveries and become more creative at solving math problems. You can then throw many of the rules away and proceed with pure logic.
If people can learn how to operate the features on their smartphones, they can learn fractions.
Thanks for explaining this.
I was always a C or C- student in math class...I just didn't get it.
But after you explained PEMDAS....I came up with the correct answer...-3/4.
BTW...it has been 39 years since I graduated.
My biggest math lesson in life has come with owning my own company.
If I made a mistake with math now...it costs me $$$...huge motivator.
love his voice and style its very kind as well as a smart man very cool
Congratulations from Brazil! Thank you for sharing your knowledge!
As an adult, I discovered that I enjoy learning math. When I was in junior high and high school I thought I had a block against math but actually, I never heard a word my teacher said. I was more interested in who was sitting next to me, what they looked like, what I looked like, etc. etc. I would make much better use of those math classes now!
You’re such a great teacher! Make things so easy to understand. Wish more teachers were like you.
You must have had some god awful teachers.
Well explained....even that my son's teacher taught them the order of operation, she was not clear about doing the operation from left to right on each group of operation ....liked and subs....thanks a lot.
thank you i feel so proud of myself for completing the problem and using step by step
very interesting - my learning came back to me! Thank you.
Thank you. First problem I got right after learning about PEMDASn68 yr young.
I'm 70 years old and a retired programmer and got the correct answer....... -3/4, I've still got it.......yippee.....lol
Ajab khan khattak.This is what we were taught in school.Excellent
Thank you so much! this is really helping me with my nursing math entrance exam :) God bless you!
The big fraction bar at the beginning messed me up. Thanks for teaching that we should simplify its numerator and its denominator separately! Great video, sir!!!
The big fraction bar implies PARENTHESES for the numerator and denominator. Calculator manufacturers started offering the “stacked fractions” to eliminate confusion when students were trying to enter an expression!
I really appreciate these videos. I am sincere when I say they’re about 55 years too late…but ..
I'm nearly 69 and I agree very much with Joanis. Thank you John☘
I got the correct answer so I guess I haven't forgotten everything (I'm 74) I spent many years as a computer programmer in different languages. It has always intrigued me how different the problem looks when you write it in one line of code. Easy enough to duplicate the hand written version until you get to the need to add a grouping so the computer knows to treat the numerator and denominator as two separate terms. Do you have a video that discusses what changes need to be made to this problem for a computer to understand?
Excellent commentary and instruction. THANK YOU!!!😇
Just loved this one.....don't remember it from school...too long ago and anything I did not understand was boring.....xx
You do an amazing job explaining this. 👏 🎉 I wish you were my math teacher in high school.
Wow, thanks a lot for making maths so easy to understand.
Thanks Fellow...🎉 Your really awesome men..
Excellent. I am 78 and I have heard of this but never knew what it meant. Thanks
GET TO THE POINT QUICKER 😏 PLEASE. LESS TALKING
Excellent teacher wish he would have been my teacher. I would have enjoyed math.😃👍🏽💯💯💯💯
Here I thought I was bad at this! Do you have cbest videos? I love how you explain stuff!
This is wonderful to find! Thank you!
Excellent presentation...!!!
... Just became a subscriber! 👍
This is your best one yet.
Hey, I think I know Algebra again. Have been out of school for several years. Thank you! It helps to work with our children on it. 😉👍
I wish you had time to do more examples…@ least, one more. I really enjoyed watching it.
Yes me too. I would loved to see another example 😊
I was a compiler writer and used many languages. Frankly I can't remember the order of operations as it changes from language to language. I always explicitly use parenthesis to force the order of operations that I want. I like APL order of operations, which is strictly left to right honoring parenthesis. (Cobol, RPG, Fortran, C, C++, Java, SmallTalk, PL/1, Rexx, APL...). I wonder how many programmers know that floating point is not necessarily associative ie A + (B+C) is not necessarily the same as (A+B) + C.
Why would order of operations change from one language to another?? Math is math... no?
@@bobshenix agreed
@@bobshenix Math is indeed math, but order of operations is not inherent to math itself but instead is just a set of conventions for achieving a shared understanding of the meaning of written formulas. Wikipedia has a very nice article on the topic, which covers numerous differences in the implementation of certain aspects of order of operations among various widely used programming languages, calculator brands (and models), spreadsheets, etc. One important and not widely known area of inconsistency is sequential exponentiation such as 2^3^2, which is evaluated as (2^3)^2 = 64 or 2^(3^2) = 512 depending on the platform. Fortunately, one can (and should) use parentheses to resolve or avoid this and any other ambiguities or inconsistencies.
Very well stated.
The expression 3(2)^2 is ambiguous. Does it refer to the product of 3 and 2 being squared or does it refer to the 2 being squared? If it refers to the 2 being squared it should be written as 3(2^2).
I am 51 lol, I got it right, I can't believe it. I was always in the lowest math class. Yay I'm going to do these every day.
After so long I understood these operations 🤩🥳
Thanks for the explanation. Somehow, I cannot recall being taught that in middle school (1968 - 1970). We used parenthesis for every part of the calculation in order "compartmentalize" each operation. I am aware that the order of operation was developed long before my middle school years, but I imagine it was not universally taught back then.
You are not alone. Math teachers, insisting that math is logical, write the problems on the board from left to right. Then, because math isn't really logical and they all seem to have taken an oath not to reveal the truth, they hatched this out of order nonsense and call it "order of operations." The catch, of course, is that math is not done in the same order written.
I went to college in the 70s and it was taught then, but it appears someone is trying is trying to trick people into a new order of operations. Math is precise and they're is not two answer for this problem. the answer is -3
@@mokooh3280 How did you get -3?
I am a senior as well. I’ve avoided math most of my life and regret it.😢 Hopefully I can learn now
Looking foward to seeing example in subject matter field.
I was one of those "mistakes" you speak about with the first operation of the numerator. It was at this point in school I got lost, and no one was able to rerail me. My question to this day is still: if 3(2)sq MEANS just the 2 is squared, why in the name of the universe is it not written: 3(2sq)???? And please don't say 1) because it just is, OR 2) those are the rules - because it (still) doesn't make sense.
Because it isn’t (3x2) squared in which case it would be 6 squared.
I think you have to think of any non-grouping parentheses as multiplication operators (x or *). If you replace the (2) with 3 x 2 and keep the exponent with the 2, it makes more sense to interpret it as 3 X 4. It's confusing because of the P in PEMDAS being "translated" as "parentheses" when it doesn't necessarily mean that.
This is the first thing that I had problems with. Does some kind of rule take care of the 3(4)² squared part? I take it that the parens around the 4 means only the 4 is to be squared, in other words any numbers occurring inside the parens would be squared first? Is that it? And then we multiply that with 3, as in 12? How exactly do we know it isn't instead 3 times 4 squared? Squaring the whole thing, which would be 144? If it was 3 times 4 squared, I take it, it would be written like this: (3 x 4)² ? Is that right?
Hi, I am a UK viewer of this video. I have always loved maths, and as an 83 year old man, would like to keep my old brain a bit more active. I wish to revise what in the UK is 'A'level maths, I don't know what the American equivalent is. Do you offer something which I could use? I find most Maths Textbooks a little daunting at my age, so I need something simple, which it appears your courses might provide. If so, what would you suggest, how much would it cost, and would it be possible to view some of the content before purchase. Many thanks. Terry Davis
When I taught it I always stressed that when dealing with the M & D or A & S, it can be done in any order as long as the "sign of operation" stays with the term (number). For example:
A&S > 6-5 (or +6-5) equals -5+6 M&D > 8/4x2 is equal to 8x2/4 with answer of 4. Note: There is no bracket around the "/4x2" because the question would be written 8/(4x2) which is wrong.
Confusing...
Oh dear....don't confuse this old brain...just got the lesson straight ....
multiply and divide in the order they occur, if ÷ comes first then divide, if × comes first then multiply
If we are following pemdas, we should multiply 4x2 which is 8 then we should divide 8 by 8 which leave 1. Therefore, the answer should be -3.
@@Tata-dj6xo PEMDAS doesn't mean multiplication first and then division comes after. It means multiplication and division (as they occur) from left to right
Hahahaha, i made that mistake with the Denominator, and got zero. Then realised left to right, and got the correct answer. Thanks for a great channel. Secrets i never learnt at school. Well, the other kids did, but i missed out on that CRUCIAL week due to flu. 😔
PEDMAS (not PEMDAS) will give you the correct answer every time, without needing to remember the left-to-right rule. In other words, doing division before multiplication always works.
If our math teachers in the Phils had taught us in college just like the way you do then most of us students could have got perfect score in the quizzes. On the contrary, our teachers- engineers tried to make it difficult for the students to understand the lessons by not explaining the concept first but go directly to the problem without letting us know what kind of animal is that or what or when to use that formula or method. In sum, our teachers don’t know applied concept of teaching thats made students confused let alone frustrated of not knowing the lessons which left us students to research and learn on our own making the teacher useless to us.
Except this guy is teaching a fallacy, see my explanation above. 3(2) = (3X2) = 6 Not 3x2 !!
I can't believe that I have not done equations since school 50 years ago ago and I can remember please excuse my aunt Sally, wow what a blast from the past.And of course always read a equation from left to right.
Just a minor point: This is an expression, not an equation.
Thank you for the clear explanation here
although, to be honest, the only bit I wasn't sure about was
the 3 (2) squared bit.
Is that 3 x 4 = 12 or 6 squared = 36 The rest I knew.
I don't understand why 3(2)^2... why not 3x2^2..?
There's no reason to put 2 in (), it's just confusing...
You’re correct BUT some people and textbooks use parentheses to imply multiplication so you should know how to handle this too!
I am 11 year old. I like maths. It is not challenging for me at all. I got the correct answer easily ❤
I did this mentally and got answer in a few seconds. I was taught the 'bodmas' rule in school in SA