With how many people on Twitter argue from a third grade understanding of sex and gender I can’t say I’m surprised See also climate deniers and Trump supporters
It is not really about lack of math knowledge, for people who are used to working with calculators that show only one number at a time it acts unpredictable
Hold up. without parenthesis that says: here's 50 of something here's 50 more of something now double it. It is worked left to right. In which case, the addition would go first. Without parenthesis, it is a different statement. It says this: 50+50×2=a ÷50 from the left is 50x2=a/50 Which is 100=a/50 Which is a=200 Or you can ÷ 100 from the left Which is 2 = a/100 Which is a=200 Without parenthesis, it is already broken down.
@@dogbreaththe3rd851 Cute. No. However, seriously, write the equation out to prove 200 is incorrect. The flow chart the video presents is not mathematics.
Ive been trying to explain to people that multiplication and division are the exact same thing. Multiplying by 2 is the same as dividing by 1/2, they are the same operation and therefore have the same order of operation. This also applies with addition/subtraction (+2=-[-2]) and exponentiation/roots (x^[1/2]=[sqrt x])
Make that 1950. The fifties were a great time for futurism. Just look at the Atomium in Brussels, which was built in 1958. A great example of the sixties is 2001: a space odyssey, where HAL9000 is an AI computer built in 1992.
@@EaglePicking You've just reminded that I have been to the Atomium. I've also been to the Dali exhibition in the Pompidou centre in Paris. HAL. In each case one letter before IBM. Back in the day, IBM meant "It's Being Mended", ICL meant "It's Coming Later", and DEC meant "Don't Even Consider". Yes, I am actually that old!
you can imagine what other things that individual is getting all sorts of wrong in his life. Including voting. You can only fear his choices if they impacted your daily life as well.
People did Maths for hundreds of years without the order of operations we mostly use now, they used different ones, or none - it's not a fundamental part of maths just an arbitrary set of rules that are relatively recent, and are not needed
Except it isn't really "math"...it's busy work. PEMDAS crap is why kids think they "hate math" or that "they're no good at math"...it is the math equivalent of diagramming sentences.
The problem here is that Apple calculator app is absolute garbage because it doesn't show you your whole input. Some people then think that it actually evaluates the 50+50 part - exactly like those cheapest single-line calculators, which evaluate every single operation as soon as possible. Apple's calculator app looks like it does the same thing, but doesn't - thus the confusion.
@@Duke_of_Lorraine I wouldn’t. I guess I’ve been using too many cheap calculators. I would use a lot of parenthesis on scientific calculators just to be sure.
She is not that wrong... Apple's calculator does not show the expression, compared to other calculators, and old calculators used to work like..... calculators! and not parsers + calculators
Calculators used to (and some still do) calculate the result each time you pressed an operator, not just equal, so if you tiped 50 + 50 then X, it will calculate to 100 (as if you pressed =), then 2 = 200
the difference is between calculators that use single-step evaluation (as pretty much all old calculators did), and newer calculators that use expression (or formula) evaluation. the Windows calculator lets you choose between single-step (Standard) and expression (Scientific/Programmer), which give the answers 200 and 150, respectively. to say that old calculators evaluate the "expression incorrectly" is not a valid statement - they don't evaluate mathematical expressions at all, they evaluate their input step-by-step (not expressions), by-design.
Bingo. Apple's looks like the simple type but acts like the advanced type. It's ridiculous to think that someone would put in a complex expression totally blind, and imagine that it's storing it all internally and then evaluating it using order of operations, with no evidence of this.
Windows default calculator interprets both the "addition" key and the "multiplication" key as also the "equals" key. But if you switch to the scientific view then you get a different result.
Yeah, this has been an issue for many years. But I'm pretty sure they used to have a calculator that did it correctly. But that was the version before they added the "Standard", "Scientific" and other modes. So, maybe 15-20 years ago. I was shocked, the first time I discovered the error and I only discovered it, because I'm good at calculating in my head. And yes, it is an error.
The issue is not expecting calculators to follow the formal order of operations, but to follow as typed. I grew up as we transitioned from the latter, which is why I use RPN calculators - they behaved in a deterministic manner.
the fact that it has to be memorized, and cannot be worked out from first principals, should tell you it is an arbitrary set of rules, and nothing really to do with maths at all
The problem is not about math but rather about interface: Apple calculator doesn't display the full expression being evaluated, just like about any simple calculator, which in turn presumes left-to-right evaluation order (pressing an action button is performing current calculation and going to input of the next argument using selected action). In Android example the expression is displayed fully, and there is no confusion.
Exactly this! Apple's calculator violates good Usability principles, specifically 'visibility of system status'. People's confusion is justified here, as the confusion is not about arithmetics.
This isn't even an order of operations problem. The first example explicitly uses the "=" key, which means "evaluate the tree so far, display the result, and treat the result as the first operand".
Yes, he completely missed the point the Twitter post was angry about. It's that clicking the "equals" button implicitly surrounds your previous expression with parentheses.
Re. the laws, isn't that mostly a matter of notation? If you change the notation conventions you'll also have to change the notation of the laws: (a) + (b) = (b) + (a) a(b + c) = (ab) + (ac) Edit: I certainly don't mean to say that would be better, just that I wonder if it's about the laws not holding vs. having to express the laws differently when conventions change
Yeah, he forgot that a left-to-right convention regardless of operation, means that a + b × c means (a + b) × c Applying the commutative law of addition as he did, he should've started with a + (b × c) which equals b × c + a And the distributive law should've been notated as a × (b + c) = a × b + (a × c) You're right. If you use a different convention, the properties still hold, they just look different. Another example, if using a convention of addition having a higher priority than multiplication, then the distributive law would be written as a × b + c = (a × b) + (a × c) or, using implied multiplication, ab + c = (ab) + (ac) I agree, even though the properties hold under different conventions, it doesn't mean they're useful.
It's a valid point that if the entire expression isn't shown on screen while you type the rest, then it's updating the total as you go along, ergo not following the order of operations.
@@mrsoisauce9017 Extensively praising Elon Musk, racism (including that against his own nationality), supporting war crimes, and arguing 16-year-olds should be allowed to get married. That's all I can remember now.
It’s a political Twitter account, so “worst” posts are going to be a highly subjective category. This one is blatantly a false post, but he can be excused as it is very much not in his area of expertise.
Commutative law part if you have (10 + 50) x 2 and change the order of the addition, you get (50 + 10) x 2. Your way of treating it as 10 + (50 x 2) = (50 x 2) + 10 is a result of the order of operation you already chosen 6:48
Distributive law: a * (b + c) = (a * b) + (a * c) in the normal-order of operation you can remove the parentheses, in the reverse you can't. If you write a law in one systems format, of course it's not going to look the same in the other system.
Why do you continue to post these same type of videos repeatedly ? In recent days, I think you've posted more bodmas problems than actual maths questions
He types 50+50 and hit equals and after that times 2 and hit equals which is 100 and later it's 200 But when he types 50+50*2 that's just 1 and not 2 different equations And the other thing which is 2nd or 3rd grade Maths: multiplications and divisions are sooner than addition or substraction
Order of operations is just grammar for math. Yes we could just decide to do it differently but then we would have a harder time understanding each other and wouldn’t know how to write equations to best be interpreted the way we intended
Love how you explained why the order of expressions is valid past the dad answer of ‘because’. Not using the order of expression will violate the Commutative and the Distributive Laws. I will be referencing this video the next time my family asks these types of math questions. Thanks for sharing.
You want to start a flame war? Multiplication by juxtaposition. There is no universal standard so sometimes there are 2 different and valid answers. Most of the world including Europe, academia, and engineering use it. Some of the world, notably North American grade schools do not. Even calculators don’t agree- some use it, some don’t, some have changed back and forth between models. Multiplication by juxtaposition, sometimes called implied multiplication, is where you multiply adjacent terms that do not have a symbol before regular addition, subtraction, multiplication, and division. People construct problems such as the examples you had at the end of the video often with text saying “most get this wrong”, that because there two answers are designed nothing more than to start an argument between two groups that cannot understand why the other group says the other answer. As multiplication by juxtaposition is more common, I say use it. But if your equation could be ambiguous, use parentheses to be explicit.
The example of swapping with commutative addition isn't accurate. a + b = b + a would not move the multiplication left if you were using left to right evaluation. It would only swap the 50s, so does not prove your point.
The customary order of operations has NOTHING to do with how calculators, spreadsheets and computer programming languages interpret math expressions. They all work a little differently (in the case of RPN, way differently). It's nice when applications follow the customary order of operations, but it is up to the user to know how the application works. As someone who does a LOT of calculations for work...calculations that are written out to be reviewed by others, they MUST be clear. Here are my humble suggestions: 1) Make ample use of brackets and parenthesis. Group operations that have priority. 2) NEVER EVER use obeluses (division signs)...if you have a rational expression, write it out as a fraction. 3) Dividing by fractions/putting fraction in the denominator of a rational expression should be avoided unless you have a damned good reason. (It does come up in algebra and calculus). Mathematic expressions are communication...if you are relying on the reader to strictly interpret your math with PEMDAS/BODMAS, you are, at best, WASTING THEIR TIME, and at worst, CREATING CONFUSION. If people have to ask what you meant, or how you got a particular result, you have expressed yourself poorly. An aside...most of the "math videos" deliberately present expressions that are, to put it nicely, problematic. They have just enough ambiguity to generate lots of clicks and comments. The comments often get very ugly. Another aside, teaching PEMDAS is one of those things I would call "essential, but otherwise unimportant". Teachers are better off teaching students how to express their math ideas clearly.
Maybe also another reason the order of operations is important to follow is because of the following (correct me if i could be wrong). -Multiplication and division are like a simplified version of addition(multiplication) or subtraction(division somewhat). -A parenthesis may be just an unsimplified mini equation. -exponentiation is a simplified version of many multiplications and/or divisions. And wouldn't it be very logical if you started off with the parenthesis since that is an unsimplified mini equation? Then the exponential since it is just a notation for multiplication/division of the same value? Then multiplication or division next since it is another notation for addition/subtraction? Then lastly addition and subtraction? Just wanted to add for your discussion about why the operations of equations are important:))
Multiplication is just a special case of addition: repeatedly adding some number, a, some other number, b, amount of times. So, multiplication can just be rewritten in terms of addition. 2 × 5 = 2 + 2 + 2 + 2 + 2. The question then becomes: why should the precedence be what it is? The commutative property of addition being true answers that. 3 + 2 × 5 = 3 + 2 + 2 + 2 + 2 + 2 Since addition is accepted as being commutative, we can rearrange the addends and evaluate some of them. If we simplify the remaining addends into multiplication, we should expect the same result because we only used addition's commutative property: 3 + 2 × 5 = 3 + 2 + 2 + 2 + 2 + 2 = 3 + 4 + 2 + 2 + 2 = 3 + 4 + 2 × 3 Sure enough, the entire expression remains equal to 13 at every step. If a left-to-right evaluation system were to be accepted as true, then either the commutative property of addition would need to be false, multiplication would have to be redefined, or BOTH. More complex equations would even be inconsistent in their rule evaluations with the constant swapping of operator precedence.
When I got to college level, the instructor was baffled that this concept was not taught in my secondary school (or I just didn't know it). No problem, I learned it then and there.
This should be apparent to anyone with basic math literacy as soon as they see the tweet. As soon as the enter button is hit, it calculates based on the order of operations from what you've input. The result, if left in for another calculation, is considered its own, separate part of a new equation. So if you enter it as two different equations, you will get two different answers if you don't do them in an order that would match the order of operations had you input it all at once. The only calculator I've ever seen to actually be incorrect and not have the order of operations correctly programmed is Casio brand calculators, which will sometimes give incorrect answers when using more than one type of operation in the same equation, but that's a topic for another video. Simply going from left to right regardless of the order of operations is simply incorrect. The order of operations exists for a reason. It would be like disregarding cooking times and ingredient amounts in a recipe. Doing it the right way will give you a delicious meal but disregarding the system will result in something very different than what the recipe is meant to yield.
First, follow PEMDAS (Perinthesis, Exponent, Multiplication and Division, ADD and SUBSTRACT) So this evaluation: 50 + 50 * 2 Is something like this: 50 + 50 * 2, 50 + 100, 150 So the answer is 150
You highlight the statement in William Oughtred's Key of the Mathematics that shows him evaluating 12x3 first before adding 4, but the very next step (23) doesn't seem to follow: he has the expression 40+3x13=572. What's going on there?
It confused me as well. What he ment to say ist the rule vor the sum of an arithmetical progression. Compare to en.wikipedia.org/wiki/Arithmetic_progression. 4 (first term); 7; 10; ....;37; 40 (thirteenth term), sum of terms (Z) = 4+7+10....+37+40 = 572/2 =286 (4+40)*13 = 572 = 2*286 Maybe the "3" in the equation was a typo and he forgot brackets.
The vinculum is *not* the horizontal bar used to represent division. The vinculum is the under or over bar used to group digits or to group operations or show conjugates or negation or various other things but *not* division for which the division bar is used.
Also, there's nothing wrong with the math in the post. It's clearly, the user expecting 200, and mechanically NOT pressing the equal sign to get 100 and then multiply by 2.
Ian Miles Cheong stated "But type on 50 + 50 * 2 and it spits out 150. What gives?" It's because the calculator uses the order of operation(PEMDAS), which means parentheses first, then exponents, next is multiplication or division after that is addition or subtraction. Which is why 50 + 50 * 2 is 150.
As a general rule, I think that calculator apps on smartphones and computers should have a display of the expression it is evaluating, and add sufficiently many parentheses so that the expression becomes unambiguous. People might disagree on how the calculator interprets the input, but the calculator will make it very clear exactly what they are calculating, so you can retype it if it follows different conventions than you do. If the user writes 50+50*2, then I think it should be rendered at 50+(50*2), just to make it even more clear that this is what it is calculating when arriving at the answer of 150. This is obviously more important with expressions like 6/2(1+2), which usually is interpreted at 6/(2(1+2)), but where a lot of people online like to disagree and claim it's (6/2)(1+2) instead.
Half of the video's MYD posts are really difficult challenges The other half is people on the internet causing a fuss because they forget order of operations
The ones at 10:18 are legitimately ambiguous, though. I had a pair of students try and consult me on one of those a few weeks ago (I am a HS Math Teacher), and I ended up telling them that there are two different problems it very much LOOKS like, but that it is unclear which one it should actually solve to (and thus which of the two popular answers is “right”).
The deeper reason is that there is an order to operations. Adding is just counting by numbers other than just 1, multiplying is adding multiple groups. Exponentiation is another order higher yet, multiple multiples if you will. And we can go on, to tetration etc. We do the highest order first unless the expression has been specifically indicated to be done first (parentheses). That being said, while sometimes you may use an operation to figure out the answer an operation isn't always what is going on. 2(1+2) does not mean 2 multiplied by (1 + 2) which would be taking 2 and adding it to itself a total of three times. 2(1+2) means that you have 2 of the value of (1+2). It describes how many of (1+2) you have and so in this case is acting as an adjective. Technically numbers are probably best considered as determiners, but they act like adjectives much of the time. The order of operations is the second thing you do when solving a problem, the first thing you do is figure out what the problem is actually saying. Calculators aren't good at that.
Calculator to me: Hallo world! Me to calculator: Sorry! I do not know how not use the calculator corrrectly! Paper to me: I am here too! Me to paper: Sorry! I do not know maths basic laws of operation! Paper and calculator to me: ask AI for help.
We need to abolish the ÷ symbol. It's needlessly confusing when we have fraction bars to express exactly where division goes in the equation's order of operations.
Ummm...yeah, no. Both the commutative law of addition and the distributive law hold under a left to right convention regardless of operation. Commutative law of addition: 20 + 50 × 2 = 70 × 2 = 140 50 + 20 × 2 = 70 × 2 = 140 20 + 50 × 2 = 50 + 20 × 2 To do what you did is 50 + (50 × 2) = 50 + 100 = 150 50 × 2 + 50 = 100 + 50 = 150 50 + (50 × 2) = 50 × 2 + 50 Distributive law: 50 × 3 = 150 50 × (1 + 2) = 150 50 × 1 + (50 × 2) = 150 If you include a nonsensical demonstration about the commutative law and distributive law - before you claim they don't hold under left to right - you need to consider your own biases. Next time be consistent using left to right, including parenthesis to group multiplication if you want it done first and it's not the left most operation. In doing so you'll realize two things: 1) The commutative law of addition and the distributive law hold under a left to right convention 2) You can't prove nor disprove a convention. The primary reason for multiplication over addition is it's usefulness in reading and writing polynomials. Other conventions would be considerably more wonkish to work with polynomials. For example if addition has a higher priority than multiplication, then you'd end up writing parenthesis around every monomial term of the polynomial.
The issue is not lack of education, or a bug with a calculator - it is simply that Order of Operations is an arbitrary set of rules that are only used to teach people in school, and to put as puzzles for people to discuss and are otherwise not used The fact that people argue over it means it's useless If you want it to be unambiguously interpreted as you wanted - use brackets, like everyone else does If you meant (50 + 50) x 2, then write that and your calculator will show the answer you expected If you meant 50 + (50 x 2), then write that and your calculator will show the answer you expected
The only possible "excuse" I could think of, why in the 21st century people still don't know the correct order of operation, is that they might be used to very primitive calculators from the electronic "stone age" in their childhood. But on the other hand: every one who has visited school for more than 2 years should know the correct rules.
It's not even related to order of operations. When you press =, it calculates whatever was entered. Any subsequent operations you do will use that result. The previous operations that gave that result don't matter anymore. If the screen displays "100" after pressing =, then "100" will be used for the next thing you do (if you enter an operator). Whatever happened previously doesn't matter.
Actually, if you happen to ever been given an assignment on programming your own calculator in AOS (Algebraic Operating System), you would find that storing the whole expression tree is unnecessary, but would only need to store two variables: one for accumulating addition/subtraction results, and one for memorizing the latest chain of multiplication/division results. For example, if you key in 4 + 4 + 3 + 2 * 2 * 3 = , as you press +, the screen displays the accumulated result(4 -> 8 -> 11), but for the next multiplications it will display the chain of multiplication (2 -> 4 -> 12), then it will be added to the accumulated variable as soon as you press equal or plus/minus.
In all my years of education and 40+yrs professional experience, that's the first time I've ever heard a justification for the Order of Operations. All I was ever taught was the Order of Operation and, "When in doubt, USE PARENTHESES!". (🤔) Thanks for that, Presh! It was a revelation.
People have problems even with just addition and subtraction. The AS in PEMDAS or BODMAS is misunderstood to mean 'Addition before Subtraction' such that people will interpret e.g. 7-3+2 as being the same as 7-(3+2).
I saw a calculator that showed this kind of expression converted to *Polish Notation," which is what any compiler or interpreter does. (I had to write one about 50 years ago.) Store 50 in list of operands, store + in operators, store another 50. Store x operator, store 2. End of expression with lists "+x" operators and 50 50 2 operands. Perform x, store 100 (replace 50 and 2), perform +. This works for any expression using any list of prioritized operators.
The problem is that people are told the order of operations but not why it is so. It is not some rule given from above but some to simplify things. It is typical that you for example buy different amounts of different items that each have a different unit price and want to calculate the total. Because multiplication is done before addition one does not need to put every multiplication in brackets. Four function calculators calculate as you go (some say left to right but that incorrect as there is no concept of left or right in the calculator. The entries are separated by time, not by location). On them you must use the memory function. M+ adds the result to the memory. Mr then gives the total.
The key here is the word "*SCIENTIFIC*". The Windows calculator will give BOTH results, depending on which MODE it is in. In STANDARD mode it adheres to "left-to-right*, but in SCIENTIFIC mode it adheres to *order-of-operations*. *Neither* method is *in-&-of-itself* wrong. It simply depends on what one wants to do. Presh Talwalkar clearly states what the STANDARD mode is typically used for. So any user *MUST* know the rules of & conventions for BOTH *left-to-right* AND *order-of-operations*. AND, if using a calculator, which mode it is set to. (I am still searching for a Help-file for the Windows calculator app...) (PS: My "smart phone" running Android has only the SCIENTIFIC mode, and also NO useful Help-file. But from its 'History' display one can deduce its mode.)
For those that are interested, there is a new book out about the history of the pocket calculator: Empire of the Sum by Keith Houston. Pretty interesting read.
Even without following the mathematical order of operations it should be easy to apply the correct order. 50 + 50 x 2 reads as follows: 50 plus two 50's. That should clarify things a bit. Obviously the answer would be 150.
Let all be kind here 😂😂, I know we all know it but give some respect for his honest question. He is willing to learn new things although it should be a basic understanding for others. Knowledge is a bliss to those who have it. I hope he got the answer and learned new things.
6:39 I am not convinced by that as it assumes the conclusion i.e. is circular. Changing the order makes sense only if we take multiplication to be higher precence.
@MindYourDecisions Thank you, Presh, for continuing to (implicitly) hammer on the need for teachers who UNDERSTAND what they are supposed to be teaching.
It makes sense for the Android calculator, but not for the Apple one. The fact that it clears the screen after the * implies that it's already calculated the result up to that point using only those first two terms.
50+50*2 = 200 ONLY if you totally ignore the priority of operations and incorrectly proceed left to right. 50+50*2=150 is correct when you do the operation properly : Do the multiplications THEN the additions.
Tbh i can see why people would get this wrong since apple's calculator doesn't show the whole expression so it looks like it's doing 50+50=answer then answer×2=200
I liked the video until Presh wrongly explained what would be wrong with the (commutative and) distributive axioms. If you change the order of operations, you need to change those axioms as well. The distributive axiom a*(b+c) = ab+bc would become ab+c = (ab)+(ac) The commutative axiom would be a bit harder because you cannot include the multiplier, but if we would have learned a different order of operations you would not do that. People would correctly apply it as a+bc = b+ac just as with our current order of operations most of us would correctly flip the order multiplicands (where it is allowed) without including the addend: ab+c = ba+c I do agree that our current order of operations (PEMDAS) is the more logical one. I just think of it as prioritizing the most "composed" operations. (Parentheses are composed of whatever is inside of them. Exponentiation can be seen as composed of multiplications e^x = e*e*...*e. Multiplication can be seen as composed of additions a*b=a+a+...+a) Of course, currently we could substitute: a*b*c = (a+a+...+a)*c But with different order of operations we would not need those parentheses: a*b*c = a+a+...+a*c Hmm, I'm curious, what would the following expression equal? e+1-1^0 Addition and subtraction first, so it becomes e^0 which is 1. Or is it exponentiation first, so it becomes e+1-1, which is e? Or maybe subtraction first, then exponentiation, then addition: e+0^0, which is either e+1 or e+0 Ah, maths discussions, fun additions to fun times.
I just tried this with the Windows calculator, which you can switch modes between "standard" and "scientific". In standard mode it would give 200 (because it evaluates left-to-right like a 2 dollar calculator would do it) while in scientific mode it would give 150 (because that's how scientists would calculate this). It's worth noting that the standard mode also shows "100" in the display as soon as you press the "×" key, indicating that it did in fact add 50+50 first, while the scientific mode still displayed "50" after hitting the "×" key (and it showed the entire "50+50×2" thing in a smaller display until the entire calculation is finalized)
I think your Proof with the communative law is wrong. The summands are Not 50 and 50*2 but 50 and 50. You are literally assuming in your Proof, that multiplication comes first.
One ambiguity in the order of operations I personally find is with trigonometry, for instance, seeing something written as: tan αβ Just based on the order of operations of trigonometry coming before multiplication, it should be (tan(α)) * (β). However, I was told it really denoted tan(αβ), because the αβ written together implicitly formed a group, equivalent to that of brackets. Which is the correct order?
the standard is usually, if you're not writing the × or • explicitly then scalars go infront of the term. In your case we would expect (tan(α))*(β) to be written as βtanα. A real annoying issue is when you have multiple functions like tan x√x which can either mean (tan(x))*(√x) or tan(x√x) but it's hopefully clear from context
Living in Kuwait 🇰🇼 I have seen a lot of non scientific normal calculators that just operate left to right directly especially in Jewelery shops just to make us pay more ( since here the currency is the costliest of the world ) Like 2 years back, i heard that someone got a jewelery which was supposed to be approx 21 Kwd but the shopkeeper used the calculator in such a way that it showed 25 KwD .... After hearing that i am sure he used the operation as 1 + 4 × 5 ( meaning he wanted four notes of 5 Kwd and 1 note of 1 Kwd but since it actually calculated addition first he got paid 4 Kwd extra and the customer was said to give *Five* notes of 5 Kwd..... ) This is One of the biggest scams So pls be aware and improve your calculations more than a Jeweller's or any other shopkeeper's calculator otherwise it may turn out that you are spending more than required.
![Spot The Difference : Can You Find Them All? [ Find The Difference #569 ]](http://i.ytimg.com/vi/gus-Qj5gfdA/mqdefault.jpg)
Isn't it wonderful that grown adults on Twitter are arguing due to lack of second grade math knowledge? What a world.
Um it’s actually called X now.
Why isn’t it called capital multiply.?
Just use bodmas
With how many people on Twitter argue from a third grade understanding of sex and gender I can’t say I’m surprised
See also climate deniers and Trump supporters
It is not really about lack of math knowledge, for people who are used to working with calculators that show only one number at a time it acts unpredictable
the initial tweet is engagement farming and nothing else
bingo
yeah, especially from that particular user
@@barb0za0 yep, i don't use twitter anymore, but i remember back in the day, he was just a troll for attention
Since X now pays users for high engagement it's becoming quite common.
I'm amazed some people are allowed to have phones.
It’s rage bait. Saw thumbnail, havnt gotten thru ad yet. Boutta dip. Don’t waste ur time. Obvious stuff
Some are allowed to run for an election having actively called his partisans to raid the congress. So, allowing people to have a phone...
Implied parenthesis are the worst, and cause non-mathematicians headaches
Hold up.
without parenthesis that says:
here's 50 of something
here's 50 more of something
now double it.
It is worked left to right. In which case, the addition would go first.
Without parenthesis, it is a different statement.
It says this:
50+50×2=a
÷50 from the left
is 50x2=a/50
Which is 100=a/50
Which is a=200
Or you can ÷ 100 from the left
Which is 2 = a/100
Which is a=200
Without parenthesis, it is already broken down.
@@dogbreaththe3rd851 Cute. No. However, seriously, write the equation out to prove 200 is incorrect.
The flow chart the video presents is not mathematics.
I'm a little tired of endlessly discussing how some folks on the internet don't understand order of operations.
I suspect they do this on purpose for attention
@@dheebanarunachalam9960 I'm not so sure since a while back fools were arguing over something similar but it involved parentheses.
@@demonwolf570 HOW COULD THEY GET IT WRONG WIH PARANTHESES!?
Ive been trying to explain to people that multiplication and division are the exact same thing. Multiplying by 2 is the same as dividing by 1/2, they are the same operation and therefore have the same order of operation. This also applies with addition/subtraction (+2=-[-2]) and exponentiation/roots (x^[1/2]=[sqrt x])
@@mher_22at last one mistake was a distribution operation which was done incorrectly
e.g.
2 * (5 + 10) / 5 becomes 10 + 20 / 5 instead of 30 / 5
1970:We'll have flying cars in the future.
2024:having to explain order of operations.
Make that 1950. The fifties were a great time for futurism. Just look at the Atomium in Brussels, which was built in 1958.
A great example of the sixties is 2001: a space odyssey, where HAL9000 is an AI computer built in 1992.
2024. Why should we bother to understand punctuation?
@@EaglePicking You've just reminded that I have been to the Atomium. I've also been to the Dali exhibition in the Pompidou centre in Paris. HAL. In each case one letter before IBM. Back in the day, IBM meant "It's Being Mended", ICL meant "It's Coming Later", and DEC meant "Don't Even Consider". Yes, I am actually that old!
I love people not understanding how basic math works lol
you can imagine what other things that individual is getting all sorts of wrong in his life. Including voting. You can only fear his choices if they impacted your daily life as well.
People did Maths for hundreds of years without the order of operations we mostly use now, they used different ones, or none - it's not a fundamental part of maths just an arbitrary set of rules that are relatively recent, and are not needed
Except it isn't really "math"...it's busy work.
PEMDAS crap is why kids think they "hate math" or that "they're no good at math"...it is the math equivalent of diagramming sentences.
The problem here is that Apple calculator app is absolute garbage because it doesn't show you your whole input. Some people then think that it actually evaluates the 50+50 part - exactly like those cheapest single-line calculators, which evaluate every single operation as soon as possible. Apple's calculator app looks like it does the same thing, but doesn't - thus the confusion.
This, yes. UI not matching UX
The real problem is that everyone has become reliant on "Artificial Incompetence".
I would expect a calculator to follow the correct rules on a single line.
I don't entirely disagree but FYI you can turn on Paper Tape mode to see your whole formula on one line (after you've hit "=").
@@Duke_of_Lorraine I wouldn’t. I guess I’ve been using too many cheap calculators. I would use a lot of parenthesis on scientific calculators just to be sure.
The number of decibels you yelled high at is the number of times I've heard this problem and thought: "how can people mess this up too!"
lol the original xeet from Ian Mile Cheong, the wrongest man on the Internet.
Rightwing troll farming ad revenue on X 😂 what a website
Xeet, lol
She is not that wrong... Apple's calculator does not show the expression, compared to other calculators, and old calculators used to work like..... calculators! and not parsers + calculators
Calculators used to (and some still do) calculate the result each time you pressed an operator, not just equal, so if you tiped 50 + 50 then X, it will calculate to 100 (as if you pressed =), then 2 = 200
Exactly. I can see the confusion coming from Gen X or Millenial. Because calculator back then worked like that
@@bigbendum8403 "back then"... most simple 4-function calculators you can buy now still work like this
Yeah some still does that, although some also have a counter at the top left/right to say which step is the calculation at
No decent calculator has ever done it the wrong way. And there are cheap $5 calculators that does it the right way.
I rushed to do the same in Excel 50+50*2=150.
How anybody can blame Apple, I don't get it.
Engagement farming
@@achintyaagrawal9819 That would be the most charming explanation 🤕
the difference is between calculators that use single-step evaluation (as pretty much all old calculators did), and newer calculators that use expression (or formula) evaluation. the Windows calculator lets you choose between single-step (Standard) and expression (Scientific/Programmer), which give the answers 200 and 150, respectively.
to say that old calculators evaluate the "expression incorrectly" is not a valid statement - they don't evaluate mathematical expressions at all, they evaluate their input step-by-step (not expressions), by-design.
Bingo. Apple's looks like the simple type but acts like the advanced type. It's ridiculous to think that someone would put in a complex expression totally blind, and imagine that it's storing it all internally and then evaluating it using order of operations, with no evidence of this.
Windows default calculator interprets both the "addition" key and the "multiplication" key as also the "equals" key. But if you switch to the scientific view then you get a different result.
Also, geez your UA-cam channel was made only one year after UA-cam was founded wow
Yeah, this has been an issue for many years. But I'm pretty sure they used to have a calculator that did it correctly. But that was the version before they added the "Standard", "Scientific" and other modes. So, maybe 15-20 years ago.
I was shocked, the first time I discovered the error and I only discovered it, because I'm good at calculating in my head. And yes, it is an error.
The issue is not expecting calculators to follow the formal order of operations, but to follow as typed.
I grew up as we transitioned from the latter, which is why I use RPN calculators - they behaved in a deterministic manner.
I purchased an HP RPN calculator 45 years ago, and it still works fine! That's the only one I use.
Please Excuse My Dear Aunt Sally
the fact that it has to be memorized, and cannot be worked out from first principals, should tell you it is an arbitrary set of rules, and nothing really to do with maths at all
From what? What did she do? 😉
The problem is not about math but rather about interface: Apple calculator doesn't display the full expression being evaluated, just like about any simple calculator, which in turn presumes left-to-right evaluation order (pressing an action button is performing current calculation and going to input of the next argument using selected action). In Android example the expression is displayed fully, and there is no confusion.
Exactly this! Apple's calculator violates good Usability principles, specifically 'visibility of system status'. People's confusion is justified here, as the confusion is not about arithmetics.
Innovation
It's not about the expression. Old calculators evaluate at each time the next operator button is hit
It's crazy that videos like this even exist...
This isn't even an order of operations problem. The first example explicitly uses the "=" key, which means "evaluate the tree so far, display the result, and treat the result as the first operand".
Yes, he completely missed the point the Twitter post was angry about. It's that clicking the "equals" button implicitly surrounds your previous expression with parentheses.
How Presh narrated the problem in starting is 😂 😃 😄 😁 🤣
Re. the laws, isn't that mostly a matter of notation? If you change the notation conventions you'll also have to change the notation of the laws:
(a) + (b) = (b) + (a)
a(b + c) = (ab) + (ac)
Edit: I certainly don't mean to say that would be better, just that I wonder if it's about the laws not holding vs. having to express the laws differently when conventions change
Yeah, he forgot that a left-to-right convention regardless of operation, means that
a + b × c means (a + b) × c
Applying the commutative law of addition as he did, he should've started with
a + (b × c) which equals b × c + a
And the distributive law should've been notated as
a × (b + c) = a × b + (a × c)
You're right. If you use a different convention, the properties still hold, they just look different.
Another example, if using a convention of addition having a higher priority than multiplication, then the distributive law would be written as
a × b + c = (a × b) + (a × c) or, using implied multiplication,
ab + c = (ab) + (ac)
I agree, even though the properties hold under different conventions, it doesn't mean they're useful.
It's a valid point that if the entire expression isn't shown on screen while you type the rest, then it's updating the total as you go along, ergo not following the order of operations.
The issue is, that's not his worst tweet. Not in the top 100 even.
How much worse does it get?
@@mrsoisauce9017 Extensively praising Elon Musk, racism (including that against his own nationality), supporting war crimes, and arguing 16-year-olds should be allowed to get married. That's all I can remember now.
It’s a political Twitter account, so “worst” posts are going to be a highly subjective category. This one is blatantly a false post, but he can be excused as it is very much not in his area of expertise.
@@Utred2012 Shouldn't need expertise to do grade school math though
@@Utred2012 Racism and war crimes aren't subjective.
Commutative law part
if you have (10 + 50) x 2
and change the order of the addition, you get (50 + 10) x 2.
Your way of treating it as 10 + (50 x 2) = (50 x 2) + 10 is a result of the order of operation you already chosen
6:48
Distributive law: a * (b + c) = (a * b) + (a * c)
in the normal-order of operation you can remove the parentheses, in the reverse you can't.
If you write a law in one systems format, of course it's not going to look the same in the other system.
What?
@@myself.0001he means order of operations
@@PugganBacklund is right
It should be (50 X 2) + (10 X 2) which is the same as (50 + 10) X 2
@@TecraTube Oh thanks 👍
Can we get Presh a trophy for standing on this soapbox, speaking the truth of Order of Operations for over 7 years at this point? 🤣🤣
Why do you continue to post these same type of videos repeatedly ? In recent days, I think you've posted more bodmas problems than actual maths questions
He's been doing it for years and years. Snore.
the bag
@@toaster4693 And still half the people don't understand it.
Bodmas problema ARE actual maths problems.
Because clearly it’s still an issue that Americans are having..
He types 50+50 and hit equals and after that times 2 and hit equals which is 100 and later it's 200
But when he types 50+50*2 that's just 1 and not 2 different equations
And the other thing which is 2nd or 3rd grade Maths: multiplications and divisions are sooner than addition or substraction
Order of operations is just grammar for math.
Yes we could just decide to do it differently but then we would have a harder time understanding each other and wouldn’t know how to write equations to best be interpreted the way we intended
Great video, and thanks for the great explanation of WHY we do multiplication and division before addition and subtraction…
Did I miss something? Did elementary schools stop teaching order of operations or something?
I assume it now depends on the school...
I guess they teach, but the student dosen't learn...
They do still teach it, but those are the type of people that sleep during classes and go on to say school is useless
"recently there was a big controversy on twitter" has to be my favorite tautology
4:57 "Here's a text from 1702" - Wow, I didn't know people were texting way back in 1702!
"1702" Isn't that two min's past five in the afternoon?
1702! is pretty far in the future, actually.
@@nightytime Only about an hour ago BST. Unless, of course, you are posting at 1702 BC.
that's why they didn't want to give them the app
Love how you explained why the order of expressions is valid past the dad answer of ‘because’. Not using the order of expression will violate the Commutative and the Distributive Laws. I will be referencing this video the next time my family asks these types of math questions. Thanks for sharing.
Whosoever tweeted that needs serious elementary education asap
You want to start a flame war? Multiplication by juxtaposition. There is no universal standard so sometimes there are 2 different and valid answers.
Most of the world including Europe, academia, and engineering use it. Some of the world, notably North American grade schools do not. Even calculators don’t agree- some use it, some don’t, some have changed back and forth between models.
Multiplication by juxtaposition, sometimes called implied multiplication, is where you multiply adjacent terms that do not have a symbol before regular addition, subtraction, multiplication, and division.
People construct problems such as the examples you had at the end of the video often with text saying “most get this wrong”, that because there two answers are designed nothing more than to start an argument between two groups that cannot understand why the other group says the other answer.
As multiplication by juxtaposition is more common, I say use it. But if your equation could be ambiguous, use parentheses to be explicit.
The example of swapping with commutative addition isn't accurate. a + b = b + a would not move the multiplication left if you were using left to right evaluation. It would only swap the 50s, so does not prove your point.
The customary order of operations has NOTHING to do with how calculators, spreadsheets and computer programming languages interpret math expressions. They all work a little differently (in the case of RPN, way differently).
It's nice when applications follow the customary order of operations, but it is up to the user to know how the application works.
As someone who does a LOT of calculations for work...calculations that are written out to be reviewed by others, they MUST be clear.
Here are my humble suggestions:
1) Make ample use of brackets and parenthesis. Group operations that have priority.
2) NEVER EVER use obeluses (division signs)...if you have a rational expression, write it out as a fraction.
3) Dividing by fractions/putting fraction in the denominator of a rational expression should be avoided unless you have a damned good reason. (It does come up in algebra and calculus).
Mathematic expressions are communication...if you are relying on the reader to strictly interpret your math with PEMDAS/BODMAS, you are, at best, WASTING THEIR TIME, and at worst, CREATING CONFUSION.
If people have to ask what you meant, or how you got a particular result, you have expressed yourself poorly.
An aside...most of the "math videos" deliberately present expressions that are, to put it nicely, problematic. They have just enough ambiguity to generate lots of clicks and comments. The comments often get very ugly.
Another aside, teaching PEMDAS is one of those things I would call "essential, but otherwise unimportant". Teachers are better off teaching students how to express their math ideas clearly.
In Lisp we dont have this problem of hidden rules of precedence, since there's prefix notation. Lisp: (+ 50 (* 2 50))
Maybe also another reason the order of operations is important to follow is because of the following (correct me if i could be wrong).
-Multiplication and division are like a simplified version of addition(multiplication) or subtraction(division somewhat).
-A parenthesis may be just an unsimplified mini equation.
-exponentiation is a simplified version of many multiplications and/or divisions.
And wouldn't it be very logical if you started off with the parenthesis since that is an unsimplified mini equation? Then the exponential since it is just a notation for multiplication/division of the same value? Then multiplication or division next since it is another notation for addition/subtraction? Then lastly addition and subtraction?
Just wanted to add for your discussion about why the operations of equations are important:))
Multiplication is just a special case of addition: repeatedly adding some number, a, some other number, b, amount of times. So, multiplication can just be rewritten in terms of addition.
2 × 5 = 2 + 2 + 2 + 2 + 2.
The question then becomes: why should the precedence be what it is? The commutative property of addition being true answers that.
3 + 2 × 5 = 3 + 2 + 2 + 2 + 2 + 2
Since addition is accepted as being commutative, we can rearrange the addends and evaluate some of them. If we simplify the remaining addends into multiplication, we should expect the same result because we only used addition's commutative property:
3 + 2 × 5 = 3 + 2 + 2 + 2 + 2 + 2 = 3 + 4 + 2 + 2 + 2 = 3 + 4 + 2 × 3
Sure enough, the entire expression remains equal to 13 at every step. If a left-to-right evaluation system were to be accepted as true, then either the commutative property of addition would need to be false, multiplication would have to be redefined, or BOTH. More complex equations would even be inconsistent in their rule evaluations with the constant swapping of operator precedence.
When I got to college level, the instructor was baffled that this concept was not taught in my secondary school (or I just didn't know it). No problem, I learned it then and there.
This should be apparent to anyone with basic math literacy as soon as they see the tweet. As soon as the enter button is hit, it calculates based on the order of operations from what you've input. The result, if left in for another calculation, is considered its own, separate part of a new equation. So if you enter it as two different equations, you will get two different answers if you don't do them in an order that would match the order of operations had you input it all at once. The only calculator I've ever seen to actually be incorrect and not have the order of operations correctly programmed is Casio brand calculators, which will sometimes give incorrect answers when using more than one type of operation in the same equation, but that's a topic for another video.
Simply going from left to right regardless of the order of operations is simply incorrect. The order of operations exists for a reason. It would be like disregarding cooking times and ingredient amounts in a recipe. Doing it the right way will give you a delicious meal but disregarding the system will result in something very different than what the recipe is meant to yield.
0:52 you can’t do math operations on math solutions like that.
First, follow PEMDAS (Perinthesis, Exponent, Multiplication and Division, ADD and SUBSTRACT)
So this evaluation:
50 + 50 * 2
Is something like this:
50 + 50 * 2,
50 + 100,
150
So the answer is 150
You highlight the statement in William Oughtred's Key of the Mathematics that shows him evaluating 12x3 first before adding 4, but the very next step (23) doesn't seem to follow: he has the expression 40+3x13=572. What's going on there?
It confused me as well. What he ment to say ist the rule vor the sum of an arithmetical progression.
Compare to en.wikipedia.org/wiki/Arithmetic_progression.
4 (first term); 7; 10; ....;37; 40 (thirteenth term), sum of terms (Z) = 4+7+10....+37+40 = 572/2 =286
(4+40)*13 = 572 = 2*286
Maybe the "3" in the equation was a typo and he forgot brackets.
That's a person who brags they went to the school of life.
The vinculum is *not* the horizontal bar used to represent division. The vinculum is the under or over bar used to group digits or to group operations or show conjugates or negation or various other things but *not* division for which the division bar is used.
This is an elementary school problem 😅 I don't remember when I learnt the priority of operators, but it was quite early, probably before I was 12...
Mnemonic device in German: Punkt vor Strich, dot before line. Punkt means dot (· for multiplication, : for division); Strich means line (-, +).
Apple: Let me guess.. you didn't finish primary school 🥵, did you ?
Also, there's nothing wrong with the math in the post. It's clearly, the user expecting 200, and mechanically NOT pressing the equal sign to get 100 and then multiply by 2.
Ian Miles Cheong doing engagement-bait? Of course, he did.
Ian Miles Cheong stated "But type on 50 + 50 * 2 and it spits out 150. What gives?"
It's because the calculator uses the order of operation(PEMDAS), which means parentheses first, then exponents, next is multiplication or division after that is addition or subtraction. Which is why 50 + 50 * 2 is 150.
As a general rule, I think that calculator apps on smartphones and computers should have a display of the expression it is evaluating, and add sufficiently many parentheses so that the expression becomes unambiguous. People might disagree on how the calculator interprets the input, but the calculator will make it very clear exactly what they are calculating, so you can retype it if it follows different conventions than you do.
If the user writes 50+50*2, then I think it should be rendered at 50+(50*2), just to make it even more clear that this is what it is calculating when arriving at the answer of 150. This is obviously more important with expressions like 6/2(1+2), which usually is interpreted at 6/(2(1+2)), but where a lot of people online like to disagree and claim it's (6/2)(1+2) instead.
Half of the video's MYD posts are really difficult challenges
The other half is people on the internet causing a fuss because they forget order of operations
The ones at 10:18 are legitimately ambiguous, though. I had a pair of students try and consult me on one of those a few weeks ago (I am a HS Math Teacher), and I ended up telling them that there are two different problems it very much LOOKS like, but that it is unclear which one it should actually solve to (and thus which of the two popular answers is “right”).
The ones at 9:10 and 9:23 are not ambiguous, though.
The deeper reason is that there is an order to operations. Adding is just counting by numbers other than just 1, multiplying is adding multiple groups. Exponentiation is another order higher yet, multiple multiples if you will. And we can go on, to tetration etc. We do the highest order first unless the expression has been specifically indicated to be done first (parentheses). That being said, while sometimes you may use an operation to figure out the answer an operation isn't always what is going on. 2(1+2) does not mean 2 multiplied by (1 + 2) which would be taking 2 and adding it to itself a total of three times. 2(1+2) means that you have 2 of the value of (1+2). It describes how many of (1+2) you have and so in this case is acting as an adjective. Technically numbers are probably best considered as determiners, but they act like adjectives much of the time. The order of operations is the second thing you do when solving a problem, the first thing you do is figure out what the problem is actually saying. Calculators aren't good at that.
Calculator to me: Hallo world!
Me to calculator: Sorry! I do not know how not use the calculator corrrectly!
Paper to me: I am here too!
Me to paper: Sorry! I do not know maths basic laws of operation!
Paper and calculator to me: ask AI for help.
Definitions of AI in context:-
Analysis : Artificial Incompetence.
Request : Artificial Indifference.
Telephone : Artificial Ignorance.
We need to abolish the ÷ symbol. It's needlessly confusing when we have fraction bars to express exactly where division goes in the equation's order of operations.
Ummm...yeah, no. Both the commutative law of addition and the distributive law hold under a left to right convention regardless of operation.
Commutative law of addition:
20 + 50 × 2 = 70 × 2 = 140
50 + 20 × 2 = 70 × 2 = 140
20 + 50 × 2 = 50 + 20 × 2
To do what you did is
50 + (50 × 2) = 50 + 100 = 150
50 × 2 + 50 = 100 + 50 = 150
50 + (50 × 2) = 50 × 2 + 50
Distributive law:
50 × 3 = 150
50 × (1 + 2) = 150
50 × 1 + (50 × 2) = 150
If you include a nonsensical demonstration about the commutative law and distributive law - before you claim they don't hold under left to right - you need to consider your own biases.
Next time be consistent using left to right, including parenthesis to group multiplication if you want it done first and it's not the left most operation. In doing so you'll realize two things:
1) The commutative law of addition and the distributive law hold under a left to right convention
2) You can't prove nor disprove a convention.
The primary reason for multiplication over addition is it's usefulness in reading and writing polynomials.
Other conventions would be considerably more wonkish to work with polynomials. For example if addition has a higher priority than multiplication, then you'd end up writing parenthesis around every monomial term of the polynomial.
In school we all learned Bedmas. Bracket, exponent, division, multiplication, addition, subtraction
The issue is not lack of education, or a bug with a calculator - it is simply that Order of Operations is an arbitrary set of rules that are only used to teach people in school, and to put as puzzles for people to discuss and are otherwise not used
The fact that people argue over it means it's useless
If you want it to be unambiguously interpreted as you wanted - use brackets, like everyone else does
If you meant (50 + 50) x 2, then write that and your calculator will show the answer you expected
If you meant 50 + (50 x 2), then write that and your calculator will show the answer you expected
The only possible "excuse" I could think of, why in the 21st century people still don't know the correct order of operation, is that they might be used to very primitive calculators from the electronic "stone age" in their childhood. But on the other hand: every one who has visited school for more than 2 years should know the correct rules.
It's not even related to order of operations. When you press =, it calculates whatever was entered. Any subsequent operations you do will use that result. The previous operations that gave that result don't matter anymore. If the screen displays "100" after pressing =, then "100" will be used for the next thing you do (if you enter an operator). Whatever happened previously doesn't matter.
Yet another unnecessary problem easily avoided with Reverse Polish Notation. Once you try Polish, you'll never go back.
Actually, if you happen to ever been given an assignment on programming your own calculator in AOS (Algebraic Operating System), you would find that storing the whole expression tree is unnecessary, but would only need to store two variables: one for accumulating addition/subtraction results, and one for memorizing the latest chain of multiplication/division results. For example, if you key in 4 + 4 + 3 + 2 * 2 * 3 = , as you press +, the screen displays the accumulated result(4 -> 8 -> 11), but for the next multiplications it will display the chain of multiplication (2 -> 4 -> 12), then it will be added to the accumulated variable as soon as you press equal or plus/minus.
Thank you for the Eureka moment. That's why multiplication/division comes first.
In all my years of education and 40+yrs professional experience, that's the first time I've ever heard a justification for the Order of Operations.
All I was ever taught was the Order of Operation and, "When in doubt, USE PARENTHESES!". (🤔)
Thanks for that, Presh! It was a revelation.
I wonder if Ian Miles Cheong was just looking for reactions. He seems like a person who should know better.
People have problems even with just addition and subtraction. The AS in PEMDAS or BODMAS is misunderstood to mean 'Addition before Subtraction' such that people will interpret e.g. 7-3+2 as being the same as 7-(3+2).
The calculator correctly followed order of operations. Multiplication always precedes addition unless mandated by using parentheses.
It's one of the basics that multiplication is done first if there are no parenthesis...
Twitter should have an entry exam before letting people speak. LOL
I saw a calculator that showed this kind of expression converted to *Polish Notation," which is what any compiler or interpreter does. (I had to write one about 50 years ago.)
Store 50 in list of operands, store + in operators, store another 50. Store x operator, store 2. End of expression with lists "+x" operators and 50 50 2 operands. Perform x, store 100 (replace 50 and 2), perform +. This works for any expression using any list of prioritized operators.
I think in these cases using the bracket is the solution to help people who aren't very good at maths understand the expressions.
It would be simpler if we adopted prefix (or postfix) instead of infix.
They are not so readable unfortunately
The problem is that people are told the order of operations but not why it is so. It is not some rule given from above but some to simplify things. It is typical that you for example buy different amounts of different items that each have a different unit price and want to calculate the total. Because multiplication is done before addition one does not need to put every multiplication in brackets.
Four function calculators calculate as you go (some say left to right but that incorrect as there is no concept of left or right in the calculator. The entries are separated by time, not by location). On them you must use the memory function. M+ adds the result to the memory. Mr then gives the total.
The key here is the word "*SCIENTIFIC*".
The Windows calculator will give BOTH results, depending on which MODE it is in.
In STANDARD mode it adheres to "left-to-right*, but in SCIENTIFIC mode it adheres to *order-of-operations*.
*Neither* method is *in-&-of-itself* wrong. It simply depends on what one wants to do. Presh Talwalkar clearly states what the STANDARD mode is typically used for.
So any user *MUST* know the rules of & conventions for BOTH *left-to-right* AND *order-of-operations*. AND, if using a calculator, which mode it is set to.
(I am still searching for a Help-file for the Windows calculator app...)
(PS: My "smart phone" running Android has only the SCIENTIFIC mode, and also NO useful Help-file. But from its 'History' display one can deduce its mode.)
For those that are interested, there is a new book out about the history of the pocket calculator: Empire of the Sum by Keith Houston. Pretty interesting read.
Even without following the mathematical order of operations it should be easy to apply the correct order. 50 + 50 x 2 reads as follows: 50 plus two 50's. That should clarify things a bit. Obviously the answer would be 150.
Please Excuse My Dear Aunt Sally. I wish teachers would teach.
Let all be kind here 😂😂, I know we all know it but give some respect for his honest question. He is willing to learn new things although it should be a basic understanding for others. Knowledge is a bliss to those who have it. I hope he got the answer and learned new things.
6:39 I am not convinced by that as it assumes the conclusion i.e. is circular. Changing the order makes sense only if we take multiplication to be higher precence.
Adults forgot that rule exists called "BODMAS"
@MindYourDecisions Thank you, Presh, for continuing to (implicitly) hammer on the need for teachers who UNDERSTAND what they are supposed to be teaching.
I remember something called “PEDMAS” from another video, so I figured out it was 50x2, and that is 100, 100+50 is 150
Glad I don't have twitter and haven't heard about this thing.
It makes sense for the Android calculator, but not for the Apple one. The fact that it clears the screen after the * implies that it's already calculated the result up to that point using only those first two terms.
The problem is we are taught BODMAS but we aren't given any explanation as to why we should follow it.
A classic case of Dunning-Kruger.
I was not aware that there are actually people who don’t know the order of operations.
50+50*2 = 200 ONLY if you totally ignore the priority of operations and incorrectly proceed left to right. 50+50*2=150 is correct when you do the operation properly : Do the multiplications THEN the additions.
Tbh i can see why people would get this wrong since apple's calculator doesn't show the whole expression so it looks like it's doing 50+50=answer then answer×2=200
I liked the video until Presh wrongly explained what would be wrong with the (commutative and) distributive axioms.
If you change the order of operations, you need to change those axioms as well.
The distributive axiom
a*(b+c) = ab+bc
would become
ab+c = (ab)+(ac)
The commutative axiom would be a bit harder because you cannot include the multiplier, but if we would have learned a different order of operations you would not do that.
People would correctly apply it as
a+bc = b+ac
just as with our current order of operations most of us would correctly flip the order multiplicands (where it is allowed) without including the addend:
ab+c = ba+c
I do agree that our current order of operations (PEMDAS) is the more logical one. I just think of it as prioritizing the most "composed" operations. (Parentheses are composed of whatever is inside of them. Exponentiation can be seen as composed of multiplications e^x = e*e*...*e. Multiplication can be seen as composed of additions a*b=a+a+...+a)
Of course, currently we could substitute:
a*b*c = (a+a+...+a)*c
But with different order of operations we would not need those parentheses:
a*b*c = a+a+...+a*c
Hmm, I'm curious, what would the following expression equal?
e+1-1^0
Addition and subtraction first, so it becomes e^0 which is 1.
Or is it exponentiation first, so it becomes e+1-1, which is e?
Or maybe subtraction first, then exponentiation, then addition: e+0^0, which is either e+1 or e+0
Ah, maths discussions, fun additions to fun times.
I just tried this with the Windows calculator, which you can switch modes between "standard" and "scientific". In standard mode it would give 200 (because it evaluates left-to-right like a 2 dollar calculator would do it) while in scientific mode it would give 150 (because that's how scientists would calculate this).
It's worth noting that the standard mode also shows "100" in the display as soon as you press the "×" key, indicating that it did in fact add 50+50 first, while the scientific mode still displayed "50" after hitting the "×" key (and it showed the entire "50+50×2" thing in a smaller display until the entire calculation is finalized)
I think your Proof with the communative law is wrong. The summands are Not 50 and 50*2 but 50 and 50. You are literally assuming in your Proof, that multiplication comes first.
One ambiguity in the order of operations I personally find is with trigonometry, for instance, seeing something written as:
tan αβ
Just based on the order of operations of trigonometry coming before multiplication, it should be (tan(α)) * (β). However, I was told it really denoted tan(αβ), because the αβ written together implicitly formed a group, equivalent to that of brackets. Which is the correct order?
the standard is usually, if you're not writing the × or • explicitly then scalars go infront of the term. In your case we would expect (tan(α))*(β) to be written as βtanα.
A real annoying issue is when you have multiple functions like tan x√x which can either mean (tan(x))*(√x) or tan(x√x) but it's hopefully clear from context
@@imanharrisidham8971So, tan αβ = tan(αβ), but tan α * β = β tan α = (tan α) * (β), correct?
my old TI-36 gives 150 with no intermediate equals button pushed.
Living in Kuwait 🇰🇼 I have seen a lot of non scientific normal calculators that just operate left to right directly especially in Jewelery shops just to make us pay more ( since here the currency is the costliest of the world )
Like 2 years back, i heard that someone got a jewelery which was supposed to be approx 21 Kwd but the shopkeeper used the calculator in such a way that it showed 25 KwD ....
After hearing that i am sure he used the operation as 1 + 4 × 5 ( meaning he wanted four notes of 5 Kwd and 1 note of 1 Kwd but since it actually calculated addition first he got paid 4 Kwd extra and the customer was said to give *Five* notes of 5 Kwd..... ) This is One of the biggest scams
So pls be aware and improve your calculations more than a Jeweller's or any other shopkeeper's calculator otherwise it may turn out that you are spending more than required.