I got 165 and did it in my head. I was lucky to get a really good education growing up. I guess it comes down to the luck of where you live and which school you get to go to. Thanks for sharing this lesson.
I am a 77 year old woman who had a couple of very intimidating math teachers in middle school so I never mastered algebra and have regretted it all these years. Thank you for your RUclips channel. I watch it every night on TV and I am determined with your help to finally be able to conquer this and cross it off my bucket list. Thank you, John, for your patient teaching.
@@LivingroomTV-me9oz I am sorry, but algebra is imaginary. It does not exist. What is a number? It is a symbol indicating how many objects, thoughts, concepts, items exist in a given space. (...) is described as the number 3. What is a letter? A letter is a symbol indicating a sound. "A" is a sound. "Three" is a word, a sound made up of letters, but "three" is NOT (...). Just as you cannot add a stone to a board or a piece of paper to a dog, you cannot add, subtract or do anything combining a (...) to a letter! It simply does not work. Yes, you COULD mulch the board and reduce the stone to sand and throw them together, but ultimately microscopically, you will ALWAYS have tiny rocks and wood fibers! I havd explained this many times and nobody seems to understand it.
@@sylvisterling8782what does that have to do with algebra? Sure someone had to come up with the concept of algebra so in that sense it is made up, but math such as algebra has useful applications in real life. Without someone doing the math you wouldn’t have a device to even watch this video. So I guess I don’t understand your point about it being made up.
@@sylvisterling8782 c'mon dude, this ain't no abstract algebra course, it's a video on order of operations. Nobody seems to understand because you're explaining to others based on what you want to hear and not explaining in a form that will compel others to listen. You're basically explaining it to impress yourself, you're not necessarily explaining something because you want others to understand. Algebra comes from "al-mukhtasar fi hisab al-jabr wa al-muqabala" the title of a book written by Abu Ja'far Muhammad ibn Musa al-Khwarizmi (which is also where the word algorithm comes from), colloquially its means "the reunion of broken parts". Originally, letters were not used represent unknowns, rather the algorithms used to solve problems were written out in steps, much like a recipe. Sometimes the algorithms were written out as poetry as a means to help better remember them.
165. Depending on the country, the name of the order of operation may differ, but the concept is the same. I learned BEDMAS... Brackets, Exponents, Division and Multiplication, Addition and Subtraction.
What's the point of a pnemonic (pedmas) to help you remember when all it does it make you do an error if you don't remember that it actually is pe(dm)(as). I would've expected more logic from math people who came up with this.
When I learned the order of operations, it was presented in a graphical form, with the various groupings on separate lines, with an arrow pointing down on the left, with the label, "Simplify," and an arrow on the right pointing up with the label, "Solve." That way it was clear that multiplication and division were in the same class of operations, and addition and subtraction were in a different class of operations from multiplication and division, but were in the same class as each other. The teacher gave extra credit on tests if you drew the graphic on the upper right side of the test paper, and he would indeed occasionally have questions where you were asked to, "Solve," instead of, "Simplify," and to get the correct answer it was necessary to reverse the order of operations. That was over 30 years ago, and I still remember every detail of that graphic, so it was entirely effective.
I have spent my life feeling stupid because I didn’t understand this stuff and now I realise that I just wasn’t taught the basics properly. I wish that I’d had a teacher like you, Sir! My life would have taken a completely different direction. This 62 year old thanks you very much!
I was taught Parentheses in order from left to right, then Exponents from left to right, then, Multiplication and Division in order from left to right, and finally Addition and Subtraction from left to right. Addition and Subtraction were equal in that you don’t prioritize one over the other and same with multiplication and division, you just do whichever appears first so 3x(5+20/2x5) 3x(5+10x5) 3x(5+50) 3x55 165 I’m really not a math fan, but my favorite math classes in school were business math and data analysis & statistics. To me they were fairly simple and the teachers I had were amazing. The business math teacher was a very kind and understanding professor who was very good at explaining it so that you got it the first time and he didn’t even make us get the book, he just read from his own and we all worked the problems out together. My data analysis and statistics professor didn’t make us get the book either and he actually introduced a lot of humor into his teaching style, but he had that really dark and sarcastic type of humor like mine, but he was never mean about it and genuinely cared about helping you learn. With the war on teachers in this country the last few years I really hope they haven’t been burnt out by it, especially since I live in a deep red, but northern red state.
I do agree as per PEMDAS rule.. but application in real world such as physics, chemistry, advance math, engineering does not follow this. juxtaposition is included in the rule. hence your answer is still wrong
Multiplication and division are of equal value and are done in the order that they appear in the equation from left to right; the same is true of addition and subtraction. It should be 3 x (5 + ((20/2) x 5)) = 3 x (5 + (10 X 5)) = 3 x 55 = 165.
The critical clarifying moment that you presented here is the insertion of the simple word "OR" in the PEMDAS sequence. I don't recall ever hearing it simplified that way by any math teacher back in the day or in any other RUclips presentations. I take my hat off to you in thanks, sir!
My teachers never got it to me either. They taught us how to do it but told us to go in order of letters, not multiplication or division. Multiplication, then division is what we were taught. I don't think my teacher was that skilled in math and just tried using the book with the answers in it. You can't teach somebody how to do something if you don't know how to do it yourself though.
This actually shocks me. I remember several teachers saying or. Another way of thinking about it is, if there is a run of multiple and division operations in a row, they all are acting on the first number.
@@brendanh8193 that's still not 100% intuitively clear. Left-to-right is necessary because division is essentially a fractional expression. 1 ÷ 4 and 1/4 is the same thing. Left-ro-right means you resolve the fraction into a whole number before multiplying by a whole number. If you go right-ro-left, you accidentally multiply the denominator by a whole number. The most intuitive way to understand this is 1 ÷ 4 × 5 is to convert it to (1/4) × (5/1). Now you're multiplying two fractions, (numerator × numerator) / (denominator × denominator). This is easier to understand when you have something like 1 ÷ 3 × 5. If you do left to right, 1 ÷ 3 doesn't resolve to a whole number. It's a fraction with repeating decimal .333333... Decimals are weird and confusing, especially repeating decimals. You run into problems of precision using them in calculations which is why representing them as fractional expressions is preferred, especially in equations with irrational numbers (pi, square root of 2, etc).
The important thing to realize is that division is just multiplication by the reciprocal and subtraction is just addition of a negative number. So really it should just be taught as PEMA and perhaps people would be less confused.
I'm 60 and had never heard of PEMDAS or wasn't listening in class. But after 2 previous videos I've watched of yours, I got this correct! Shocked and proud of myself. I wish you were my teacher 45 years ago!
Wow! I hated math, but I remember PEMDAS. I specifically remember the mnemonic, Please Excuse My Dear Aunt Sally =PEMDAS! I teach it to my grandkids today! My granddaughter is gifted in math & way ahead of her peers! She's 10. Proud grandma here, sorry! 🤭
I am older and we were taught the rules for equations; however it was never referenced as PEMDAS or any other acronym. We just remembered it by the function names.
I am so excited! I got165! YES! I do not remember being taught this loooooong ago! (I remembered it from one of your previous videos, I think!). Thanks!
To solve this expression, you need to follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and square roots, etc.), Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right). In this expression: 3 * (5 + 20 / 2 * 5) Let's break it down step by step: First, evaluate the expression inside the parentheses: 5 + 20 / 2 * 5 Now, follow the order of operations within the parentheses: a. Divide 20 by 2: 20 / 2 = 10 b. Multiply 10 by 5: 10 * 5 = 50 c. Add 5 to the result: 5 + 50 = 55 So, the expression inside the parentheses simplifies to 55: 3 * 55 Finally, multiply 3 by 55: 3 * 55 = 165 So, the answer is 165.
Unlesss you are a maths teacher, how on earth could you remember that rule? (I won't say you looked it up). I worked in pensions admin, actuarial, finance and insurance all my life but couldn't recall all that you laid out.
Practical comment: As a 35+ year engineer… just use extra sets of parentheses. Or break it up into smaller parts. Or both. Other people may be looking at your work. Regardless of the correct “rules” it’s better to clearly communicate what you are doing … don’t assume that the other people know the rules as well as you do.
"As a 35+ year engineer… just use extra sets of parentheses." And then everyone would get the same answer and it would not be clickbait. There's dozens of these videos with minor variations so we can argue about it.
Very true, be explicit in how you want the problem to proceed. The best way is to design the problem so that it will give the right answer if it is fed into any computer on the planet. If it will not, then clarify.
As a fellow engineer, (since Mar 1980, 43 years 5 months) I totally agree with you, I haven't even watched this video yet but I can clearly see that the equation is very poorly expressed. Just the part inside the parenthesis can be solved as 55 or 7. I'm leaning towards 7 because the video description shows 3 times ( 5 + 20 / 2 x 5 ) and because it's expressed as a fraction, you should solve the denominator first. Then, you have 5+20/10 or 5+2=7 Making the overall equation 3(7) or 21. Now I'll watch it and I'm probably wrong. Yeah, according to the video, I was wrong. But the fraction 20/2X5 does equal 2 and then, 5+2=7. At least he admits that math teachers do try to trick their students. He says it's to see who was paying attention in class, However, he doesn't go into the actual psychology behind this, which gives you the real reason, they do it to boost their own EGOs. They do it to feel smarter than their students, by tricking them. Tricking them doesn't make them better teachers. Rather, it allows them to ease their own inferiority complex and feel better about themselves (probably because they were called nerds, or geeks, so often in high school). It has nothing to do actually with teaching the students. I hope he was able to boost his own EGO with this video and then, he can feel better about himself. 3(5(20/2)+5) would have been a much better way to express the intent of this equation. It communicates the intent more clearly because you're not trying to trick your intended audience. I gave your comment a like. Have yourself a great day!
Hello, I am British and we use BODMAS, eg Brackets, Of (to the power of), Division, Multiplication, Addition, Subtraction. Using this mnemonic means you don’t have to complicate the process further by having to remember to check on the order of the division and multiplication within the brackets. Division is always carried out first ie before multiplication.
No in Bodmas what you do is based on going left to right in the equation in this case divsion comes first in the equation (going from left to right) so you do division first but if the multiplication came first left to right then multiplication would come first.
@@FranklinThe1You’re right but they’re not wrong. Doing division first always gives the correct answer because it’s simply multiplication by the reciprocal of the number following the division symbol, and it doesn’t matter what order you multiply in. There’s no reason to go left to right. Just understand what division actually is and you’ll be fine. I hate the people just mindlessly repeat rules they’ve learned without understanding them.
I did that totally wrong by addition first and dividing the sum by the multiplied sum. 3(25/10)=7.5. That’s quite a difference. Thanks for reminding me of the order.
This is the way i was taught at school. After four decades in business i never get my figures wrong. I would be interested when and where the maths was changed.
My lord if you were my teacher I would be great at math. Your voice isn't threatening and your teaching is superb. I commend you and I thank you for posting your knowledge and your spirit comes through to teach younger people and adults like myself how to properly understand math. I applaud you, your parents and all of your teachers. 👏🏿👏🏿👏🏿👏🏿🎉😊
Agree ... we need more efficient teachers. I have a friend who is becoming a teacher and she can't spell. That immediately limits her effectiveness as a teacher.
@@nukasnook1561Nothing worse than an illiterate teacher. I had an English teacher about 50 years ago who couldn’t pronounce Yosemite, she called it Yo-see-mite but she was thankful when I told her the correct pronunciation Yo-sim-a-tee.
@@JohnFourtyTwo Another way of saying "Yosemite" is "the most fabulously beautiful place to visit" - especially in the months of May and June when the snowmelt fills the waterfalls and Merced River. Great that you taught the teacher how to say the name of this most wonderful place.
John, I love your math channel. I am a math person as well! Numbers & Math are the universal language. I think we should connect one day, I believe we would get along extremely well! Hope you channel continues to prosper!
Wow, I just realized how much I had forgotten in regards to basic math. Thanks for the video. I got it totally wrong. I worked left to right in the parentheses, then multiplied by 3.
Plus and minus come in which ever order they come first X and : come in which ever order they come first. In this, here is the 4 second easy calculation that ran in my head: 20/2=10 10x5=50 5+50=55 3x55=110+55=165
Yes, 165. Did it in my head thanks to learning from this guy for the last months. Im 60yrs and never learnt this type of math at school. Thankyou. I love Aunt Sally😂.
Sure wish you were my math teacher back in the day. Now I lament that I can’t do math and my brain cracks. I enjoy your videos. I don’t feel that I am not capable. Thanks.
I was part of the 21 answer crowd, unfortunately, but I’m grateful this video explained why I was wrong and how to not make the same mistake again. Thank you. I liked and subscribed.
Another method to help you with PEMDAS (or confuse you more ;-) ) is keeping in mind that a **division is just a multiplication of the inverse value or reciprocal so that will transform your problem to: 3 ( 5 + 20 * 1/2 * 5 ) or 3(5 + 20*.5 * 5) , so now the division disappears and you do left to right multiplications in order first. 3 ( 5 + 10 * 5 ) => 3 * (5 + 50) , 3 (55) = 165 or when you are down to 3*( 5 + 50 ) , you could use the distributive principle you use in algebra of a (b+c) = (ab+ac); (3*5 + 3*50) = (15+150) = 165 to verify that you answer is right. Keep in mind that PEMDAS is just a trick for your to remember order of operations, but as you learn more math there are other tools that will help you gain speed or find easier ways to solve problems that might be more relatable on how your own brain works. This is fine example of how simple arithmetic is a foundation block for algebra, geometry, trigonometry, pre-calc + more. **Note: this is mostly true with integers and rational numbers, you run into some issues later in life in computing, software, with irrational and imaginary numbers like pi. :P
I have been a machinist and a fabricator and a carpenter in my lifetime and I’ve never run up on one situation where I used any equation like this. I couldn’t figure out in school why they were teaching me this and now I’m 52 and still don’t know why.
You might think you have not have used what you learned in math, but you've probably used the logic and problem solving skills you learned without realizing.
@@rthompson7282 It's not so much the basic math is of no use. It's that writing a practical problem in this way is something a non-mathematics professional would never do. Effectively as he mentions around 10:25 it's made in a way that is intentionally deceptive. In most practical applications of math, you end up being held accountable for the result of the use of the math, so if something is written in a way that could seemingly done multiple ways and the wrong one is chosen, liability for the outcome becomes a concern. Mathematician's don't have this issue. Like @larrybuckner8619 mentioned, machinist, fabricator, and carpenter, his head or a coworkers head would be on the chopping block should something unfortunate happen due to writing an equation in this way. At best, this use of presentation in math, is a good example of what NOT to do in terms of learning logic and problem solving skills, because it eschews common logic and practical use in favor of requiring rote memorization and convoluted presentation to create a problem in need of solving, neither of which is of any direct practical use.
I found maths very challenging at school, but I LOVED this video - got it wrong first time, but I learnt a lot! Great explanation - wish you'd been my maths teacher!
The teacher you have makes such a difference to your learning skills, some can impart their knowledge and you totally get it. Never too old to learn though. 👍
My sister loved math for the same reason you have. She liked the challenge. In contrast to my philosophy, I woke up every school morning conceding defeat in every aspect under the title "Schoolwork". Lol
This is the first video of yours that I have seen, and I WILL be subscribing just to try and re-learn what I've forgotten from 9th grade Algebra I in 1973. I struggled with math beginning in 4th grade. Our teacher was Asian, his IQ was probably at least 200, the whispers in my class were that he could make a perfect circle on the chalk board, and they were right. His accent, his IQ, and the speed of what he wrote on the blackboard was faster than I could understand, and he didn't repeat things. That was my first year of fractions, and with each year after that, I struggled so hard, and when it was time to sign up for classes in 9th grade (still junior high) for math, there were 2 options. General Math or Algebra I. That was an easy choice for me, General Math. On day 1, I was nervous and happy all at the same time because I felt like it was something that would be easy for me. Sort of like some of my other classes were. My teacher was probably around the age of 60, and very easy to pay attention to. After day 2, he asked me to stay after class, and I was petrified. I went to his desk as the class emptied, and he asked me "why did you sign up for this class"? I hung my head (I was terrified of my own shadow) and told him of my difficulties with math and that I thought I would do better in General Math. He then told me that he also taught the Algebra 1 class, and he was sure that I could do it, and he wanted me to give it a try, and if I couldn't do it, I could go back to the simpler math. Having him tell me that he thought I could do it was something I wasn't very used to hearing, but I went to Algebra I the next day and I stayed in his class, never getting below an A- on anything. I was even raising my hand to answer questions-that was new for me also. That man made me believe in myself more than any other person in my life including my parents. So for High School, I joined my classmates in Algebra II. Totally different teacher, and I fell behind quickly. I barely got through the semester without failing, I dropped it after that first semester, and never took another math class. Little did I know how much math would be part of my life for 18 years of working in Ophthalmology. It was only dealing with positive and negative numbers, but I could rattle those numbers off, I had a great understanding of how crucial my numbers were for the surgeons, and while I never needed Algebra II, I climbed the ladder to the top rung one step at a time, always grateful for that one teacher who believed in me. Sorry for the book, I will sub you now that I've learned something from you. Your voice is calm just like my teacher who I wish I could have thanked for what he did for a farm girl who didn't think she would go far in life, but I did. God bless good teachers everywhere.
For someone that has had difficulty with understanding basic algebra. This is the third video I watched and ta da. I got it right. Woo hoo. Thank you.thank you,thank you.
I was taught PEMDAS (Please Excuse My Dear Aunt Sally) and got 165. 3(5 +20/2 x 5) = 3(5 +10 x 5) = 3(5 +50) = 3(55) = 165 Edit: I was taught PEMDAS in 6th grade and reminded again in Algebra
I was never great at math and I as well was taught this in 6th grade and my achilles heel Algebra as well. So proud of myself I got it right too! And remembered it!
BODMAS brackets Of. As in ‘power of’ Division Multiplication Addition Subtraction Following these rules, I got 165 I know BODMAS is different to BEDMAS or PEDMAS, but it means the same thing and I’ve remembered BODMAS for 40 or more years! So my teacher managed to jam this into my head that’s lasted almost half a century
I'm in the U.S. and I also came up with 7.5. We used parentheses within brackets, so it was very clear which formulas were used first. Always got As in algebra. No need to make it so complicated. I've seen how they've changed the way math is taught (with my grandchildren) in the last 20 years, and yet math scores across the U.S. continue to decline.
@@bvm3925, from what I learned in elementary school arithmetic more than 50 years ago in NY, you solve bracketed sections first, multiplication and division first from left to right, and then addition and subtraction from left to right. So you would first divide the 20 by the 2 which equals 10, and then multiply that by 5 which equals 50, and then add the 5, which equals 55, and then multiply that by 3, which equals 165. Hopefully that is the way the instructor in the video solves it. Another alternate method is to distribute the 3 into the bracketed section which would result in 15 + 60 ÷ 6 × 15, which equals 15 + 10 × 15, which equals 15 + 150, which equals 165.
I am actually quite proud of myself. NO ONE could ever make math make sense to me in school; At first I solved it incorrectly but as soon as I saw it written with a proper division sign opposed to the forward slash, which I also recognized as divide; I knew to do the division before the multiplication and got it right. And all in my head. Major accomplishment for me!!😀 I'm quite sure I couldn't pass a grade 8 math exam though....
Delirious here. Got it right! You’re a great teacher, but I needed clarification and listened to another educator who said we always move from left to right and m/d means either procedure , but if division comes first, do division.. you’re good, thank you! Wanna give us some homework?
I love this!!! Back in college, I majored in math and I love solving problems so this was easy for me. Needless to say, my nieces and nephews and grandkids all call me when they need help with their math homework - because according to them, I explain it "way" better than their teachers can! However, trying to help them solve complex math problems over the phone is a pain - especially when I'm at work or at the grocery store! Because well, when solving any math problem, it's all about the visuals! Sadly, I'd say that 95% of people who think they're bad at math, really aren't. They've just never had the benefit of a great math teacher to visually explain the proper steps to follow when solving a problem. I tell my grandkids to always follow each step and that a single problem can take up to a half a page to solve, and extremely complex problems will take up the entire page - front and back! Knowing the proper steps and following those steps exactly, will ensure success. After watching your videos, I have to tell you that you sir, are a fantastic math teacher! Not only is your voice very calming, your visuals are the best I've seen! This is exactly the way I have shown my kids and grandkids how to solve a problem - only this is better! Your use of the green "chalkboard" style screen, combined with your use of fonts and explanation of proper procedure is extremely effective. It's so easy to understand, follow and comprehend. I just forwarded your channel to my entire family! The kids will be starting school in a couple weeks, so I told their parents to subscribe to your channel and to start watching one or two of your videos every day. I told them to make a game out of each video by having everyone solve the problem on their own, then watch the video to see who got it right! By turning it into a game, it makes it fun for the entire family and the kids (and parents) get a refresher course so they're prepared when they go back to school - creating an everlasting boost to their confidence. I'm so thankful I found your channel. You are a Godsend to both parents and kids who struggle with math! Your channel is a game changer! Thank you so, so much! 💙💯
I used to find I didn't understand the way our teachers explained things - this was New Zealand in the 1970s - but I easily understood the way my father explained how to do the equations - he was taught in England, 1930s/40s. I don't understand the modern ways at all and I not only enjoy maths/arithmetic but am generally fairly good at it - don't like using calculators though - and I can't understand why people now say that the ways they were taught in the UK as kids give different answers to those I get because my dad was educated there and the ways he used and taught me were the same as our teachers used in NZ, but which now appear to be totally different to those taught in the UK. Very confusing and can only guess they changed their teaching methods some time after the 1940s for some reason.
When a teacher asked me to explain why something's done in a certain way, my only response was "because you said so". Beyond basic arithmetic, math makes absolutely no sense (and I was never good at word problems, even in basic arithmetic). I majored in Computer Science in college, but I wasn't able to take any programming courses because I couldn't pass Algebra. (Well, I took JavaScript from another college based on a technicality; the professor didn't know why I was in the class since I was already good at JavaScript, but I thought it would be an easy elective; I got in a tiny argument because the textbook said to use document.write() in an XHTML document and brought up that write() is part of the HTML DOM but not the XML DOM so you have to use methods like createElement(), createTextNode(), and appendChild() to properly add new content to an XHTML document (eh, I did it properly regardless of what the textbook and the professor had to say about it)).
OPERATIONS A linking of elements within a set and resulting within that set for all elements of that set is an operation. There exist monary, binary, trinary, … linkings. In mathematic: +,-,•,: are binary operations within the set of rational numbers. As soon as you introduce radical you enlarge the set to the irrational numbers. R and I build the real number set. Here you have the operators +,-,•,:,exp,log. Notice that the introduction of PI, e can not be generated by using operators. Those numbers are transcend. There are exactly 11 AXIOMS which define the set of real numbers. The set is called FIELD.
I was also taught that multiplication had equal priority to division, but another respondent said that division comes before. I can’t agree with that as they are interconnected functions.
Thank you teacher! I'm a frenchman of 71. I never heard about PEMDAS or equivalent in french before you spoke about it! And though my english is far to be perfect, i understood your whole explanations and i'm very glad of this. I have to precise that when i was young, i hated mathematics and the teachers in this discipline. Now i notice that i understand very easily, and in english! So i have to consider nowadays, that i am a little bit smarter than a nut... What a great satisfaction !😊😉
La première fois que j'ai appris l'ordre des opérations, c'était en français, mais je viens des États-Unis. Mon école primaire avait un programme d'immersion, donc mes cours de mathématiques et de sciences étaient tous en français pendant cinq ou six ans. Quelle coïncidence intéressante ! (pardonnez-moi s’il vous plaît d'utiliser un programme de traduction, mais je fais encore moins confiance à ma grammaire sans lui. Cela fait longtemps que je n'ai pas pratiqué!)
I've got to review all of this stuff since I have a four year old grandchild that is exceptionally bright and all to soon he will be wanting to learn. In my view this guy is just what the doctored ordered. I don't know that he would agree but I've found that fifty per cent of learning Algebra on up is just learning the formula!
Instead of PEMDAS I taught my students PEMoDAoS, the little "o" stands for OR, when confronted by the same level of operation the one that comes first working left to right (the same direction we read) is the one acted upon. I had the kids make up their own sayings to remind themselves, the best was "Perform Each Math Operation During Algebra On Schedule". When the kids become invested they own it!!
Brilliant ! Your students mnemonic makes more sense than any others I've seen. Congratulations. You are the kind of math teacher that can open their minds to the joy of numbers! I salute you.
Thank you, I was never taught PENDAS. Graduated in 1982, I’m learning it now on RUclips. I thought it was set in stone. I’m happy to know that it’s not. Thank you for this information.
PEDMAS has been taught to everyone who has ever attended school way before we were born. Just because you don't remember doesn't mean you weren't taught it
Remembering the rules of pemdas and not overthinking it, I came up with 165 in my head in about 20 seconds. I’ve noticed people forget that addition and subtraction are equal, as are multiplication and division.
165 in no y brain before I even started the video. PEMDAS. I learned advanced math calcs on a circular slide rule in the early 80’s while navigating jet aircraft. We had a sextant, pressure differential (radar bs barometric altitudes), and Ded Reckoning. Nothing like today.
Whenever I'm in doubt in cases like this, I convert the divisions into multiplications. So it would be : 3 ( 5 + 20 x ½ x 5) = ? With that, the mistake that leads you to 21 can't happen. 20 x ½ x 5 = ? 10 x 5 = 50 -- or -- 20 x ½ x 5 = ? 20 x 2.5 = 50 -- or even -- 20 x ½ x 5 = ? 100 x ½ = 50 This approach also creates some freedom to choose the simplest calculation.
2 does not = 1/2. 2 in fractional representation is 2/1. 1/2 is .5 in fraction. This person is also incorrect the actual answer according to simple math is 21 because multiplication always comes before division in simple math order of operations, to get the answer they wanted you have to either use brackets or put the 3(5+20/2x5) then the answer works out to what they are getting at, the notation was done in a shitty way to trick people the problem is with that notation the answer is 21, complex math or higher meth is different and that comes when you are a physicist or a mathematician and regular order of operations has the problem of creating a paradox. People are being assholes.
Multiply first So 20/10 = 2 5 + 2 = 7 3 x 7 = 21 Do you understand no one writes expressions in this format? Expression should read 3[ 5 + 20/10] Why make it a puzzle when it is only a multiply and divide and addition expression?
.... so... i did this via algebra expansion... 3(5+20/2*5) becomes (3*5) + (3*20) / (3*2) * (3*5), becomes 15+60/6*15, becomes 15+10*15, becomes 15+150, becomes 165.... Completely different method of dealing with the brackets but the same ultimate answer :)
I'm 59 now. Math has always been my strong suit! I did not know the technical word for the order of operations, but definitely knew how to calculate the correct answer (of 165). My curiousity, in regards to all of the people who came up with the correct answer, is wondering how many of you were able to solve the question within your head (i.e. not using pen/paper; calculator; etc.)?
I just see the answer. Not sure how. It works for me with calculus also. I do have to work at DiffEq though. I am high functioning (autistic spectrum) and test at very high IQ levels. The latter indicates a high level of inductive reasoning and logical thinking. The former indicates I am neural-divergent (don't think like a "normal" person).
oh, with their natural organic intelligence, nahhhhhhhhhhhhh no way, artificial intelligence is their go to in 2023---lol 165=1+6+5=12 as you come from the 12th creation/dimension pure celestial being,from the expression of the one, and from the highest level of reality^
I correctly worked out the right answer in my head but realistically it's a pedestrian calculation. I tried to also work out the wrong answer in my head but got 187.5 not 21. I found it interesting how 21 was derived in the video and it was not something I would have thought of. When I looked at the question I do not see a division symbol in my mind, such as "a" divided by "b" but I always see it as a multiplication such as "a" times "1/b" or alternatively "b^-1" In most semi advanced mathematics the divide symbol is not used probably for that reason. The divide is either a full bar clearly showing the numerator and denominator or alternatively a "/" symbol and parenthesis.
I think some people get confused about the MDAS part. That means that Multiplication/Division are on the same level as well as Addition/Subtraction. They are worked right to left-M/D or D/M first-depending how the problem is written. That’s what tripped me up when I first started doing these types of problems.
what to be confuse of? prentice's , multiplication, division addition subtraction. that's the rule. so in this case the parenthesis makes it 9 then you do the multiplication makes it 18 then addition makes the sawer 21
@@respectbigman3133The answer is 165. Multiplication and division are on the same level. You don’t necessarily multiply before you divide. You just work left to right whichever comes first. So first you do everything in the parentheses. Working left to right, divide and multiply first, and then subtract and add, left to right. Then work outside the parentheses. The answer is 165, not 21.
@@ChasOnErieYou have made up your own rule. The problem is you’re going to get the wrong answer many times. The true rule does not say to always multiply before divide. You work left to right, dividing and multiplying first and then subtracting and adding. The answer is 165.
An alternative way, which still honors PEMDAS is to distribute the 3, thereby removing the parenthesis in one step. 3(5 + 20 / 2 x 5) --> 15 + 60 / 6 x 15 Then follow PEMDAS just like he shows for the rest: 15 + 10 x 15 15 + 150 165
@@kdizzle901 Brackets vs. Parentheses... same thing, just different words. It's like bathroom vs washroom vs water closet vs loo etc. You're really trying to say the same thing, just using different words depending on where you're from. As for the switch of the D and M, they're the same grouping, so it really doesn't matter which order they go in. Maybe in PEMDAS rolled off the tongue more easily for your region...
@@dulcinealee3933 Yes math is still a universal language, but English is not. Specifically, words used varies depending on the region you're from. The perfect example is your use of the word maths vs my use of the word math. Same thing, slightly different word based on where we're from.
Saw the video title and image, did the math in my head, went to the end of the video and....kudos to my elementary school teachers. Whatever you did, it stuck.
Per the distributive property, you COULD execute the parenthesis by multiplying 3 times every item within the parenthesis and then do the MDAS order operation as described....you'll still get 165. 15 + 60 / 6 * 15 = 165.
@@vladdawoken4181 they actually are not :) one is a straight multiplication, the other is a parenthesis multi,juxtaposed, implied multi. There are cases where they would give different answers :/
If you see the parenthetical part first and then see not a division problem, but a fraction: 20/2, it works out. 3[5 + (20/2) * 5] =. It's a good idea to always think of a division symbol to mean a fraction.
Not a bad idea, but not flexible enough. Let's say we change the question to 3(5 + 20 / 2 X 5 / 10), thinking of it as a fraction might add more confusion like 3(5 + (20/2) x (5/10)) while the correct form would be 3(5 + ((20/2) x 5)/10). It works out but also add some complexity.
When i did math in the sixties the way this is written the answer would be 7.5 . We were taught to figure inside the parentheses first. 5*20 =25 divided by 2*5 =10 answer 2.5 *3 =7.5
Any operation within parentheses is attempted first. However, given that division and multiplication share the same importance, we attempt those operations from left to right. So 20/2 = 10. Then multiply the result by 5, which yields 50. Only then can we add 5, which gives us 55. Lastly, multiply 3 by 55, which totals 165.
As a programmer, I always use parentheses to separate math logic so there is no ambiguity. If it’s not clear to most people, that means the equation is poorly written. The author must make it clear what the intentions are.
I remember doing various strings of if...then functions and similar in various programming, spreadsheet and print formatting languages. In 1981 was in the last class at my uni to use punch cards & Fortran in Computing 101 😂😂 but it was useful later in setting up reports in accounting programs that were still text based into the 2000s. After 2010-2015 that started changing, too so it's been useful for a looooong time. Also helped with complicated spreadsheet functions & macros.
You can see in the comments exactly why the International Organisation of Standardisation exists and why specifically ISO-80000-1 exists. It says when writing division on one line with multiplication or division directly after that brackets are *required* to remove ambiguity. Never write 20÷2×5 It is (20÷2)×5 or 20÷(2×5). Those are acceptable. Many are taught M is higher priority than D and some books do use that convention (and I don't just mean for multiplication by juxtaposition specifically) and that leads to the general mistake of 20÷2×5 = 20÷10. Avoid the mistake by writing properly on the first place. Use two line fractions as these are best practice.
It's written as twenty over two times five which equals two. If it were written as twenty over two, times five it would equal fifty. BOMDAS and PEMDAS are tools more than rules. Brackets matter and cannot be arbitrarily added or subtracted without changing the equation.
Wouldn't one comma clear it up enough? While 20 over 2 times 5 is ambiguous. Does 20, over 2 times 5 imply 20/(2×5)? although I can see 20, over, 2 times 5 being better for 20/(2×5) 20 over 2, times 5 is pretty clear to be (20/2)×5 though even though you could write 20, over 2, times 5 either. So, maybe one or two commas, depending on the situation?
If you actually understand the fact that multiplication and division are the same operation then it makes no sense for one to have priority over the other. The problem is that people try to remember PEMDAS and don't actually understand what they're doing.
Canadian who learned order of operations back in the 1970s. My school didn't bother with any mnemonic device at the time, which may have been a good thing. Always clear to me that multiplication and division had equal priorities with each other (as did addition with subtraction). The PEDMAS mnemonic sounds as confusing as it is helpful, which, when you think about that, means it is a HORRIBLE mnemonic.
tbf, we learned it as BEDMAS (or BODMAS, depending on terms used) in the 90's and that was a perfect layout of the order of operations. Also, when did PEMDAS become the new norm and who needs to be flogged for messing up something so simple? Or was it keeping in line with the overcomplication/revamp of basic math they did at one point?
Also Canadian, but we were also taught MD in the order they appear, and AS in the order they appear. I don't know if they still teach that way but it was cemented in our heads from grade 6 on (learned in 90s). Also why make such a big deal over P or B? Parentheses are Brackets. It makes no difference. Also if you were taught in the 70s you probably learned with BODMAS Brackets Orders Multiplacation and Division (in the order they appear) Addition and Subtraction in the (order they appear). My mother and father taught me BODMAS when I was 8. By time I was in highschool it had become BEDMAS (as exponents made more functional sense as a term then Orders) ....they learned it in the 70s as BODMAS, so you would have to.
@@TheTicoune Since the internet spread Americana to everyone. BEDMAS is popular in British English Schooling (Canada, New Zealand, Australia, UK), where as PEDMAS is an American spin on it because despite being anglophone they choose to be different. They are the exact same thing. Parentheses = Brackets.
@@kurtmooreca PEDMAS would make sense, but its not spelled out that way for whatever reason: PEMDAS is the official way...even though it makes no sense and creates confusion rather than helping it.
@@TheTicoune Why would it make more sense to say division before multiplication? These 2 are equal, you dont do either one specifically before the other.
I got 165 in my head. As a music and math teacher, I've taught both PEMDAS of BIDMAS. I stick with PEMDAS with the emphasis PE(MD)(AS) you showed. I tell my students multiplication and division are actually the same thing, just expressed as inversions that lead to the same result. As with AS, instead of taking away like subtraction, I rephrase it as adding a negative. So in the problem above, I can easily see how kids get 21, because they are taught to do multiply first instead of divide, no matter where the multiplication operation is in the problem. Any time there is an order of operations problem, I tell my students to convert every division operation to multiplication, and every subtraction operation to addition. Then solve PEMA left to right. It's an extra step, but they soon eliminate those extra steps once they realize MD and AS are grouped to together.
Something is not OK in teaching math if these kind of problems exist. Parenthesis are used to clarify things in case any doubts . Programming had caused this problem.
Interesting- in Canada they teach it as BEDMAS. (B standing for brackets or parentheses) and the rest is the same as this version. My husband taught math for 30 years, so I heard this a lot!
@@TheOtherKine The DM is not backwards since the ordering doesn't matter. MD and DM are correct as long as you read the equation from left to right. Their here is probably referring to the USA. USA typically does PEMDAS while places like Britain and Canada use BEDMAS.
In my school we were taught BODMAS (brackets, other, division, multiplication, addition, subtraction) but also that the 'DM' didn't swap, division was always before multiplication. Because of this I had to pause to work out how someone would come to your example of a wrong answer.
I was taught in the UK in the 80's and we didn't learn any misleading acronym. We were just taught the order of operation. Division and multiplication have the same order, and so are done left to right.
@@thor4u no, 165 is the answer I came to using BODMAS, I was mostly commenting on the division and multiplication being interchangeable, while I was under the impression that they weren't. If a similar sum with those two functions swapped were the example I would have got it wrong if dictated left to right.
Got this one right, even though math used to be my worst subject ^-^ After getting a very bad grade at algebra, I started practicing it alot and actually started to enjoy it alot. Eventually I got one of the highest grades of the class and was alot of fun, like just making puzzles. Glad to see some still stuck ^^
Agreed. in the UK brackets etc remove any ambiguity. Also if you were programming it you would also put in brackets. its good practice and makes for ease of maintenance.
@Dead_Goat did you watch the video? 21 is the wrong answer because the division takes priority over the multiplication because it shows up first. If an expression has two or more operations of the same priority, do those operations from left to right.
The problem with PEMDAS (easy to forget the M & D happen together and the A & S happen together, so you start thinking you always do Multiplication before Division) is why one of my middle-school teachers always emphasized that M & D are actually the same operations written different ways and ditto with A & S, resulting in just PEMA.
But when they are the same operation Multiplication-Division then Addition-Subtraction it's simple, you do left to right. The left to right order of operation is the most BASIC order you learn when beginning in math. The first level of math is addition-subtraction. You learn you do that left to right. 4+2-3+6-1-2=6. Then you move to Multiplication-Division and you still do it left to right. 2x6/3x2=8. Then you get to the next level combining all four. 4+2x6/3+6-8/2+4x2=20 Multiplication-Division and Addition-Subtraction. We learn you do M-D first, still doing left to right, then you do Addition-Subtraction left to right. Next, you learn Parenthesis and Exponents to complete PEMDAS. Complete the Equation in Parenthesis first still using PEMDAS (4+2(8/4+2^2))+(8-4/2)^2=52 It really is not that difficult.
@@LeSyd1984Part of the order you learned 40 years ago and I learned 50 years ago was left to right so, you would have gotten 165 if you followed those rules correctly since it hasn't changed.
I didn't have a good math teacher until my freshman year in college. For years I had struggled with math, although I had the GPA I needed to be accepted by the university. This one professor cleared up the mystery...from that class onward, the rest of my classes were a snap! My 8th grade math teacher was also helpful, but I still had headaches with math. My freshman math prof made all the difference.
Greetings. The correct answer is definitely 165. First we consider the bracketed figures. In the brackets, we will first divide 20 by 2 to get 10, thereafter multiply 10 by 5 to get 50. We will then add 50 to 5 to get 55 and finally we multiply 55 by 3 to arrive at the answer of 165.
When you express the division operation like a fraction it is much easier to see what should be done first. Placement of the division bar makes it much easier to see different groupings than the elementary school division symbol you used in the original expression. I think when I went to college I rarely if ever saw the elementary school notation. We always used a fraction bar that you could position so as to minimize any ambiguity. Also when my teachers taught PEMDAS, they always made it clear that multiplication was first and addition was second and each were performed LEFT TO RIGHT.
If it is rendered as vertical fraction, with a horizontal line through the middle between numerator and denominator, which clearly shows the extent of the overall fraction, then yes definitely. But fractions are more likely to be renedered in typed text with a 'front slash' which is no clearer than using the division symbol used here.
@@MrDannyDetailin which case use parentheses to do the grouping that would normally be represented by the positioning of the numerator/denominator. If you were writing this in LaTeX you'd have to use those parentheses anyway.
I'm going back a long time now, roughly 37 years but I was taught bodmas, meaning B. brackets O. of D. division M. multiplication A. addition S. subtraction. Which would be a completely different answer due to a different process. So with all that said are you telling me that I was taught wrong.
Thanks, that makes a lot of sense. I was actually taught wrong in school. My teachers were insistent that M came before D. Now I know why I failed a couple of math sections in test for various jobs over the years. Thank you, public education system.
They should be writing it as PE(MD)(AS) or some thing. Then again, in today's common core world, they probably teach an incredibly stupid and unintuitive way on purpose.
@@BlitzkriegOmegaIf you write it as PE(MD)(AS) then you create a paradox. Cause parenthesis are first, but the MD and AS are in parenthesis. So is the P first or the MD Because its in parenthesis
@@BlitzkriegOmegaalso it's still wrong because it should be p(er)(MD)(as) But..roots are reverse of exponents... PEMA, roots are reverse of exponents, division is reverse of multiplication, subtraction is reverse of multiplication... There only 3 operation families. 2 operations per family... And parenthesis are essentially just a highlight
Got it right. Was taught order of operations, here in 80s/90s UK, as BODMAS. Brackets, orders, division, multiplication, addition, subtraction. May have been saved as I was taught DM not MD, this was a great refresher!
I was always taught in school bit was called BEDMAS? Brackets, Exponents, Division, Multiplication, Addition, Subtraction. Now it's all wrong??? Why do rules keep changing.
@@coju8543 In German we say 'point operations before stroke operations'. Division is usually written as a colon, not the stylised fraction, multiplication as a dot, making the kind of operation easily groupable.
@@Notir072 yep! and same for subtraction and addition. whichever is first is what you do first. if 5+4-3 you would do 5+4 first if it was 5-6+4 same goes. 5-6 goes first.
I didn't enjoy math in high school, but I only had basic business math. When I stated college part-time, I had to take pre-algebra and learned to love quadratic equations. BUT outside of school and the fields of science and engineering, does this truly matter. I must say that after taking my math classes required with my degree, I never needed to use it again.
The best way to deal with problems where there is a division symbol followed by a number is to replace it with multiplication by the reciprocal of the number. Then you get (5 + 20 x 1/2 x 5). doing the multiplications first gets you 5 + 50 in the parentheses, and leads to the correct answer. Even better would be for the problem to be written unambiguously from the start!
Just because some don't learn arithmetic properly does not mean the problem is ambiguous. "Ambiguous" would be if people who learned it properly disagreed with how to complete it.
@@Ddrhl Even people who were taught properly can forget how to solve problems or make mistakes when the problem is poorly stated, like this one. If you're being pedantic, it maybe isn't ambiguous, but the fact that a lot of people apparently get it wrong means it is not stated clearly. It it were written 3(5 + (20 x 5)/2) the sequence of operations would be obvious and I suspect everyone would get the same, correct, answer.
@@ceejay0137 Learning math properly is not pedantic...it IS the crux of the matter. Are you saying that since "nuclear" is mispronounced by so many people that it is mispelled? You don't forget order of operations...ever...when you LEARN them.
23 years since I have had to do any Algebra. I was stuck until I got to the PEDMAS part. Had completely forgotten how to do this. It is true if you don't use it, you lose it. I will be digging through these videos as a refresher course.
Since multiplication and division have equal weight, I did the 20÷2×5 part from left to right to reduce that to 50. Then I added 5 to the resulting 50 inside the parentheses to reduce that to one term, 55. Then just multiply the 3 on the far left by that. The answer is 165.
Clearly does not have equal weight. If they had equal weight, you could multiply first in the "20/2*5", get 2 as a result and you would be right. You would be wrong though.
@@seph. Yeah they do have equal weight. But you always solve from left to right. Therefore you do first the division and then the multplication. (20/2*5 => 10*5 => 50)
Commenting at 0:01. Easy answer. Equations in order of calculation. 20/2 = 10 10 x 5 = 50 50 + 5 = 55 This solves the bracket (5+ 20/2 x 5) 3x55 = 165 Resolving the equation. Edit: Post video watch. I think the problem is most people don't rewrite the equation every time they do a calculation. 3(5+20/2x5) = everytime you knock out a calculation you rewrite. 1. 3(5+20/2x5) = 2. 3(5+10x5) = 3. 3(5+50) = 4. 3(55)= 5 165. If you don't understand math to the point you can't knock out operations in your head, rewrite the equation every time you get rid of a X, / , +, - and its easier to keep track of. Exponents and Squares can also be more easily understood when written by hand. For example 3^2(5+20/2x5)/2 is the same answer as the above. (exponents are just factorials multiplied to themselves) 1. 3x3(5+20/2x5)/2 2. 6(5+10x5)/2 3. 6(5+ 50)/2 4. 6(55)/2 5. 330/2 6. 165. SQRT 9 (5+20/2x5) (find common factorials for the square and divide) 1. 9/3(5+20/2x5) 2. 3(5+20/2x5) 3. 3(5+10x5) 4. 3(5+50) 5. 3(55) 6. 165 I swear calculators have ruined Mathematics, and thus Science today (in people, computers handle them just fine).
Interesting, and there seems to still be confusion in the comments below. But i was taught in UK to use BODMAS (Brackets, Order, Div, Multi,Add, Subtract) so while this order worked fine for me and i got the right answer, i did not realise that the Div/Multi (and Add/Subtract) were on a left to right basis. So had it been written the other way around i would have still done the Divide first. Guess you learn something new every day :D
Great video! I never could remember how to do these type of problems. After watching your video its perfectly clear…. And ive been out of school for 40 years! Thanks
I am 62 years old from India, and we were given BODMAS to follow. B-Brackets, O- off(multiplication), D-divison, M-multiplication, A-addition, S-subtraction, to be strictly followed in order. Never failed to get at the right answers.
*In Canada we were taught "BEDMAS" (Brackets, Equations, Division, Multiplication, Addition, Subtraction).* *The ONE thing that I was completely stumped by was the "3(" Now I know that it means "3 TIMES". I always found this confusing because there was no symbol to tell me what to do.*
This is why I failed geometry. I was taught to do inside the parenthesis first in the following order: plus, minus, multiply then divide; then apply the numbers outside the parenthesis. So, 5 + 20 = 25; there is no minus, so then multiply 2 times 5 = 10; then divide 25 by 10 which is 2.5; finally multiply 2.5 times 3 which equals 7.5. And that, ladies and gentlemen, is why I did not enroll in mathematics beyond the level of geometry.
Your process arriving at 7.5 was "as taught" when I attended such classes in High School in the 70's ... (in our very poor School District that was later taken over by the State, due to teaching vacancies our Gym Teacher was also the Health and Math Teacher ... great guy but way out of his depth for Math)
Nah, geometry is pure memorization of theorems and postulates and application. totally different. I have a great memory so memorizing things comes easy for me. a+b+c is where my brain puts up a block. Just no....3 math tutors and I always got C's in Algebra. I took that C and was proud of it. Though it killed my GPA.
Wow, your videos have shown me exactly where I stopped learning math around the eighth grade. (Where I was still getting in trouble for working the problems in my head.) I never learned PEMDAS, but it was not for a lack of people trying to teach me. I just didn't much care about school. Not knowing PEMDAS must be what doomed me to failure in pretty much all higher levels of math, I somehow passed algebra one, parts one and two, in ninth and tenth grades. I failed algebra two as a junior, and took geometry, (which I actually enjoyed and did well) as a senior. This is the third video of yours I've watched now, and the first one which I was able to answer correctly!
To solve the expression 3 times (5 + 20 / 2 x 5), you should follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and square roots, etc.), Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right). In this case: Start with the parentheses: 5 + 20 / 2 x 5 Perform the division inside the parentheses first: 5 + 10 x 5 Next, perform the multiplication inside the parentheses: 5 + 50 Finally, multiply the result by 3: 3 * 55 = 165 So, the answer is 165. Says Chat GPT
This is the correct answer says my high-school algebra from 2003, my college algebra and yeah that's about the only time I have ever really used this. But I got the same answers following this order.
@@Robert53area 1982 Algebra from me, still remember parts of it, did watch a video on how to do some of what we learn back then in the head, sure wish we had videos like this back then, I like using Chat GPT to solve a lot of my math problems, I wanted to know what size building will it take to give every person in the united states a 2000 sq foot living area it came up with the answer for me, I like mega structure videos
We learned these 3 simple rules since elementary. 1. Left to right 2. If there are parentheses, do them FIRST. (Left to right) 3. Multiplication OR Division FIRST but ALWAYS remember rule 1, LEFT TO RIGHT. I hope those SIMPLE rules helped a bit. ☺️😉 3(5+20:2x5) 3(5+10x5)... parenthesis first, Division/multiplication first, left to right ALWAYS 3(5+50) 3(55) 3x55 165 😊👍🏾
I remember MDAS - my dear aunt sue. Multiply, then divide, then add then subract. Parentheses first. I came up with 21, but clearly I am wrong. 2X5 = 10. 20/10 = 2. 2+5 = 7. 3X7 = 21.
@@titansrule72we learned PEMDAS: please excuse my dear aunt sally. Parentheses, exponents, multiplication and division left to right, addition and subtraction left to right.
165 (20/2) = 10 10 * 5 = 50 50 + 5 = 55 (calculated inside the parentheses first with multiplication or division read left to right first come first serve) Then 55 * 3 Even though the multiplication math operator is missing from the written equation it is in the written text. 165 is answer
I actually got it right the first time I went through it, BUT then I did it again and again, and got 21 and 7.5 (figure that one out Mr. Math Teacher). In the end, my dear Aunt Sally told me to stay with 165 and I did.😊
On my first try I figured out your '7.5' all by myself, as it turned out by doing EVERYTHING inside the parenthesis exactly backwards! I had just begun to watch the solution explanation in this video when my iPad Facetime rang. It was my Math-teacher daughter from across the country. I flipped the camera around to show her the operation and without knowing the given answer, she got it right, '165', immediately. We laughed a lot. I still can't get over that crazy coincidence(?).
It’s amazing how many people didn’t pay attention in school. I’m 61. Last algebra class I had was college in the early 1980s. The people that argue that “that’s not the way we learned it in school”…good grief. Whether we heard of “PEMDAS” or not, the order of operation was always there to be followed.
Exactly. I never understood how having to remember an acronym and what each letter meant and how to apply it was easier than just learning the correct order of operations. Perhaps graded and discussed/counseled homework is a thing of the past?
Agree .. the acronyms make no difference to the law of order ... it's a learning aide and that's all. The order is burned into my brain from school ... but I struggle to remember the acronyms. But I'm just weird.
I got 165 and did it in my head. I was lucky to get a really good education growing up. I guess it comes down to the luck of where you live and which school you get to go to. Thanks for sharing this lesson.
I am a 77 year old woman who had a couple of very intimidating math teachers in middle school so I never mastered algebra and have
regretted it all these years. Thank you for your RUclips channel. I watch it every night on TV and I am determined with your help
to finally be able to conquer this and cross it off my bucket list. Thank you, John, for your patient teaching.
Nobody tell her that this isn’t algebra…
@@LivingroomTV-me9oz I am sorry, but algebra is imaginary. It does not exist. What is a number? It is a symbol indicating how many objects, thoughts, concepts, items exist in a given space. (...) is described as the number 3.
What is a letter? A letter is a symbol indicating a sound. "A" is a sound. "Three" is a word, a sound made up of letters, but "three" is NOT (...). Just as you cannot add a stone to a board or a piece of paper to a dog, you cannot add, subtract or do anything combining a (...) to a letter! It simply does not work. Yes, you COULD mulch the board and reduce the stone to sand and throw them together, but ultimately microscopically, you will ALWAYS have tiny rocks and wood fibers!
I havd explained this many times and nobody seems to understand it.
@@sylvisterling8782what does that have to do with algebra? Sure someone had to come up with the concept of algebra so in that sense it is made up, but math such as algebra has useful applications in real life. Without someone doing the math you wouldn’t have a device to even watch this video. So I guess I don’t understand your point about it being made up.
@@sylvisterling8782 c'mon dude, this ain't no abstract algebra course, it's a video on order of operations. Nobody seems to understand because you're explaining to others based on what you want to hear and not explaining in a form that will compel others to listen. You're basically explaining it to impress yourself, you're not necessarily explaining something because you want others to understand.
Algebra comes from "al-mukhtasar fi hisab al-jabr wa al-muqabala" the title of a book written by Abu Ja'far Muhammad ibn Musa al-Khwarizmi (which is also where the word algorithm comes from), colloquially its means "the reunion of broken parts". Originally, letters were not used represent unknowns, rather the algorithms used to solve problems were written out in steps, much like a recipe. Sometimes the algorithms were written out as poetry as a means to help better remember them.
This is arithmetic not algebra
165.
Depending on the country, the name of the order of operation may differ, but the concept is the same. I learned BEDMAS... Brackets, Exponents, Division and Multiplication, Addition and Subtraction.
Yep. I learned BODMAS as well (of just meant exponent) :) Got 165 as well.
What's the point of a pnemonic (pedmas) to help you remember when all it does it make you do an error if you don't remember that it actually is pe(dm)(as). I would've expected more logic from math people who came up with this.
When I learned the order of operations, it was presented in a graphical form, with the various groupings on separate lines, with an arrow pointing down on the left, with the label, "Simplify," and an arrow on the right pointing up with the label, "Solve." That way it was clear that multiplication and division were in the same class of operations, and addition and subtraction were in a different class of operations from multiplication and division, but were in the same class as each other.
The teacher gave extra credit on tests if you drew the graphic on the upper right side of the test paper, and he would indeed occasionally have questions where you were asked to, "Solve," instead of, "Simplify," and to get the correct answer it was necessary to reverse the order of operations.
That was over 30 years ago, and I still remember every detail of that graphic, so it was entirely effective.
Yeah I solved this with bedmas as well 👐
@@mkovis8587*mnemonic
1) Divide 20 by 2 = 10
2) Multiply 10 x 5 = 50
3) Add 5 + 50 = 55
4) Multiply 3 x 55
5) Answer - 165
42. The answer to everything in the universe .. except this. It's 165
3(5 + 20 / 2 x 5) = 3(5 + 10 x 5) = 3(5 + 50) = 3(55) = 165
I have spent my life feeling stupid because I didn’t understand this stuff and now I realise that I just wasn’t taught the basics properly. I wish that I’d had a teacher like you, Sir! My life would have taken a completely different direction. This 62 year old thanks you very much!
Me too! Im 63
I'm from overseas and I noticed most teachers are the same THEY DON'T KNOW HOW TO EXPLAIN MATH & SAID IT YEARS AGO
Yes! this teacher was born to be teacher
Don't feel bad.
The dude F'd Up the grammar of the opening statement. So he's no genius 😂
@@tonyferreira6679
See, another english scholar.
I was taught Parentheses in order from left to right, then Exponents from left to right, then, Multiplication and Division in order from left to right, and finally Addition and Subtraction from left to right.
Addition and Subtraction were equal in that you don’t prioritize one over the other and same with multiplication and division, you just do whichever appears first so
3x(5+20/2x5)
3x(5+10x5)
3x(5+50)
3x55
165
I’m really not a math fan, but my favorite math classes in school were business math and data analysis & statistics. To me they were fairly simple and the teachers I had were amazing. The business math teacher was a very kind and understanding professor who was very good at explaining it so that you got it the first time and he didn’t even make us get the book, he just read from his own and we all worked the problems out together. My data analysis and statistics professor didn’t make us get the book either and he actually introduced a lot of humor into his teaching style, but he had that really dark and sarcastic type of humor like mine, but he was never mean about it and genuinely cared about helping you learn. With the war on teachers in this country the last few years I really hope they haven’t been burnt out by it, especially since I live in a deep red, but northern red state.
3(5 + 20 / 2 x 5) brackets first .. and 20/2 first
3(5 + 10 x 5) then 10 x 5
3(5 + 50) then 5 + 50
3(55) then 3 x 55
165
Totally agree.
I do agree as per PEMDAS rule.. but application in real world such as physics, chemistry, advance math, engineering does not follow this. juxtaposition is included in the rule. hence your answer is still wrong
165
Multiplication and division are of equal value and are done in the order that they appear in the equation from left to right; the same is true of addition and subtraction. It should be 3 x (5 + ((20/2) x 5)) = 3 x (5 + (10 X 5)) = 3 x 55 = 165.
I came in to type 165. You are quite correct.
PEMDAS is probably understood correctly in some countries.
BEDMAS removes confusion, where B refers to brackets or parentheses.
@@pandaycorpWe referred to this as BODMAS; Brackets of, Division, Multiplication, Addition, Subtraction.
@@pandaycorpI was taught BODMAS as the order of operations; brackets, order/exponent, division, multiplication, addition, subtraction.
Yeah, I got this correct answer on my 2nd try. I was trying to figure out using PEMDAS and of course that is incorrect.
The critical clarifying moment that you presented here is the insertion of the simple word "OR" in the PEMDAS sequence. I don't recall ever hearing it simplified that way by any math teacher back in the day or in any other RUclips presentations. I take my hat off to you in thanks, sir!
My teachers never got it to me either. They taught us how to do it but told us to go in order of letters, not multiplication or division. Multiplication, then division is what we were taught. I don't think my teacher was that skilled in math and just tried using the book with the answers in it. You can't teach somebody how to do something if you don't know how to do it yourself though.
This actually shocks me. I remember several teachers saying or. Another way of thinking about it is, if there is a run of multiple and division operations in a row, they all are acting on the first number.
@@brendanh8193 that's still not 100% intuitively clear. Left-to-right is necessary because division is essentially a fractional expression. 1 ÷ 4 and 1/4 is the same thing. Left-ro-right means you resolve the fraction into a whole number before multiplying by a whole number. If you go right-ro-left, you accidentally multiply the denominator by a whole number. The most intuitive way to understand this is 1 ÷ 4 × 5 is to convert it to (1/4) × (5/1). Now you're multiplying two fractions, (numerator × numerator) / (denominator × denominator). This is easier to understand when you have something like 1 ÷ 3 × 5. If you do left to right, 1 ÷ 3 doesn't resolve to a whole number. It's a fraction with repeating decimal .333333... Decimals are weird and confusing, especially repeating decimals. You run into problems of precision using them in calculations which is why representing them as fractional expressions is preferred, especially in equations with irrational numbers (pi, square root of 2, etc).
It’s even easier in Canada we were taught Bedmas. Which dosent allow for the mistake of doing the M first.
The important thing to realize is that division is just multiplication by the reciprocal and subtraction is just addition of a negative number. So really it should just be taught as PEMA and perhaps people would be less confused.
I'm 60 and had never heard of PEMDAS or wasn't listening in class. But after 2 previous videos I've watched of yours, I got this correct! Shocked and proud of myself. I wish you were my teacher 45 years ago!
Nicely done.
Wow! I hated math, but I remember PEMDAS. I specifically remember the mnemonic, Please Excuse My Dear Aunt Sally =PEMDAS! I teach it to my grandkids today! My granddaughter is gifted in math & way ahead of her peers! She's 10. Proud grandma here, sorry! 🤭
Same, but I know I was never taught this,which would have made maths lessons so much easier……# sigh
I am older and we were taught the rules for equations; however it was never referenced as PEMDAS or any other acronym. We just remembered it by the function names.
We were taught BODMAS. I too have never heard PEMDAS
I am so excited! I got165! YES! I do not remember being taught this loooooong ago! (I remembered it from one of your previous videos, I think!). Thanks!
Got it this time! Yippee!!...❤...
To solve this expression, you need to follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and square roots, etc.), Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right). In this expression:
3 * (5 + 20 / 2 * 5)
Let's break it down step by step:
First, evaluate the expression inside the parentheses:
5 + 20 / 2 * 5
Now, follow the order of operations within the parentheses:
a. Divide 20 by 2:
20 / 2 = 10
b. Multiply 10 by 5:
10 * 5 = 50
c. Add 5 to the result:
5 + 50 = 55
So, the expression inside the parentheses simplifies to 55:
3 * 55
Finally, multiply 3 by 55:
3 * 55 = 165
So, the answer is 165.
Unlesss you are a maths teacher, how on earth could you remember that rule? (I won't say you looked it up). I worked in pensions admin, actuarial, finance and insurance all my life but couldn't recall all that you laid out.
but the m comes before the d. so why dont you multiply the 2 x 5 first and then divide into 10?
@@johnbeard3733because the rule is you go left to right. Multiply or divide (whichever comes first), then add or subtract next (whichever comes first)
Thanks Peggy
Because he does not understand@@johnbeard3733
Practical comment: As a 35+ year engineer… just use extra sets of parentheses. Or break it up into smaller parts. Or both. Other people may be looking at your work. Regardless of the correct “rules” it’s better to clearly communicate what you are doing … don’t assume that the other people know the rules as well as you do.
"As a 35+ year engineer… just use extra sets of parentheses."
And then everyone would get the same answer and it would not be clickbait. There's dozens of these videos with minor variations so we can argue about it.
@@thomasmaughan4798 they are nice, though, but of little practical use.
Very true, be explicit in how you want the problem to proceed. The best way is to design the problem so that it will give the right answer if it is fed into any computer on the planet. If it will not, then clarify.
As a fellow engineer, (since Mar 1980, 43 years 5 months) I totally agree with you, I haven't even watched this video yet but I can clearly see that the equation is very poorly expressed. Just the part inside the parenthesis can be solved as 55 or 7. I'm leaning towards 7 because the video description shows 3 times ( 5 + 20 / 2 x 5 ) and because it's expressed as a fraction, you should solve the denominator first. Then, you have 5+20/10 or 5+2=7 Making the overall equation 3(7) or 21. Now I'll watch it and I'm probably wrong. Yeah, according to the video, I was wrong. But the fraction 20/2X5 does equal 2 and then, 5+2=7. At least he admits that math teachers do try to trick their students. He says it's to see who was paying attention in class, However, he doesn't go into the actual psychology behind this, which gives you the real reason, they do it to boost their own EGOs. They do it to feel smarter than their students, by tricking them. Tricking them doesn't make them better teachers. Rather, it allows them to ease their own inferiority complex and feel better about themselves (probably because they were called nerds, or geeks, so often in high school). It has nothing to do actually with teaching the students. I hope he was able to boost his own EGO with this video and then, he can feel better about himself. 3(5(20/2)+5) would have been a much better way to express the intent of this equation. It communicates the intent more clearly because you're not trying to trick your intended audience. I gave your comment a like. Have yourself a great day!
Spot on!
Hello, I am British and we use BODMAS, eg Brackets, Of (to the power of), Division, Multiplication, Addition, Subtraction. Using this mnemonic means you don’t have to complicate the process further by having to remember to check on the order of the division and multiplication within the brackets. Division is always carried out first ie before multiplication.
No in Bodmas what you do is based on going left to right in the equation in this case divsion comes first in the equation (going from left to right) so you do division first but if the multiplication came first left to right then multiplication would come first.
@@FranklinThe1You’re right but they’re not wrong. Doing division first always gives the correct answer because it’s simply multiplication by the reciprocal of the number following the division symbol, and it doesn’t matter what order you multiply in. There’s no reason to go left to right. Just understand what division actually is and you’ll be fine. I hate the people just mindlessly repeat rules they’ve learned without understanding them.
Yes thats right we use BODMAS in UK and use the nifty expression Bugger Old Dad! Mums Arse Sags - so as to handily recall it when doing operations
I did that totally wrong by addition first and dividing the sum by the multiplied sum. 3(25/10)=7.5. That’s quite a difference. Thanks for reminding me of the order.
Me too. 7.5
@@alicejackson7676, I thought I was alone. It’s so nice to have company. 😁
That's exactly the way I was taught back in the 60s and 70s and I still think it's the right way. I nearly always get different answers to this guy.
This is the way i was taught at school. After four decades in business i never get my figures wrong. I would be interested when and where the maths was changed.
That’s what I got too. 7.5
My lord if you were my teacher I would be great at math. Your voice isn't threatening and your teaching is superb.
I commend you and I thank you for posting your knowledge and your spirit comes through to teach younger people and adults like myself how to properly understand math. I applaud you, your parents and all of your teachers. 👏🏿👏🏿👏🏿👏🏿🎉😊
My son had a young lady fresh out of teaching college who taught high school math. She was awesome. He was an engineer.
Agree ... we need more efficient teachers. I have a friend who is becoming a teacher and she can't spell. That immediately limits her effectiveness as a teacher.
@@nukasnook1561Nothing worse than an illiterate teacher. I had an English teacher about 50 years ago who couldn’t pronounce Yosemite, she called it Yo-see-mite but she was thankful when I told her the correct pronunciation Yo-sim-a-tee.
@@JohnFourtyTwo Another way of saying "Yosemite" is "the most fabulously beautiful place to visit" - especially in the months of May and June when the snowmelt fills the waterfalls and Merced River. Great that you taught the teacher how to say the name of this most wonderful place.
Heh I live in New Zealand and I know the correct rendering of Yosemite.
Learned PEMDAS from you yesterday and solved this one quickly!
John, I love your math channel. I am a math person as well! Numbers & Math are the universal language. I think we should connect one day, I believe we would get along extremely well! Hope you channel continues to prosper!
3[5+(20÷2)×5] --> 3[5+(10×5)] --> 3(5+50) --> 3×55 = 165
ya took me less time than you to write that.
I agree, this is basic order of precedence.
@@weebee6922me too.
Thank you
Wow, I just realized how much I had forgotten in regards to basic math. Thanks for the video. I got it totally wrong. I worked left to right in the parentheses, then multiplied by 3.
I did the same thing. Why wouldn’t you just put them in order of how you’re supposed to work it out?
That would make sense, but I remember math had it's own set of rules. I just pretty much forgot all of them.@@Inquisitor_Vex
Plus and minus come in which ever order they come first
X and : come in which ever order they come first.
In this, here is the 4 second easy calculation that ran in my head:
20/2=10
10x5=50
5+50=55
3x55=110+55=165
That’s what came into my head right away too.
Thank you Mesiah. I have finally found someone who has taugh basic arithmetic to me!
The order of plus and minus doesn't matter
Im an electrician and im always confused with plus and minus
In early teaching, ÷ said any function to the right first then the ÷ so 20 ÷ (2 x 5).
Yes, 165. Did it in my head thanks to learning from this guy for the last months. Im 60yrs and never learnt this type of math at school. Thankyou. I love Aunt Sally😂.
Sure wish you were my math teacher back in the day. Now I lament that I can’t do math and my brain cracks. I enjoy your videos. I don’t feel that I am not capable. Thanks.
I'm 75 and terrible in math but I'm doing these to work my old brain. Thank you!
I got 65
75 .. your a kid😀😀
I was part of the 21 answer crowd, unfortunately, but I’m grateful this video explained why I was wrong and how to not make the same mistake again. Thank you.
I liked and subscribed.
Another method to help you with PEMDAS (or confuse you more ;-) ) is keeping in mind that a **division is just a multiplication of the inverse value or reciprocal so that will transform your problem to: 3 ( 5 + 20 * 1/2 * 5 ) or 3(5 + 20*.5 * 5) , so now the division disappears and you do left to right multiplications in order first. 3 ( 5 + 10 * 5 ) => 3 * (5 + 50) , 3 (55) = 165 or when you are down to 3*( 5 + 50 ) , you could use the distributive principle you use in algebra of a (b+c) = (ab+ac); (3*5 + 3*50) = (15+150) = 165 to verify that you answer is right. Keep in mind that PEMDAS is just a trick for your to remember order of operations, but as you learn more math there are other tools that will help you gain speed or find easier ways to solve problems that might be more relatable on how your own brain works. This is fine example of how simple arithmetic is a foundation block for algebra, geometry, trigonometry, pre-calc + more. **Note: this is mostly true with integers and rational numbers, you run into some issues later in life in computing, software, with irrational and imaginary numbers like pi. :P
a faster way to do this in this example is
3 ( 5 + 20 / 2 * 5 ) = 3x5 (1+10) = 15 x 11 = 165
Thank you, this is great. I don’t really need it, but I love knowing how to do it. Even though I could have used it 45 years ago.👍🏻
I have been a machinist and a fabricator and a carpenter in my lifetime and I’ve never run up on one situation where I used any equation like this. I couldn’t figure out in school why they were teaching me this and now I’m 52 and still don’t know why.
You might think you have not have used what you learned in math, but you've probably used the logic and problem solving skills you learned without realizing.
@@rthompson7282 It's not so much the basic math is of no use. It's that writing a practical problem in this way is something a non-mathematics professional would never do. Effectively as he mentions around 10:25 it's made in a way that is intentionally deceptive. In most practical applications of math, you end up being held accountable for the result of the use of the math, so if something is written in a way that could seemingly done multiple ways and the wrong one is chosen, liability for the outcome becomes a concern. Mathematician's don't have this issue. Like @larrybuckner8619 mentioned, machinist, fabricator, and carpenter, his head or a coworkers head would be on the chopping block should something unfortunate happen due to writing an equation in this way. At best, this use of presentation in math, is a good example of what NOT to do in terms of learning logic and problem solving skills, because it eschews common logic and practical use in favor of requiring rote memorization and convoluted presentation to create a problem in need of solving, neither of which is of any direct practical use.
the beauty of mathematics and how finite it is in a disorderly society has an appeal. wish i was better at it but i do understand the appeal
If you would have done an electrical apprenticeship, you'd understand why...
Me too . I worked in dentistry and never used it , not in the last 22 years anyway
I found maths very challenging at school, but I LOVED this video - got it wrong first time, but I learnt a lot!
Great explanation - wish you'd been my maths teacher!
The teacher you have makes such a difference to your learning skills, some can impart their knowledge and you totally get it.
Never too old to learn though. 👍
“Maffs” that’s you
@@mikeb8013 not exactly...I'm an English teacher, and my pronunciation is pedantically clear and precise!
My sister loved math for the same reason you have. She liked the challenge. In contrast to my philosophy, I woke up every school morning conceding defeat in every aspect under the title "Schoolwork". Lol
@NA-fe4yy both are correct. In the UK they say maths. In the US, we say math.
This is the first video of yours that I have seen, and I WILL be subscribing just to try and re-learn what I've forgotten from 9th grade Algebra I in 1973. I struggled with math beginning in 4th grade. Our teacher was Asian, his IQ was probably at least 200, the whispers in my class were that he could make a perfect circle on the chalk board, and they were right. His accent, his IQ, and the speed of what he wrote on the blackboard was faster than I could understand, and he didn't repeat things. That was my first year of fractions, and with each year after that, I struggled so hard, and when it was time to sign up for classes in 9th grade (still junior high) for math, there were 2 options. General Math or Algebra I. That was an easy choice for me, General Math. On day 1, I was nervous and happy all at the same time because I felt like it was something that would be easy for me. Sort of like some of my other classes were. My teacher was probably around the age of 60, and very easy to pay attention to. After day 2, he asked me to stay after class, and I was petrified. I went to his desk as the class emptied, and he asked me "why did you sign up for this class"? I hung my head (I was terrified of my own shadow) and told him of my difficulties with math and that I thought I would do better in General Math. He then told me that he also taught the Algebra 1 class, and he was sure that I could do it, and he wanted me to give it a try, and if I couldn't do it, I could go back to the simpler math. Having him tell me that he thought I could do it was something I wasn't very used to hearing, but I went to Algebra I the next day and I stayed in his class, never getting below an A- on anything. I was even raising my hand to answer questions-that was new for me also. That man made me believe in myself more than any other person in my life including my parents. So for High School, I joined my classmates in Algebra II. Totally different teacher, and I fell behind quickly. I barely got through the semester without failing, I dropped it after that first semester, and never took another math class. Little did I know how much math would be part of my life for 18 years of working in Ophthalmology. It was only dealing with positive and negative numbers, but I could rattle those numbers off, I had a great understanding of how crucial my numbers were for the surgeons, and while I never needed Algebra II, I climbed the ladder to the top rung one step at a time, always grateful for that one teacher who believed in me. Sorry for the book, I will sub you now that I've learned something from you. Your voice is calm just like my teacher who I wish I could have thanked for what he did for a farm girl who didn't think she would go far in life, but I did. God bless good teachers everywhere.
For someone that has had difficulty with understanding basic algebra. This is the third video I watched and ta da. I got it right. Woo hoo. Thank you.thank you,thank you.
I was taught PEMDAS (Please Excuse My Dear Aunt Sally) and got 165.
3(5 +20/2 x 5) =
3(5 +10 x 5) =
3(5 +50) =
3(55) =
165
Edit: I was taught PEMDAS in 6th grade and reminded again in Algebra
I got it right to! 😉👍=165
I was never great at math and I as well was taught this in 6th grade and my achilles heel Algebra as well. So proud of myself I got it right too! And remembered it!
I thought it was BEDMAS- BRACKETS EXPONENTS DIVISION MULTIPLICATION ADDITION SUBTRACTION. There is not a aunt Sally in math. At least it is in Canada
3(5+20/2x5)
PEMDAS
Inside parenthesis
Parentheses: ...
Exponents: ....
Multiplication: 2x5=10
Division: 20/10=2
Addition: 5+2=7
Subtraction: ...
Outside Prentheses
P: ...
E: ...
M: 3x7=21
D: ...
A: ...
S: ...
The answer is 21.
BODMAS
brackets
Of. As in ‘power of’
Division
Multiplication
Addition
Subtraction
Following these rules, I got 165
I know BODMAS is different to BEDMAS or PEDMAS, but it means the same thing and I’ve remembered BODMAS for 40 or more years! So my teacher managed to jam this into my head that’s lasted almost half a century
I had a lot of maths at secondary school about 45 years ago, in Poland. According to the rules we used back then, the correct answer would be 7.5.
Me too, in UK. This makes no sense.
There goes the theory that math is the universal language.
@@JohnFourtyTwo Hahahahaha! Cracked me up, John. Good comment.
I'm in the U.S. and I also came up with 7.5. We used parentheses within brackets, so it was very clear which formulas were used first. Always got As in algebra. No need to make it so complicated. I've seen how they've changed the way math is taught (with my grandchildren) in the last 20 years, and yet math scores across the U.S. continue to decline.
@@bvm3925, from what I learned in elementary school arithmetic more than 50 years ago in NY, you solve bracketed sections first, multiplication and division first from left to right, and then addition and subtraction from left to right. So you would first divide the 20 by the 2 which equals 10, and then multiply that by 5 which equals 50, and then add the 5, which equals 55, and then multiply that by 3, which equals 165. Hopefully that is the way the instructor in the video solves it. Another alternate method is to distribute the 3 into the bracketed section which would result in 15 + 60 ÷ 6 × 15, which equals 15 + 10 × 15, which equals 15 + 150, which equals 165.
I am actually quite proud of myself. NO ONE could ever make math make sense to me in school; At first I solved it incorrectly but as soon as I saw it written with a proper division sign opposed to the forward slash, which I also recognized as divide; I knew to do the division before the multiplication and got it right. And all in my head. Major accomplishment for me!!😀 I'm quite sure I couldn't pass a grade 8 math exam though....
Delirious here. Got it right! You’re a great teacher, but I needed clarification and listened to another educator who said we always move from left to right and m/d means either procedure , but if division comes first, do division.. you’re good, thank you! Wanna give us some homework?
I love this!!! Back in college, I majored in math and I love solving problems so this was easy for me. Needless to say, my nieces and nephews and grandkids all call me when they need help with their math homework - because according to them, I explain it "way" better than their teachers can! However, trying to help them solve complex math problems over the phone is a pain - especially when I'm at work or at the grocery store! Because well, when solving any math problem, it's all about the visuals!
Sadly, I'd say that 95% of people who think they're bad at math, really aren't. They've just never had the benefit of a great math teacher to visually explain the proper steps to follow when solving a problem. I tell my grandkids to always follow each step and that a single problem can take up to a half a page to solve, and extremely complex problems will take up the entire page - front and back! Knowing the proper steps and following those steps exactly, will ensure success.
After watching your videos, I have to tell you that you sir, are a fantastic math teacher! Not only is your voice very calming, your visuals are the best I've seen! This is exactly the way I have shown my kids and grandkids how to solve a problem - only this is better! Your use of the green "chalkboard" style screen, combined with your use of fonts and explanation of proper procedure is extremely effective. It's so easy to understand, follow and comprehend. I just forwarded your channel to my entire family!
The kids will be starting school in a couple weeks, so I told their parents to subscribe to your channel and to start watching one or two of your videos every day. I told them to make a game out of each video by having everyone solve the problem on their own, then watch the video to see who got it right! By turning it into a game, it makes it fun for the entire family and the kids (and parents) get a refresher course so they're prepared when they go back to school - creating an everlasting boost to their confidence. I'm so thankful I found your channel. You are a Godsend to both parents and kids who struggle with math! Your channel is a game changer! Thank you so, so much! 💙💯
answer is easy 21
I used to find I didn't understand the way our teachers explained things - this was New Zealand in the 1970s - but I easily understood the way my father explained how to do the equations - he was taught in England, 1930s/40s. I don't understand the modern ways at all and I not only enjoy maths/arithmetic but am generally fairly good at it - don't like using calculators though - and I can't understand why people now say that the ways they were taught in the UK as kids give different answers to those I get because my dad was educated there and the ways he used and taught me were the same as our teachers used in NZ, but which now appear to be totally different to those taught in the UK. Very confusing and can only guess they changed their teaching methods some time after the 1940s for some reason.
i only read like 2 sentences but i’m gonna go ahead and guess you’re a english major also cuz damn that’s an essay.
When a teacher asked me to explain why something's done in a certain way, my only response was "because you said so". Beyond basic arithmetic, math makes absolutely no sense (and I was never good at word problems, even in basic arithmetic). I majored in Computer Science in college, but I wasn't able to take any programming courses because I couldn't pass Algebra. (Well, I took JavaScript from another college based on a technicality; the professor didn't know why I was in the class since I was already good at JavaScript, but I thought it would be an easy elective; I got in a tiny argument because the textbook said to use document.write() in an XHTML document and brought up that write() is part of the HTML DOM but not the XML DOM so you have to use methods like createElement(), createTextNode(), and appendChild() to properly add new content to an XHTML document (eh, I did it properly regardless of what the textbook and the professor had to say about it)).
OPERATIONS
A linking of elements within a set and resulting within that set for all elements of that set is an operation. There exist monary, binary, trinary, … linkings. In mathematic: +,-,•,: are binary operations within the set of rational numbers. As soon as you introduce radical you enlarge the set to the irrational numbers. R and I build the real number set.
Here you have the operators +,-,•,:,exp,log. Notice that the introduction of PI, e can not be generated by using operators. Those numbers are transcend. There are exactly 11 AXIOMS which define the set of real numbers. The set is called FIELD.
Correction......."if we have both multiplication and division, neither has priority and we work from left to right". So the answer is 165.
I was also taught that multiplication had equal priority to division, but another respondent said that division comes before. I can’t agree with that as they are interconnected functions.
In my head
Mathematically any order will be correct. It's just important that everyone follow the same rules.
165
But to avoid confusion you would always add extra brackets if you are a good communicator.
I'm a web developer and I do this all the time to avoid confusion.
agreed
But to avoid confusion you would always add extra brackets; if you are a good communicator. :)
basically the one who made the question are bad communicator.
No, I feel that brackets can only add confusion. The rules of math already dictate the order of operations.
*At 66 years old, it's never too late to re-energize one's brain, thank you, professor!* 👍
good vintage 😁
You are a kid at 66😀😀
Thank you teacher! I'm a frenchman of 71. I never heard about PEMDAS or equivalent in french before you spoke about it! And though my english is far to be perfect, i understood your whole explanations and i'm very glad of this. I have to precise that when i was young, i hated mathematics and the teachers in this discipline. Now i notice that i understand very easily, and in english! So i have to consider nowadays, that i am a little bit smarter than a nut... What a great satisfaction !😊😉
12765 .......ahh close, but no sigar
@@RS-Amsterdam ???
I believe other teachers I forgot where teaching B.O.D.M.A.S rather than P.E.M.D.A.S
@@alfredvikingelegant9156 🤪
La première fois que j'ai appris l'ordre des opérations, c'était en français, mais je viens des États-Unis. Mon école primaire avait un programme d'immersion, donc mes cours de mathématiques et de sciences étaient tous en français pendant cinq ou six ans. Quelle coïncidence intéressante ! (pardonnez-moi s’il vous plaît d'utiliser un programme de traduction, mais je fais encore moins confiance à ma grammaire sans lui. Cela fait longtemps que je n'ai pas pratiqué!)
I've got to review all of this stuff since I have a four year old grandchild that is exceptionally bright and all to soon he will be wanting to learn. In my view this guy is just what the doctored ordered. I don't know that he would agree but I've found that fifty per cent of learning Algebra on up is just learning the formula!
Appreciate this content! Wholesome, true, and even though I got 21 initially: you were not condemning.❤
Likewise here...
Instead of PEMDAS I taught my students PEMoDAoS, the little "o" stands for OR, when confronted by the same level of operation the one that comes first working left to right (the same direction we read) is the one acted upon. I had the kids make up their own sayings to remind themselves, the best was "Perform Each Math Operation During Algebra On Schedule". When the kids become invested they own it!!
Brilliant ! Your students mnemonic makes more sense than any others I've seen. Congratulations. You are the kind of math teacher that can open their minds to the joy of numbers! I salute you.
Thank you, I was never taught PENDAS. Graduated in 1982, I’m learning it now on RUclips.
I thought it was set in stone. I’m happy to know that it’s not.
Thank you for this information.
PEDMAS has been taught to everyone who has ever attended school way before we were born. Just because you don't remember doesn't mean you weren't taught it
1981 grad and have never heard of it either. Life would have been easier with pemdas!
@@RenéeinVirginia - right!
I took algebra in college and I was taught to use 6 different type of formulas to solve such a problem.
Remembering the rules of pemdas and not overthinking it, I came up with 165 in my head in about 20 seconds.
I’ve noticed people forget that addition and subtraction are equal, as are multiplication and division.
Tu solo lo haces MAS COMPLICADO; MUCHO BLA,BLA,BLA,BLA,¡¡¡¡
Not true. This guy got it wrong!
165 in no y brain before I even started the video.
PEMDAS.
I learned advanced math calcs on a circular slide rule in the early 80’s while navigating jet aircraft.
We had a sextant, pressure differential (radar bs barometric altitudes), and Ded Reckoning.
Nothing like today.
I got 165 too, we were taught BODMAS at school. Brackets, orders, Division, Multiplication, Addition, Subtraction.
Same, but I learned BOMDAS 😅
@@gravyz2cute4u Which just shows you, It's just an agreed method.
Whenever I'm in doubt in cases like this, I convert the divisions into multiplications. So it would be : 3 ( 5 + 20 x ½ x 5) = ?
With that, the mistake that leads you to 21 can't happen.
20 x ½ x 5 = ?
10 x 5 = 50
-- or --
20 x ½ x 5 = ?
20 x 2.5 = 50
-- or even --
20 x ½ x 5 = ?
100 x ½ = 50
This approach also creates some freedom to choose the simplest calculation.
2 does not = 1/2. 2 in fractional representation is 2/1. 1/2 is .5 in fraction. This person is also incorrect the actual answer according to simple math is 21 because multiplication always comes before division in simple math order of operations, to get the answer they wanted you have to either use brackets or put the 3(5+20/2x5) then the answer works out to what they are getting at, the notation was done in a shitty way to trick people the problem is with that notation the answer is 21, complex math or higher meth is different and that comes when you are a physicist or a mathematician and regular order of operations has the problem of creating a paradox.
People are being assholes.
@@nocturnal101ravenous6 🤣
Before watching the video:
20 / 2 = 10
10 x 5 = 50
5 + 50 = 55
3 x 55 = 165
[edit] And I was correct. I win... something. Probably.
My answer was the same and I followed the same steps (MDAS).
Multiply first
So 20/10 = 2
5 + 2 = 7
3 x 7 = 21
Do you understand no one writes expressions in this format?
Expression should read 3[ 5 + 20/10]
Why make it a puzzle when it is only a multiply and divide and addition expression?
Answer is 165. Took me few seconds to solve this and learned trick by watching your other video. Thank you for sharing your knowledge.
.... so... i did this via algebra expansion...
3(5+20/2*5) becomes (3*5) + (3*20) / (3*2) * (3*5), becomes 15+60/6*15, becomes 15+10*15, becomes 15+150, becomes 165....
Completely different method of dealing with the brackets but the same ultimate answer :)
This is the way I was taught. Its So much easier this way.
Distributive property
@@FirstNameLastName-yc5sz that's your opinion, right or wrong your allowed to have it. You can do it your way, and I will do it my way.
I'm 59 now. Math has always been my strong suit! I did not know the technical word for the order of operations, but definitely knew how to calculate the correct answer (of 165).
My curiousity, in regards to all of the people who came up with the correct answer, is wondering how many of you were able to solve the question within your head (i.e. not using pen/paper; calculator; etc.)?
it's a dying skill, but a person SHOULD be able to solve the equation without any assistance (i.e. in your head).
I just see the answer. Not sure how. It works for me with calculus also. I do have to work at DiffEq though. I am high functioning (autistic spectrum) and test at very high IQ levels. The latter indicates a high level of inductive reasoning and logical thinking. The former indicates I am neural-divergent (don't think like a "normal" person).
oh, with their natural organic intelligence, nahhhhhhhhhhhhh no way,
artificial intelligence is their go to in 2023---lol
165=1+6+5=12 as you come from the 12th creation/dimension
pure celestial being,from the expression of the one, and from the highest level of reality^
I got both answers in my head, but wasn’t sure whether to do multiplication or division first.
I correctly worked out the right answer in my head but realistically it's a pedestrian calculation. I tried to also work out the wrong answer in my head but got 187.5 not 21. I found it interesting how 21 was derived in the video and it was not something I would have thought of. When I looked at the question I do not see a division symbol in my mind, such as "a" divided by "b" but I always see it as a multiplication such as "a" times "1/b" or alternatively "b^-1" In most semi advanced mathematics the divide symbol is not used probably for that reason. The divide is either a full bar clearly showing the numerator and denominator or alternatively a "/" symbol and parenthesis.
I think some people get confused about the MDAS part. That means that Multiplication/Division are on the same level as well as Addition/Subtraction. They are worked right to left-M/D or D/M first-depending how the problem is written. That’s what tripped me up when I first started doing these types of problems.
DOES NOT MATTER HOW THE PROBLEM IS WRITTEN …MULTIPLICATION FIRST THAN DIVISION..
Least complex to most !!
what to be confuse of? prentice's , multiplication, division addition subtraction. that's the rule. so in this case the parenthesis makes it 9 then you do the multiplication makes it 18 then addition makes the sawer 21
@@ChasOnErie Wrong - multiplication is first only if it appears first when read left to right.
@@respectbigman3133The answer is 165. Multiplication and division are on the same level. You don’t necessarily multiply before you divide. You just work left to right whichever comes first. So first you do everything in the parentheses. Working left to right, divide and multiply first, and then subtract and add, left to right. Then work outside the parentheses. The answer is 165, not 21.
@@ChasOnErieYou have made up your own rule. The problem is you’re going to get the wrong answer many times. The true rule does not say to always multiply before divide. You work left to right, dividing and multiplying first and then subtracting and adding. The answer is 165.
An alternative way, which still honors PEMDAS is to distribute the 3, thereby removing the parenthesis in one step.
3(5 + 20 / 2 x 5) --> 15 + 60 / 6 x 15
Then follow PEMDAS just like he shows for the rest:
15 + 10 x 15
15 + 150
165
This comment needs more attention!
It's how I did it in my head
I learned BEDMAS back in the day. Brackets, Exponents, Division, Multiplication, Addition, Subtraction. 👌
that's the method our high school math teacher taught us as well
Yep that is what I learnt as well . Is maths not a universal language anymore?
See I was taught PEMDAS
@@kdizzle901 Brackets vs. Parentheses... same thing, just different words.
It's like bathroom vs washroom vs water closet vs loo etc. You're really trying to say the same thing, just using different words depending on where you're from.
As for the switch of the D and M, they're the same grouping, so it really doesn't matter which order they go in. Maybe in PEMDAS rolled off the tongue more easily for your region...
@@dulcinealee3933 Yes math is still a universal language, but English is not. Specifically, words used varies depending on the region you're from.
The perfect example is your use of the word maths vs my use of the word math. Same thing, slightly different word based on where we're from.
I was never taught any of this and got 187.5. Thank you for the lesson!
Yikes we must be on a similar brainwave as I got the same answer as you when I did it before watching the actual video.
That is what I thought is that correct?
Agree with this number
This is the same # I got as well
@@hcox1111No
Saw the video title and image, did the math in my head, went to the end of the video and....kudos to my elementary school teachers. Whatever you did, it stuck.
Per the distributive property, you COULD execute the parenthesis by multiplying 3 times every item within the parenthesis and then do the MDAS order operation as described....you'll still get 165.
15 + 60 / 6 * 15 = 165.
Hahaha... and I read that as a fraction, so now I get 0.8333, lol!
Damn imperial system... :/
That’s how I learned to do this type of problem.
This is why 3(2) is not the same as 3*(2)
And why many "viral" math problem confuse people...
@@jawstrock2215 pretty sure those are the same bro...
@@vladdawoken4181 they actually are not :)
one is a straight multiplication, the other is a parenthesis multi,juxtaposed, implied multi.
There are cases where they would give different answers :/
If you see the parenthetical part first and then see not a division problem, but a fraction: 20/2, it works out. 3[5 + (20/2) * 5] =. It's a good idea to always think of a division symbol to mean a fraction.
Not a bad idea, but not flexible enough.
Let's say we change the question to 3(5 + 20 / 2 X 5 / 10), thinking of it as a fraction might add more confusion like 3(5 + (20/2) x (5/10)) while the correct form would be 3(5 + ((20/2) x 5)/10). It works out but also add some complexity.
Easy calculation straight you get 165 with this nicely bracket in there
When i did math in the sixties the way this is written the answer would be 7.5 . We were taught to figure inside the parentheses first. 5*20 =25 divided by 2*5 =10 answer 2.5 *3 =7.5
Any operation within parentheses is attempted first. However, given that division and multiplication share the same importance, we attempt those operations from left to right. So 20/2 = 10. Then multiply the result by 5, which yields 50. Only then can we add 5, which gives us 55. Lastly, multiply 3 by 55, which totals 165.
As a programmer, I always use parentheses to separate math logic so there is no ambiguity. If it’s not clear to most people, that means the equation is poorly written. The author must make it clear what the intentions are.
I remember doing various strings of if...then functions and similar in various programming, spreadsheet and print formatting languages. In 1981 was in the last class at my uni to use punch cards & Fortran in Computing 101 😂😂 but it was useful later in setting up reports in accounting programs that were still text based into the 2000s. After 2010-2015 that started changing, too so it's been useful for a looooong time. Also helped with complicated spreadsheet functions & macros.
Yes, parentheses within parentheses establishes function order, otherwise it could be misinterpreted.
@@kathydurow6814i😂
This is the correct answer.
This is the Mathematical equivalent of the Oxford Comma.
I despise the Oxford Comma...
You can see in the comments exactly why the International Organisation of Standardisation exists and why specifically ISO-80000-1 exists.
It says when writing division on one line with multiplication or division directly after that brackets are *required* to remove ambiguity.
Never write 20÷2×5
It is (20÷2)×5 or 20÷(2×5).
Those are acceptable.
Many are taught M is higher priority than D and some books do use that convention (and I don't just mean for multiplication by juxtaposition specifically) and that leads to the general mistake of
20÷2×5 = 20÷10.
Avoid the mistake by writing properly on the first place.
Use two line fractions as these are best practice.
It's written as twenty over two times five which equals two. If it were written as twenty over two, times five it would equal fifty. BOMDAS and PEMDAS are tools more than rules.
Brackets matter and cannot be arbitrarily added or subtracted without changing the equation.
I won't refer to the international standard here, however, a comma in the correct position, makes your comment far less ambiguous.
@@violettownmicroenterprises1528 actually there should be two commas. Don't point out an error with another error :)
Wouldn't one comma clear it up enough?
While
20 over 2 times 5 is ambiguous.
Does
20, over 2 times 5
imply 20/(2×5)?
although I can see
20, over, 2 times 5 being better for
20/(2×5)
20 over 2, times 5 is pretty clear to be
(20/2)×5 though even though you could write
20, over 2, times 5 either.
So, maybe one or two commas, depending on the situation?
If you actually understand the fact that multiplication and division are the same operation then it makes no sense for one to have priority over the other. The problem is that people try to remember PEMDAS and don't actually understand what they're doing.
Canadian who learned order of operations back in the 1970s. My school didn't bother with any mnemonic device at the time, which may have been a good thing. Always clear to me that multiplication and division had equal priorities with each other (as did addition with subtraction). The PEDMAS mnemonic sounds as confusing as it is helpful, which, when you think about that, means it is a HORRIBLE mnemonic.
tbf, we learned it as BEDMAS (or BODMAS, depending on terms used) in the 90's and that was a perfect layout of the order of operations. Also, when did PEMDAS become the new norm and who needs to be flogged for messing up something so simple? Or was it keeping in line with the overcomplication/revamp of basic math they did at one point?
Also Canadian, but we were also taught MD in the order they appear, and AS in the order they appear. I don't know if they still teach that way but it was cemented in our heads from grade 6 on (learned in 90s). Also why make such a big deal over P or B? Parentheses are Brackets. It makes no difference. Also if you were taught in the 70s you probably learned with BODMAS Brackets Orders Multiplacation and Division (in the order they appear) Addition and Subtraction in the (order they appear). My mother and father taught me BODMAS when I was 8. By time I was in highschool it had become BEDMAS (as exponents made more functional sense as a term then Orders) ....they learned it in the 70s as BODMAS, so you would have to.
@@TheTicoune Since the internet spread Americana to everyone. BEDMAS is popular in British English Schooling (Canada, New Zealand, Australia, UK), where as PEDMAS is an American spin on it because despite being anglophone they choose to be different. They are the exact same thing. Parentheses = Brackets.
@@kurtmooreca PEDMAS would make sense, but its not spelled out that way for whatever reason: PEMDAS is the official way...even though it makes no sense and creates confusion rather than helping it.
@@TheTicoune Why would it make more sense to say division before multiplication? These 2 are equal, you dont do either one specifically before the other.
Basic computing: from left to right 1) multiplication 2) division 3) addition 4) subtraction. Work inside parentheses first.
Multiply and divide have the same precedence as do add and subtract.
I got 165 in my head. As a music and math teacher, I've taught both PEMDAS of BIDMAS. I stick with PEMDAS with the emphasis PE(MD)(AS) you showed. I tell my students multiplication and division are actually the same thing, just expressed as inversions that lead to the same result. As with AS, instead of taking away like subtraction, I rephrase it as adding a negative. So in the problem above, I can easily see how kids get 21, because they are taught to do multiply first instead of divide, no matter where the multiplication operation is in the problem. Any time there is an order of operations problem, I tell my students to convert every division operation to multiplication, and every subtraction operation to addition. Then solve PEMA left to right. It's an extra step, but they soon eliminate those extra steps once they realize MD and AS are grouped to together.
Very good explanation.
I learned PEMAL, ‘M’ultiplication, ‘A’ddition, from ‘L’eft to right
Where division is just multiplication and subtraction is just addition
Something is not OK in teaching math if these kind of problems exist. Parenthesis are used to clarify things in case any doubts . Programming had caused this problem.
You're absolutely correct. The only operations are multiplication and addition. For that matter, multiplication is just a quicker addition.
Interesting- in Canada they teach it as BEDMAS. (B standing for brackets or parentheses) and the rest is the same as this version. My husband taught math for 30 years, so I heard this a lot!
I learned it in elementary school. It’s impossible to forget so I don’t understand how so many don’t do this right.
It’s PEMDAS here. P for parentheses lol :)
@@Withjoyfulsenescence Here where? The reason why PEMDAS is wrong is because you put the DM backwards, is why BEDMAS is correct
@@TheOtherKine It could be BEDMSA or PEDMAS and it would be right as MD are equals and AS are equals and are solved from left to right in the equation
@@TheOtherKine The DM is not backwards since the ordering doesn't matter. MD and DM are correct as long as you read the equation from left to right. Their here is probably referring to the USA. USA typically does PEMDAS while places like Britain and Canada use BEDMAS.
In my school we were taught BODMAS (brackets, other, division, multiplication, addition, subtraction) but also that the 'DM' didn't swap, division was always before multiplication. Because of this I had to pause to work out how someone would come to your example of a wrong answer.
Yep, BODMAS was what I was taught.
Same here in NZ
I was taught in the UK in the 80's and we didn't learn any misleading acronym. We were just taught the order of operation. Division and multiplication have the same order, and so are done left to right.
@@thor4u no, 165 is the answer I came to using BODMAS, I was mostly commenting on the division and multiplication being interchangeable, while I was under the impression that they weren't. If a similar sum with those two functions swapped were the example I would have got it wrong if dictated left to right.
Got this one right, even though math used to be my worst subject ^-^ After getting a very bad grade at algebra, I started practicing it alot and actually started to enjoy it alot. Eventually I got one of the highest grades of the class and was alot of fun, like just making puzzles. Glad to see some still stuck ^^
Yup, immediately realized people get it wrong because they're doing the addition first.
We were never taught PEDMAS. Using parentheses and brackets eliminated any confusion about the sequence of operations. That’s why it had to go.
YES! This is ridiculous, memorizing rules.
Please excuse my dear aunt Sally is pictures they are cool wrong and there's nothing over
Agreed. in the UK brackets etc remove any ambiguity. Also if you were programming it you would also put in brackets. its good practice and makes for ease of maintenance.
Thanks John, I got 21. I am 60 and vaguely remembered PEMDAS, but had forgotten reading from left to right takes priority.
I learned BEDMAS here in Canada. Brackets, Exponents, Division or Multiplication, Addition or Subtraction.
21 is right.
It is 21. The problem happens due to how it is written. the division symbol implies it is over the upcoming portion of the equation.
@Dead_Goat did you watch the video? 21 is the wrong answer because the division takes priority over the multiplication because it shows up first. If an expression has two or more operations of the same priority, do those operations from left to right.
@@Dead_Goatno it doesn’t.
The problem with PEMDAS (easy to forget the M & D happen together and the A & S happen together, so you start thinking you always do Multiplication before Division) is why one of my middle-school teachers always emphasized that M & D are actually the same operations written different ways and ditto with A & S, resulting in just PEMA.
Funny 'cuz I casually calculated 165 and then I remembered about the "order" I was thaught 40 yrs ago and got 21.
But when they are the same operation Multiplication-Division then Addition-Subtraction it's simple, you do left to right. The left to right order of operation is the most BASIC order you learn when beginning in math. The first level of math is addition-subtraction. You learn you do that left to right. 4+2-3+6-1-2=6. Then you move to Multiplication-Division and you still do it left to right. 2x6/3x2=8. Then you get to the next level combining all four. 4+2x6/3+6-8/2+4x2=20 Multiplication-Division and Addition-Subtraction. We learn you do M-D first, still doing left to right, then you do Addition-Subtraction left to right. Next, you learn Parenthesis and Exponents to complete PEMDAS. Complete the Equation in Parenthesis first still using PEMDAS (4+2(8/4+2^2))+(8-4/2)^2=52
It really is not that difficult.
@@LeSyd1984Part of the order you learned 40 years ago and I learned 50 years ago was left to right so, you would have gotten 165 if you followed those rules correctly since it hasn't changed.
Yeah, so, you didn't provide an answer. There are two answers based on your comment, so which one to you is correct?
Better than PEDS I guess.
I didn't have a good math teacher until my freshman year in college. For years I had struggled with math, although I had the GPA I needed to be accepted by the university. This one professor cleared up the mystery...from that class onward, the rest of my classes were a snap! My 8th grade math teacher was also helpful, but I still had headaches with math. My freshman math prof made all the difference.
Greetings. The correct answer is definitely 165. First we consider the bracketed figures. In the brackets, we will first divide 20 by 2 to get 10, thereafter multiply 10 by 5 to get 50. We will then add 50 to 5 to get 55 and finally we multiply 55 by 3 to arrive at the answer of 165.
Simple and easy explanation! Plus a nice refresher for anyone who’s forgotten the PEMDAS formula.
When you express the division operation like a fraction it is much easier to see what should be done first. Placement of the division bar makes it much easier to see different groupings than the elementary school division symbol you used in the original expression.
I think when I went to college I rarely if ever saw the elementary school notation. We always used a fraction bar that you could position so as to minimize any ambiguity.
Also when my teachers taught PEMDAS, they always made it clear that multiplication was first and addition was second and each were performed LEFT TO RIGHT.
If it is rendered as vertical fraction, with a horizontal line through the middle between numerator and denominator, which clearly shows the extent of the overall fraction, then yes definitely. But fractions are more likely to be renedered in typed text with a 'front slash' which is no clearer than using the division symbol used here.
@@MrDannyDetailin which case use parentheses to do the grouping that would normally be represented by the positioning of the numerator/denominator. If you were writing this in LaTeX you'd have to use those parentheses anyway.
I'm going back a long time now, roughly 37 years but I was taught bodmas, meaning B. brackets O. of D. division M. multiplication A. addition S. subtraction. Which would be a completely different answer due to a different process. So with all that said are you telling me that I was taught wrong.
Thanks, that makes a lot of sense. I was actually taught wrong in school. My teachers were insistent that M came before D. Now I know why I failed a couple of math sections in test for various jobs over the years. Thank you, public education system.
I thought the same thing until I was corrected in Middle School by one of my teachers fortunately.
They should be writing it as PE(MD)(AS) or some thing.
Then again, in today's common core world, they probably teach an incredibly stupid and unintuitive way on purpose.
@@BlitzkriegOmegaIf you write it as PE(MD)(AS) then you create a paradox. Cause parenthesis are first, but the MD and AS are in parenthesis. So is the P first or the MD Because its in parenthesis
@@BlitzkriegOmegaalso it's still wrong because it should be p(er)(MD)(as)
But..roots are reverse of exponents...
PEMA, roots are reverse of exponents, division is reverse of multiplication, subtraction is reverse of multiplication... There only 3 operation families. 2 operations per family... And parenthesis are essentially just a highlight
M IS D and A IS S.
Got it right. Was taught order of operations, here in 80s/90s UK, as BODMAS. Brackets, orders, division, multiplication, addition, subtraction. May have been saved as I was taught DM not MD, this was a great refresher!
I was always taught in school bit was called BEDMAS? Brackets, Exponents, Division, Multiplication, Addition, Subtraction.
Now it's all wrong??? Why do rules keep changing.
Lol for me it was GEMS. Grouping, exponents, multiplication/division and subtraction/addition
@@coju8543 In German we say 'point operations before stroke operations'. Division is usually written as a colon, not the stylised fraction, multiplication as a dot, making the kind of operation easily groupable.
And you are wrong !
Division had same priority as multiplication, and so they go from left to right order.
@@Notir072 yep! and same for subtraction and addition. whichever is first is what you do first. if 5+4-3 you would do 5+4 first if it was 5-6+4 same goes. 5-6 goes first.
In Britain it’s BIDMAS - Brackets, Indices, Divide, Multiply, Add, Subtract. I think that’s easier, but whatever method works for you is best.
Pemdas- Parathises exponents multiplication division addition subration idk what they teaching you guys nowadays
Canada: BEDMAS - Brackets, exponents, division, multiplication, addition, subtraction.
.....that's literally the same thing with two words replaced by synonyms.
@@vct454 Not really, one has multiplication first and the other has division first. It makes a difference with this problem
Used to be BODMAS (O for orders)
Maths is about clear expression. Define the problem in clear terms. Do not set out to confuse.
I didn't enjoy math in high school, but I only had basic business math. When I stated college part-time, I had to take pre-algebra and learned to love quadratic equations. BUT outside of school and the fields of science and engineering, does this truly matter. I must say that after taking my math classes required with my degree, I never needed to use it again.
The best way to deal with problems where there is a division symbol followed by a number is to replace it with multiplication by the reciprocal of the number. Then you get (5 + 20 x 1/2 x 5). doing the multiplications first gets you 5 + 50 in the parentheses, and leads to the correct answer. Even better would be for the problem to be written unambiguously from the start!
Right. The original expression of the problem has no practical use...
Just because some don't learn arithmetic properly does not mean the problem is ambiguous. "Ambiguous" would be if people who learned it properly disagreed with how to complete it.
@@Ddrhl Even people who were taught properly can forget how to solve problems or make mistakes when the problem is poorly stated, like this one. If you're being pedantic, it maybe isn't ambiguous, but the fact that a lot of people apparently get it wrong means it is not stated clearly.
It it were written 3(5 + (20 x 5)/2) the sequence of operations would be obvious and I suspect everyone would get the same, correct, answer.
👍👍👍👍👍
@@ceejay0137 Learning math properly is not pedantic...it IS the crux of the matter. Are you saying that since "nuclear" is mispronounced by so many people that it is mispelled? You don't forget order of operations...ever...when you LEARN them.
23 years since I have had to do any Algebra. I was stuck until I got to the PEDMAS part. Had completely forgotten how to do this. It is true if you don't use it, you lose it. I will be digging through these videos as a refresher course.
Hahahaha…PEMDAS
Paranthesis
Exponents
Multiplication
Division
Addition
Subtraction
Algebra?
Since multiplication and division have equal weight, I did the 20÷2×5 part from left to right to reduce that to 50. Then I added 5 to the resulting 50 inside the parentheses to reduce that to one term, 55. Then just multiply the 3 on the far left by that.
The answer is 165.
Clearly does not have equal weight. If they had equal weight, you could multiply first in the "20/2*5", get 2 as a result and you would be right. You would be wrong though.
@@seph. Yeah they do have equal weight. But you always solve from left to right. Therefore you do first the division and then the multplication. (20/2*5 => 10*5 => 50)
@@nIghtorius shouldn't i be able to solve right to left, if equal weight?
@@seph. when equal weight you solve from left to right.
@@nIghtorius i want to do right to left though. Equal weight, so shouldn't matter.
Commenting at 0:01. Easy answer. Equations in order of calculation.
20/2 = 10
10 x 5 = 50
50 + 5 = 55
This solves the bracket (5+ 20/2 x 5)
3x55 = 165
Resolving the equation.
Edit: Post video watch.
I think the problem is most people don't rewrite the equation every time they do a calculation.
3(5+20/2x5) =
everytime you knock out a calculation you rewrite.
1. 3(5+20/2x5) =
2. 3(5+10x5) =
3. 3(5+50) =
4. 3(55)=
5 165.
If you don't understand math to the point you can't knock out operations in your head, rewrite the equation every time you get rid of a X, / , +, - and its easier to keep track of.
Exponents and Squares can also be more easily understood when written by hand.
For example
3^2(5+20/2x5)/2 is the same answer as the above.
(exponents are just factorials multiplied to themselves)
1. 3x3(5+20/2x5)/2
2. 6(5+10x5)/2
3. 6(5+ 50)/2
4. 6(55)/2
5. 330/2
6. 165.
SQRT 9 (5+20/2x5)
(find common factorials for the square and divide)
1. 9/3(5+20/2x5)
2. 3(5+20/2x5)
3. 3(5+10x5)
4. 3(5+50)
5. 3(55)
6. 165
I swear calculators have ruined Mathematics, and thus Science today (in people, computers handle them just fine).
This is the way
Interesting, and there seems to still be confusion in the comments below. But i was taught in UK to use BODMAS (Brackets, Order, Div, Multi,Add, Subtract) so while this order worked fine for me and i got the right answer, i did not realise that the Div/Multi (and Add/Subtract) were on a left to right basis. So had it been written the other way around i would have still done the Divide first. Guess you learn something new every day :D
I am exactly in the same position. You summarised it perfectly 👍
I'm from uk too. and i'm sticking to our way.
Ok, so what if they switched the x and /?
The point is that MD and AS have equal standing. Thus left to right here..
All that, but you always go from left to right.
@@jeanettecardinal790There's no "our way" when it comes to math. There's proper math, and then there's people who do it wrong.
Bidmas in the U.K. You can also multiply everything inside the brackets by three and work it out that way too.
Great video! I never could remember how to do these type of problems. After watching your video its perfectly clear…. And ive been out of school for 40 years! Thanks
I am 62 years old from India, and we were given BODMAS to follow. B-Brackets, O- off(multiplication), D-divison, M-multiplication, A-addition, S-subtraction, to be strictly followed in order. Never failed to get at the right answers.
Yes, BODMAS here in UK too (or used to be!)
This is correct, except that mult/div are perfor,ed left to write within the parenthesis.
2.5
Pmdas here. But same answer
*In Canada we were taught "BEDMAS" (Brackets, Equations, Division, Multiplication, Addition, Subtraction).*
*The ONE thing that I was completely stumped by was the "3(" Now I know that it means "3 TIMES". I always found this confusing because there was no symbol to tell me what to do.*
This is why I failed geometry. I was taught to do inside the parenthesis first in the following order: plus, minus, multiply then divide; then apply the numbers outside the parenthesis. So, 5 + 20 = 25; there is no minus, so then multiply 2 times 5 = 10; then divide 25 by 10 which is 2.5; finally multiply 2.5 times 3 which equals 7.5. And that, ladies and gentlemen, is why I did not enroll in mathematics beyond the level of geometry.
Your process arriving at 7.5 was "as taught" when I attended such classes in High School in the 70's ... (in our very poor School District that was later taken over by the State, due to teaching vacancies our Gym Teacher was also the Health and Math Teacher ... great guy but way out of his depth for Math)
No, you failed because of your lack of understanding of maths. This has nothing to do with geometry, it's basic arithmetic
Nah, geometry is pure memorization of theorems and postulates and application. totally different. I have a great memory so memorizing things comes easy for me. a+b+c is where my brain puts up a block. Just no....3 math tutors and I always got C's in Algebra. I took that C and was proud of it. Though it killed my GPA.
Yep. I got 21. I went into denial. Then frustration. Then acceptance. Then I agreed with you. It's 165. LOL 😂
No
Wow, your videos have shown me exactly where I stopped learning math around the eighth grade. (Where I was still getting in trouble for working the problems in my head.) I never learned PEMDAS, but it was not for a lack of people trying to teach me. I just didn't much care about school. Not knowing PEMDAS must be what doomed me to failure in pretty much all higher levels of math, I somehow passed algebra one, parts one and two, in ninth and tenth grades. I failed algebra two as a junior, and took geometry, (which I actually enjoyed and did well) as a senior. This is the third video of yours I've watched now, and the first one which I was able to answer correctly!
To solve the expression 3 times (5 + 20 / 2 x 5), you should follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and square roots, etc.), Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right).
In this case:
Start with the parentheses: 5 + 20 / 2 x 5
Perform the division inside the parentheses first: 5 + 10 x 5
Next, perform the multiplication inside the parentheses: 5 + 50
Finally, multiply the result by 3: 3 * 55 = 165
So, the answer is 165.
Says Chat GPT
This is the correct answer says my high-school algebra from 2003, my college algebra and yeah that's about the only time I have ever really used this.
But I got the same answers following this order.
@@Robert53area 1982 Algebra from me, still remember parts of it, did watch a video on how to do some of what we learn back then in the head, sure wish we had videos like this back then, I like using Chat GPT to solve a lot of my math problems, I wanted to know what size building will it take to give every person in the united states a 2000 sq foot living area it came up with the answer for me, I like mega structure videos
We learned these 3 simple rules since elementary.
1. Left to right
2. If there are parentheses, do them FIRST. (Left to right)
3. Multiplication OR Division FIRST but ALWAYS remember rule 1, LEFT TO RIGHT.
I hope those SIMPLE rules helped a bit. ☺️😉
3(5+20:2x5)
3(5+10x5)... parenthesis first, Division/multiplication first, left to right ALWAYS
3(5+50)
3(55)
3x55
165
😊👍🏾
i got 187.5 lol i still got it wrong going left to right!
I remember MDAS - my dear aunt sue. Multiply, then divide, then add then subract. Parentheses first. I came up with 21, but clearly I am wrong. 2X5 = 10. 20/10 = 2. 2+5 = 7. 3X7 = 21.
@@titansrule72we learned PEMDAS: please excuse my dear aunt sally. Parentheses, exponents, multiplication and division left to right, addition and subtraction left to right.
I was correct. All thanks to the tutoring my father, a civil engineer, gave me from grade school through college. God I miss him.
165 (20/2) = 10
10 * 5 = 50
50 + 5 = 55
(calculated inside the parentheses first with multiplication or division read left to right first come first serve)
Then 55 * 3
Even though the multiplication math operator is missing from the written equation it is in the written text.
165 is answer
I actually got it right the first time I went through it, BUT then I did it again and again, and got 21 and 7.5 (figure that one out Mr. Math Teacher). In the end, my dear Aunt Sally told me to stay with 165 and I did.😊
On my first try I figured out your '7.5' all by myself, as it turned out by doing EVERYTHING inside the parenthesis exactly backwards! I had just begun to watch the solution explanation in this video when my iPad Facetime rang. It was my Math-teacher daughter from across the country. I flipped the camera around to show her the operation and without knowing the given answer, she got it right, '165', immediately. We laughed a lot. I still can't get over that crazy coincidence(?).
@Robert Mac, i made it 7.5 too. yet i was good at maths. We obviously looked at it the same way.
@@jeanettecardinal790 Sometimes I cannot explain how I arrive at an answer. But I'm happy I'm not alone!
It’s amazing how many people didn’t pay attention in school. I’m 61. Last algebra class I had was college in the early 1980s. The people that argue that “that’s not the way we learned it in school”…good grief. Whether we heard of “PEMDAS” or not, the order of operation was always there to be followed.
Exactly. I never understood how having to remember an acronym and what each letter meant and how to apply it was easier than just learning the correct order of operations. Perhaps graded and discussed/counseled homework is a thing of the past?
Agree .. the acronyms make no difference to the law of order ... it's a learning aide and that's all. The order is burned into my brain from school ... but I struggle to remember the acronyms. But I'm just weird.