3( 5 + 20 / 2 x 5 ) Use the ORDER of OPERATIONS to solve… (BECAREFUL)
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ISO 80000-2-9.6 says "The symbol ÷ should not be used."
But please go ahead and break the rules when you test if your students know the rules.
Ibid: "If there is any risk of confusion, parentheses should always be inserted."
Pretty much rules out this kind of meaningless gotcha exercise.
I don't remember any basic problem like this where the parentheses were not used to make the whole thing unambiguous. When did this kind of thing get more complicated?
165 is my answer. Perform the operation inside the parenthesis first following MDAS. So, 3(5+10×5)= 3(5+50)= 3(55)=165
Yep, good job. When presented with M & D like they have here, you perform operations from left to right, just like you did.
How I did it. But not sure of the answer with out writing it out first. Or using the calculator. Just know its close to but more than 150. But I just woke up. And had not thought to add the 15 in yet. 😅
Well the answer I got was 21. 3(5+20÷2×5). Multiply 2×5=10, then divide that by 20 which=2+5=7. Then 3×7=21.
@@matthewmaning4859 You need to perform 20/2 first. When multiplication and division are inline with one another you perform whichever is to the left first.
@@matthewmaning4859 you do the 20 ÷ 2 first. Or think of it as (20 × 1/2 × 5). If it were written (20 ÷ (2 × 5)) then you would get 21. 165 is the correct answer.
It's a good academic discussion but you should write an equation using proper parentheses, fraction notation, and other appropriate symbology so that people DO NOT have to use order-of-operations to interpret it. Doing it any other way is just asking for trouble. As an engineer, if one of my guys ever has that on a document, it's going to get circled in red with a terse note, "Write this equation so that it is non-ambiguous, i.e. not open to some sort of interpretation." If you're making somebody remember or look up order of operations, you're doing it wrong!
Sheriff Lobo: As a retired engineer, I wish I could give this multiple likes. Students' time should not be wasted on teaching them to write in a form that requires interpretation; instead they should be taught to write unambiguosly. These days, it is more important to learn how to enter formulas in spreadsheet software rather than intuiting what some ambiguous notation meant.
Hurray!
Consider ac/b vs. a/bc. One of these is better than the other even though both are technically equivalent if using the grade-school order of operations.
Absolutely! It is a futile exercise.
Amen brotha (engineer)! When your practice (company) or license is on the line or peoples lives are at stake, leave nothing to chance. Academic exercisers don’t have to worry about such things.
if somebody asked me to do this problem…… I would refuse and say it was poorly formatted and not worth doing
Oh, how I love the response. With that, I am dropping out of this discussion.
Absolutely correct, sloppily written equations should be thrown in the bin.
@@nigelmansfield3011 It is not a sloppily written equation. It is not even an equation.
Explanation occurs at 12:50
PEDMAS. Parentheses, exponents, division, multiplication, addition and subtraction. Division and multiplication are equivalent calculations as are addition and subtraction. My answer 165.
I took general math in school , that is also what I got
Its what I got...165
Talks too much in the beginning.
One way to remember the order of operations is to note that division is the inverse of multiplication, and subtraction is the inverse of addition (e.g. dividing by two is the same as multiplying by one half, and subtracting two is the same as adding negative two). Thus you could replace the “/2” with “*0.5” in this equation without changing it, and once you do that, it’s all parentheses, multiplication, and addition.
However, division is frequently expressed with fraction bars (which double as grouping symbols) to avoid this sort of ambiguity.
Exactly. Addition and subtraction are the same operation. Multiplication and division are the same operation.
It is worthwhile noting that subtraction, in algebra, is defined as addition of the inverse and division, in algebra, is defined as multiplication by the reciprocal. Accordingly, with some pre-manipulation, changing subtractions to additions and divisions to multiplication, one could shorten the mnemonic to PEMA.
This is the important point, multiplication and division is the same operation, as well as addition and subtraction is the same operation. PEMDAS is confusing, I would only ever use PEMA or no mnemonic at all. Teaching "PEMDAS" to students is like confusing them on purpose.
I agree, PEMDAS isn't even consistent because if we're including the inverse operations, shouldn't we be including roots to make PERMDAS?
@@TheHammer305 Roots / radicals are part of "Exponents" (Indices). I agree it should be PEMA, or PFEMA if you include factorials.
@@darbyl3872 If the logic used by schools is that the R is excluded because it is included in with E, then shouldn't schools apply that same logic to the rest of the letters? I was just pointing out the inconsistency of the way that it is taught in schools. For consistency sake it should be all (PERMDAS) or nothing (PEMA). And like I already said in my previous comment, preferably PEMA.
@@TheHammer305 Or it should be PFERLMDAS, if factorials go before exponents, and logarithms are part of exponents.
I was taught BEDMAS, which was also written BE(DM)(AS). That is, Brackets, then Exponents, then Division and Multiplication IN THE ORDER THEY APPEAR, then Addition and Subtraction (in order again).
Me too. I guess it doesn't matter since t's in the order, but changing these familiar mnemonics leads to confusion.
I was also taught be BEDMAS. I think BEDMSA would be best though as then you only need to use left to right rule when dealing with operations of the same priority and can assume division and subtraction are stronger if you like.
A 3 minute video would have been enough to explain this. 13 mins pure overhead.
The other way to eliminate the parenthesis is to distribute the 3. You still come up with 165 after that.
Yep, 3(5+50)=15+150=165.
Distributing the 3 first results in 15 + 60 ÷ 6 × 5... 165.
On can actually do the multiplication from the 3 outside the parentheses thus eliminating the parentheses.
I think the thing that confuses people is the obelus (÷). In my head I automatically eliminate it => 3(5 + (20/2) * 5). When 20/2 is written as a fraction people know not to multiply 2 by 5. Also when it is written as a fraction you can divide the fraction, 20/2 then multiply by 5 which gives 50 ... or you can multiply 20 by 5 then divide by by which ALSO gives you 50.
I agree that there are many ways it could be written to make it more clear. I'm tired of all the PEMDAS videos. Just write equations so they can't be misunderstood.
Yep. I honestly feel like the division symbol should just be abolished and we just use fractions.
if you know PEMDAS, then no question or confusion. Ans is 165.
btw..The first column of evaluation you showed was weird!
I got the right answer because I was taught that division is the same as multiplication of the inverse, or 20 divided by 2 = 20 times 1/2. Therefore division and multiplication have the same order performed left to right.
That is correct. There is no division. Merely, multiplication by the multiplicative inverse. Same with subtraction; it's merely adding the additive inverse.
Correct - you simply multiply by the number or its reciprocal
PEMDAS is the general guide, but not the only rule for order of operations. The other main rule is the left to right rule when dealing with operations that are considered of equal importance. Any operation that is the inverse (they would undo each other) of another operation is considered of equal importance. Multiplication and division, addition and subtraction, exponents and logarithms, etc. Therefore, any math problem has a correct solution, even if the expression might be ambiguously written such as this one.
Order for Addition and subtraction does not matter at all, so long as you interpret/understand the "Addition and subtraction" terms as only being addition, and treat the operators ( +/- ) as signs on the terms instead.
Left to right:
5 - 20 + 30 - 50 + 10 = 25
Left to Right or right to left:
5 + -20 + 30 + -50 + 10 = 25
-20 + 5 + 30 + 10 + -50 = 25.
Additionally, because this works for Addition swallowing subtraction, it logically follows it must be true somehow for multiplication and division, which it is.
You can interpret/understand all multiplication and division terms as fractions that are multiplied together by setting any multiplication term as N/1 and setting any division term as 1/N. Once you do this, as wirh addirion and subtraction the operations can be considered in any arbitrary order you like.
Left to right:
100 * 5 / 50 = 10
Right to left or left to right:
100/1 * 5/1 * 1/50 = 10/1 = 10
100/1 * 1/50 * 5/1 = 10/1 = 10
Once you are used to this you might prefer to shorthand just the division terms as 1/N and leave multiplication as N as a matter of notation, so long as you actually remember to act on each one as a fraction.
Ie
"100 * 5 * 1/50"
@@qsquared8833 This is really the right way to think about it. The only true binary operations we need are + and * but we use other operations as short hand to make it easier to write expressions.
This is why you should always put parentheses around chains of multiplications and divisions. And why you should always use the horizontal line ("viniculum") for divisions, not the weird division symbol that you literally NEVER see used after grade school. This is literally the de facto rule I've seen followed in every math class after 6th grade, from Algebra 1 to Differential Geometry.
Literally EVERY "gotcha" I've ever seen with PEMDAS and order of operations comes down to some prick using a string of divides and multiplies with that plain divide symbol and missing parentheses. So just don't do it. Just explicitly teach kids the way you're supposed to write down equations, the de facto rules that everyone in higher math, science, and engineering already has to pick up via osmosis anyway.
In the old days many equations or mathematical expressions were written by hand and used blank areas to show where the break in a chain was if parentheses weren't used. The problem only came into being writing single lines of code for computers eliminating the spaces. As soon as I heard of this "new" order of operations for such one line expressions I knew it would cause all the confusion people have today. Really, just add the parentheses, and everyone should get it right. How would someone using PEMDAS etc read a historical text with blanks?
They're not "pricks". You just need to know the rules. It's pretty simple.
@@toby9999 No they definitely are pricks. There's no reason to use an ambiguous notation when there's an alternative. The types of equations they use to trick students don't appear anywhere else.
These are all over the Internet. I'm an engineer and use a fair amount of math in my job. Who would write an equation this way?
A pedant
No one. That's why these are exercises and not real world problems. That being said, I got an A+.
No one because it is not an equation.
@@cbesthelper404 It is when it's solved.
@@robertcameronjones It's an expression that is being simplified. So many are incorrectly referring to this as an equation.
There is no left to right in mathematics, it’s all about what that division symbol means, the two dots and the line are the same as if you had written it as a fraction, 20/2, and you should immediately rewrite that division symbol as a fraction to avoid confusion, then the problem becomes 3(5+20/2*5)=3(5+(20*5)/2)=3(5+50)=3*55=165.
Yes, my way is tedious, but you progress sequentially and you can never make a mistake, and you always know why you are doing what you are doing, it’s not some hokey rule!
I first encountered the left-to-right rule when programming equations in fortran and BASIC decades ago. If you paid strict attention to the order of operations, you could eliminate pairs of parentheses and end up with a program that would execute just a tiny bit faster.
@@clarencegreen3071
Precisely! I remember doing FORTRAN II problem sets of writing Statements whose goal was fastest execution. The same for Assembly Language coding. This was back in mid 1960’s. IBM RELEASED FORTRAN II in 1958.
@@clarencegreen3071
That’s totally different than the operations in mathematics itself, yes there are rules you must adhere to when programming, just like you must know how your calculator manages operations and must input information accordingly, HP was different than Texas Instruments, just like Excel was different than Quattro or Lotus, and when we got programs like Grapher, Mathematica, or Minitab.
The first thing we learned as engineers is to be careful when inputting information into computer programs, and know how to calculate your problems by hand and test your programs before you put any stock in the answers that were rendered.
Today we have simulators and the like that need little consideration when you input information, and unskilled engineers relying on computing power instead of actual experience and understanding of basic principles leads to poor engineering analysis and even poorer conclusions.
Remember, we have mathematical principles so we can communicate with each other our solutions to problems. It would be total chaos if we all had our own way and our own basic principles. We all must be able to reach the same results or our solutions are useless.
From Wikipedia in Order of Operations under the pneumonics section...
The "Addition/Subtraction" in the mnemonics should be interpreted as that any additions and subtractions should be performed in order from left to right.
You write "there is no left to right"?
Perhaps you need review the Order of Operations.
I would have been remiss in my duties as a Math Instructor at ASU to not teach the Order of Operations properly. It is engrained in my brain.
Takes about 5secs of mental arithmetic if you know the rules. And this example shows why it's so important to know the rules which remove ambiguity.
Well say. if you know the rules the result is just 165
I came up with both answers, but had forgotten ‘order of appearance left to rightI’…so I couldn’t explain why 165 was correct…thanks for the reminder!
By 4:00 I am so fed up with the chit-chat I couldn't care less about learning the answer. Bye!
Thank you for your videos. But I am a practical man. I have been teaching (lower level) math to trades students for almost twenty years. A math problem laid out as this is written by a math teacher.... in the real world a problem needs to be written in a way that anyone will understand. Throw in another set of brackets or whatever is needed.
After 25 years in industry, followed by college level teaching I never heard of BEDMAS until I started teaching math to my trades students, yet I don't believe there was ever a redo at a gas plant or oil rig construction or any other job I worked on... Just like weld symbols or blueprints keeping it simple, and mistakes are minimized. As I said, I like (and have learned from) your vids. But even 45 years ago in school I hated questions that were written as 'math' questions. I know the need to 'tests a student, but real world work uses way that don't depend on memorized rules.
Pardon my typing.
You're correct in terms of real world useage but as you'd know, this was designed to test people's understanding of the rules and as such I thinks it's fine.
@@toby9999 A rule is not a rule if there are multiple versions of it.
I solve the problem by using parentheses liberally. That way I force the order and eliminate any misunderstandings. Btw, I do know the order of operations and I was a programmer for many years and don’t blindly trust compilers.
I have been aware of the order of operations for a long time now [70 years old] but I honestly don't recall ever having been taught the PEMDAS acronym. Nor do I remember being taught other mnemonics like Roy G Biv - or the English version: Richard of York gave battle in vain. Maybe I just have a poor memory for mnemonics LOL
Yes, I got it right and am 78 and I never heard of any of those things either, that I recall
I'm pretty sure that I was taught the order of operations in 9th grade Algebra I, but I had completely forgotten it until recently being made aware of it. I have never had to solve a quadratic equation IRL.
In high school, I studied algebra (3 levels) then Euclidean geometry, solid geometry, and trigonometry, in the 1950s. I got advanced placement upon entering university and studied symbolic logic and calculus. I became a translator and never looked back until 60 years later. When seeing modern algebraic expressions, my first questions was, "Why aren't the operations grouped non-ambiguously, with parentheses, brackets, braces, and rarely, vinculums." Then I noticed mentions of PEDMAS and eventually learned what that meant. It is certainly a more compact method for writing expressions than what I was taught, but can be very ambiguous. I am now updating my knowledge of the subject by working through "Algebra for College Students" by Lial, Hornsby and McGinnis. No doubt, I will find other things that have changed since the old days.
The thing about algebra is that it is a language and, like all languages, it has grammatical rules that have been developed over the years to improve clarity.
3( 5 + 20 / 2 x 5 )
Do the most inner parenthesis first. There is division being indicated, so we must complete that first.
= 3(55)
= 165
In my head : 165
From my high-school : Parenthesis from inner to outer, then powers, then multiplications and divisions as they appear as they have the same priority, then addition and subtraction as they appear as they also have the same priority.
On the face of it this feels like debugging uncommented code you haven't written - the intended logic isn't self evident. It may run, but checking the results correctly makes sense afterwards is another matter! Whilst I appreciate the academic value of this video, a practical approach is to not write your equations in a form which relies on humans remembering (as that alone is just asking for trouble) the finer points of the PEDMAS mnemonic. Sprinkling a few clarifying but 'technically superfluous' parentheses around can help communicate your thought logic by grouping equation elements related to particular parameters you're mathematically modeling. Incidentally this also makes relationships easy to navigate during later refinement of the equation, so do it for future you too!
There's more to maths than just numbers and operators, there's almost always an associated logic. Yes you can add a temperature to a velocity vector, and maths will let you do it with the numbers, but it makes no logical sense. It's also very easy to be out due to not accommodate a parameter's unit (just ask NASA re Mars Climate Orbiter) , and these can be a bugger to spot in equations where the intended logic is not immediately apparent. Equations also get interesting when dividing by temperatures around 273.15°K expressed in °C.
You need the logic, not just the maths.
are you a robot from the future?
Did this in less than 10 seconds in my head.
That's why when you write software code you have to be specific and leave no ambiguity. Absolute use of relevant parentheses is needed if you wish the software to track your intentions.
Yes, I totally agree. I remember assisting a person with a coding issue (and this was an experienced coder). He couldn't get a table to show a 'dash' when there was a blank with no numeric result. I said to him "have you tried a nested if statement"? The next day I had a box of chocolates on my desk. I said to him, you just need to remember computers are stupid and they need their instructions to be 'bleedingly' obvious - think like a computer when the computer isn't giving you the result you want.
We learned "Please Excuse My Dear Aunt Sally" which is PEMDAS but in a way cooler way of saying it.
I'm just getting back into math as a substitute. I was excited to learn PEMDAS. Now I know the rest of the story. TY
It is bad practice to present a math question in this way.
With the correct use of brackets, which may include small ones within larger ones , plus the use of numerators and denominators where appropriate, preclude any necessity for priority rules and head scratching ambiguity.
Actually, this is pretty standard for math teachers.
Greetings. The answer is 165. The bracketed portion works out to 55. Thereafter, multiplying 55 by 3 gives 165.
I draw up maths and English notes for students to use alongside my subject matter notes (I do not teach maths, but we certainly use maths in class! ;-) ),. In them, I point out that division is essentially the same as multiplication (Just invert and multiply.), and subtraction is essentially the same as addition (Just add the negative.).
Student tend to understand.
Maybe it's because I'm a former Army sergeant, and act accordingly..... ;-)
Good lord, 16 minutes to say this...
Follow this order:
1. Parentheses
2. Exponents
3. (Left to right) Multiplication and/or Division
4. (Left to right) Addition and/or Subtraction
I'm not even sure he actually states what the acronym means.
Bonus points: it's also known as BOMDAS (brackets/order/mult/dev/add/sub where 'order' or 'of' is another way to say exponents)
and BEMDAS which is the same as PEMDAS but with "brackets" instead of "parentheses"
Where do these guys come from? Mathematics is a strict science, 1 + 1= 2. There is no other way. Yet still this guy is admitting that the problem resented has various methods. If that is so, the problem is not that there are various ways but the people have no idea of how to use the one and only correct order of operations order. There is only one order of solving these problems, not various. No wonder the level of mathematics taught in schools have dropped to the lowest ever compared to other countries.
Thank you for the laugh (operation), I got both answers 21 and 165 (correct) but how you said: it doesn't matter which is first M or D and A or S they are the same. Happy New Year 2022.
The answer to this algebra problem is 165. Using PEMDAS you solve the inside of the(first the first thing you do is to buy the 20 by 22 get 10 and you multiply the 10xfive you get 50 you add 252 the 50 you get 55 then you multiply that by the three on the outside of the parens which is 165 that is the answer and that is the proper order using PEMDAS to solve an equation.
You’re wrong - the answer is 21 - PEMDAS - multiplication comes first, not division
@@JustMe-ob3nw No, you are wrong. Charles is absolute correct.
this made the problem MORE confusing
Subtraction can be considered adding a negative number (5-3 is equivalent to
5+(-3)) so they are actually equivalent processes as are division and multiplication.
20 ÷ 2 can be written as 20/2 or 20 × 1/2. Knowing this equivalency you just have to know which takes priority. In school you learn to add and subtract before learning multiplication and division, so remember they are a
higher level than adding(subtacting) so higher level takes presidence.
You should probably let people know that "order of operations" as explained here ceases to be very relevant after elementary school. It is useful for passing tests in junior grades, but in the real world it is superseded by other rules that are more practical and useful for scientists and engineers to use when writing and communicating with each other.
As one who practiced engineering for almost 50 years; I learned to use parenthesis if the expression were ambiguous and not rely on people remembering arbitrary rules.
@@srsykes Thank you!
@ib9rt Exactly! And well stated. Whenever I see such a problem as this, my first thought is that the presenter/poster has never dealt with advanced math in the real world.
Thank you sir. I was confused about M and D sequence.
They are interchangeable depending on what is first from left to right.
This helped a lot.
Will watch your interesting lessons.
They are the same operation. A-B= A+ -B.
It took almost nine minutes before you got to the actual mathematics of the video.
That is why a lot of people get bored in math class - the teacher tends to over-explain stuff that is basically already inherently understood by most of the students.
Maybe try to throw the concept out there, and then see if some of the students need further clarification from there, instead of tuning 90% of the class out just to make sure that you try to make sure that last 10% has a better chance of grasping it on the first explanation.
My theory is that impatience is why so many people are challenged by math. They don't want to hear context or logic or the "Why?" Little do they know that if they listen and integrate math into a narrative rather than rushing off to the numbers, they'd understand better.
I've heard it,, referred to as PEDMAS, or in the UK, BODMAS, which I was taught in maths back in the '60s. I've no idea why the D and M are different here, especially as you do division before multiiplication.
The D and M (and the A and S) do not dictate order, only that operators DM have higher precedence the AS. The rule says evaluate terms with equal precedence from left to right. Not sure whether this is what you were referring to?
" you do division before multiiplication." is INCORRECT.
Multiplication and division have equal status, and are done left-to-right.
Same for addition and subtraction, although there it makes no difference.
3*(5+20/2*5)=?;=> If We Perform Arithmetic Operations According to Operation Priority!
3*(5+20/2*5)=?;=> 3*(5+(20/(2*5)))=?;=> 3*(5+(20/10))=?;=> 3*(5+2)=?;=> 3*7=?;=> = 21; İt Will Be İn Form!
Division is inverse multiplication
for example, (÷2) = (1/2) = (0.5)
therefore, 20÷2×5 = 20×0.5×5 = 50
Similarly, subtraction is the addition of negative numbers
It follows that PEMDAS reduces to PEMA.
Or, do what is taught in engineering school, use more parentheses for clarity. Mistakes matter in engineering, regardless of the reasons. Lives and money matter.
eg, 3(5+(20(1/2)(5)) = ...
Thank you.
On this side of the Atlantic we teach BIDMAS - brackets, indices, and I'm sure you can guess the rest. We just work through the letters in that order. I've never heard of PEMDAS and having M before D could confuse some students? But a good video. (retired maths teacher)
There is no "order of operations" in real math. The so-called "order-of-operations" is a convention that was made up, but nothing in math suggests, for example, that multiplication comes "before" addition. Real mathematicians don't write ambiguous equations. If the real-world problem dictates that an addition, subtraction, multiplication, or other operation should be done in a certain order, then the mathematician would use brackets to make it completely clear. The so-called "order of operations" was dreamed up and has no real practical application.
Think of the four lines of the Order of Operations as 1) P 2) E 3)M/D 4 A/S If their are multiple operations on the same line, go from left to right. Work within grouping symbols first. I used to tell my students it's like school lunch - it works it's way from the inside out.
I write PEMDAS a bit differently - the D and M on top of one another, same with A S. And I tell them that each pair of those stacked operations should be looked at from left to right. Another thought I share, dividing by two is the same as multiplying by 1/2 which would illuminate all doubt because now you only have multiplies. It’s funny how we can have new ideas how to teach this old topic.
I learned the OoO quite a few years ago, and the way you describe it is how I see it in my head. I feel quite a few younger people would understand it better if it was written out you described.
Why not teach how to write unambiguous statements?
@@ronaldtownsend5745 Great question! Teach proper grouping with ( ), etc., get rid of the classic division sign, and avoid the ambiguity.
@@ronaldtownsend5745 - Yes, but. Even as students are solving simple equations, order of operations is important. The problems that hit TH-cam are often ambiguous, or at least, ones that don't really occur as presented. My comment about multiplication/division having same priority, as does adding/subtracting is still an important observation, one that needs to be learned.
@@JoeTaxpayer You'd be surprised how many people I've encountered that could not divide by 1/2 much less add a -2.
I wasn't sure where you were going. I got confused. Then I saw your merch , You are not an educature you are a merchant. Best of luck Mr Math Class.
Apply Bedmas withbin the Bracket.
3 x(5+ 20÷2 x5)
= 3× (5 + 10x5)
= 3x( 5 + 50)
= 3 x 55 = 165
It's been a long time, but i'm from the uk, and we use (I think) BODMAS, so i did -
3(5+20/2x5) - remove brackets -
15+60/6x15 - Do the division -
15+10x15 - do the multiplication -
15+150 - do the addition -
165 - Which is the answer.
Now I don't know if this a fluke but I get what the video says is the right answer. Woo Hoo.
@@stephenc.120 No fluke. You simply distributed the factor of 3 which violates no rule at all.
Pemdas is like classical Latin where all the verbs are at the end of the sentence, and you have figure out where they go.
Or using a sentence without proper punctuation.
Use as many brackets as needed. Then the Oder becomes so clear George Jetson could figure it out.
Or if there are set formulae, teach how the formulae work. I do not think in the real world one would just get page of expressions to figure out.
Plus I do not think Pemdas would help with FOIL or factoring of quad equations
The issue isn't PEMDAS per se, but the additional "left to right" rule that has to be tacked on to handle this pathological single-line equation syntax. A syntax NOBODY ACTUALLY USES. Everything gets much clearer and less prone to error if you simply ALWAYS use "---" lines for division and don't cram everything on a single row of text- AKA the real way everyone is taught to read and write equations after elementary school, anyway. In the real world, people also use as many brackets and horizontal rows as they need.
These pathological expressions are a waste of everybody's time. The kids waste time mastering an equation syntax that nobody actually uses in practice, and teachers waste time because the full PEMDAS rules are made more complicated than the need to be.
Topic starts at 5:00
A few decades ago it was taught as BEDMAS. brackets, exponents, etc.
Yup, same here. BEDMAS, but similarly to his lesson, D&M and A&S swap places with each other as needed working from left to right.
That's the way I learned too. I came out with 165.
I learnt it as BODMAS... Brackets, Of, Division, Multiplication, Addition, Subtraction.
@@shanelawson5072 same here but now it's taught as BIDMAS over here in schools.
I got it right and I haven't studied math for over 35 years and I don't have a photographic memory. I didn't learn the pemdas either this is the first time I have seen that. I like math because the rules are absolute with no grey areas like some other subjects. Some stuff just sticks in my brain forever and math is one. And yes I did take a lot of notes in class. If the instructor writes in on the board it should be in your notes.
Do by pemdas(parentheses, exponents, multiply, divide, add, and subtract.
A firm grasp of the algebraic calculation rules of algebra ensures mistakes don't percolate upwards into partial solutions that will contaminate final calculations and conclusions.
Well, at one time or another, Newton, Planck and Einstein each evaded
scientific journal publishers after realizing submissions contained arithmetic errors in partial theory solutions. Corrected, the papers were released from hostage and soon published. :-)
Similar to the system that ! was taught. "BODMAS' was used--brackets, of, (division), division, multiplication, addition, subtraction.
I was taught Brackets out, then division ......
@@stephenc.120 That is the same system as mine. The term "of" represents division. eg: 1/4 of ....
I'm a retired old man, but like to keep my analytics skills sharp, and why not do it with daily math problems.
And watching this videos is even easier to understand it.
To avoid this type of confusion brackets should be used and division should be expressed as x/y, not x÷y.
It is equally valid to say X times 1/Y as X/Y.
I think you're missing the point of this test.
There recently was one of these blatant “order of operations” problems on Facebook. The two sides debated the two possible solutions with great vigor. Now< I know which one should have been correct. Thank you.
This is called BODMAS in India.
Bracket, of , division, multiplication, addition, subtraction.
No, the order of operations is not a pure mathematical necessity..if you arrive at one number for yourself or your team, then that is the correct answer..order doesn't matter.. it's that a number is used to benchmark by..I still believe mathematics is way overblown, made far more complicated than it should be..make the pure concepts part of a required course of study..much of mathematics is purely abstract and artistic..not just raw numbers
@@mitchelll3879 So if you need >30 micro liters of anesthesia to not be killed (made up number) and the medical arrives at 60 micro liters and gives you that and you die….
Are they still right because that’s the number they came up with? Of course not.
Your comment was wrong on so many levels and I don’t even know how to begin to explain that to you.
I will say this, no one listen to what that guy just said.
That was borderline flat earth logic right there.
Step 1: 20/2=10
Step 2: 10 x 5 = 50
Step 3: 50 + 5 = 55
Step 4: 55 x 3 = 165
The reason I don’t distribute the 3 first is because according to PEMDAS OR GEMDAS you start with Grouping or Parenthesis first.
165, division is left of multiply so 20/2 =10 x 5 = 50 +5 = 55 x 3 = 165
I study math. I always tell ppl, multiplication and division are the same (excluding the number 0, can't divide by 0). Dividing by 2 is the same as multiplying by 0.5. Same with addition and subtraction. Subtracting 2 is the same as adding by negative 2.
Real math is about communication among mathematicians. Is it really correct to write ac/b as a/bc? They are the same with PEMDAS/PEDMAS. F=ma so F/ma is 1? Or is it?
My grandfather explained the obelus (÷) to me 70 years ago when I was 8 and he was over 80. He said it was a symbol he was taught at age 10. It could occur only once in an expression and it was performed last in that expression so 3(5 + 20 ÷ 2 * 5) would have been evaluated as 3((5+20)/(2*5)) in 1890. He would have answered 7.5. Think of it as a horizontal bar with the stuff to the left above that bar and the stuff on the right below it.
Why are you introducing inner brackets ? You should instead 'kill' the original brackets as you sail towards the solution. By injecting inner brackets you have changed the meaning of the expression completely. Insertion of inner brackets must be done with care to avoid distortion of the original question. Math is always true forget about your grandfather limitations.
@@joshuaorenge I was showing with the brackets how my grandfather would have interpreted the question. I was remarking on the history of the symbol and its historic meaning. But let's just skip the history and maybe take a shot at -- Is it really correct to write ac/b as a/bc?* They are the same with PEMDAS/PEDMAS.
Say x=ma is established in some paper. Then x/ma is what? That depends, of course. Especially in an electrical engineering paper where 'ma' is milli-amperes.
Math can be about the formal grammar of a string of symbols. The order-of-operations rules are such a grammar. Nevertheless, the best advice was given by Sheriff Lobo in another comment. Always be clear as to what your string of symbols is intended to mean. That any reader can get it wrong means that you're doing it wrong. The problem is further confused by the use of the obelus (÷) instead of slash (/). It had an historic meaning. It allowed the typesetter to use a single line instead of using a vinculum saving 2 lines of space. The obelus is not the same as the slash historically.
A program (like Wolfram Alpha) may well have PE(DM)(AS) built-in. You can take advantage of this if you know the rule and save yourself some brackets.
___
* For many ordinary algebraists the implied multiplication by adjacency is before the division. a/bc would mean a/(bc) to them. Sheriff Lobo would always write a/(bc), a/(b*c) or (a/b)*c or (a*c)/b depending on what was intended. (Of course, (A/B)*C and (A*C)/B can be differently evaluated using integer variables in a computer.)
3(5+20/2x5) = 3 x ( 5 + 20 x (1/2) x 5 ) = 3 x ( 5 + (20 x (1/2) x 5) ) = 3 x ( 5 + 50 ) = 3 x ( 55 ) = 3 x 55 = 165, because there is no division; merely, multiplication by the multiplicative inverse, and other than exponentiation, operators are evaluated left-to-right by convention in the absence of parentheses.
multiplication by the reciprocal instead of division is good practise but the formula is simple enough, so either way works.
Having been a programmer for 30 years and understanding of how computers do the operations I aced it.
Just make fractions with the multiplies on the top (numerator) and divides on the bottom (denominator)
Confused 😕 why switch division first than multiple when it is pemdas
i would honestly do the parenthesis from right to left so 3(5+2) = 21
Of course. That's what the rules dictate.
But if you write it as 3(5+20/2a) where a=5 is ambiguous. It is just because I wrote it inline and not as a fraction with a 2a under a horizontal line.
In South Africa we were taught to multiply the number outside the parenthesis "into" the brackets...thus eliminating the number outside the parentheses, and only having to deal with the normal order of operations within the parenthesis...if that makes any sense.
P.S. W(hy)TF the mnemonic PEMDAS? How's about the basic rules of logic?
You are correct that you can manipulate the equation as you say.
You still must do the multiplication and division in order from left to right.
The best practice is to make an equation that cannot be misinterpreted.
Whoever rights equations like that should not be teaching math. In the engineering world these sloppy practices have cost lives. Just don't write like this!
@@johnlangenecker5664 What is sloppy is referring to this as an equation when it is not.
If this Left to Right law was implied eons ago, 21 wouldn’t be coming up as an answer 🤦♂️, Always done multiplication first then division then add then subtract
There is no division. That's the problem. Rote application of a rule without deeper understanding. Like FOIL.
5+20=25, 2x5=10, 25 divided by10=2.5, 3x2.5=7.5
Good grief this guy just perfectly represents everything wrong with modern education:
1. Passes off PEMDAS as a mathematical property when it's really just a convention. A convention that only seems to ever be used on ambigous problems designed to deliberately confuse students. Every teacher ever seems to fall into this trap.
2. A video 3-5 times longer than it needs to be. Like dude, you should know that the students who learn this stuff for the first time already have a horrible attention span. Maybe your students would stop using their phones in your class and take better notes if you just got to the point so they know what's actually important to write down. Instead they have to listen to you ramble and switch bac and forth between autopilot mode and "this might be important" mode.
3. Clickbaity title and half the video is just advertising his online courses. He's probably the same kind of person who writes his own propriety textbook for a college course, changes the edition every semester, and then forces his students to buy it for his course while he charges them up the wazoo for it.
you got the wrong answer didn't you?
@@davem45 I'd say you did the math - LOL!
@@davem45 LOL!!!! You gave me the best laugh I've had all day.
@@felixlinquist A good one!
I thought parentheses first meant DISTRIBUTE the 3 first... (15+60/6*15). (15+10*15). (15+150)=165
I did it this way also
A number right next to parentheses implies that you should multiply; it just does it without using a multiplication sign. However, using the Distributive Property would be optional here. However, you made 2 mistakes in your distribution, but they canceled each other out (not something you can count on happening all of the time) and you did end up with the correct answer.
In the Distributive Property, a(b+c)=ab+ac, the stronger multiplication is outside of the parentheses with the weaker addition inside to start. When a is distributed, it is multiplied by each of the things being added. So in this problem, 3(5+20÷2•5), the 3 can be distributed to each of the things being added. Since 20÷2•5 must be simplified before it can be added to 5, it will be treated as one chunk of information. So 3 will be multiplied with 5 and with 20÷2•5. Thus, using the Distributive Property:
3(5+20÷2•5)
= 3•5 + 3•20÷2•5
= 15 + 60÷2•5
= 15 + 60÷2•5
= 15 + 30•5
= 15 + 150
= 165
Since you distributed the 3 to each of the numbers in 20÷2•5, your work was wrong. What saved your answer was that, when you multiplied 2 and 5 by 3, the 2 was being divided by and the 5 was being multiplied by. So when you multiplied 2 by 3, what you were dividing by got 3 times bigger (making the number 3 times smaller), but when you multiplied 5 by 3, what you were multiplying by got 3 times bigger. So getting 3 times smaller and 3 times bigger canceled each other out. If it weren't those opposite operations in the same chunk of information, your answer would have been wrong.
I hope this helps. If not, I will say this, it is almost always better to just follow the order of operations if you have no variables. The Distributive Property is most helpful when there are variables.
@@MrBurfordNCS I am fully aware of the correct way to use the order of operations, I just liked the fact that the multiplication followed by division canceled out and it allowed me to use the three incorrectly and still get the correct answer. I would say it was almost sarcastic but there was a certain amount of enjoyment I received by doing it wrong. I do like your detailed explanation and that was exactly what I noticed when I did the problem incorrectly. I even thought to myself of a number of examples in which it would not work just out of morbid curiosity. 😁
@@Frie_Jemi Hey, if you knowingly did it wrong because you knew that it would come out right, who am I to complain? :)
PEMDAS (order of Multiplication and Division are determined by what comes first, going Left to right):
Question: Does the same apply to Addition and Subtraction?? In other words, if moving left to right, Subtraction comes first, then do you implement subtraction rather than addition? Please answer - this is a very important question.
@@davhwd So, Multiplication and Division is determined by Left to right, and Addition and Subtraction is not determined from Left to right. This is correct?
As John was explaining , after going from parenthesis , exponents/ when going from left to right if division is encountered it is applied but if multiplication comes first then it is applied then swing around and apply division/ moving forward from left to right if addition comes first it is applied but if subtraction is encountered then it is applied then after addition is applied.
A little confusing, but follow the sequence and you'll get it right. Peace
@@victorsoto2188 In sum, Multiplication / division, and Addition / Subtraction are interchangeable in the Order of Operations when working left to right. (Thank you
Multiplication and division are not interchangeable. Neither are addition and subtraction. The PEMDAS acronym should be stated: Parentheses, exponents, multiplication OR division whichever comes first from left to right, addition OR subtraction whichever comes first from left to right.
@@cynthiamitchell2705 Wrong. If Division occurs first, working left to right, the Division takes priority over Multiplication -
The way I explain it to my students when it has the division then multiplication is to tell them to look at it line by line. 3(5 + 20/2 * 5)
20 over 2 puts the 2 on line 2. So work line 1 20 * 5 then divide by 2 which is on line 2. Then complete the rest.
There is no "order of operations" in real math. The so-called "order-of-operations" is a convention that was made up, but nothing in math suggests, for example, that multiplication comes "before" addition. Real mathematicians don't write ambiguous equations. If the real-world problem dictates that an addition, subtraction, multiplication, or other operation should be done in a certain order, then the mathematician would use brackets to make it completely clear. The so-called "order of operations" was dreamed up and has no real practical application.
@@RexWeylerMusic Just something to confuse some people while making others look smarter than they really are. All that operations is useless in real world because it's not everyone that uses it.
It's P then E then [M or D] then [A or S]
Now I remember why I hated math class and junior high school and high school!
Videos would be better if there weren't so many words (yak, yak, yak) but instead proceeded directly to the problem.
Please Remember My Dear Aunt Sally - Powers Roots Multiplication Division Addition Subtraction
I got it wrong. I had to verify my answer with my own software calculator. The RPN (Reverse Polish notation) solution came up with 165 answer. Thanks for the lesson.
RPN is the best way to remove ambiguity ;-)
This is a problem written down by someone who didn't know what they were doing. If a problem depends on order of operations and there's no widely understood "order of operations" rule, then the problem is meaningless as there is no "answer".
There is nothing wrong with the way this is written. Mathematics is based on rules. Without rules there would be ambiguity. The rules here are very simple and unambiguous.
This problem was written by a man trying to teach algebra to teenagers. How would you teach teens?
If you were a math teacher, you would realize how reckless your statement is.
It should be PLUS then MULTIPLY,then SUBTRACT AND THE DIVIDE.in that order.
No. There needs to be parenthesis inside the parenthesis to define order in that set.
We were taught BODMAS that is, brackets off, division, multiplication,addition abd substrsction.
And never forget the left to right rule.
I learnt it BOMDAS. I don’t remember left to right, multiply came before divide. Answer to this problem would have been 21.
There seems to be a lot of confusion about whether PEMDAS (or PEDMAS as I learned it) is a "law". Math is a logical construct that can only produce unambiguous answers when performed correctly. This is a valid problem if you have learned all the rules and if you think it's ambiguous you have not. The problem is that people remember the mnemonic but forget the actual rule which specifies that M and D are equal priority as was explained in the video therefore should be performed left to right. If all you remember is the mnemonic you were taught for this rule you missed the details. If adding parenthesis makes it less ambiguous for you go ahead, but they aren't necessary for the problem's validity.
No, it only seems so because you don't appreciate that multiplication and division are identical calculations ( X divided by Y is X times 1/Y) and addition and subtraction are the same ( X-Y is X+ -Y)
Why do they change the order of operations inside the parentheses? Seems contradictive.
3(5+20÷2×5)
3(5+20÷10)
3(5+2)
3(10)
Answer 30
Here's a fun way...... 3x5+3x20÷3x2x3x5
15+60÷6x15
15+10x15
15+150
=165
So, what if the expression were written 3(5-20/2x5) with the 2 written above the 2x5?
If you meant put the 20 above the 2x5 then that would be a different question. The denominator would group the 2x5 as if it were inside ()
Illigal for calc.
Skip to 12:50 is where the solution is.
I will have to disagree with parts of this. There is no rule for left to right. 2x3x4 4x3x2. As Armchair Tin-Kicker has said well below, there is no real difference in subtraction and addition.
One way to never make an mistake is to always think of the number after the division marker as times 1/x or writing it all using one division line for all the terms.
3(5+20*(½)*5) or 3(5 +(20*5)/2)
edit: formula not really working in the comment, so had to change it by adding brackets and a / for division.
Very very helpful. Time to do some exercises.
It’s time to retire bad PEMDAS acronym and make it something like PEMA (where M stands for both multiplication and division and A for Add and Subtract )
First 3 minutes of painful self indulgence.
perhaps the reason i got this one right is because i learned the order directly,
(NOT the mnemonic "PEMDAS", which is what seems to have confused some ppl)