I always had a hard time with math. After I got out of the Air Force, I went to a local college and the teacher was wonderful. He could explain things so simply, I wondered why I never got it in the first place. A teacher has a lot to do with how well slower students grasp the subject matter. I will never forget this man. His wife was also a math teacher.
Yes. A teacher should be able to help even the weakest of the weak in the class. That was a "must" for the teachers where I taught in the Primary section.
In Australia I was taught BODMAS with B meaning Brackets - ( ), and O meaning Order - square root or indices. Division and Multiplication are of equal importance, so should be completed in order of left to right. It is the same with Addition and Subtraction. My answer would also be 25.
@@jesperlykkeberg7438 No, you are wrong. Watch the video again. Multiplication and Division have equal standing so they are therefore carried out from left to right in the order they appear. Likewise Addition and Subtraction have equal standing and are carried out L-R in the order they appear. So 5 + 4 x 4 ÷ 2 - 3 can be rewritten as: 5 + (4 x 4) ÷ 2 - 3 5 + (16 ÷ 2) - 3 5 + 8 - 3 = 10
So finally, at 64 next Monday I had never heard of PEMDAS. I ALWAYS said, "I must have missed something in 4th grade!" This has been embarrassing all my life, not knowing this. Especially being a computer college professor. My co-worker, a math professor could never figure out how I could do that and not know this! I retired last year but I am texting her with so much excitement!! If she just would have told me about PEMDAS (Please Excuse My Dear Aunt Sally.) In your, I'll call it, "Many Will Get Wrong" Series I just got 2 right in a row. You just don't (maybe others will) know the feeling of joy and not being stupid. I always knew the basic 4 +×÷- but never able to do these kind of problems. I hope there are more like this. I read in the comments, from someone who knew this and said why does it take 13 minutes to get the answer?? Cuz we didn't know PEMDAS!! Bless you John! ❤
My math teacher always said to think of the operations as different tiers. Brackets, braces, and parenthesis are the highest tier, so they are done first. Powers/exponents are the second highest tier, so they are done second. Multiplication and division are the third highest tier, so they are done third while addition and subtraction are the lowest tier, so they are done last. And everything is done left to right.
I was taught BIDMAS (In the UK) B - Brackets I - Index / Indices D - Division M - Multiplication A - Addition S - Subtraction However, we were told to keep in mind that addition, subtraction and multiplication, division (opposite operations) are on the same levels, so if they should appear, just solve from left to right! Have a nice day!
@garrysysling445 I disagree. The answer is 25. If you are using PEMDAS, you are applying it incorrectly. Multiplication and Division, if present in the same equation, are of the SAME level. And therefore you do them in the order in which they appear from LEFT to RIGHT. In this case DIVISION is done FIRST not MULTIPLICATION.
And this becomes one of the many reasons why mathematics are loathed by myriad students. This problem isn't testing one's knowledge of true arithmetic principles, it's trying figure out if you can apply some hair-brained acronym and then remember the "special rule" that makes the two letters equal, so just do it left to right. What a crock... if you want the answer of 25, write the problem as (10 / 2) x 5. I mean, what's a few keystrokes between friends, right?@@topkatz58
@StiyaShanthan Yes, it has the same meaning as PEMDAS. P=B and E=I in our different acronyms. M and D same level. A and S same level. When it's simplified, work left to right.
I tested at a 12th grade level in reading and math in the 6th grade. got 4 A's in basic math as a freshman in high school. that's all we had to take. I was done in 10 minutes while the rest of the class took the whole period. you would think the teacher would have encouraged me to take advanced math classes but never even suggested it. he wasn't a teacher, he was a babysitter.
Same here. I was chastised for asking a question in algebra class. I always ranked in state tests etc. but was never encouraged to go to college. No counselors in my poorer fam community school.
@michaelmacpherson-wm6mh and bluefidle, I am so very, very sorry that your teachers did not affirm your capabilities and encourage, and even help you, to further develop your skills.
You could follow PEMDAS and still come to 1. All depends on how you interpret PEMDAS. In PEMDAS multiplication comes before Division, and then there are people who say, 'yeah but even in PEMDAS they are equal, so you do them left to right, after the Parenthesis and exponents.
I'm 67, retired English teacher. I chose the correct answer, 25, because you're a good teacher. From your teaching, I know to go from left to right, AND the M and D in PEMDAS means which ever comes first. In my head I wrote (10/2)5=25.
As a 58 year old Engineer, this is the best explanation of PEMDAS I have seen. Nice job I've had High School math teachers tell me that 25 is the wrong answer. Sad....
THANK YOU! The left to right decision regarding multiplication vs division and addition vs subtraction was never explained to me. I am 67. I always struggle with these little math challenges because I thought PEMDAS was 100% the order of operations.
Pemdas....I took geometry as a sophomore but am 52 now....got to keep fresh 25 is the answer aunt sally! I honestly never heard of pemdas till now in your videos but it is helpful.
I had never heard of it before, either, despite being in Grammar School (in England the highest secondary school after primary school). I just always knew that brackets and exponents came first. I later moved to Germany and took a maths course. There I learned what they refer to as “point calculation (M and/or D) before line calculation (A and/or S)”, which is basically PEMDAS (multiplication is indicated with a simple . in Germany, as opposed to an x and division is indicated with a colon :, which confused me terribly at first, but hence the “point calculation”).
My intentions are to go back to school for my associates degree now that I'm retired. I always had a very tough time math. Maybe it was the teachers or me. Anywhere I loved your explanations I will be tuning in. Thank you!!
Multiplication and division have the same hierarchy in PEMDAS because they are basically the same operation. Dividing by 2 is the same as multiplying by 1/2. Likewise, subtracting a number is the same as adding its opposite. It helps to know WHY rules are the way they are instead of just memorizing IMHO.
@nancy668 They actually did change. Division and multiplication have same value. Parentheses first. Then mult. or division from left to right - whichever came first. In this case, division is first, so it's 10/2, then × 5.
Wow. I was taught PEMDAS. I was never told about the MD and AS exception. I thought the answer was 1. I'm almost 50. Not too late to learn. Thank you for this video!
@@jimpark5591 To be quite honest, everything we have been taught, is a lie. I kid you not. We have been big time deceived by the “powers that be”. You must be born into God’s family to see with spiritual eyes, how the earth “shaped up” after Noah’s flood. It will blow you away.
@@jimpark5591 Just to come back and check that my comment that I made to you got deleted. I know 100 percent that the censorship has hit the charts. Liars hate the truth. satan and his filthy demons know that their days are numbered and they don’t want anyone to know the truth.
Thank you for having these videos explaining PEMDAS because explaining the grouping of MD and AS has helped me as a teacher. I can now explain it correctly to my students. 😊😊😊
I am 73 years old. I went through the New Math era starting in the 8th grade (Fall 1963 to Spring 1964) and survived. I have a very good memory but I do not remember PEMDAS. I was able to to come up with the correct answer using another order of operations I learned somewhere along the way to graduating with a BSME in May of 1973.
The New Math system was horrible and I believed it crippled many student's early understanding of basic algebra.and geometry. I know it did mine as I had to fill in the gaps by my own efforts.
I am 71, and despite hating maths all my life, I got it right, by doing nothing fancy just starting at the beginning and continuing.I am a bit chuffed.
Your comment is exactly my point Bradley. PEMDAS was not taught in the "New Math". It was mostly group and ring theory along with mathematical "proofs" which was ridiculously pre mature for high school students.
At 68 and retired and hating math for most of my life I now find an interest in math. Looking back it may have had something to do with teaching methods. I have discovered that the math teacher is important.
Me too, except for any new "interest". Made it thru a two year engineering degree because I understood the "Concepts" (even in Physics). The one thing in later years I learned, was that "Math" is just a Tool; not an end in itself, not unless you're "intuitive", then more power to them. The late Physicist Richard Feynman, pointed out something too regarding "teachers"...most all math is taught Wrong! He's well worth looking up here on the "Tube", as a side note, he worked on the Manhattan Project as well, and had quite a sense of humor...he took great delight in putting Top Secret Papers back on the desktop of one of the top scientists after he had locked them up in a drawer before leaving for the night (lap drawer firmly locked). Feynman finally told him how he did it....just reached up and around the lap drawer and pulled them out :-).
@@festeradams3972 yes I'm aware of Feynman. I remember seeing him on TV back in the early 70's I think. I didn't read much about him until fairly recently. Sounds like he had great sense of humor.
Answer is 1 This is another fine example of an ambiguously written expression or problem. All the acronyms are well and good, but you'll always get the wrong answer if the original problem is unclear to begin with! In this case, whenever we see an obelus --- the dot-dot-division sign --- we always need to remember that division, like addition, subtraction and multiplication, are BINARY operations. This means that whatever is on the left of the obelus is divided by whatever is on the right. In this case, all the stuff on the right is 2 x 5. This should be a red flag!! Because a binary operation usually means take this number and operate on it by the other number. Here, we have two numbers and another operator on the right! AMBIGUITY ALERT!! Once we remember that division is like a fraction --- some quantity over another quantity --- and that its sign (the vinculum or long bar) is a grouping symbol, this problem can only logically be written as: 10 / (2 x 5) 10 / 10 1 I'm not at all surprised that I got this "wrong", but that's because I used the Order of Operations, and I've learned to understand how the underlying math works. It's not an argument over whether I'm right and you're wrong. The sole argument here is: are you presenting an unambiguous mathematical problem, or are you intentionally writing this problem in a way that can only sow confusion? Since Mr TH-cam Math Man says the answer is 25, let's help him write the expression so that the answer will actually be 25! (10 / 2) x 5 (5) x 5 25 There! It wasn't so hard to just draw a couple of grouping symbols on there and make this a nice unambiguous problem, now was it!
Thank you. His written expression followed by the proposed answer didn't make sense to me with how it was presented. Your written expression follows the classical guidelines for mathematical alignment.
Simple if you have division, and multiplication work from left to right. So, 10÷2×5 (left to right) because, there is only division, and multiplication.
We were taught (Germany) from the inside out (brackets), then top (exponents) and then from left to right keeping in mind that dots come before lines. (• is multiplication, : is division, + addition and - subtraction). For me it was always straight forward but then, I do love math.
I was taught (Netherlands) to strictly stick to "Meneer Van Dalen Wacht Op Antwoord" (Dutch version of PEMDAS) and to not switch half way through to 'from left to right' So: first Power (Machtsverheffen), Multiplication (Vermenigvukdigen), Divison (Delen) Rooting (Worteltrekken), Addition (Optellen), Subtraction (Aftrekken). Seems way more logic to me, but, it is all about what system one chooses. When in doubt, use parenthesis
We can say that in PEMDAS is fine as priority but Multiplaction and divion has same priority just as multilication and division. The order ofevaluation of operators of same priority goes from left to right
When I was at school late 1940 early 1950 we didnt use acronyms. I've never heard of them. We would do the maths in order of appearance. So the above would be 25. 10÷2×5=25 if the answer was to be 1, it would be written as 2×5÷10. And that's how it was back in the 1940s/1950s So much simpler then.
I grew up with BODMAS too, but I always thought it was division before multiplication, and addition before subtraction. Seems I was wrong all along, unless it is different for different countries. I am from the UK. But that is not to say everyone in the UK was taught that. I may have just misunderstood.
We used BODMAS. Bodmas stands for B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, S-Subtraction. PEMDAS is new to me and is not as straightforward as BODMAS
Pemdas states that the multiplication/division step is done from left to right as they are considered of equal value, so first: 10/2 = 5 so we’re left with 5 x 5 which is 25. So the answer is 25
I received the best education ever in American history in the 1950's in Central Valley CA. This is such an easy math problem that does not need the acronym. Straight forward
25 is the answer simply because you read the equation like a sentence from left to right. You would have to group 2 x 5 in brackets if you wanted to divide by the whole quantity of that product.
Thank you for this! I was like well isn’t there supposed to be brackets? What if there is brackets? Lol 😂 school was a long time ago and I certainly forgot my math skills 😂☺️
@@fiveoctaves That is true. I know when I was first taught this in class the teacher did explain the grouping of MD and AS could be done in either order. I am an engineer, so this stuff is etched into my mind.
This entry was written on 9/15/'23. In order to get the answer 1 properly, The number 10 would have to be in the numerator of a fraction, and 2 X 5 would have to be in the denominator. Or written another way: 10/(2X5)
In UK in 1940s and '50s we were taught the acronym BODMAS (Brackets, Of, Divide, Multiply, Add, Subtract) which has always given the correct result for my level of maths. This was used left to right as written. I was a Surveyor / Valuer / Architect - so no rocket science formulae to worry about. Best wishes to you.
The O stands for Order, not Of, but yes, it was the way we were taught back in the day, although for the life of me I cannot remember the acronym being used back then!!
@@peterhead9981 In Australia we were taught and use BOMDAS _ where this bodmas comes from is a bit sus. B _ brackets O _ treat of as a bracket M _ multiplication D _ division A _ addition S _ subtraction
BODMAS is an acronym to help children remember the order of mathematical operations - the correct order in which to solve maths problems. Bodmas stands for B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, S-Subtraction.
I did indeed learn something, thank you! I had never heard of 'PEMDAS'! I always treated mathematics as reading, just go left to right. Well, even at 66, I'm still learning something new every day! Very many thanks , Sir.
@PaulDredge1815 I'm 55 and didn't know it either . Which would explain why I struggled in algebra , albeit did great at geometry :\ But in your left to right understanding . You knew enough intuitively to do the brackets and powers first ? So really this acronym arbitrary rule ... is a tack on to an intuitive function in math formulation. Where knowing the real world application to these data points , and how to compute them. Renders this late 19th century math rule , pointless , and actually a cause for more confusion errors with computing . Just thinking to one of my real world uses in calculating the cubic yards of cement for a basement floor .
@@gordonhill8164 Well it certainly does not stop errors from being introduced by the admin that collected and formulated the data into an equation. And looks like a nifty way to hide or siphon money by knowingly swapping around the order of operations .
I'm 65 and have had algebra and three semesters of calculus in the US. This kind of problem is just a stupid scribble and should be ignored. If you see a thing with a division sign and NO CLEAR MEANING to the numerator and denominator, you are being TROLLED. Run away and enjoy your life, cause you don't need this endless bickering. You have been set up.
Okay: I came up with 25. However, if you do what you say to do- order of oerations- where multiply precedes divide, then the answer is 1. However, without parenthesis, or any other indicators, your operation starts at the left and goes to the right, solving as you go. Therefore, the answer is 25.
I'm a math teacher and I always tough my students P ER MD AS 'R' for radicals. I also teach about the implied parentheses in something like 5/3+1 (written vertically with '3+1' in the denominator).
I've always sucked at math. My motto is "Numbers are not my friends."😄 However, I did reach the answer of 25 with no problem....then waited nervously to see what you said.😬 I've never heard of PEMDAS.
@HarryHewitt-lh8xxIt is if you just bear in mind that M and D are one group, both operators with equal priority, so whichever comes first is solved first. The same applies to A and S.
Even though we use PEMDAS to solve these, you still have to read the problem from left to right. So in this case because the division sign is before the multiplication sign, you have to decide first. Therefore the answer is 25.
Ok, I'm doing this a 2nd time and my answer before hearing the PEMDAS is 25. I'll find out if I'm correct. I guess I'm going to subscribe again, but I'm going to stick with problems that appear easier before jumping in the deep end because if I ignore what you say that has nothing to do with the problem at hand, I AM learning again. Last night I was in tears over my incompetence, but today as I go through a few simple problems, repetition of the order of operations from L-R is actually giving me a little confidence. I don't like hearing right away that "most of you will get this wrong" because that convinces me that I will get it wrong. I heard enough negative things like that as a kid, and it stuck, so it made it very hard to believe in myself.
25 I think PEMDAS should be PEPS (Parenthesis, Exponential, Product, Summation) with left to right being the prerequisite. Division is the inverse and multiplication of the second argument, and subtraction is the sum of a negative number. These operations begin in the innermost parenthesis. Exponents are also a shorthand for multiplication. PEMDAS was over-explictily created for elementary school children to address the four arithmetic operations. It meant PE(M/D)(A/S) with the slash meaning either/or and not mathematical division. "Limited" computer math line interpreters began the confusion whereas humans knew how to sort discrepancies. Good explanation, and intellectuals should watch this.
I like your PEPS idea, would solve this - as you wouldn't guess the amounts of arguments I have had over questions like this. People seem to know the PEMDAS rule but never apply it correctly. So I can see the value in what you purpose. As the amount of times I have tried to explain that, with OUT the brackets, you simply go left to right through the equation in the order it is written in the equation. As in math, brackets are used to manipulate the order of operation to give the output you require. i.e in this case, if you wanted the answer to be 1, the sum would be written as 10 / (2x5) = 1.
My thing with PEMDAS is only in a its lack of consistency. Ok, P,E,(MD)(AS) I get it, you group the inverses. But then it should be P(ER)(MD)(AS) Parentheses Exponents and Roots. Multiply and Divide. Add and Subtract
You are correct. The PROBLEM GIVER should make all division parts clear to you. The numerator, the denominator, if not, then the answer is "you didn't ask this right, fix it and ask me again". There is no clear answer. We might also look into the value of 1/0 and sqrt(-1)
Regarding 6:15 PEMDAS. Division has equal order of operation as Multiplication, because Division is actually Multiplication by its reciprocal. Subtraction has equal order of operation as Addition, because Subtraction is actually negative Addition. This means PEMDAS (Please Excuse My Dear Aunt Sally) has equal order of operation as PEDMSA (Please Excuse Dear My Silly Aunt). In other words, PEMDAS = PEDMSA.
Agreed. There is really no 10 / 2, it is 10 * (1/2) ---- You can go all thru algebra and calc without needing this more than the PEMA part and do well. Its the internet, youtube, social websites and memes that people argue forever about the rest.
Well I am 67 and that is the first time I think I understood that PEMDAS. I did not know about the multiplication and division order. I always use Multiplication then division. Thanks Great job teaching this old man.
BEDMAS and PEMDAS are the exact same thing, just abbreviated differently: B or P - brackets/parenthesis E - Exponents D/M or M/D - divisions and multiplication in the order they appear from left to right A/S - addition or subtraction in the order they appear from left to right. It doesn't matter which of the 2 abbreviations for the order of operations is used, they are done in the same way.
@@ThePsychosocialite BODMAS is best of all three. (Brackets, Of, Division, Multiplication, Addition, Subtraction). Cos its British, by Jove, now fetch me a muffin and a cup of Earl Grey!
So, it’s points before lines (at least we say it that way in Germany), if their are only Dots, then you would use (… ) to show which should be calculated first. As also this is not shown, it’s from left to right and that means 25.
This was very confusing. I was taught BODMAS in Australia. And now I see that there is also PEMDAS. For a exact discipline such as mathematics, it would be inconceivable that these two ways of ordering equations would result in different answers. So, assuming that they both give the same result, what is the difference. The only difference I can see is that the D and M are reversed ie division and multiplication are in a different order. If they produce the same result, then there must be a way to determine objectively the correct order. From other sources, I find that ranking of operations are: 1 Parentheses, 2 Exponential, 3 Multiplication and Division, and 4 Addition and Subtraction, AND for equal rankings, they are to performed from left to right. So, in the example given, the order of ranking 3 should be left to right - division then multiplication. This gives the answer of 25, which agrees with the solution. As I initially thought the answer was 1, I have been misinterpreting BODMAS for the last 60 years. Thanks for the education, Mr TabletClass Math.
20 years ago in algebra class we were taught, multiply and divide both have priority over plus or minus. Unless parentheses are used you work left to right in this equation.
I don’t think anyone reading this didn’t get both answers. But I’ve also heard it argued that blind adherence to PEMDAS is a flawed sort of consistency. I’ve seen some great the division like a fraction making the problem 10 / (2*5) in which the answer would inarguably be 1
I was told these 2 groups are reciprocal operations. Funny how mostly we all get the gist of the big picture, even though it was taught in different ways. The more linear that some were, the more wrong and confused they were with their equations. 👍
I am a retired teacher. I made up a song about the order of operations for my students: Please Excuse My Dear Aunt Sally. She doesn’t know what to do first. Please Excuse My Dear Aunt Sally - Her memory is really the worst! Just remember Dear Aunt Sally When doing math homework tonight: Parentheses, Exponents, Multiply and Divide* Then Add and Subtract* *Left to Right!
The problem with the MDAS part is that in any real world application you should hopefully know which ones should be done first and then you'd indicate that with parenthesis. I certainly do this with any formula I put in a spreadsheet so I don't have to depend on the software doing things in the order I think it's going to. A lot of times it will also be obvious that an answer is wrong. If you want to know much food to divide among 10 people when two people each have five pounds you should know the order to do that and that the answer is not 25. Likewise, if it has taken you ten minutes to complete two tasks and you want to know how long it take to complete five more, you should know the order of that and that the answer is not one minute. The same thing would apply if there was a situation with addition or subtration, you'd think it through before doing the calculation. Students should not be confused with questions like these, but rather given a problem where those numbers actually represent something and there's a question to be answered. The purpose of learning math should be to know how to solve problems and answer questions, not to learn things that don't have any real world application unless you're going to be a math teacher.
Perfect my friend. The only comment here that makes sense. People just want to memorize rules without trying to think and understand the real world application of a calculation. Engineers are trained to think if the results makes sense while math teacher are trained to memorize rules of math operations.
Yeah. Exactly because this is just confusing. The order of operations acronym only applies until it doesn't ... i mean what ? That just confuses things to the point of asking well why have that acronym in the furst place? Make up a better one. I used to make up my own. And the point is. Once learned these acronyms, to later find they don't fully apply in all circumstances. The danger is that some, if not most will end up just ditching the whole concept and loose interest in maths
PEMDAS/BODMAS/BEDMAS are wrong as they mislead into the concept that multiplication & division, as well as addition and subtraction, are different operations thus order matters. If you simply use them correctly, order does NOT matter as division is multiplication & subtraction is addition. At least PEMDAS is a bit better as it doesn’t put subsets ahead of the overarching set by putting division ahead of multiplication, but I still wouldn’t teach it except maybe as PEMdAs parenthesis (in this case brackets may be a better label); exponents; multiplication, including division; addition, including subtraction. 10 * 1/2 * 5 = 10 * 5 * 1/2 = 1/2 * 5 * 10 = 1/2 * 10 * 5 = 5 * 1/2 * 10 = 5 * 10 * 1/2
Then, when do you work the exponents in that method? I'm from the USA and taught math in this century. I grew up in the 60s and 70s in school but don't remember which method was taught.
25 is the answer. This is exactly how I was taught, way back in the 70s, in the US. Yes, parenthesis (or brackets) eliminate the confusion, but the MD and AS are equal components of the PEMDAS order of operations.
Thank you for this refresher course.. I must have missed this day in math class because I've had trouble my whole life with this very issue.. in all of my classes through high school and college.. anything with math.. I understood the principles but could not get the grade on tests. . Algebra geometry physics all sub par But I made it through and am retired now but still curious. .
@@wrongfullyaccused7139 The rules of mathematics are not that complicated multiplication and division have the same priority so you solve the equation from left to right.
Hubby and I in our late 70!’s Both looked at it at different times and said 25! Then thought wonder what the new math comes up with. There must be a trick to it we thought. Old math wins! 😂
Lol. The comment section is confusing to me. Straight forward operation, no paratheses. One obvious answer. I went to the k.i.s.s school. Keep it simple, stupid Yay, old maths and logic !!!
There's no such thing as new math or old math. There really hasn't been any changes in math for hundreds of years. What HAS changed is the method for teaching it and the way teachers approach teaching the subject. Instead of rote memorization which was the way for longer than most of us have been alive, they have decided to teach students different ways of approaching math problems. The trouble is, they didn't teach these new methods to the parents, so the students are left with nobody to help them understand these concepts other than their overworked teachers, who themselves may, or may not, understand these new methods. Some academics somewhere thought it would be good to create this new system and call it Common Core. It was partly inspired by political and social issues rather than being a solely mathematical endeavor. The politically and socially motivated educators thought it would narrow the racial and socio-economic gaps between students. This is, of course, a terrible way to develop an educational system, especially a mathematical one. To further complicate things, the students being taught these new concepts are in for a rude awakening when they get to higher education and the work force, as both of those institutions still rely on the previous methods of doing math, so now students must relearn math the old way. Common Core must die and never be brought back. Teachers need to return to the old system so we can bring back the success we used to have. We can find other ways to solve the racial and socio-economic issues involved.
We counted actual beans in primary school. The visual aspect helped me. Convoluted process gets lost in my head. Now I just tell people “don’t math at me” 😅😅😅
HP Prime CAS says the answer is "1". It has been stated by The American Physical Society in their "Physical Review Style and Notation Guide" that when confusion might result from the way a problem is written, parentheses must be used to clarify the order desired. The correct way to write this problem to get your answer would be (10/2)*5=?. Most people, including my trusty HP Prime, write it as 10/(2*5)=? . The American Physical Society - Physical Review Style and Notation Guide, p. 21: (e) When slashing fractions, respect the following conventions. In mathematical formulas this is the accepted order of operations: (1) raising to a power, (2) multiplication, (3) division, (4) addition and subtraction. According to the same conventions, parentheses indicate that the operations within them are to be performed before what they contain is operated upon. Insert parentheses in ambiguous situations. For example, do not write a/b/c; write in an unambiguous form, such as (a/b)/c or a/(b/c); as appropriate.
In the UK we use BODMAS... The US uses PEMDAS Both use left to right rules and follow the calculation rule of the respective letters P - Parentheses First ** B - Brackets First E - Exponents ** O - Orders M - Multiplication ** D - Division D - Division ** M - Multiplication A - Addition ** A - Addition S - Subtraction ** S - Subtraction Even today, people still make errors in calculations because we are fundamentally lazy and use calculators
@@BobbyJardine-vs8yc No, because the acronym you learned is not the problem. Some were also taught BOMDAS, or BIMDAS,. All you need to know regardless of what acronym you learned is that multiplication and division are worked together equally no matter what order they happen to appear in the equation from left to right and the same goes for addition and subtraction. Refer to the OP's post.
The symbol “÷” was introduced when calculators were invented. It symbolizes a fraction where the dots are placeholders for the nominator and denominator. If you can write an actual fraction, please do so and avoid this symbol. I.e. just write 10/2 instead of 10÷2. This is how it's done in “proper” mathematics outside of high-school. The rules for calcualting with fractions are much less ambiguous, avoiding confusing cases like the one described in this video, which are basically just bad notation. Furthermore: The sign “⨯” is reserved for the cross-product in vector algebra. If you want to notate multiplication, please just use the centered dot “⋅”. In general, when writing down mathematics, it is good to think about the reader and not try to “test” him how smart he is. Therefore, I would write down the formula as follows: (10/2)⋅5 . Crystal clear and no PEMDAS needed! (The parentheses are only there because I cannot write a proper fraction inside this text box.)
I'm looking at ISO 80000-1. An INTERNATIONAL standard, not a style guide from some university. Direct quote from ISO 80000-1-7.3.3: "These provisions can be extended to cases where the numerator, denominator or both are themselves products or quotients. In such a combination, a solidus (/) shall not be followed by a multiplication sign or a division sign on the same line unless parentheses are inserted to avoid any ambiguity." Oh, and by ISO 80000-2-9.6 "The symbol ÷ should not be used." DON'T USE "GOTCHA" QUESTIONS TO CHECK IF YOUR STUDENTS HAVE UNDERTOOD YOUR HOME MADE RULES.
A scene from the "Martian" that never was: Matt Damon looks in a manual. "Read gauges A, B and C. Set thrust leaver D according to the formula D = A ÷ B × C. Press "IGNITION". GOOD LUCK! You only got ONE chance." As you all may remember he has no means of communication. How about that?
When I was in school many years ago, for clarity, every math problem included parentheses (n), brackets [n] and braces {n}, in that order. Engineers despise ambiguity. Everything must be precise for a given thing to work as expected. If it doesn't fly, we failed. Period.
Agreed! Give me the parentheses. Even if I know the proper order of operations, I wouldn't assume that the person writing it knows the correct order and is conveying it properly. As an engineer, if something came to me like this, I would request written clarification.
We never learned order of operation in math and I had great math teachers from 6th grade on up. We used the parentheses, brackets, braces too. I graduated in 1986.
@@cdykstra6 WOW and this out of the mouth of an engineer. You can write this 15/(4+1) and everything is fine but if you write this (10/2)X5 I would dearly doubt your profession, sure for an everday joe this may make sense and delete confusion but in as an engineer this looks highly unproffessional. Even worse if I give you this 10/2X5 and you ask for clarification I again would deeply doubt your profession and I couldn´t take you serious as an engineer anymore...
was just thinking this!.... This guy is an engineer and works with other engineers and is talking ab not knowing basic math and not trusting other engineers to know basic math. Scary.@@reinerhoch1357
One math teacher in Hong Kong was extremely strict. If you write down the statement (10 - (5 x 3)) + 2 you will get a big "X" and zero marks for your answer. It has to be [10 - (5 x 3)] + 2. Personally I find that a bit extreme - she basically cared more about form vs. function. In Canada I have not run into a teacher that will deduct marks for using the first example.
I didnt use Bodmas or pemdas but i used my own as and this is what i was taught. Change the ÷ to × Nd invert the divisor. 10×1/2 × 5 = 25. Not much talking but simple things we were taught by excellent teachers in primary school.
Great explanation. I've been retired for over 5 years and my math skills still haunt me. I managed to squeak through college with a BS in Business. Every math class I was required to take, I had to take it twice and sometimes more. To me, a math equation might as well be in Chinese writing - it makes no sense to me at all. It took me 5 attempts to pass Algebra with a D. It has always been a source of embarrassment to admit how bad I am in math (Not arithmetic - add subtract multiply and divide) it always has been wheat I refer to as "Abstract Math". I always felt that the problem with Math teachers was their complete inability to explain why or how I would need to know it. Wish I would have found you 55 years ago
This is interesting from the perspective of say setting a mathematical puzzle for the fun of it but I was taught from a different perspective. Just always use brackets where there's potential ambiguity. It's useful to know multiplication and division take precedence over addition and subtraction to avoid cluttering up very simple expressions with brackets, but brackets always took precedence over having to remember rules. Using an expression such as this in a professional capacity would be frowned upon, and when I studied maths at degree level we always used brackets rather than having to remember rules like this, they just detract from actual problem at hand.
Yeah your correct, bracket and parenthesis must always be used in actual and exact/normal application to avoid confusion, only in tricks and carnaval / fancy events a problems like this occur/// i know pemdas/bidmas but dont give problems like this especially to common non math enthusiast ///
I would never pose a problem like this where the outcome is questionable. That is, I would always use parentheses to avoid confusing my readers. Period. 10 ÷ (2 X 5) = 1 and (10 ÷ 2) X 5 = 25. The more symbols that are strung together in a complex expression, the more important the parentheses become. Don't expect your readers to have memorized operation priority rules just because you are too lazy to use parentheses or to split up complex expressions into multiple assignments. I see writers often making this mistake a + b / c when they obviously meant (a + b) / c. It really wouldn't hurt to write a + (b / c) when you really mean it if you think a + b / c might confuse some readers.
The outcome here is not questionable. I see your point that where you are speaking to people with very limited math education, you may want to separate out the sub-calculations - but recall that not everyone of that limited education will handle parens comfortably. Assuming your audience HAS the least smattering of algebra, they may reasonably be expected to know precedence or how to look it up. Failing to use parens where not required is not "lazy", it is properly spare, and reduces clutter. There may indeed be cases where unrequired parens do improve clarity, but for a problem statement such as this, not so. Me are xpected to use Good english gramer when talking at youse, and you will notice if I don't. Same with math.
The outcome of this mathematical equations is not “questionable”, as the answer depends on an un-ambiguous rigidly prescribed order of steps to solve said equation. And ‘priority rules’ are just as important as any other mathematical and/or arithmetic rules. And parenthesis are part and parcel of priority rules. Why would anyone be expected to ‘know the priority rule’ that ‘parenthesis come first’ but not ‘know’ the rest of the orders?
PEMDASFLTR - “Please excuse my dear aunt Sally for losing the radishes” was what I learned - parentheses, exponents, multiplication, division, addition, subtraction, from left to right. I like that md and as can be flipped 🎉
As a former math teacher, this topic was covered thoroughly in class in far less time. Diluting your presentation with endless, extraneous side commentary greatly reduces its effectiveness.
Different countries, different systems. Living in the Netherlands I learned in the 1960/1970 Mijnheer Van Dalen Wacht Op Antwoord. And in that strict order. Machtsverheffen (Index) first Vermenigvuldig (Multiply) before Delen (Devide) Wortel trekken (Indices) Optellen (Add) Aftrekken (Subtraction) So according to the rules back then I came to the answerr 1. I read a bit about it and found out, that the rules where changed to something equal to PEMDAS due to the upcoming computers and that they had a different order. So thanks, I learned something new.
@@olivierlohman En dus komt worteltrekken op een heel andere plaats. Dus elke vergelijking zo opschrijven, met haakjes, zodat er geen gekke discussie kan ontstaan. Bijna metrisch zou ik zeggen.
That "whatever you see first" thing tripped me up! who invented these rules and also how were these operation symbols + - x etc invented? was here some kind of big meeting thousands of years ago?
I got the answer right, although I was at school before they taught BODMAS. We were taught the correct way to do sums, but the acronym was not used in the 70s.
That's why I always use parenthesis to remove the ambiguity in these types of problems. They don't cost you anything and they prevent someone from getting the wrong answer which can be quite costly.
I am so glad you use parentheses. For non English speakers and languages that read and write NOT from left to right, I can imagine the use of parentheses is important to show order of importance.
In this case an inverted notation would make the answer correct even without brackets: "5 x 10 / 2 = 25" Understood as either as 50/2=25. or as 5x5=25. Same answer, making brackets redundant.
@@jesperlykkeberg7438 --- In this case, yes, the brackets are redundant: (5 x 10) / 2 would be equivalent to 5 (10 / 2). Doesn't work the other way, which is the whole issue!
PEMDAS is just order of operation but there was an item that was not really mentioned. Multiply and divide are treated equally and addition and subtraction are treated equally. Parenthesis and exponents are completed first by priority but the others are done left to right with multiple/divide being completed first. Since the question does not contain any other components, it’s just done left to right normally.
We got taught BEDMAS in the western provinces of Canada, like many of the others quoting PEDMAS and BIDMAS and BODMAS, etc. This time the E = exponents, but it all means the same thing. Oh. And the answer is 10/2= 5 thus 5x5=25
So I went to school and was taught pemdas, the correct answer is 1, that’s what we were taught in school you do multiply then divide And if you think I’m wrong I’m a licensed water treatment operator and have to do math every single day, and the test I took was made up of 100 questions with half of them being math questions and having to use the pemdas method, you need a 80 percent on that exam to pass to receive your water operator certification
That’s too bad because you are wrong. I don’t think you understand the full definition of any of the acronyms, PEMDAS, PEDMAD, BODMAS, they all when used properly come up with the same answer. It isn’t just the letters. M&D have the same precedence and are handled left to right. A&S have the same precedence and are done left to right. Go to the source, look up Order of Operations and read the definition. I hope any mistakes you have made in the past haven’t resulted in someone getting hurt.
When teaching the order of operations, emphasize MD or DM, whichever comes first and AS or SA, whichever comes first. Use this consistently in the first year this is taught and it will become part of learners permanent memory. Create a silly rhyme or dance from it, and you'll have a powerful memory tool.
Yea for me the teacher said "Multiplication and Division are treated equally just like Addition or Subtraction, you solve whatever comes first on the line" And that was a very easy and simple rule to remember
Except there is no such thing as subtraction. It is really adding a negative so AS is commutative. But Multiplication and division are not. Division is a fraction and the denominator must be calculated as a unit. Here you have 10/2X5 2X5 is the denominator. It is not 10 div 2 and then the result multiplied by 5. Division is not commutative. Because 2X5 is the same as 5X2 it can very well be 10/5X2.
In my mind, Division and Subtraction do not exist (in this context). Division is really just inverted multiplication and subraction is just adding a negative. So, a better acronym might be PEMA.
This is why grouping is important. Is it 10 / (2 x 5), or (10 / 2) x 5? When writing an equation, it is incumbent on the writer to compose a clear expression leaving no room for misinterpretation.
If you know the order of operations, parentheses are not necessary and could actually confuse the issue in a simple problem like this. I think the acronym may need to be clarified-PE M/D A/S or PE[MD][AS], something like that.
I saw this and thought the answer was 25 because things are done left to right. Don't know why a person would jump over a thing to go to another thing and then back to the first one. Side note- I've never heard of, or seen, that PEMDAS tip before. I've been out of school for 30+ years and am happy to not have to think about any of it 🥳❤️
@@mybluemars Correct, it does work, and that's my point. Why would a person not do it that way? Adding in ( x ) is a completely different thing (that is done 1st). If they get the left to right part, they need to start learning things from the beginning 😉👍
@@busaj383 because those who were taught PEMDAS think multiplication is done before division. But my teachers made it clear multiplication and division were equal, as well as addition and subtraction were equal to each other. So you do whichever comes first. But not everyone was taught they were equal or forgot, so they think multiplication and addition have priority in an equation.
Basically Multiplication and division is the same operation (division by 2 is the same as multiplication by 1/2), so there cannot be any superiority of one over another. Left to right is the only way if no brackets present :)
I hated maths as a child and would put a barrier up refusing to go there. If I had a maths teacher like you things would have been different. You’re clear and explain well. I did get the question right ⭐️ and I watched the whole video. I envy those who find maths easy. I still feel that fear even now. It’s the, find the square root, type I always dreaded. If you know the language of maths and understand it you’re half way there! I might watch more of YOUR videos and see if you can turn that mathematical key! 🤷🏻♀️😉
@@scottw5253 Hey, it’s just how everyone said it. How it was printed on the week’s schedule and given to me! No one seems to have a kind word or a warm heart anymore and that saddens me. Maybe someone should have taught you better manners!! You need to know how your negativity has compounded a situation. I’ve just lost a close friend and I’m grieving. Taking my mind off it for a little while I watched a few videos and thanked them for taking the time to share and lift my spirits. Then you go and spoil that moment of peace. Think before you speak, and if you haven’t got anything good to say, keep it firmly SHUT! 😡
@@cu4wur6023I’m sorry Carol for the rudeness. I had to take Algebra for my science classes pre-Nursing. I had an India tutor and a Vietnamese teacher. They were so awesome that I took a next level course just for the fun of it 🤪
@@scottw5253 Maybe you could have benefited from knowing that “maths” is a more British term while “math” is more American. It is much like colour or color. She’s not wrong, but the term indicates that she has a British influence so she learned “maths.” My late wife was Canadian, so we ran into these differences often.
I figured it out in like 2 seconds of looking at it. I was always horrible at math at school but had some great teachers who helped me understand. to me this is very simple
When I was at school quite a long time ago this was a pretty basic mathematics calculation. & Providing there is simply multiplication & or division with no brackets etc. Then simly draw a line first put all the multiples above the line & all the divisibles below the line and wolla. The answer 😮
![[TH] VALORANT Champions Seoul - Grand Final - EDG vs TH](http://i.ytimg.com/vi/WvObMc9VelI/mqdefault.jpg)
I always had a hard time with math. After I got out of the Air Force, I went to a local college and the teacher was wonderful. He could explain things so simply, I wondered why I never got it in the first place. A teacher has a lot to do with how well slower students grasp the subject matter. I will never forget this man. His wife was also a math teacher.
Yes. A teacher should be able to help even the weakest of the weak in the class. That was a "must" for the teachers where I taught in the Primary section.
100% it all starts with the teacher and the attitude!! It takes a certain teacher to make it click!!! So true!!!
I got stuck @ Trinomials...
Math is easy. Just practice it and learn the rules/tricks to solve the problems.
I agree 💯.. a really good teacher is one who makes things understandable and simple for each & everyone in the class
In Australia I was taught BODMAS with B meaning Brackets - ( ), and O meaning Order - square root or indices. Division and Multiplication are of equal importance, so should be completed in order of left to right. It is the same with Addition and Subtraction. My answer would also be 25.
Exactly what I was taught in UK
Yes way we learnt in New Zealand (BODMAS)
Learned BODMAS in Singapore too.
Which is wrong.
@@jesperlykkeberg7438 No, you are wrong. Watch the video again. Multiplication and Division have equal standing so they are therefore carried out from left to right in the order they appear. Likewise Addition and Subtraction have equal standing and are carried out L-R in the order they appear. So 5 + 4 x 4 ÷ 2 - 3 can be rewritten as:
5 + (4 x 4) ÷ 2 - 3
5 + (16 ÷ 2) - 3
5 + 8 - 3 = 10
So finally, at 64 next Monday I had never heard of PEMDAS.
I ALWAYS said, "I must have missed something in 4th grade!" This has been embarrassing all my life, not knowing this. Especially being a computer college professor.
My co-worker, a math professor could never figure out how I could do that and not know this! I retired last year but I am texting her with so much excitement!!
If she just would have told me about PEMDAS
(Please Excuse
My Dear Aunt Sally.)
In your, I'll call it, "Many Will Get Wrong" Series I just got 2 right in a row. You just don't (maybe others will) know the
feeling of joy and not being stupid.
I always knew the basic 4 +×÷- but never able to do these kind of problems.
I hope there are more like this. I read in the comments, from someone who knew this and said why does it take 13 minutes to get the answer??
Cuz we didn't know PEMDAS!!
Bless you John! ❤
My math teacher always said to think of the operations as different tiers. Brackets, braces, and parenthesis are the highest tier, so they are done first. Powers/exponents are the second highest tier, so they are done second. Multiplication and division are the third highest tier, so they are done third while addition and subtraction are the lowest tier, so they are done last. And everything is done left to right.
So the answer is 25 (people make it sometimes to difficult) If there where braces () it would be 1.
I was taught BIDMAS
(In the UK)
B - Brackets
I - Index / Indices
D - Division
M - Multiplication
A - Addition
S - Subtraction
However, we were told to keep in mind that addition, subtraction and multiplication, division (opposite operations) are on the same levels, so if they should appear, just solve from left to right!
Have a nice day!
There are no brackets and the answer is 1 it's obvious
@garrysysling445
I disagree. The answer is 25. If you are using PEMDAS, you are applying it incorrectly.
Multiplication and Division, if present in the same equation, are of the SAME level.
And therefore you do them in the order in which they appear from LEFT to RIGHT.
In this case DIVISION is done FIRST not MULTIPLICATION.
And this becomes one of the many reasons why mathematics are loathed by myriad students. This problem isn't testing one's knowledge of true arithmetic principles, it's trying figure out if you can apply some hair-brained acronym and then remember the "special rule" that makes the two letters equal, so just do it left to right. What a crock... if you want the answer of 25, write the problem as (10 / 2) x 5. I mean, what's a few keystrokes between friends, right?@@topkatz58
@StiyaShanthan Yes, it has the same meaning as PEMDAS. P=B and E=I in our different acronyms. M and D same level. A and S same level. When it's simplified, work left to right.
They didn't say there are brackets, they were simply stating how they were taught@@garrysysling445
I tested at a 12th grade level in reading and math in the 6th grade. got 4 A's in basic math as a freshman in high school. that's all we had to take. I was done in 10 minutes while the rest of the class took the whole period. you would think the teacher would have encouraged me to take advanced math classes but never even suggested it. he wasn't a teacher, he was a babysitter.
Same here. I was chastised for asking a question in algebra class. I always ranked in state tests etc. but was never encouraged to go to college. No counselors in my poorer fam community school.
Maybe both of you did not use proper PRONOUNS!! School is not about education anymore it is about indoctrination!! LOL
@@johnb-us6bf class of '78. we only had boys and girls when I went to school.
@michaelmacpherson-wm6mh and bluefidle, I am so very, very sorry that your teachers did not affirm your capabilities and encourage, and even help you, to further develop your skills.
@@jannh29 I know nothing about algebra at all. may as well be Chinese. I think geometry would have been interesting to learn.
Mr. Math TH-cam Professor! This time I got 25 as the answer without using a calculator. I followed PEMDAS.
You have great teaching methods.
Kudos!
Its all adds.
Wow!
You could follow PEMDAS and still come to 1. All depends on how you interpret PEMDAS. In PEMDAS multiplication comes before Division, and then there are people who say, 'yeah but even in PEMDAS they are equal, so you do them left to right, after the Parenthesis and exponents.
@@Ed19601yea i followed it in order glad 1 got some remeidial math here
I'm 67, retired English teacher. I chose the correct answer, 25, because you're a good teacher. From your teaching, I know to go from left to right, AND the M and D in PEMDAS means which ever comes first. In my head I wrote (10/2)5=25.
Yea! I got the right answer. I have not forgotten how to do this, and I'm almost 90 yrs old. I had great teachers!!
I'm 70, so just a youngster, but got it right too. Now for some Trigonometry.. .
70, too, got it!👍
Going on 70 so I gave two answers just in case. 😂 My dad was the Father of New Math.
We get it right because we went to schools that actually taught subjects rather than social ideology. Lol.
This was easy for me and I am kissing 80 next week.
As a 58 year old Engineer, this is the best explanation of PEMDAS I have seen. Nice job
I've had High School math teachers tell me that 25 is the wrong answer. Sad....
Unless was written that way.
10/( 2 x 5 )=1
If it was written like this video. Than 25 is correct.
Because they didn't know BODMAS(from UK or EU).
1
THANK YOU! The left to right decision regarding multiplication vs division and addition vs subtraction was never explained to me. I am 67. I always struggle with these little math challenges because I thought PEMDAS was 100% the order of operations.
@@xbman1 Actually, the way it's written is rather ambiguous.
Pemdas....I took geometry as a sophomore but am 52 now....got to keep fresh
25 is the answer aunt sally! I honestly never heard of pemdas till now in your videos but it is helpful.
I had never heard of it before, either, despite being in Grammar School (in England the highest secondary school after primary school). I just always knew that brackets and exponents came first. I later moved to Germany and took a maths course. There I learned what they refer to as “point calculation (M and/or D) before line calculation (A and/or S)”, which is basically PEMDAS (multiplication is indicated with a simple . in Germany, as opposed to an x and division is indicated with a colon :, which confused me terribly at first, but hence the “point calculation”).
My intentions are to go back to school for my associates degree now that I'm retired. I always had a very tough time math. Maybe it was the teachers or me. Anywhere I loved your explanations I will be tuning in. Thank you!!
Multiplication and division have the same hierarchy in PEMDAS because they are basically the same operation. Dividing by 2 is the same as multiplying by 1/2. Likewise, subtracting a number is the same as adding its opposite.
It helps to know WHY rules are the way they are instead of just memorizing IMHO.
Especially when a prior set of rules has been used for years before PEMDAS was devised.
@nancy668 They actually did change. Division and multiplication have same value. Parentheses first. Then mult. or division from left to right - whichever came first. In this case, division is first, so it's 10/2, then × 5.
@@MR-lq7ssthe chicken came first😂
@@Cancionera40I nevr heard of either, but got it right just doing L to R gave me 25
@@awillis244 Eggsactly!
Wow. I was taught PEMDAS. I was never told about the MD and AS exception. I thought the answer was 1. I'm almost 50. Not too late to learn. Thank you for this video!
really ? I am crap at maths but for me this was obviously 25
I thought the answer was 1 too so you are not alone. Lol 😂
LOL, I'm 56 and just learned it too! Better late than never! ;)
@@jimpark5591
To be quite honest, everything we have been taught, is a lie. I kid you not. We have been big time deceived by the “powers that be”. You must be born into God’s family to see with spiritual eyes, how the earth “shaped up” after Noah’s flood. It will blow you away.
@@jimpark5591
Just to come back and check that my comment that I made to you got deleted. I know 100 percent that the censorship has hit the charts. Liars hate the truth. satan and his filthy demons know that their days are numbered and they don’t want anyone to know the truth.
I wanted to say thank you, I had my Aptitude test for C.A.F. today and your videos really helped me a lot on my math skills!
Thank you for having these videos explaining PEMDAS because explaining the grouping of MD and AS has helped me as a teacher. I can now explain it correctly to my students. 😊😊😊
I am 73 years old. I went through the New Math era starting in the 8th grade (Fall 1963 to Spring 1964) and survived. I have a very good memory but I do not remember PEMDAS. I was able to to come up with the correct answer using another order of operations I learned somewhere along the way to graduating with a BSME in May of 1973.
I'm 68, and I also learned under New Math... which I loved. (FYI: BODMAS is PEMDAS using different words.)
The New Math system was horrible and I believed it crippled many student's early understanding of basic algebra.and geometry. I know it did mine as I had to fill in the gaps by my own efforts.
I am 71, and despite hating maths all my life, I got it right, by doing nothing fancy just starting at the beginning and continuing.I am a bit chuffed.
Your comment is exactly my point Bradley. PEMDAS was not taught in the "New Math". It was mostly group and ring theory along with mathematical "proofs" which was ridiculously pre mature for high school students.
Me too Brad...the acronym didn't exist yet.
At 68 and retired and hating math for most of my life I now find an interest in math. Looking back it may have had something to do with teaching methods. I have discovered that the math teacher is important.
Me too, except for any new "interest". Made it thru a two year engineering degree because I understood the "Concepts" (even in Physics). The one thing in later years I learned, was that "Math" is just a Tool; not an end in itself, not unless you're "intuitive", then more power to them. The late Physicist Richard Feynman, pointed out something too regarding "teachers"...most all math is taught Wrong! He's well worth looking up here on the "Tube", as a side note, he worked on the Manhattan Project as well, and had quite a sense of humor...he took great delight in putting Top Secret Papers back on the desktop of one of the top scientists after he had locked them up in a drawer before leaving for the night (lap drawer firmly locked). Feynman finally told him how he did it....just reached up and around the lap drawer and pulled them out :-).
@@festeradams3972 yes I'm aware of Feynman. I remember seeing him on TV back in the early 70's I think. I didn't read much about him until fairly recently. Sounds like he had great sense of humor.
A book about him covers that. It's called "Surely you're joking Mr. Feynman".@@robdavidson4945
Answer is 1
This is another fine example of an ambiguously written expression or problem. All the acronyms are well and good, but you'll always get the wrong answer if the original problem is unclear to begin with!
In this case, whenever we see an obelus --- the dot-dot-division sign --- we always need to remember that division, like addition, subtraction and multiplication, are BINARY operations. This means that whatever is on the left of the obelus is divided by whatever is on the right. In this case, all the stuff on the right is 2 x 5. This should be a red flag!! Because a binary operation usually means take this number and operate on it by the other number. Here, we have two numbers and another operator on the right!
AMBIGUITY ALERT!!
Once we remember that division is like a fraction --- some quantity over another quantity --- and that its sign (the vinculum or long bar) is a grouping symbol, this problem can only logically be written as:
10 / (2 x 5)
10 / 10
1
I'm not at all surprised that I got this "wrong", but that's because I used the Order of Operations, and I've learned to understand how the underlying math works.
It's not an argument over whether I'm right and you're wrong. The sole argument here is: are you presenting an unambiguous mathematical problem, or are you intentionally writing this problem in a way that can only sow confusion?
Since Mr TH-cam Math Man says the answer is 25, let's help him write the expression so that the answer will actually be 25!
(10 / 2) x 5
(5) x 5
25
There! It wasn't so hard to just draw a couple of grouping symbols on there and make this a nice unambiguous problem, now was it!
Thank you. His written expression followed by the proposed answer didn't make sense to me with how it was presented. Your written expression follows the classical guidelines for mathematical alignment.
Simple if you have division, and multiplication work from left to right.
So, 10÷2×5 (left to right) because, there is only division, and multiplication.
So many words for such simple and straightforward task.
I was thinking the exact same thing..
Pad it out to over 10 min for that sweet, sweet monetization.
But the words you use mean nothing
exactly! 👍
@bujgirl did in fifty words what he couldn't in eleven minutes. lol
We were taught (Germany) from the inside out (brackets), then top (exponents) and then from left to right keeping in mind that dots come before lines. (• is multiplication, : is division, + addition and - subtraction). For me it was always straight forward but then, I do love math.
As a RoT (Rule of Thumb) something like 'dots come before lines' makes sense. But ONLY if one uses a specific set of symbols.
I was taught (Netherlands) to strictly stick to "Meneer Van Dalen Wacht Op Antwoord" (Dutch version of PEMDAS) and to not switch half way through to 'from left to right' So: first Power (Machtsverheffen), Multiplication (Vermenigvukdigen), Divison (Delen) Rooting (Worteltrekken), Addition (Optellen), Subtraction (Aftrekken). Seems way more logic to me, but, it is all about what system one chooses. When in doubt, use parenthesis
We can say that in PEMDAS is fine as priority but Multiplaction and divion has same priority just as multilication and division.
The order ofevaluation of operators of same priority goes from left to right
Correct…
When I was at school late 1940 early 1950 we didnt use acronyms. I've never heard of them. We would do the maths in order of appearance.
So the above would be 25. 10÷2×5=25 if the answer was to be 1, it would be written as 2×5÷10. And that's how it was back in the 1940s/1950s So much simpler then.
In India we grew up usingBODMAS. Brackets Off division multiplication addition subtraction.
So nothing about exponents?
@@TheaKaSaToRi The exponents is the O in BODMAS. Meaning "Orders" or "Power Of"
In the Philippines we use PEMDAS to solve multiple equations
I grew up with BODMAS too, but I always thought it was division before multiplication, and addition before subtraction. Seems I was wrong all along, unless it is different for different countries. I am from the UK. But that is not to say everyone in the UK was taught that. I may have just misunderstood.
25
We used BODMAS. Bodmas stands for B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, S-Subtraction. PEMDAS is new to me and is not as straightforward as BODMAS
I was looking for this comment.
Brackets would be equivalent to parenthesis and Exponents is the same as Order, Both of which are not in the equation.
25 !
💯💯
Yes I was taught PEMDAS. The public school system failed me 😂😂
Pemdas states that the multiplication/division step is done from left to right as they are considered of equal value, so first: 10/2 = 5 so we’re left with 5 x 5 which is 25. So the answer is 25
Does math recognize more than one kind of bracket? What is the order for this? (A+B) * [C+D] * {E+F}
I received the best education ever in American history in the 1950's in Central Valley CA. This is such an easy math problem that does not need the acronym. Straight forward
Me 2. Central Valley here.
I taught elementary school students with learning disabilities. Using the acronym was especially helpful for them. Whatever works!
I agree❣
Too easy? Aren’t you special 😂
@@eagle-eye29 Jealous?
25 is the answer simply because you read the equation like a sentence from left to right. You would have to group 2 x 5 in brackets if you wanted to divide by the whole quantity of that product.
Thank you for this! I was like well isn’t there supposed to be brackets? What if there is brackets? Lol 😂 school was a long time ago and I certainly forgot my math skills 😂☺️
Yeah, but apparently, some people believe PEMDAS is literally done in that order.
@@fiveoctaves That is true. I know when I was first taught this in class the teacher did explain the grouping of MD and AS could be done in either order. I am an engineer, so this stuff is etched into my mind.
@@scottguitar8168 Same for me. We had better teachers than some others...or some people didn't pay attention or forgot!
Understanding how to read the equation also helps. And you can change the equation and maintain the equality. 10÷2×5 can also be written as 10/2 × 5
This entry was written on 9/15/'23. In order to get the answer 1 properly, The number 10 would have to be in the numerator of a fraction, and 2 X 5 would have to be in the denominator. Or written another way: 10/(2X5)
In school I learned pemdas
P-parenthesis
E-exponents
M-multiply
D-divide
A-add
S-subtract
Never heard of this We just did it....
That is why I always use parentheses to make it explicitly clear what I mean. Especially when I find myself reading code I wrote years ago.
This is important.... Because the answers are very different, depending on the way one is taught.
25?
@@Atheist_Rhapsody (10/2)5
In UK in 1940s and '50s we were taught the acronym BODMAS (Brackets, Of, Divide, Multiply, Add, Subtract) which has always given the correct result for my level of maths. This was used left to right as written. I was a Surveyor / Valuer / Architect - so no rocket science formulae to worry about. Best wishes to you.
In early 60's Australia we were taught BOMDAS not BODMAS this is just another example of a time slip people talk abt.
The O stands for Order, not Of, but yes, it was the way we were taught back in the day, although for the life of me I cannot remember the acronym being used back then!!
@@peterhead9981 In Australia we were taught and use BOMDAS _ where this bodmas comes from is a bit sus.
B _ brackets
O _ treat of as a bracket
M _ multiplication
D _ division
A _ addition
S _ subtraction
@@iandaniel2153 - strange, Ian. Australia seems more in tune with the American PEMDAS. Why we should be different is anyone's guess!
Don’t remember any anagrams at school in the U.K. in the 1980’s, but the answer is 25.
BODMAS is an acronym to help children remember the order of mathematical operations - the correct order in which to solve maths problems. Bodmas stands for B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, S-Subtraction.
It's PEMDAS... Parentheses, Exponents, Multiply/Divide, Add/Subtract
Watching all of the people in the comments still insist the answer is 1 even after it’s explained to them is infuriating
On the other hand, if you give them £1 in change instead of £25 they should be happy, and so will you.
I did indeed learn something, thank you! I had never heard of 'PEMDAS'! I always treated mathematics as reading, just go left to right. Well, even at 66, I'm still learning something new every day! Very many thanks , Sir.
And this equation works left to right but not all of them do.
@PaulDredge1815 I'm 55 and didn't know it either . Which would explain why I struggled in algebra , albeit did great at geometry :\
But in your left to right understanding . You knew enough intuitively to do the brackets and powers first ?
So really this acronym arbitrary rule ... is a tack on to an intuitive function in math formulation.
Where knowing the real world application to these data points , and how to compute them.
Renders this late 19th century math rule , pointless , and actually a cause for more confusion errors with computing .
Just thinking to one of my real world uses in calculating the cubic yards of cement for a basement floor .
@@Mk101T Stupid rules with no explanation should NOT make you feel inadequate.
@@gordonhill8164 Well it certainly does not stop errors from being introduced by the admin that collected and formulated the data into an equation.
And looks like a nifty way to hide or siphon money by knowingly swapping around the order of operations .
I'm 65 and have had algebra and three semesters of calculus in the US. This kind of problem is just a stupid scribble and should be ignored. If you see a thing with a division sign and NO CLEAR MEANING to the numerator and denominator, you are being TROLLED. Run away and enjoy your life, cause you don't need this endless bickering. You have been set up.
Okay: I came up with 25. However, if you do what you say to do- order of oerations- where multiply precedes divide, then the answer is 1.
However, without parenthesis, or any other indicators, your operation starts at the left and goes to the right, solving as you go. Therefore, the answer is 25.
I hated math in high school and college, so I was quite pleased when I immediately got this one right.
I'm a math teacher and I always tough my students
P
ER
MD
AS
'R' for radicals. I also teach about the implied parentheses in something like 5/3+1 (written vertically with '3+1' in the denominator).
I've always sucked at math.
My motto is "Numbers are not my friends."😄
However, I did reach the answer of 25 with no problem....then waited nervously to see what you said.😬
I've never heard of PEMDAS.
The "P" in PEDMAS stands for "work inside the parentheses first", but the original problem doesn't have any.
We never learned PEDMAS. I learned this way , and before this was the old way that I still use. There’s no symbol I can find on my keyboard.
ditto
Me too. Biology was my friend
Great answer 🤣🤣
In short, PEMDAS doesn't mean squat, or, more exactly, it means left to right except where it doesn't. Real helpful.
I agree
This is absolutely BS. If you have a rule PEMDAS, then it should be followed, and to support your argument you totally disregard the rule
@@jonathanraven5939So you don't understand the rule. Got it. He just explained it for you.
I thought I knew it.
@HarryHewitt-lh8xxIt is if you just bear in mind that M and D are one group, both operators with equal priority, so whichever comes first is solved first. The same applies to A and S.
Even though we use PEMDAS to solve these, you still have to read the problem from left to right. So in this case because the division sign is before the multiplication sign, you have to decide first. Therefore the answer is 25.
Ok, I'm doing this a 2nd time and my answer before hearing the PEMDAS is 25. I'll find out if I'm correct. I guess I'm going to subscribe again, but I'm going to stick with problems that appear easier before jumping in the deep end because if I ignore what you say that has nothing to do with the problem at hand, I AM learning again. Last night I was in tears over my incompetence, but today as I go through a few simple problems, repetition of the order of operations from L-R is actually giving me a little confidence. I don't like hearing right away that "most of you will get this wrong" because that convinces me that I will get it wrong. I heard enough negative things like that as a kid, and it stuck, so it made it very hard to believe in myself.
25
I think PEMDAS should be PEPS (Parenthesis, Exponential, Product, Summation) with left to right being the prerequisite. Division is the inverse and multiplication of the second argument, and subtraction is the sum of a negative number. These operations begin in the innermost parenthesis. Exponents are also a shorthand for multiplication.
PEMDAS was over-explictily created for elementary school children to address the four arithmetic operations. It meant PE(M/D)(A/S) with the slash meaning either/or and not mathematical division.
"Limited" computer math line interpreters began the confusion whereas humans knew how to sort discrepancies.
Good explanation, and intellectuals should watch this.
I like your PEPS idea, would solve this - as you wouldn't guess the amounts of arguments I have had over questions like this. People seem to know the PEMDAS rule but never apply it correctly. So I can see the value in what you purpose. As the amount of times I have tried to explain that, with OUT the brackets, you simply go left to right through the equation in the order it is written in the equation.
As in math, brackets are used to manipulate the order of operation to give the output you require. i.e in this case, if you wanted the answer to be 1, the sum would be written as 10 / (2x5) = 1.
@@rianmacdonald9454 Thankyou. I've been heard by the internet 👏👏👏. You're a wise man 👍
You make my head ache.👍🤣🤣🤣
My thing with PEMDAS is only in a its lack of consistency.
Ok, P,E,(MD)(AS) I get it, you group the inverses.
But then it should be P(ER)(MD)(AS)
Parentheses
Exponents and Roots.
Multiply and Divide.
Add and Subtract
@@MrGreensweightHist Yep, same idea.
I always think of it as PE[MD][AS]. M and D are inverses. A and S are inverses. So within those two sets are Left to Right.
You are correct. The PROBLEM GIVER should make all division parts clear to you. The numerator, the denominator, if not, then the answer is "you didn't ask this right, fix it and ask me again". There is no clear answer.
We might also look into the value of 1/0 and sqrt(-1)
We were taught bodmas brackets of division, multiplication, addition subtraction. Therefore 25
Regarding 6:15 PEMDAS. Division has equal order of operation as Multiplication, because Division is actually Multiplication by its reciprocal. Subtraction has equal order of operation as Addition, because Subtraction is actually negative Addition. This means PEMDAS (Please Excuse My Dear Aunt Sally) has equal order of operation as PEDMSA (Please Excuse Dear My Silly Aunt). In other words, PEMDAS = PEDMSA.
Agreed. There is really no 10 / 2, it is 10 * (1/2) ---- You can go all thru algebra and calc without needing this more than the PEMA part and do well. Its the internet, youtube, social websites and memes that people argue forever about the rest.
Well I am 67 and that is the first time I think I understood that PEMDAS. I did not know about the multiplication and division order. I always use Multiplication then division. Thanks Great job teaching this old man.
My too. I was taught X always was done before /
When multiplication and division are encountered without parentheses, they are performed left to right. The same goes for addition and subtraction.
In NZ we were taught BEDMAS (brackets, exponents, division, multiplication, addition, subtraction) which avoided the confusion using PEMDAS.
BEDMAS and PEMDAS are the exact same thing, just abbreviated differently:
B or P - brackets/parenthesis
E - Exponents
D/M or M/D - divisions and multiplication in the order they appear from left to right
A/S - addition or subtraction in the order they appear from left to right.
It doesn't matter which of the 2 abbreviations for the order of operations is used, they are done in the same way.
@@ThePsychosocialite
BODMAS is best of all three.
(Brackets, Of, Division, Multiplication, Addition, Subtraction).
Cos its British, by Jove, now fetch me a muffin and a cup of Earl Grey!
@@jasonyoung7705 We had the O as Orders, ie indices.
@@TifSC
We were taught it was 'of', as in, power of, or root of. maybe thats the same thing.
With no brackets it is confusing unless you do it in exact order written.
So, it’s points before lines (at least we say it that way in Germany), if their are only Dots, then you would use (… ) to show which should be calculated first. As also this is not shown, it’s from left to right and that means 25.
This was very confusing. I was taught BODMAS in Australia. And now I see that there is also PEMDAS. For a exact discipline such as mathematics, it would be inconceivable that these two ways of ordering equations would result in different answers. So, assuming that they both give the same result, what is the difference. The only difference I can see is that the D and M are reversed ie division and multiplication are in a different order. If they produce the same result, then there must be a way to determine objectively the correct order. From other sources, I find that ranking of operations are: 1 Parentheses, 2 Exponential, 3 Multiplication and Division, and 4 Addition and Subtraction, AND for equal rankings, they are to performed from left to right. So, in the example given, the order of ranking 3 should be left to right - division then multiplication. This gives the answer of 25, which agrees with the solution.
As I initially thought the answer was 1, I have been misinterpreting BODMAS for the last 60 years. Thanks for the education, Mr TabletClass Math.
20 years ago in algebra class we were taught, multiply and divide both have priority over plus or minus. Unless parentheses are used you work left to right in this equation.
Good. Correct.
I am 65 years old RN. Never in my adult life have I ever had to use any algebra.
@@TC-eo5eb i am a semi truck mechanic. I use it frequently.
@@TC-eo5eb I'm about to turn 50, and I have...numerous times.
This is not Algebra it’s standard school mathematics.
I learnt at school, long time ago, that to get the result 25 was to write this way:
(10:2)X5=25. That was what we learnt in the sixties in France.
Makes much better sense to me than the above!
good to give the order of operation than the math genius showing off.
I don’t think anyone reading this didn’t get both answers. But I’ve also heard it argued that blind adherence to PEMDAS is a flawed sort of consistency. I’ve seen some great the division like a fraction making the problem 10 / (2*5) in which the answer would inarguably be 1
For this ref BODMAS rule, means Bracket of Division, Multiplication, Addition and lastly Subtraction.
10÷2*5 = x
(10÷2)*5 = x
5*5 = 25 Answer
Don't forget folks, M and D are just inverses of each other and have the exact same priority. Same thing with A and S.
I was told these 2 groups are reciprocal operations. Funny how mostly we all get the gist of the big picture, even though it was taught in different ways. The more linear that some were, the more wrong and confused they were with their equations. 👍
So some people were not taught that some powers of operations are equal and must be calculated left to right. What bad math teachers they had!
I am a retired teacher. I made up a song about the order of operations for my students:
Please Excuse My Dear Aunt Sally.
She doesn’t know what to do first.
Please Excuse My Dear Aunt Sally -
Her memory is really the worst!
Just remember Dear Aunt Sally
When doing math homework tonight:
Parentheses, Exponents,
Multiply and Divide*
Then Add and Subtract*
*Left to Right!
Poor Aunt Sally.!
66 Here
0
The problem with the MDAS part is that in any real world application you should hopefully know which ones should be done first and then you'd indicate that with parenthesis. I certainly do this with any formula I put in a spreadsheet so I don't have to depend on the software doing things in the order I think it's going to. A lot of times it will also be obvious that an answer is wrong. If you want to know much food to divide among 10 people when two people each have five pounds you should know the order to do that and that the answer is not 25. Likewise, if it has taken you ten minutes to complete two tasks and you want to know how long it take to complete five more, you should know the order of that and that the answer is not one minute. The same thing would apply if there was a situation with addition or subtration, you'd think it through before doing the calculation. Students should not be confused with questions like these, but rather given a problem where those numbers actually represent something and there's a question to be answered. The purpose of learning math should be to know how to solve problems and answer questions, not to learn things that don't have any real world application unless you're going to be a math teacher.
Perfect my friend. The only comment here that makes sense. People just want to memorize rules without trying to think and understand the real world application of a calculation. Engineers are trained to think if the results makes sense while math teacher are trained to memorize rules of math operations.
The answer is 1. Remember the rule in order, 1st (X), 2nd (/), 3rd (+), 4th (-); exception if include bracket ( )
Here in the UK, I was taught BODMAS - Brackets, Orders (indices, square roots etc) Division, Multiplication, Addition, Subtraction.
Yes that’s the one
The same in Australia.
in phil it is MDAS❤
Yeah. Exactly because this is just confusing. The order of operations acronym only applies until it doesn't ... i mean what ? That just confuses things to the point of asking well why have that acronym in the furst place? Make up a better one. I used to make up my own.
And the point is. Once learned these acronyms, to later find they don't fully apply in all circumstances. The danger is that some, if not most will end up just ditching the whole concept and loose interest in maths
PEMDAS/BODMAS/BEDMAS are wrong as they mislead into the concept that multiplication & division, as well as addition and subtraction, are different operations thus order matters. If you simply use them correctly, order does NOT matter as division is multiplication & subtraction is addition. At least PEMDAS is a bit better as it doesn’t put subsets ahead of the overarching set by putting division ahead of multiplication, but I still wouldn’t teach it except maybe as PEMdAs parenthesis (in this case brackets may be a better label); exponents; multiplication, including division; addition, including subtraction.
10 * 1/2 * 5 = 10 * 5 * 1/2 = 1/2 * 5 * 10 = 1/2 * 10 * 5 = 5 * 1/2 * 10 = 5 * 10 * 1/2
In the UK we had BOMDAS, which was : Brackets ; OF ; Multiplication ; Division ; Addition ; Subtraction. It was the order of usage.
In India we follow the same method BODMAS
I was taught BOMDAS in school, South Africa following UK standard apparently. When did the change come about?
@@kanabapuka Even in PEMDAS the multiplication comes first. The wind must have changed direction.
Then, when do you work the exponents in that method? I'm from the USA and taught math in this century. I grew up in the 60s and 70s in school but don't remember which method was taught.
do you mean BODMAS? Not BOMDAS...
I always use fractions whenever I have these issues. So it gets easier on which approach to take.
The answer is 1. PEMDAS. Parenthesis, exponents, multiplication, division, addition, subtraction. 2×5=10. 10÷10=1
25 is the answer. This is exactly how I was taught, way back in the 70s, in the US. Yes, parenthesis (or brackets) eliminate the confusion, but the MD and AS are equal components of the PEMDAS order of operations.
1
Thank you for this refresher course.. I must have missed this day in math class because I've had trouble my whole life with this very issue.. in all of my classes through high school and college.. anything with math.. I understood the
principles but could not get the grade on tests. . Algebra geometry physics all sub par
But I made it through and am retired now but still curious.
.
@@mikederiggi2523 : What stipulates that the multiplication is performed first?
@@mikederiggi2523 : Wrong. 25. The problem is solved left to right.
@@wrongfullyaccused7139 The rules of mathematics are not that complicated multiplication and division have the same priority so you solve the equation from left to right.
Hubby and I in our late 70!’s Both looked at it at different times and said 25! Then thought wonder what the new math comes up with. There must be a trick to it we thought. Old math wins! 😂
Lol. The comment section is confusing to me. Straight forward operation, no paratheses. One obvious answer.
I went to the k.i.s.s school.
Keep it simple, stupid
Yay, old maths and logic !!!
There's no such thing as new math or old math. There really hasn't been any changes in math for hundreds of years. What HAS changed is the method for teaching it and the way teachers approach teaching the subject. Instead of rote memorization which was the way for longer than most of us have been alive, they have decided to teach students different ways of approaching math problems. The trouble is, they didn't teach these new methods to the parents, so the students are left with nobody to help them understand these concepts other than their overworked teachers, who themselves may, or may not, understand these new methods. Some academics somewhere thought it would be good to create this new system and call it Common Core. It was partly inspired by political and social issues rather than being a solely mathematical endeavor. The politically and socially motivated educators thought it would narrow the racial and socio-economic gaps between students. This is, of course, a terrible way to develop an educational system, especially a mathematical one. To further complicate things, the students being taught these new concepts are in for a rude awakening when they get to higher education and the work force, as both of those institutions still rely on the previous methods of doing math, so now students must relearn math the old way. Common Core must die and never be brought back. Teachers need to return to the old system so we can bring back the success we used to have. We can find other ways to solve the racial and socio-economic issues involved.
We counted actual beans in primary school. The visual aspect helped me. Convoluted process gets lost in my head. Now I just tell people “don’t math at me” 😅😅😅
I am your generation and my old math tells me it is 1 🙂
Apply BODMAS, which also says operations of equal priorities must be done left to right.
Thus 10/5 =5, then 5x5 =25, which is the answer
HP Prime CAS says the answer is "1".
It has been stated by The American Physical Society in their "Physical Review Style and Notation Guide" that when confusion might result from the way a problem is written, parentheses must be used to clarify the order desired. The correct way to write this problem to get your answer would be (10/2)*5=?. Most people, including my trusty HP Prime, write it as 10/(2*5)=? .
The American Physical Society - Physical Review Style and Notation Guide, p. 21:
(e) When slashing fractions, respect the following conventions. In mathematical formulas this is the accepted order of operations:
(1) raising to a power,
(2) multiplication,
(3) division,
(4) addition and subtraction.
According to the same conventions, parentheses indicate that the operations within them are to be performed before what they contain is operated upon. Insert parentheses in ambiguous situations.
For example, do not write a/b/c; write in an unambiguous form, such as
(a/b)/c
or
a/(b/c);
as appropriate.
Yes it is appropriate to use parentheses for clarification. These kinds of examples are to show you how to process a poorly written expression.
We start by 10÷2=5×5=25
My pet peeve, John puts examples up; then erases them w/o a solution.
My pet peeve… 10/2 is not equal to 5 X 5. Mathematically, 25 = (10/2) X 5.
@@DaveHarris75yeah that is wrong and you don't need the parentheses. So you can just do 10 ÷ 2 × 5 is the same cause you go left to right.
The answer is 1. Multiply first then division
@@joannejennings7649 you do the order from left to right. If you need to do the multiply first the you need to add parentheses around it.
In the UK we use BODMAS...
The US uses PEMDAS
Both use left to right rules and follow the calculation rule of the respective letters
P - Parentheses First ** B - Brackets First
E - Exponents ** O - Orders
M - Multiplication ** D - Division
D - Division ** M - Multiplication
A - Addition ** A - Addition
S - Subtraction ** S - Subtraction
Even today, people still make errors in calculations because we are fundamentally lazy and use calculators
Do you see how BODMAS is correct while PEMDAS is misleading??
i really dont see how anyone gets this wrong
@@BobbyJardine-vs8yc No, because the acronym you learned is not the problem. Some were also taught BOMDAS, or BIMDAS,.
All you need to know regardless of what acronym you learned is that multiplication and division are worked together equally no matter what order they happen to appear in the equation from left to right and the same goes for addition and subtraction. Refer to the OP's post.
In Canada it's BEDMAS
Yes you are right. We use in India same. BODMAS. It is easy to remember as it means rascal in Hindi.
The symbol “÷” was introduced when calculators were invented. It symbolizes a fraction where the dots are placeholders for the nominator and denominator. If you can write an actual fraction, please do so and avoid this symbol. I.e. just write 10/2 instead of 10÷2. This is how it's done in “proper” mathematics outside of high-school. The rules for calcualting with fractions are much less ambiguous, avoiding confusing cases like the one described in this video, which are basically just bad notation.
Furthermore: The sign “⨯” is reserved for the cross-product in vector algebra. If you want to notate multiplication, please just use the centered dot “⋅”.
In general, when writing down mathematics, it is good to think about the reader and not try to “test” him how smart he is. Therefore, I would write down the formula as follows: (10/2)⋅5 . Crystal clear and no PEMDAS needed! (The parentheses are only there because I cannot write a proper fraction inside this text box.)
I'm looking at ISO 80000-1. An INTERNATIONAL standard, not a style guide from some university.
Direct quote from ISO 80000-1-7.3.3: "These provisions can be extended to cases where the numerator, denominator or both are themselves products or quotients. In such a combination, a solidus (/) shall not be followed by a multiplication sign or a division sign on the same line unless parentheses are inserted to avoid any ambiguity."
Oh, and by ISO 80000-2-9.6 "The symbol ÷ should not be used."
DON'T USE "GOTCHA" QUESTIONS TO CHECK IF YOUR STUDENTS HAVE UNDERTOOD YOUR HOME MADE RULES.
A scene from the "Martian" that never was:
Matt Damon looks in a manual.
"Read gauges A, B and C.
Set thrust leaver D according to the formula D = A ÷ B × C.
Press "IGNITION".
GOOD LUCK!
You only got ONE chance."
As you all may remember he has no means of communication.
How about that?
As a accountant, just tell me the answer you want and I will make it work for you
You must be Trump's accountant.
Love it 😂
Absolutely love this. So true.
And people think accountants are not creative 😊
Answer is 25
When I was in school many years ago, for clarity, every math problem included parentheses (n), brackets [n] and braces {n}, in that order. Engineers despise ambiguity. Everything must be precise for a given thing to work as expected. If it doesn't fly, we failed. Period.
Agreed! Give me the parentheses. Even if I know the proper order of operations, I wouldn't assume that the person writing it knows the correct order and is conveying it properly. As an engineer, if something came to me like this, I would request written clarification.
We never learned order of operation in math and I had great math teachers from 6th grade on up. We used the parentheses, brackets, braces too. I graduated in 1986.
@@cdykstra6 WOW and this out of the mouth of an engineer. You can write this 15/(4+1) and everything is fine but if you write this (10/2)X5 I would dearly doubt your profession, sure for an everday joe this may make sense and delete confusion but in as an engineer this looks highly unproffessional. Even worse if I give you this 10/2X5 and you ask for clarification I again would deeply doubt your profession and I couldn´t take you serious as an engineer anymore...
was just thinking this!.... This guy is an engineer and works with other engineers and is talking ab not knowing basic math and not trusting other engineers to know basic math. Scary.@@reinerhoch1357
One math teacher in Hong Kong was extremely strict. If you write down the statement (10 - (5 x 3)) + 2 you will get a big "X" and zero marks for your answer. It has to be [10 - (5 x 3)] + 2. Personally I find that a bit extreme - she basically cared more about form vs. function.
In Canada I have not run into a teacher that will deduct marks for using the first example.
I didnt use Bodmas or pemdas but i used my own as and this is what i was taught. Change the ÷ to × Nd invert the divisor. 10×1/2 × 5 = 25. Not much talking but simple things we were taught by excellent teachers in primary school.
Great explanation. I've been retired for over 5 years and my math skills still haunt me. I managed to squeak through college with a BS in Business. Every math class I was required to take, I had to take it twice and sometimes more. To me, a math equation might as well be in Chinese writing - it makes no sense to me at all. It took me 5 attempts to pass Algebra with a D. It has always been a source of embarrassment to admit how bad I am in math (Not arithmetic - add subtract multiply and divide) it always has been wheat I refer to as "Abstract Math". I always felt that the problem with Math teachers was their complete inability to explain why or how I would need to know it. Wish I would have found you 55 years ago
1
This is interesting from the perspective of say setting a mathematical puzzle for the fun of it but I was taught from a different perspective. Just always use brackets where there's potential ambiguity. It's useful to know multiplication and division take precedence over addition and subtraction to avoid cluttering up very simple expressions with brackets, but brackets always took precedence over having to remember rules. Using an expression such as this in a professional capacity would be frowned upon, and when I studied maths at degree level we always used brackets rather than having to remember rules like this, they just detract from actual problem at hand.
Yeah your correct, bracket and parenthesis must always be used in actual and exact/normal application to avoid confusion, only in tricks and carnaval / fancy events a problems like this occur/// i know pemdas/bidmas but dont give problems like this especially to common non math enthusiast ///
The main reason for the existence of such a RoT (Rule of Thumb) is when forced to write a maths statement as were it a sentence.
Which fingers do I count as brackets? 🤔
@@WtWm-fw7wo All 20. I you look at it the Spanish way...🥸
@@WtWm-fw7wo 😂
I would never pose a problem like this where the outcome is questionable. That is, I would always use parentheses to avoid confusing my readers. Period. 10 ÷ (2 X 5) = 1 and (10 ÷ 2) X 5 = 25. The more symbols that are strung together in a complex expression, the more important the parentheses become. Don't expect your readers to have memorized operation priority rules just because you are too lazy to use parentheses or to split up complex expressions into multiple assignments. I see writers often making this mistake a + b / c when they obviously meant (a + b) / c. It really wouldn't hurt to write a + (b / c) when you really mean it if you think a + b / c might confuse some readers.
The outcome here is not questionable. I see your point that where you are speaking to people with very limited math education, you may want to separate out the sub-calculations - but recall that not everyone of that limited education will handle parens comfortably.
Assuming your audience HAS the least smattering of algebra, they may reasonably be expected to know precedence or how to look it up. Failing to use parens where not required is not "lazy", it is properly spare, and reduces clutter. There may indeed be cases where unrequired parens do improve clarity, but for a problem statement such as this, not so. Me are xpected to use Good english gramer when talking at youse, and you will notice if I don't. Same with math.
Very well put. Use parentheses if you want to be clear.
The outcome of this mathematical equations is not “questionable”, as the answer depends on an un-ambiguous rigidly prescribed order of steps to solve said equation.
And ‘priority rules’ are just as important as any other mathematical and/or arithmetic rules.
And parenthesis are part and parcel of priority rules.
Why would anyone be expected to ‘know the priority rule’ that ‘parenthesis come first’ but not ‘know’ the rest of the orders?
I completely agree, the way it’s presented is confusing. However I got 25.
@@annelarrybrunelle3570No. No mathematician will ever write such nonsense.
PEMDASFLTR - “Please excuse my dear aunt Sally for losing the radishes” was what I learned - parentheses, exponents, multiplication, division, addition, subtraction, from left to right.
I like that md and as can be flipped 🎉
As a former math teacher, this topic was covered thoroughly in class in far less time. Diluting your presentation with endless, extraneous side commentary greatly reduces its effectiveness.
Different countries, different systems.
Living in the Netherlands I learned in the 1960/1970
Mijnheer Van Dalen Wacht Op Antwoord. And in that strict order.
Machtsverheffen (Index) first
Vermenigvuldig (Multiply) before
Delen (Devide)
Wortel trekken (Indices)
Optellen (Add)
Aftrekken (Subtraction)
So according to the rules back then I came to the answerr 1.
I read a bit about it and found out, that the rules where changed to something equal to PEMDAS due to the upcoming computers and that they had a different order.
So thanks, I learned something new.
tegenwoordig: Hoe Komen Wij Van Deze Onvoldoendes Af...Haakjes, kwadraat, wortel, vermenigvuldigen, delen, optellen, aftrekken
@@olivierlohman En dus komt worteltrekken op een heel andere plaats.
Dus elke vergelijking zo opschrijven, met haakjes, zodat er geen gekke discussie kan ontstaan. Bijna metrisch zou ik zeggen.
1
That "whatever you see first" thing tripped me up! who invented these rules and also how were these operation symbols + - x etc invented? was here some kind of big meeting thousands of years ago?
In our language, We read from left to right. Also, there is always that "exception to the rule" in spelling correctly. Mash that together & voila!
PEMDAS Parenthesis, Exponents, Multiplication, Division, Adding, Subtracting
I got the answer right, although I was at school before they taught BODMAS. We were taught the correct way to do sums, but the acronym was not used in the 70s.
That's why I always use parenthesis to remove the ambiguity in these types of problems. They don't cost you anything and they prevent someone from getting the wrong answer which can be quite costly.
I am so glad you use parentheses. For non English speakers and languages that read and write NOT from left to right, I can imagine the use of parentheses is important to show order of importance.
@@danc.5509 I am a software engineer so eliminating ambiguity helps reduce errors in coding.
Not using parenthese is just lazy
In this case an inverted notation would make the answer correct even without brackets:
"5 x 10 / 2 = 25"
Understood as either as 50/2=25. or as 5x5=25. Same answer, making brackets redundant.
@@jesperlykkeberg7438 --- In this case, yes, the brackets are redundant: (5 x 10) / 2 would be equivalent to 5 (10 / 2). Doesn't work the other way, which is the whole issue!
PEMDAS is just order of operation but there was an item that was not really mentioned. Multiply and divide are treated equally and addition and subtraction are treated equally. Parenthesis and exponents are completed first by priority but the others are done left to right with multiple/divide being completed first. Since the question does not contain any other components, it’s just done left to right normally.
Thank you! I was wondering when they would get to 25.
I dont know if you listen to his explanations but he did tell us that!
Yeah, he explained that.
Exactly. This is arithmetic - no bidmas needed.
You are 100% correct. Now, if we could only get the High School math teachers to listen...
We got taught BEDMAS in the western provinces of Canada, like many of the others quoting PEDMAS and BIDMAS and BODMAS, etc. This time the E = exponents, but it all means the same thing.
Oh. And the answer is 10/2= 5 thus 5x5=25
So I went to school and was taught pemdas, the correct answer is 1, that’s what we were taught in school you do multiply then divide
And if you think I’m wrong I’m a licensed water treatment operator and have to do math every single day, and the test I took was made up of 100 questions with half of them being math questions and having to use the pemdas method, you need a 80 percent on that exam to pass to receive your water operator certification
That’s too bad because you are wrong. I don’t think you understand the full definition of any of the acronyms, PEMDAS, PEDMAD, BODMAS, they all when used properly come up with the same answer. It isn’t just the letters. M&D have the same precedence and are handled left to right. A&S have the same precedence and are done left to right. Go to the source, look up Order of Operations and read the definition. I hope any mistakes you have made in the past haven’t resulted in someone getting hurt.
How many of you can still remember "BODMAS" that was taught in Maths class in our childhood days?
I only knew PEMDAS
How many of you actually learned math and not just acronyms and shortcuts?
@@shawnkearney2004not me 😢
What do the B and O stand for?
B = Bracket
O = Of
When teaching the order of operations, emphasize MD or DM, whichever comes first and AS or SA, whichever comes first. Use this consistently in the first year this is taught and it will become part of learners permanent memory. Create a silly rhyme or dance from it, and you'll have a powerful memory tool.
Thank you for this explanation.
Yea for me the teacher said "Multiplication and Division are treated equally just like Addition or Subtraction, you solve whatever comes first on the line"
And that was a very easy and simple rule to remember
Except there is no such thing as subtraction. It is really adding a negative so AS is commutative. But Multiplication and division are not. Division is a fraction and the denominator must be calculated as a unit. Here you have 10/2X5 2X5 is the denominator. It is not 10 div 2 and then the result multiplied by 5. Division is not commutative. Because 2X5 is the same as 5X2 it can very well be 10/5X2.
Greetings. The answer is 25.
The expression given can be rewritten as (10÷2)×5. That gives
(10/2)×5=(5)×5=5×5=25.
In my mind, Division and Subtraction do not exist (in this context). Division is really just inverted multiplication and subraction is just adding a negative. So, a better acronym might be PEMA.
This is why grouping is important. Is it 10 / (2 x 5), or (10 / 2) x 5? When writing an equation, it is incumbent on the writer to compose a clear expression leaving no room for misinterpretation.
It is neither of your examples. It is 10 ÷ 2 x 5, quite simple. It's not looking for any parentheses or brackets to be added.
@@martinglenn27 In a pig's eye.
@@martinglenn27 It's actually the second example, because removing the parentheses does not change the order of the operations.
If you know the order of operations, parentheses are not necessary and could actually confuse the issue in a simple problem like this. I think the acronym may need to be clarified-PE M/D A/S or PE[MD][AS], something like that.
@debbietroyer9480 why do you feel the need to change it? It is quite straight forward already.
I saw this and thought the answer was 25 because things are done left to right. Don't know why a person would jump over a thing to go to another thing and then back to the first one. Side note- I've never heard of, or seen, that PEMDAS tip before. I've been out of school for 30+ years and am happy to not have to think about any of it 🥳❤️
A few years ago on FB is the first time I ever heard of PEMDAS , don't ever recall it in school back in the 50's . I did know how to do it
I believe PEMDAS was brought into use because most math teachers couldn't.
For this example simple "left-to-right" logic works fine, but it wouldn't if you had parentheses and/or exponents, which is the point of this video.
@@mybluemars Correct, it does work, and that's my point. Why would a person not do it that way? Adding in ( x ) is a completely different thing (that is done 1st). If they get the left to right part, they need to start learning things from the beginning 😉👍
@@busaj383 because those who were taught PEMDAS think multiplication is done before division. But my teachers made it clear multiplication and division were equal, as well as addition and subtraction were equal to each other. So you do whichever comes first. But not everyone was taught they were equal or forgot, so they think multiplication and addition have priority in an equation.
Basically Multiplication and division is the same operation (division by 2 is the same as multiplication by 1/2), so there cannot be any superiority of one over another. Left to right is the only way if no brackets present :)
Everyone who got 1 like me were taught that multiplication comes before division in order of operations
Exactly.
I hated maths as a child and would put a barrier up refusing to go there. If I had a maths teacher like you things would have been different. You’re clear and explain well. I did get the question right ⭐️ and I watched the whole video. I envy those who find maths easy. I still feel that fear even now. It’s the, find the square root, type I always dreaded. If you know the language of maths and understand it you’re half way there! I might watch more of YOUR videos and see if you can turn that mathematical key! 🤷🏻♀️😉
“Maths” with an s? Obviously British or maybe Australia.
@@jamesdennis2058 oh yes, 🇬🇧 you say Math 🙂
@@scottw5253 Hey, it’s just how everyone said it. How it was printed on the week’s schedule and given to me! No one seems to have a kind word or a warm heart anymore and that saddens me. Maybe someone should have taught you better manners!! You need to know how your negativity has compounded a situation. I’ve just lost a close friend and I’m grieving. Taking my mind off it for a little while I watched a few videos and thanked them for taking the time to share and lift my spirits. Then you go and spoil that moment of peace. Think before you speak, and if you haven’t got anything good to say, keep it firmly SHUT! 😡
@@cu4wur6023I’m sorry Carol for the rudeness.
I had to take Algebra for my science classes pre-Nursing. I had an India tutor and a Vietnamese teacher. They were so awesome that I took a next level course just for the fun of it 🤪
@@scottw5253 Maybe you could have benefited from knowing that “maths” is a more British term while “math” is more American. It is much like colour or color. She’s not wrong, but the term indicates that she has a British influence so she learned “maths.” My late wife was Canadian, so we ran into these differences often.
I figured it out in like 2 seconds of looking at it. I was always horrible at math at school but had some great teachers who helped me understand. to me this is very simple
I hate maths with a passion and have dyscalculia (the dyslexia of maths), I still don't understand whats hard about this it's very basic.
Ok, so what was your answer?
Empty claim....
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@@mrbmp09
@hereandthere6001 duscalculia......never heard of it. Another made up term for someone who is just crap at math
@@hereandthere6001 I assume that you are not math Prof at yale now???
When I was at school quite a long time ago this was a pretty basic mathematics calculation. & Providing there is simply multiplication & or division with no brackets etc. Then simly draw a line first put all the multiples above the line & all the divisibles below the line and wolla.
The answer 😮
excellent explanantion....after 54 years i understand it now.