In Canada our teachers call it BEDMAS, but essentially it turns out to be the same thing. BEDMAS starts with brackets, then exponents, then division or multiplication, whichever comes first, and finally addition or subtraction. So BEDMAS is the Canadian equivalent to PEMDAS. I'm not sure if this is of British-European origin, or if it is uniquely Canadian.
I think BEDMAS is also common in Australia and New Zealand. BODMAS (Orders rather than Exponents - just a different name for the same thing) is common in a lot of places. In the UK we teach BIDMAS (I for Indices). There are lots of variations of the acronym but they all mean the same thing.
Just thought I'd also point out - using BEDMAS has gotten me the correct answer each time without having to change the order of operations to suit the question.
Around the world all other methods follow the order DMAS with just different choices of the first two abbreviations/words but still brackets then powers. PEMDAS and PEDMAS aren’t the same as multiple and divide are swapped. PEMDAS is the only one in the world that has them incorrectly ordered.
Mr topkatz. Your method is simple. Change ÷ to × and invert. Avoids complication as whether × first or divide first and left to write. Maths is simple. We complicate it. Thanks❤
Why change anything around, just remember Order of Operations, it isn’t that difficult. Think about what you are saying. You are going to 10÷2, invert and multiply which gives you 10 over 2. The same damn thing, then reduce to 5. All you did was add in one extra step. 😂😂😂😂😂
I think PEMDAS and all the other versions just cause more problems than they solve. I was never taught them in the 70s but I always get these things as I was taught what to do and why.
Me too. I have a vague memory of the acronym BODMAS being mentioned in passing as a way to remember the order of operations, but it wasn't stressed. We simply learned the order of operations.
@@thenetsurferboy It's literally impossible to "confuse BODMAS with BOMDAS". They are exactly the same thing. BODMAS, BOMDAS, PEMDAS, PEDMAS, BIDMAS, GEMDAS, BEDMAS, PEMA, BIPS, BOPS, GEMS, etc... They're all just different names for the same thing. There are lots of variations of the acronym but they all refer to the same calculation process. Your misconception is the entire reason the 4 letter variations exist. You are blindly following the sequence of letters in the acronym instead of following the rules the acronym refers to.
In my country we use parentheses to avoid this problem. There is no global agreement on how to deal with this, so a professor I heard said he could not answer such math problems! He did not understand why not using parentheses! Math is difficult enough as it is, no need to make it worse, he said. But USA seems to be so fond of it. Strange:)
@@dellymathsconcepts8652 thats the problem. division and multiplication. because in the beginning there was multiplication first only then you can divide. these people invented new math i guess.
@@dellymathsconcepts8652 So you would do addition and subtraction before multiplication or division. Read Pemdas and Bomdas from left to right or right the expression correctly arithmetically
Ezelsbruggetje : 'Hoe Moeten We Van Die Onvoldoendes Afkomen" [Haakjes (), Machten X², Worteltrekken √, Vermenigvuldigen *, Delen /, Optellen +, Aftrekken - ] Whats comes first from left to right: the opposite operation pairs [Exponentiation, Root] [Multiplication, Division] [Addition, Substraction]
I have a question. Is 10 ÷ 2 x 5 the same as 10 ÷ 2(5)? We're told we need to clear up the parentheses first, in which case we would just go from left to right in the first expression but in the second expression, since there are still parentheses present, would we do the multiplication first to get rid of the parentheses? Or would we still just start with the division and then do the multiplication?
No it isn’t the same if the parentheses are not there. You would never add parentheses around one value. If you wanted the multiply to occur first you would have to right it as (2*5).
tl;dr 10/2(5) is silly ambiguous notation. Don't write like that. "Clear up parentheses" is fundamentally wrong. That idea comes from careless and misconceived teaching. The P step in PEMDAS is to evaluate expressions INSIDE parentheses. Parentheses cannot give priority to anything outside them. If you think about when PEMDAS is introduced, at that point children probably don't know yet that implied multiplication syntax even exists ("implied multiplication" is the name for when multiplication is indicated by writing two terms next to each other, like you did, without an explicit multiplication symbol). So when PEMDAS is introduced you wouldn't see something like 10/2(2+3). It would be 10/2×(2+3). And in that case, when you've finished the P step of PEMDAS you have 10/2×5. Yes, the parentheses have gone, but that's just because they're not needed any more. You could write 10/2×(5) but those parentheses are completely redundant. Unfortunately, lazy teaching has invented this misconceived notion of "clearing up" the parentheses. With the simple expressions that children are using when they learn PEMDAS, it is true that there are no remaining parentheses at the end of the P step. But that's not because there is any sort of imperative to clear up parentheses - it's simply because any remaining parentheses would be redundant. In 10/2(5), there is no expression inside parentheses to evaluate so nothing to do for the P step in PEMDAS. But the parentheses have to still be there because they are NOT redundant. They are essential. Without them, it would say "ten divided by twenty-five". To evaluate 10/2(5) using PEMDAS, you do the multiplication and division from left to right, exactly as you do with 10/2×5, giving the answer 25. There is no mechanism in the PEMDAS process capable of distinguishing between implied multiplication and explicit multiplication. But... It is a common convention to give implied multiplication higher priority than division. By that convention you would evaluate 2(5) first, leaving you with 10/10 = 1. If you get hold of any calculator that says 10/2(5) = 1 and look up its order of operations you will see this is how it works. It's like PEMDAS but with an extra step between E and MD. Ultimately there is no universal standard or convention for what 10/2(5) means. It's a well known issue that goes round the internet on silly clickbait memes all the time. Hence what I said at the start: don't write like that.
This is a shorthand problem. 2(5) implies "the quantity of"; the answer would equal 1 (formally it would be written as 10 / (2x5) ). The original question is 10 divided by 2 times 5; the answer equals 25. Opponents do not recognize the implied form, thus causing confusion, and that is why they insist on full formal form. All through college the implied form is recognized and used in lengthy derivations and solving.
@@louf7178 but isn’t that primarily when variables are involved? Accepted ways of doing things change when dealing with variables. If you have an and b and write ab everyone knows that means a*b. But no one would assume that 23 is actually 2*3. So people are able to differentiate when conditions require it. If only numbers are inside parentheses they can be resolved allowing the parentheses to disappear. And leave a standard arithmetic expression. That can’t occur with variables so they have to be tied to the 2 outside the parentheses.
Ii understand. Except division precedes multiplication or multiplication precedes division. In your example, it matters. There is ambiguity so the use of parentheses is an excellent tactic.
No ambiguity. First off it is intended to be training exercise to help people understand how it works so that they know where to add parentheses. And M&D are a group and are handled left to right.
After many decades, I think the phrase should be PEMA since division is a form of multiplication, and subtraction is a form of addition. On this problem if someone really wants to multiply first they can set it up as 10x5/2 = 50/2 = 25.
4:39 Parentheses OR A GROUPING SYMBOL Grouping can also be indicated without any symbol. Grouping is indicated by juxtaposition: 2x, 2θ, 2π, 2(3), 20, and 2cos.
Juxtaposition is not a grouping symbol! It's a way of indicating multiplication. Examples of other things that ARE grouping symbols, so would be covered by the G step if your preferred acronym is GEMDAS rather than PEMDAS, are a vinculum (e.g. in a fraction or as part of the radical symbol) or the absolute value symbol. Juxtaposition, aka implied multiplication, is just multiplication. There is no mechanism in the PEMDAS process capable of distinguishing between implied multiplication and explicit multiplication. The PEMDAS priority rules give the same precedence to all multiplication, whether implied or explicit. But it's a common convention to treat implied multiplication with higher precedence than division, so 1/2π would be 1/(2π) rather than (1/2)π. In PEMDAS terms that is an extra step in the process, after E and before MD. It's commonly referred to with the acronym PEJMDAS" with J for Juxtaposition.
@@gavindeane3670: Juxtaposition is grouping without a symbol. It is the most common way that grouping is indicated. It can indicate multiplication or addition. Grouping gets priority no matter how it is indicated.
@@markprange2430 Juxtaposition is a way of writing multiplication. It is no more correct to call it a grouping symbol than it is to call × or • a grouping symbol. Where do you think juxtaposition indicates addition???
@@gavindeane3670: Juxtaposition is not a grouping symbol? Juxtaposition is grouping without a symbol. 20 ≡ (2 × 10 + 0 × 1). 20, 2θ, & 2π are operated on as groups because they are shown grouped. You know that 360° ÷ 2π ≠ (360° ÷ 2)π because 2π was shown as a group. Operating left to right, you know that Sin 2θ ≠ (Sin 2)θ. Because 2θ was shown in group form. It doesn't need brackets to be grouped. Grouping symbols are used when necessary, convenient, or to be explicit or emphatic. But stipulating with juxtaposition is quicker and usually sufficient.
Around the world all other abbreviations follow the order DMAS with just different choices of the first two letters/words but still brackets then powers (BODMAS, PEDMAS, etc). PEMDAS and PEDMAS aren’t the same as multiple and divide are swapped. PEMDAS is the only one in the world that has them ordered differently.
No it isn't. There's also GEMDAS. And with several of the common forms of the acronym there is also the alternative variation with M and D the other way around. For example, while PEMDAS and BODMAS are common, you sometimes see people using PEDMAS or BOMDAS too. PEMDAS and PEDMAS (and BODMAS and BOMDAS and GEMDAS and BIDMAS and BEDMAS and BEMDAS and PEMA and BOPS and BIPS and GEMS etc...) are the same. They're all the same. They're all just different ways of referring to the same calculation process. The only thing that is in any way different is that the acronyms starting with G cover more grouping symbols than just brackets/parentheses (G stands for Groupings).
PEMDAS P-arentheses E-xponent M-ultiplication D-ivide A-dd S-ubtract kinda is misleading as it suggests that multiplication happens BEFORE division. In this problem the division appears first, left to right. Still that's how it's to be done: 10÷2 = 5 5×5 = 25
@@petersearls4443 and you are right.. My point is to promote the generous usage of parentheses as there's less confusion. I.E. I hate PEMDAS... IF ever a confusing equation is entered into a Google search line you'll see the first step is to insert/employ parentheses. For this problem: 10÷2×5 yields (10/2)×5 = 25
@@tomtke7351 but that is the point of the video. To show people how to take a poorly written expression. Understand how it will be processed. Then you can add parentheses to clarify.
@@tomtke7351"Generous" usage of parentheses can just lead to an unreadable mess. And indeed an unwritable mess. It's not uncommon for computer tools to highlight parentheses as you're typing, so you can see where the matching ( is when you type a ). Many people will be familiar with this from Microsoft Excel. They do that because when you are writing an expression with a generous amount of parentheses, it is easy to lose track and misplace one. The best way to handle this problem is not more parentheses. It's to write division in a proper vertical layout, not inline. So: 10 ------ 2×5
Yes, I agree with you. However, there is a very important point to remember. Even though “M” comes before “D” in PEMDAS, multiplication and division are performed from left to right, regardless of which one comes first. So, in this particular problem, division comes before multiplication, moving from left to right. So, we have to do division first. Similarly, addition and subtraction are done moving from left to right, regardless of which one comes first. It is like how we usually read something from left to right!
In the UK we were never taught PEMDAS because it leads to confusion. Instead we were taught the rules. And never made that kind of error. Also, use "/" not "÷".
When were you taught? I learned BODMAS in the UK towards the end of the 1980s. The National Curriculum had been introduced fairly recently and I think it was part of that.
How does replacing ÷ with / remove the confusion??? It's exactly the same! You certainly should replace ÷ with / because / is the correct symbol for division in mathematical notation. But that doesn't do anything to address the precedence issue. If someone thinks multiplication has higher precedence than division, they're still going to get the answer 1.
@@johnutting9615 How does writing it as 10/2×5 help? Yes, that is how it should be written, because the proper symbol for division in mathematical notation is / not ÷. But if someone thinks multiplication has higher precedence than division (perhaps because they've been mistaught a silly acronym like PEMDAS) they will still think the answer is 1.
That's not what PEMDAS/BOMDAS says. That's a common and understandable misconception, but you are blindly following the sequence of letters in the acronyms instead of following the rules that the acronyms refer to. PEMDAS/BOMDAS is a 4 step process not a 6 step process. In the MD step you calculate all the multiplications and divisions working left to right with equal priority. That means division first in this case.
Why do you use PEMDAS? It is one of the most confusing "rules" in math. You draw a rectangle around MD and around AS. How does that follow from the word PEMDAS? Why not rectangles around PE around MDA and a circle around S? Except the expression PEMDAS you have to include those other restrictions in the rule. And that is why the rule as you write it is confusing for a lot of students. Just the word PEMDAS does not tell them how to perform the operations. A rule like P-E-MD-AS does that in a much better way.
That's probably the biggest problem with these silly six letter acronyms. It's the reason why the 4 letter variations like PEMA (Parentheses Exponents Multiplicative Additive) exist.
I've never really understood the need for an acronym in the first place. It's easy enough to explain the order of operations and why it exists without one. The first two steps relate to a "problem within a problem." We do inside brackets first because they're not a value we can calculate with until simplified. Then we do exponents because ditto. After that it's a case of working from complex to simple Division and multiplication because (a) they're two sides of the same coin (which is why we can divide by multiplying the reciprocal) and (b) they're a series of repeated simpler actions: addition or subtraction. Then, finally, addition and subtraction. Which can be performed in any convenient order, since all they consist of is steps up and down the number line. Obviously there're complications which would need to be explored later when variables are involved (you can't fully simplify a bracketed term if there's an x ii there for instance), but that's the basics, and the logic of the order is almost childishly simple.
@@dazartingstall6680I agree. One of the problems with these acronyms is they make this stuff seem more complicated than it is. They're certainly not universally liked by teachers. You can include exponents in the "complex to simple" concept too, since exponentiation is repeated multiplication in the same way that multiplication is repeated addition. Then "complex to simple" explains the entire E-MD-AS hierarchy, which is actually the order of operations bit. There are five types of mathematical operation involved and the EMDAS part of the acronym covers them all. Then you just have the P, which is something fundamentally different. P isn't a mathematical operation at all. I think of the P in the acronym as an instructiom to recursively apply EMDAS until you have the answer. But I like your "problem in a problem" description.
@@gavindeane3670 On the other hand, exponents , if expanded into a multiplication, would need to be bracketed, so they're kind half way between the two states, if that makes sense. (Which it probably doesn't. I'm all woolly headed with some kind of lurgy.)
@@dazartingstall6680If you are actually replacing it in the expression, the need for brackets would depend on context I suppose. 3+4² is fine. That's 3+4×4. But 1/4² isn't 1/4×4, it's 1/(4×4). Sometimes brackets would be required and sometimes they wouldn't. But then that would be the same for replacing multiplication with repeated addition. Sometimes you wouldn't need brackets, e.g. 1+4×3 is 1+4+4+4. But sometimes you would, e.g 4×3/2 is not 4+4+4/2, it's (4+4+4)/2. I wasn't imagining literally replacing exponentiation with repeated multiplication though, or literally replacing multiplication with repeated addition. I was just thinking in terms of the nature of the operations.
But “PEMDAS” doesn't work in your example because you do division first! I’m 60 years old, I have three college degrees, and I’m still plucked when it comes to basic math! There are too many exceptions to the “rules”!
@@bobthompson551 The entire point of this video seems to be to teach what the notation means without parentheses. Adding parentheses would rather defeat the object.
In real life, nearly all arithmetic expressions are fully understood by the user because they wrote them themselves. If they receive an expression from someone else, then it should be clear and unambiguous. The example given in this video could have been made perfectly clear with one additional set of brackets. If it isn't clear and unambiguous then it should be rejected for that reason. Exam questions testing order of operations serve no useful purpose other than knowing a set of unnecessary rules! Mr TabletClass seems to be making a huge meal out of what is in the real world (i.e. outside of education) of very little importance.
The problem with your explanation is the use of the word “should”. Should does not always happen in real life. You go into maintain a piece of software which was written 3 years ago by someone who left two years ago. You are the one that needs to fix it and make it clear for future coders.
@@petersearls4443 Is that an analogy or are you saying that incorrect order of operations of arithmetic expressions can be difficult to find and fix in computer coding?
@@abstragic4216 I’m saying poorly written code that produces the right results needed be modified to clarify what was happening in case future changes needed to be made to the expression. Most companies did rudimentary testing and no source code standards enforcement. That includes Jet Propulsion Laboratories, Lockheed, First Interstate Bank, North American Aircraft and Holland America Cruise Line. I’m sure more companies do it today, but I bet it is still below 50%.
@@petersearls4443 I believe that understanding the process is the most important step, and if you can do that, then describing it accurately is not difficult. It can be tedious doing things like comments in code and user instructions but it needs to be done. From what you're saying, taking shortcuts has been going on for some time in some highly regarded companies.
This is perhaps the most important lecture he could ever give. Many people, even advanced mathematics still confuse the order of operations, especially forgetting that with MD it's not M first but whichever of M or D that comes first, from left to right. Ditto A and S too.
@@gavindeane3670 No, they aren't. Even if they were universally agreed upon, they're an encouragement to eschew the unambiguous and easy-to-read use of nested parentheses. Whether studying physics & astronomy or calculating parameters for electronic circuitry, I would never have contemplated doing without brackets.
@@gerardjlaw Parentheses are fine, but easy to read is not an absolute. Multiple levels of nested parentheses are error prone when both writing and reading. There's a reason why some of the tools we use have been designed to highlight the matching "(" when you type a ")". But the point I was making is that the precedence grammar of mathematical notation is logical and simple, whereas these silly acronyms make this stuff seem more complex than it is, and they come with a needlessly rigid process, and they lead to some common misconceptions.
You draw these videos out soooooooo loooooooonnnnnngggg......... You would get more watches if you get rid of the pointless babble and get to the point!
You can if you decide what the ÷ sign means. But I agree, it's not used in the real world because we have / for inline division. And also because division is not normally written inline anyway.
@gavindeane3670 If it's not used in the real world, why teach it? The PEMDAS post appeared in my TH-cam feed for some unknown reason. I just find the discussion of pemdas distressing. It's a dead end in terms of advancing in mathematics, and life. A speed for example is written as miles/hour, not miles ÷ hours.
@@RobertCanova-sn4sh I have no idea why he uses the ÷ symbol instead of the / symbol. You'll have to ask him. But that's got nothing to do with PEMDAS.
Hehehe they are the exact same thing. Multiply and divide are grouped and processed left to right as encountered. All of the mnemonics give you the same answer.
It's BODMAS and PEMDAS and BIDMAS and BEDMAS and GEMDAS and PEMA and BOPS and BIPS and GEMS and... There are lots of variations of the acronym but they all mean the same thing.
It's the same rule. PEMDAS, PEDMAS, BODMAS, BIDMAS, GEMDAS, BEDMAS, PEMA, BOPS, BIPS, GEMS, etc... There are lots of variations of the acronym but they all mean the same thing.
I would have written it as I intended it to be evaluated and not depend so much on precedence. In this simple case (40/10) x 2 Too much time talking in video. After the first problem you could have said "Again start with PEMDAS" and retained more audience.
@@petersearls4443 Yes and I am suggesting people write equations so as not to cause confusion. Working in a field where mistakes are painful promotes caution.
@@gavindeane3670 Teach yes. So people can read the body of mathematics that exist. Use in industry and research. No. Fully qualified expressions is a best practice in both mathematical, engineering and programming contexts.
Echen a la basura esa PEMDAS y usen la Aritmética. 10 : 2x5 = 10 : 5x2 = 10 : 10 = UNO (1) ¡¡NO TENEIS NI PUÑETERA IDEA!! No deis clases, vayan a la Escuela a recibirla.
There is no freaking way to use division this way. The order of operations is clearly PEMDAS which outlines what to do FIRST to work the problem.. in this problem Multiplying is first then the division. Please take this post down before you confuse our children that’s up learning algebra.
The video is fine. PEMDAS is not the order of operations. PEMDAS is just an acronym intended to help you remember the order of operations. But it's a very misleading acronym because it gives the impression that multiplication has higher precedence than division when in fact they have equal precedence. Ditto for addition and subtraction. It's a 4 step process not a 6 step process: P-E-MD-AS. If the scrum is causing you to remember the rules incorrectly then just ditch the acronym. You don't need it. Just remember the rules - they're not complicated.
I am bad at math. Why don’t you do the problem on the board, then explain it? I don’t understand what you’re doing or saying. I am very good at English. I have an idea, pretend some of your students are dumb. I am speaking for myself of course.
@@gavindeane3670 It would seem so, as I don't know you I can't say. One needs to know when to use BODMAS. It's not required for this problem, something the video maker is ignorant of...
Ok 10 / 5x = 25 Simplify 2/x = 25 Multiply boths side by 2 x = 50 ≠ 2 Algebra proves 25 is not the answer 10 / 5x = 1 Simplify 2/x = 1 Multiple both sides by 2 x = 2 Original equation 10 / 2 * 5
@@chrisdissanayake6979 algebra. If 10 / 2 * 5 = 25 Then we check our answer using algebra 10 / x * 5 = 25 x * 5 = 5x Thus, 10 / 5x = 25 Why? 10 / 2 * 5 = x The circularity of math and the equal sign permit moving x to ensure the truth of the equation. For example, 2 * 2 = 4 Therefore, 2x = 4 x = 2
@@lochnesswes1 10/x *5 means 10/x times 5. That is 10 * 5 -- x --------- The given problem is 10➗ 2 x 5 OR 10 ➗ 2 * 5 Working from left to right, 10 divided by 2 is 5 Then, 5 times 5 is 25.
@@chrisdissanayake6979 no, it doesnt. x * 5 = 5x 10 / x * 5 = 2 / x * 1 (dividing the numerator and denominator by 5. Commutative property: a * b = b * a. So, 10 / 5 * x = 2/1 * x. Division equals multiplication by the inverse (10/1) * (1 / 5 * x)
10:2 = 5 x 5 = 25
25
10 divided by 2, 5 times five=25, 10 divided by {2 times five} =1, 10 divided by 2{5} =1
Covering all your bases. 😂 first one was right.
In Canada our teachers call it BEDMAS, but essentially it turns out to be the same thing. BEDMAS starts with brackets, then exponents, then division or multiplication, whichever comes first, and finally addition or subtraction. So BEDMAS is the Canadian equivalent to PEMDAS. I'm not sure if this is of British-European origin, or if it is uniquely Canadian.
I think BEDMAS is also common in Australia and New Zealand. BODMAS (Orders rather than Exponents - just a different name for the same thing) is common in a lot of places. In the UK we teach BIDMAS (I for Indices).
There are lots of variations of the acronym but they all mean the same thing.
Just thought I'd also point out - using BEDMAS has gotten me the correct answer each time without having to change the order of operations to suit the question.
Around the world all other methods follow the order DMAS with just different choices of the first two abbreviations/words but still brackets then powers. PEMDAS and PEDMAS aren’t the same as multiple and divide are swapped. PEMDAS is the only one in the world that has them incorrectly ordered.
In Australia we are taught BIMDAS. The I stands for Indices, which has the same meaning as Exponents 😊
Mr topkatz. Your method is simple. Change ÷ to × and invert. Avoids complication as whether × first or divide first and left to write. Maths is simple. We complicate it. Thanks❤
yep that is how I was taught. Also make subtraction addition with the rule x -y is the same as -y + x
Why change anything around, just remember Order of Operations, it isn’t that difficult.
Think about what you are saying. You are going to 10÷2, invert and multiply which gives you 10 over 2. The same damn thing, then reduce to 5. All you did was add in one extra step. 😂😂😂😂😂
I think PEMDAS and all the other versions just cause more problems than they solve. I was never taught them in the 70s but I always get these things as I was taught what to do and why.
Me too. I have a vague memory of the acronym BODMAS being mentioned in passing as a way to remember the order of operations, but it wasn't stressed. We simply learned the order of operations.
I agree. This confusion about M and D is a common problem but certainly not the only common problem with these acronyms.
10:5=5×5=25
I was taught BODMAS in the 70s, this works for me even today.
because PEMDAS is wrong. not sure BODMAS was all that good either. i think it was better.
@@goldendome-l1lPEMDAS and BODMAS are exactly the same thing.
@@gavindeane3670 as far as I remember, there is a difference in order of operations I think. But, thanks.
Your teacher confused Bodmas with Bomdas
I learnt Bomdas in the early fifties
@@thenetsurferboy It's literally impossible to "confuse BODMAS with BOMDAS". They are exactly the same thing. BODMAS, BOMDAS, PEMDAS, PEDMAS, BIDMAS, GEMDAS, BEDMAS, PEMA, BIPS, BOPS, GEMS, etc...
They're all just different names for the same thing. There are lots of variations of the acronym but they all refer to the same calculation process.
Your misconception is the entire reason the 4 letter variations exist.
You are blindly following the sequence of letters in the acronym instead of following the rules the acronym refers to.
You ramble off too much making it hard to listen to you.
In my country we use parentheses to avoid this problem. There is no global agreement on how to deal with this, so a professor I heard said he could not answer such math problems! He did not understand why not using parentheses! Math is difficult enough as it is, no need to make it worse, he said. But USA seems to be so fond of it. Strange:)
Do the research and you will see that division and multiplication are on the same level so anyone comes 1st from left to right MUST BE DONE 1ST...
much ado about nothing!result is 25. Children in grade 4 know that
@@dellymathsconcepts8652 thats the problem. division and multiplication.
because in the beginning there was multiplication first only then you can divide.
these people invented new math i guess.
@@dellymathsconcepts8652 So you would do addition and subtraction before multiplication or division. Read Pemdas and Bomdas from left to right or right the expression correctly arithmetically
@@jerrysimik2336 You have not reached grade 3 yet
Answer is 1
No other option
Ezelsbruggetje : 'Hoe Moeten We Van Die Onvoldoendes Afkomen" [Haakjes (), Machten X², Worteltrekken √,
Vermenigvuldigen *, Delen /, Optellen +, Aftrekken - ]
Whats comes first from left to right: the opposite operation pairs [Exponentiation, Root] [Multiplication, Division] [Addition, Substraction]
I have a question. Is 10 ÷ 2 x 5 the same as 10 ÷ 2(5)? We're told we need to clear up the parentheses first, in which case we would just go from left to right in the first expression but in the second expression, since there are still parentheses present, would we do the multiplication first to get rid of the parentheses? Or would we still just start with the division and then do the multiplication?
No it isn’t the same if the parentheses are not there. You would never add parentheses around one value. If you wanted the multiply to occur first you would have to right it as (2*5).
tl;dr 10/2(5) is silly ambiguous notation. Don't write like that.
"Clear up parentheses" is fundamentally wrong. That idea comes from careless and misconceived teaching. The P step in PEMDAS is to evaluate expressions INSIDE parentheses. Parentheses cannot give priority to anything outside them.
If you think about when PEMDAS is introduced, at that point children probably don't know yet that implied multiplication syntax even exists ("implied multiplication" is the name for when multiplication is indicated by writing two terms next to each other, like you did, without an explicit multiplication symbol).
So when PEMDAS is introduced you wouldn't see something like 10/2(2+3). It would be 10/2×(2+3). And in that case, when you've finished the P step of PEMDAS you have 10/2×5. Yes, the parentheses have gone, but that's just because they're not needed any more. You could write 10/2×(5) but those parentheses are completely redundant.
Unfortunately, lazy teaching has invented this misconceived notion of "clearing up" the parentheses. With the simple expressions that children are using when they learn PEMDAS, it is true that there are no remaining parentheses at the end of the P step. But that's not because there is any sort of imperative to clear up parentheses - it's simply because any remaining parentheses would be redundant.
In 10/2(5), there is no expression inside parentheses to evaluate so nothing to do for the P step in PEMDAS. But the parentheses have to still be there because they are NOT redundant. They are essential. Without them, it would say "ten divided by twenty-five".
To evaluate 10/2(5) using PEMDAS, you do the multiplication and division from left to right, exactly as you do with 10/2×5, giving the answer 25. There is no mechanism in the PEMDAS process capable of distinguishing between implied multiplication and explicit multiplication.
But...
It is a common convention to give implied multiplication higher priority than division. By that convention you would evaluate 2(5) first, leaving you with 10/10 = 1. If you get hold of any calculator that says 10/2(5) = 1 and look up its order of operations you will see this is how it works. It's like PEMDAS but with an extra step between E and MD.
Ultimately there is no universal standard or convention for what 10/2(5) means. It's a well known issue that goes round the internet on silly clickbait memes all the time. Hence what I said at the start: don't write like that.
This is a shorthand problem. 2(5) implies "the quantity of"; the answer would equal 1 (formally it would be written as 10 / (2x5) ). The original question is 10 divided by 2 times 5; the answer equals 25. Opponents do not recognize the implied form, thus causing confusion, and that is why they insist on full formal form. All through college the implied form is recognized and used in lengthy derivations and solving.
It doesn't have parenthesis?
@@louf7178 but isn’t that primarily when variables are involved? Accepted ways of doing things change when dealing with variables. If you have an and b and write ab everyone knows that means a*b. But no one would assume that 23 is actually 2*3. So people are able to differentiate when conditions require it. If only numbers are inside parentheses they can be resolved allowing the parentheses to disappear. And leave a standard arithmetic expression. That can’t occur with variables so they have to be tied to the 2 outside the parentheses.
10÷2=5×5=25. 25
Ii understand. Except division precedes multiplication or multiplication precedes division. In your example, it matters. There is ambiguity so the use of parentheses is an excellent tactic.
No ambiguity. First off it is intended to be training exercise to help people understand how it works so that they know where to add parentheses. And M&D are a group and are handled left to right.
25 is awnser
After many decades, I think the phrase should be PEMA since division is a form of multiplication, and subtraction is a form of addition. On this problem if someone really wants to multiply first they can set it up as 10x5/2 = 50/2 = 25.
You are begging for trouble if you get in the habit of moving things around when it isn’t necessary.
4:39 Parentheses OR A GROUPING SYMBOL
Grouping can also be indicated without any symbol.
Grouping is indicated by juxtaposition: 2x, 2θ, 2π, 2(3), 20, and 2cos.
Juxtaposition is not a grouping symbol! It's a way of indicating multiplication.
Examples of other things that ARE grouping symbols, so would be covered by the G step if your preferred acronym is GEMDAS rather than PEMDAS, are a vinculum (e.g. in a fraction or as part of the radical symbol) or the absolute value symbol.
Juxtaposition, aka implied multiplication, is just multiplication. There is no mechanism in the PEMDAS process capable of distinguishing between implied multiplication and explicit multiplication. The PEMDAS priority rules give the same precedence to all multiplication, whether implied or explicit.
But it's a common convention to treat implied multiplication with higher precedence than division, so 1/2π would be 1/(2π) rather than (1/2)π. In PEMDAS terms that is an extra step in the process, after E and before MD. It's commonly referred to with the acronym PEJMDAS" with J for Juxtaposition.
@@gavindeane3670: Juxtaposition is grouping without a symbol. It is the most common way that grouping is indicated. It can indicate multiplication or addition. Grouping gets priority no matter how it is indicated.
@@markprange2430 Juxtaposition is a way of writing multiplication. It is no more correct to call it a grouping symbol than it is to call × or • a grouping symbol.
Where do you think juxtaposition indicates addition???
@@gavindeane3670: Juxtaposition is not a grouping symbol. It is grouping without a symbol.
20 ≡ (2 × 10 + 0 × 1).
@@gavindeane3670: Juxtaposition is not a grouping symbol? Juxtaposition is grouping without a symbol.
20 ≡ (2 × 10 + 0 × 1).
20, 2θ, & 2π are operated on as groups because they are shown grouped. You know that 360° ÷ 2π ≠ (360° ÷ 2)π because 2π was shown as a group.
Operating left to right, you know that Sin 2θ ≠ (Sin 2)θ. Because 2θ was shown in group form. It doesn't need brackets to be grouped.
Grouping symbols are used when necessary, convenient, or to be explicit or emphatic. But stipulating with juxtaposition is quicker and usually sufficient.
Around the world all other abbreviations follow the order DMAS with just different choices of the first two letters/words but still brackets then powers (BODMAS, PEDMAS, etc). PEMDAS and PEDMAS aren’t the same as multiple and divide are swapped. PEMDAS is the only one in the world that has them ordered differently.
No it isn't.
There's also GEMDAS. And with several of the common forms of the acronym there is also the alternative variation with M and D the other way around.
For example, while PEMDAS and BODMAS are common, you sometimes see people using PEDMAS or BOMDAS too.
PEMDAS and PEDMAS (and BODMAS and BOMDAS and GEMDAS and BIDMAS and BEDMAS and BEMDAS and PEMA and BOPS and BIPS and GEMS etc...) are the same. They're all the same. They're all just different ways of referring to the same calculation process.
The only thing that is in any way different is that the acronyms starting with G cover more grouping symbols than just brackets/parentheses (G stands for Groupings).
They are all the same. Multiply and divide are handled left to right as encountered. And you forgot BOMDAS.
PEMDAS
P-arentheses
E-xponent
M-ultiplication
D-ivide
A-dd
S-ubtract
kinda is misleading as it suggests that multiplication happens BEFORE division. In this problem the division appears first, left to right. Still that's how it's to be done:
10÷2 = 5
5×5 = 25
If you look up the definition of the various mnemonics they usually mention the grouping of M&D and A&S.
@@petersearls4443 and you are right.. My point is to promote the generous usage of parentheses as there's less confusion. I.E. I hate PEMDAS... IF ever a confusing equation is entered into a Google search line you'll see the first step is to insert/employ parentheses.
For this problem:
10÷2×5
yields
(10/2)×5
= 25
@@tomtke7351 but that is the point of the video. To show people how to take a poorly written expression. Understand how it will be processed. Then you can add parentheses to clarify.
@@tomtke7351"Generous" usage of parentheses can just lead to an unreadable mess. And indeed an unwritable mess.
It's not uncommon for computer tools to highlight parentheses as you're typing, so you can see where the matching ( is when you type a ). Many people will be familiar with this from Microsoft Excel.
They do that because when you are writing an expression with a generous amount of parentheses, it is easy to lose track and misplace one.
The best way to handle this problem is not more parentheses. It's to write division in a proper vertical layout, not inline. So:
10
------
2×5
Yes, I agree with you.
However, there is a very important point to remember.
Even though “M” comes before “D” in PEMDAS, multiplication and division are performed from left to right, regardless of which one comes first.
So, in this particular problem, division comes before multiplication, moving from left to right. So, we have to do division first.
Similarly, addition and subtraction are done moving from left to right, regardless of which one comes first.
It is like how we usually read something from left to right!
You can say: please excuse my dear Aunt Sally, or please excuse Daisy Mae, Sally Ann!
Deu 25.
40:10=4×2=8
In the UK we were never taught PEMDAS because it leads to confusion. Instead we were taught the rules. And never made that kind of error. Also, use "/" not "÷".
When were you taught? I learned BODMAS in the UK towards the end of the 1980s. The National Curriculum had been introduced fairly recently and I think it was part of that.
@@gavindeane3670 yes I wasn't taught it in 70s but my nephew who I coached in the 90s was.
You can also switch operations and get the same result
If you simply replace ÷2 with ×1/2 you get
10 × 1/2 × 5 = 25
Or replace the ÷ with a / there is no confusion.
10/2×5
How does replacing ÷ with / remove the confusion??? It's exactly the same!
You certainly should replace ÷ with / because / is the correct symbol for division in mathematical notation. But that doesn't do anything to address the precedence issue. If someone thinks multiplication has higher precedence than division, they're still going to get the answer 1.
If this quation was written correctly there would be no confusion. Write it like so 10/2×5 then operateleft to right.
@@johnutting9615 How does writing it as 10/2×5 help?
Yes, that is how it should be written, because the proper symbol for division in mathematical notation is / not ÷. But if someone thinks multiplication has higher precedence than division (perhaps because they've been mistaught a silly acronym like PEMDAS) they will still think the answer is 1.
it's not an equation...
My answer is (b) for this latest problem
Thank you that is what I do wrong
10/2*5 25
1
Pemdas bomdas say multiplication first
So it becomes 10/10 =1
The only possible answer
That's not what PEMDAS/BOMDAS says. That's a common and understandable misconception, but you are blindly following the sequence of letters in the acronyms instead of following the rules that the acronyms refer to.
PEMDAS/BOMDAS is a 4 step process not a 6 step process. In the MD step you calculate all the multiplications and divisions working left to right with equal priority. That means division first in this case.
25 is answer
My answer is 21
Why do you use PEMDAS? It is one of the most confusing "rules" in math.
You draw a rectangle around MD and around AS. How does that follow from the word PEMDAS? Why not rectangles around PE around MDA and a circle around S? Except the expression PEMDAS you have to include those other restrictions in the rule. And that is why the rule as you write it is confusing for a lot of students. Just the word PEMDAS does not tell them how to perform the operations. A rule like P-E-MD-AS does that in a much better way.
That's probably the biggest problem with these silly six letter acronyms. It's the reason why the 4 letter variations like PEMA (Parentheses Exponents Multiplicative Additive) exist.
I've never really understood the need for an acronym in the first place. It's easy enough to explain the order of operations and why it exists without one.
The first two steps relate to a "problem within a problem."
We do inside brackets first because they're not a value we can calculate with until simplified.
Then we do exponents because ditto.
After that it's a case of working from complex to simple
Division and multiplication because (a) they're two sides of the same coin (which is why we can divide by multiplying the reciprocal) and (b) they're a series of repeated simpler actions: addition or subtraction.
Then, finally, addition and subtraction. Which can be performed in any convenient order, since all they consist of is steps up and down the number line.
Obviously there're complications which would need to be explored later when variables are involved (you can't fully simplify a bracketed term if there's an x ii there for instance), but that's the basics, and the logic of the order is almost childishly simple.
@@dazartingstall6680I agree. One of the problems with these acronyms is they make this stuff seem more complicated than it is. They're certainly not universally liked by teachers.
You can include exponents in the "complex to simple" concept too, since exponentiation is repeated multiplication in the same way that multiplication is repeated addition. Then "complex to simple" explains the entire E-MD-AS hierarchy, which is actually the order of operations bit. There are five types of mathematical operation involved and the EMDAS part of the acronym covers them all.
Then you just have the P, which is something fundamentally different. P isn't a mathematical operation at all. I think of the P in the acronym as an instructiom to recursively apply EMDAS until you have the answer. But I like your "problem in a problem" description.
@@gavindeane3670 On the other hand, exponents , if expanded into a multiplication, would need to be bracketed, so they're kind half way between the two states, if that makes sense. (Which it probably doesn't. I'm all woolly headed with some kind of lurgy.)
@@dazartingstall6680If you are actually replacing it in the expression, the need for brackets would depend on context I suppose. 3+4² is fine. That's 3+4×4. But 1/4² isn't 1/4×4, it's 1/(4×4). Sometimes brackets would be required and sometimes they wouldn't.
But then that would be the same for replacing multiplication with repeated addition. Sometimes you wouldn't need brackets, e.g. 1+4×3 is 1+4+4+4. But sometimes you would, e.g 4×3/2 is not 4+4+4/2, it's (4+4+4)/2.
I wasn't imagining literally replacing exponentiation with repeated multiplication though, or literally replacing multiplication with repeated addition. I was just thinking in terms of the nature of the operations.
But “PEMDAS” doesn't work in your example because you do division first! I’m 60 years old, I have three college degrees, and I’m still plucked when it comes to basic math! There are too many exceptions to the “rules”!
The rule works. The rule tells you to do the division first here. It's just the acronym that's misleading.
Enclosing 10 ÷2 in parentheses might simplify things. I've seen many poorly constructed problems in these PEMDAS exercises.
I learned it as PEDMAS. I've never seen PEMDAS
Look at the top of this page. They're teaching PEMDAS in schools now. Pedals seems to apply in this case. But parentheses would clarify things.
@@bobthompson551 The entire point of this video seems to be to teach what the notation means without parentheses. Adding parentheses would rather defeat the object.
In real life, nearly all arithmetic expressions are fully understood by the user because they wrote them themselves. If they receive an expression from someone else, then it should be clear and unambiguous. The example given in this video could have been made perfectly clear with one additional set of brackets. If it isn't clear and unambiguous then it should be rejected for that reason. Exam questions testing order of operations serve no useful purpose other than knowing a set of unnecessary rules! Mr TabletClass seems to be making a huge meal out of what is in the real world (i.e. outside of education) of very little importance.
The problem with your explanation is the use of the word “should”. Should does not always happen in real life. You go into maintain a piece of software which was written 3 years ago by someone who left two years ago. You are the one that needs to fix it and make it clear for future coders.
@@petersearls4443 Is that an analogy or are you saying that incorrect order of operations of arithmetic expressions can be difficult to find and fix in computer coding?
@@abstragic4216 I’m saying poorly written code that produces the right results needed be modified to clarify what was happening in case future changes needed to be made to the expression. Most companies did rudimentary testing and no source code standards enforcement. That includes Jet Propulsion Laboratories, Lockheed, First Interstate Bank, North American Aircraft and Holland America Cruise Line. I’m sure more companies do it today, but I bet it is still below 50%.
@@abstragic4216 and as you can see from the arguments on TH-cam, there are more than a few people that don’t understand the process.
@@petersearls4443 I believe that understanding the process is the most important step, and if you can do that, then describing it accurately is not difficult. It can be tedious doing things like comments in code and user instructions but it needs to be done. From what you're saying, taking shortcuts has been going on for some time in some highly regarded companies.
For Heaven's sake, stop this unwanted lecture.Time is precious.
This is perhaps the most important lecture he could ever give. Many people, even advanced mathematics still confuse the order of operations, especially forgetting that with MD it's not M first but whichever of M or D that comes first, from left to right. Ditto A and S too.
@@gilos928He could solve that particular issue by not using these silly acronyms when he delivers this lesson.
TALK,TALK,TALK
No one who used mathematics professionally relies on these cretinous rules; we use brackets. (Physics degree, then career in engineering.)
It's the cretinous acronyms that are the problem. The rules are fine.
@@gavindeane3670 No, they aren't. Even if they were universally agreed upon, they're an encouragement to eschew the unambiguous and easy-to-read use of nested parentheses. Whether studying physics & astronomy or calculating parameters for electronic circuitry, I would never have contemplated doing without brackets.
@@gerardjlaw Parentheses are fine, but easy to read is not an absolute.
Multiple levels of nested parentheses are error prone when both writing and reading. There's a reason why some of the tools we use have been designed to highlight the matching "(" when you type a ")".
But the point I was making is that the precedence grammar of mathematical notation is logical and simple, whereas these silly acronyms make this stuff seem more complex than it is, and they come with a needlessly rigid process, and they lead to some common misconceptions.
Get to the point
You draw these videos out soooooooo loooooooonnnnnngggg......... You would get more watches if you get rid of the pointless babble and get to the point!
The division sign is never used in the real world. You cannot do Algerbra if the ÷ sign is used.
You can if you decide what the ÷ sign means.
But I agree, it's not used in the real world because we have / for inline division. And also because division is not normally written inline anyway.
@gavindeane3670 If it's not used in the real world, why teach it? The PEMDAS post appeared in my TH-cam feed for some unknown reason. I just find the discussion of pemdas distressing. It's a dead end in terms of advancing in mathematics, and life. A speed for example is written as miles/hour, not miles ÷ hours.
@@RobertCanova-sn4sh I have no idea why he uses the ÷ symbol instead of the / symbol. You'll have to ask him.
But that's got nothing to do with PEMDAS.
It is used millions of times a day all over the world. Apple calculators use the obelus, so does windows 11. Most online calculators I’ve seen use it.
@@petersearls4443 yea, the ÷ appears on calculators.
The answer is 25
it's BODMAS, not PEMDAS.. and it's simple.. Pemdas is the American way to confusion. Just do by BODMAS method & you will never make a mistake ..
Hehehe they are the exact same thing. Multiply and divide are grouped and processed left to right as encountered. All of the mnemonics give you the same answer.
It's BODMAS and PEMDAS and BIDMAS and BEDMAS and GEMDAS and PEMA and BOPS and BIPS and GEMS and...
There are lots of variations of the acronym but they all mean the same thing.
@@gavindeane3670 Exactly! 💯👍
I learned it as PEDMAS. This rule is not universal.
It's the same rule.
PEMDAS, PEDMAS, BODMAS, BIDMAS, GEMDAS, BEDMAS, PEMA, BOPS, BIPS, GEMS, etc...
There are lots of variations of the acronym but they all mean the same thing.
I would have written it as I intended it to be evaluated and not depend so much on precedence. In this simple case (40/10) x 2
Too much time talking in video. After the first problem you could have said "Again start with PEMDAS" and retained more audience.
It is written this way to be a learning experience.
@@petersearls4443 Yes and I am suggesting people write equations so as not to cause confusion. Working in a field where mistakes are painful promotes caution.
@@danharold3087That's not an argument for not bothering to teach people what mathematical notation means though.
@@gavindeane3670 Teach yes. So people can read the body of mathematics that exist. Use in industry and research. No. Fully qualified expressions is a best practice in both mathematical, engineering and programming contexts.
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Echen a la basura esa PEMDAS y usen la Aritmética. 10 : 2x5 = 10 : 5x2 = 10 : 10 = UNO (1)
¡¡NO TENEIS NI PUÑETERA IDEA!! No deis clases, vayan a la Escuela a recibirla.
There is no freaking way to use division this way. The order of operations is clearly PEMDAS which outlines what to do FIRST to work the problem.. in this problem Multiplying is first then the division. Please take this post down before you confuse our children that’s up learning algebra.
The video is fine.
PEMDAS is not the order of operations. PEMDAS is just an acronym intended to help you remember the order of operations.
But it's a very misleading acronym because it gives the impression that multiplication has higher precedence than division when in fact they have equal precedence. Ditto for addition and subtraction.
It's a 4 step process not a 6 step process: P-E-MD-AS.
If the scrum is causing you to remember the rules incorrectly then just ditch the acronym. You don't need it. Just remember the rules - they're not complicated.
Too much talk and no action
I am bad at math. Why don’t you do the problem on the board, then explain it? I don’t understand what you’re doing or saying. I am very good at English. I have an idea, pretend some of your students are dumb. I am speaking for myself of course.
How can you have taught maths for decades and don't know when to use BODMAS?...a really pathetic claim...
What are you talking about? The entire video is about using it.
@@gavindeane3670 Read my post very carefully again but this time very carefully...
@@gavindeane3670 read my post again...
@@Ignoranceisbliss-i2eIt's a long video. Did I miss the bit you're referring to?
@@gavindeane3670 It would seem so, as I don't know you I can't say. One needs to know when to use BODMAS. It's not required for this problem, something the video maker is ignorant of...
the answer is 25
25
Ok
10 / 5x = 25
Simplify
2/x = 25
Multiply boths side by 2
x = 50 ≠ 2
Algebra proves 25 is not the answer
10 / 5x = 1
Simplify
2/x = 1
Multiple both sides by 2
x = 2
Original equation
10 / 2 * 5
@@lochnesswes1 how did you get 10 / 5x ?
@@chrisdissanayake6979 algebra.
If 10 / 2 * 5 = 25
Then we check our answer using algebra
10 / x * 5 = 25
x * 5 = 5x
Thus,
10 / 5x = 25
Why?
10 / 2 * 5 = x
The circularity of math and the equal sign permit moving x to ensure the truth of the equation. For example,
2 * 2 = 4
Therefore,
2x = 4
x = 2
@@lochnesswes1 10/x *5 means 10/x times 5.
That is 10 * 5
--
x
---------
The given problem is
10➗ 2 x 5
OR
10 ➗ 2 * 5
Working from left to right,
10 divided by 2 is 5
Then, 5 times 5 is 25.
@@chrisdissanayake6979 no, it doesnt.
x * 5 = 5x
10 / x * 5 = 2 / x * 1 (dividing the numerator and denominator by 5. Commutative property: a * b = b * a.
So,
10 / 5 * x = 2/1 * x.
Division equals multiplication by the inverse
(10/1) * (1 / 5 * x)
25
25
25
25
25
25
25
25
25
25