Good to know I haven't lost any of my math skills after all these years. I was wrong then and I'm wrong now.

@XXXXXX-dy5fs

3 жыл бұрын

This video is wrong. The anwer is 6.

@NeoiconMintNet

3 жыл бұрын

The correct answer is 24. 60÷5(7-5)=12(7-5)=12(2)=24. You are still correct, the other person is wrong.

@CarlMCole

3 жыл бұрын

You weren't wrong, he is.

@NeoiconMintNet

3 жыл бұрын

@@CarlMCole you are wrong, including about your false claim of genius.

@violetultravioletta

3 жыл бұрын

I'll stick to the old way. So 24

This problem is the reason why you should use fractions instead of the "divide"symbol: makes it completely unambiguous. Either the (7-5) is in the lower part of the fraction (denominator in English?), making the answer 6, or the (7-5) is completely outside of the fraction, making the answer 24.

@sinub801

3 жыл бұрын

you would need to write as 60:(5(7-5)) to make the whole thing the lower part of fraction. Otherwise, modern way to calculating will give u 24.

@GermanCarFan22

3 жыл бұрын

agreed entirely. written with a division symbol introduces ambiguity

@soilmanted

3 жыл бұрын

There is no reason you can't switch the position of the 5 and the (7-5). Then you would have 60 in the numerator, and the 7-5 in the denominator. What next you would do is calculate 60 divided by 2, which is 30. Then you would multiply 30 times 5, to get 150.

@frederf3227

3 жыл бұрын

Fractions are not interchangeable with division. 1 vinculum 2 is the fraction one-half 1 solidus 2 is the division 1 divided by 2 You cannot just replace one with the other willy nilly.

@briant7265

3 жыл бұрын

@@sinub801 60 ----------- 5(7-5)

When I entered the formula into Excel I got the message, “there is a problem with this formula.” In order to get Excel to make the calculation, the user must add parentheses to clarify the order of calculation. So yes, the formula as written is ambiguous and the person needs to clarify how the problem should be solved. In other words, don’t leave all of the decision making to a calculator.

@universaldatasupplies5125

4 ай бұрын

there's a difference between how a computer calculator reads and how mathematics is done by hand by a person. When we are writing a division sign by hand, we use the traditional division sign ÷, but for a computer calculator we end up using the /..which can also be interpreted by a computer calculator as a division sign separating the numerator and the denominator..so for this question, it was written as 60 ÷ 5(7-4) which is the correct way to write this question for the answer to be 36. If you want the answer to be 4, it should be written by hand like this: 60 ÷ (5(7-4)). This has always been how mathematicians do math by hand. Using the / sign on computers, laptops, phones is what is causing the confusion. People are so used to seeing the / on digital devices, they think it's creating a fraction and start thinking numerator and denominator.

I asked my father who was an engineer for 45 years and literally helped build parts for the space program and the nuclear programs, and he said the answer is 6. He explained that there are 2 elements. 60 and 5(7-5), these values represent something and are not just numbers. So, there are only 2 expressions. The equation should be 60 / (5(7-5)). This shows how setting an equation up correctly is most important. Given the fact that these guys sent several capsules to the moon and back, I'm going to go with his answer.

@malcolmbrewis5582

9 ай бұрын

I agree with your conclusion. I was taught that Mathematicians, Engineers and Physicists preferred where possible to rewrite an equation without the division ÷ sign to avoid ambiguity. If mathematical conventions are being changed to suit Calculators preferences, surely an honest person would consider that a very dangerous precedent. I am willing to be corrected.

@mattsmith7490

9 ай бұрын

@@malcolmbrewis5582 One other thing I did to test my dad's conclusion was I googled pictures of famous mathematic problems and equations. Secretly I was hoping to prove the old man wrong, lol. But I could not. I could not find a ÷ symbols on any of those blackboards. I took that to mean this issue of confusing how to write an equation had come up before, so to be clear and accurate, they did not use them. It makes since that they would not want to have their proofs interrupted in different ways. The same issue could easily surface in grammar as well by including or omitting punctuation like comma's.

@Gadottinho

8 ай бұрын

In physics I haven't seen a single time the ÷ symbol being used, it's always a fraction, like V=∆s/∆t

@calebfuller4713

7 ай бұрын

Almost anyone who works in STEM or has higher education will give the answer of 6. Japanese calculators also give the answer of 6. Anyone who only did high school, American high school teachers, and newer American calculators, will give the answer of 24. Make of that what you will.

@asdfqwerty14587

7 ай бұрын

The reason I treat the answer as 6 is simple - if I see an equation like "x/2y = 1" then I don't think it should ever be interpreted to actually mean "xy/2 = 1", which is basically the same question. Nobody who ever said an equation like that would mean for it to be interpreted that way (unless they're deliberately trying to trick you), and having rules that make it function differently will only ever make things more convoluted than they need to be for no practical benefit. If you wanted to write 60/5(2) to mean you're dividing by 5, then instead write it the sane way as 60(2)/5 instead.

When using excel, i always “over use parentheses “ to force excel to evaluate exactly what i want. I can’t afford surprises.

@DarkstarAcadia

4 жыл бұрын

I so the same thing.

@Volkbrecht

4 жыл бұрын

When using Excel, all you need to do is be sure of your maths. I know your "parentheses syndrome" because I suffer from it, too. But the truth is that I'm just not good enough at intuitively simplifying fractions, so I force the program to jump through all the hoops I need to be sure I got it right ;)

@Solitaire001

4 жыл бұрын

I see the need to do that too to ensure I get the correct answer. Although it might be a bit more complicated, it is worth to to avoid later headaches.

@johnhamillton6045

3 жыл бұрын

Plug this into Excel =60/5*(7-5) answer =24

@lynskyrd

3 жыл бұрын

ABSOLUTELY agree.

People aren't passionate about mathematics - they're passionate about arguing.

@dlevi67

5 жыл бұрын

I'll dispute that. Passionately.

@maumbu

5 жыл бұрын

Buckhorn Cortez NO, I’m not!

@forevertheaii

5 жыл бұрын

I know I'm passionate about arguing.💗 But I'm always drawn to problems that require solving.

@IStoleYourSandwich

5 жыл бұрын

Passionate about correcting people that i know are incorrect*

@elixiriskindofpotion1319

5 жыл бұрын

I am passionate about truth

The kicker is the "divided by" operator in its presented form. (At school in Germany in the 70s we used : for division). This sign however suggests a fraction with 60 in the numerator and everything that follows the division sign, hence 5(7-5), in the denominator. That would be 6 then. In our school we were encouraged to express divisions in fractions because they are visually easier to resolve when they become large and contain many variables. It seems like the sequential PEMDAS convention is the generally accepted one mainly because of computers.

@Nempo13

10 ай бұрын

That symbol has meant divide from before the 70's. In true math, one does not use fractions...ever. One uses decimals. 1/2 in a math is indicated as 0.5 in order to be absolutely clear. It leads to less problems, and in programming it leads to a lot less problems.

@Cdaragorn

10 ай бұрын

Sorry but nothing about a division sign suggests a fraction at all. It sounds more like you were given a bad suggestion by someone trying to make things seem easier. This is also not a restriction from computers. They could just as easily have been programmed to solve it following the second pattern but they weren't because that has been wrong for more than a century now (predating computers).

@R2BMusicCH

10 ай бұрын

@@Nempo13 What do you mean, no fractions ever? How do you write x/y in decimals?

@R2BMusicCH

10 ай бұрын

@@Cdaragorn That's not true. A division 5÷3 (or 5:3 as we did in my school) can be written as a fraction 5/3 or in words five over three.

@Cdaragorn

10 ай бұрын

@@R2BMusicCH Yes of course you can convert it to a fraction. The fact that you can convert it does not mean it's implied to be that at all. Your original conversion was wrong. The fact that you did it wrong does not mean it was implied that it should be that way. It just means you don't understand how to convert between those representations. A correct conversion would be 60/5*(7-5)

If you trust Texas Instruments' calculators, then the rule changed between 1993 and 1996. My TI-83Plus user's manual (page 1-24) says implied multiplication has the same priority as regular multiplication and division, so 1/2x is evaluated as (1/2)x, *but* the TI-82 gives a higher priority to implied multiplication so 1/2x is evaluated as 1/(2x). According to Wikipedia, the TI-82 was released in 1993 while the TI-83 in 1996. Modern TI-85Plus also has same precedence for implied and explicit multiplications, so they give answer 24. But modern Casio (at least my fx-CG50) work like old TI-82 and gives answer 6.

@markprange2430

4 ай бұрын

Don't key expressions unthinkingly, verbatim. Electronic calculators are not to be trusted that much. That is learned very early. The insertion of brackets is often needed. Rewriting with or without a fractional exponent can be useful. Sometimes, as in 1° 1', a "+" must be inserted to show addition. Juxtaposition can mean different things. 3pi indicates multiplication. 31 indicates the addition (of 3 × 10 plus 1 × 0). An electronic calculator frequently need to be told how to operate.

Seems i was thought the 1917 version. My result was 6 too. Maybe you could do a follow up video on why the modern version is now used. What advantage does that interpretation bring?

@garymartin9777

3 жыл бұрын

In large part because expressions cannot be presented to computers by use of a divide bar that clearly shows what is in the numerator and what is in the denominator thereby showing grouping. Computer languages demand expressions all be in-line and there is no way to group subexpressions other than with explicit use of parenthesis.

@lubanskigornik282

3 жыл бұрын

it is manipulating the mathematics as they do it with everything this days. All depends who is calculating and for whom. If that was you assessed by tax office it would be 24 but if that tax would be calculated for Bill G. it would be 6. - 😏 the sentence when be written as a fraction with 60 on the top and the rest in the bottom and the result is obvious.

@WillieStubbs

3 жыл бұрын

@@lubanskigornik282 And I just know if I buy Bitcoin, somewhere along the line my payout is going to use the New Math and end up dividing my payout by 24 instead of 6.

@aspenrebel

3 жыл бұрын

Correct!! But then I was in school in 1917!!! I think it is used to save space and characters in computer. 5(7-5) uses 1 less character than 5x(7-5). New Math!! You know, 2+2=5.

@stanzofka6114

3 жыл бұрын

Left to right, what a nonsense. The fact there is no multiplication sign between bracket and the 5 is a clear indicator, that this is just one term, that the 5 and the bracket belong together, period. Anything else is sophism. 6 is the solution, period.

24, didn’t even watch the video.

@CaptainMarci104

5 жыл бұрын

I watched the video, just to find out what else answer might be correct. And i laughed so hard as 6 was given as a possible solution. Yeah, with outdated, medieval math, 6 is a solution. But we live in 2018 :D

@IStoleYourSandwich

5 жыл бұрын

Exactly...

@taeghanjo4870

5 жыл бұрын

Same

@krishgupta8596

5 жыл бұрын

IKR same

@nooneeveryone1023

5 жыл бұрын

Same

Although we have modern PEMDAS to adjudicate how to interpret such expressions, this is really an inherent language flaw, as you pointed out mid video. It is rooted in the idea that you can omit the multiplication symbol between and number and an opening parenthesis. If you write it as 60 ÷ 5 * (7 - 5), you still need PEMDAS to interpret it, but it is much less tempting to get it wrong.

@glennwright9747

4 ай бұрын

I am old as dirt. I always distinguished a difference between N*(a-b) and N(a-b) With N(a-b) == (N(a-b))==(N*f(x)) Just my shorthand.

The problem I have with this kind of problem is that it is not really math. It’s grammar. Just write the darn expression in unambiguous way so we can do actual math. We have more interesting concepts to learn in geometry, trig, calculus, etc.

@GanonTEK

10 ай бұрын

100%

@UniversalS757

2 ай бұрын

I wholeheartedly agree

@UniversalS757

2 ай бұрын

@@jakemccoy Yea, I agree.

@jakemccoy

2 ай бұрын

@@UniversalS757 Don’t worry. Math grammar has correct answers too, but math grammar is different than math concepts. I have been an engineer working in the real world for 30 years. Not once have I debated stuff like this on the job. I will just put parentheses in there and keep it moving. This is a discussion that may be fun, but it needs to stay on academia.

@UniversalS757

2 ай бұрын

@@jakemccoy ok

I’m 70, and I’m just thrilled to find out I still remember being taught this! And no, I’m not a math geek. I’m a little old lady who has stayed motivated to keep learning all my life!

@clarkeugene5727

3 жыл бұрын

So true Lynn. We may never need this particular equation in our everyday life, but it's nice to know the method anyway.

@mothermary3200

3 жыл бұрын

Hi Lynn, you and me, both.

@Jake-by9ly

3 жыл бұрын

I'm 66 and went to one of top 20 High Schools and the then top Accounting and business University in the nation. The answer is 6.

@Cuzzzo

3 жыл бұрын

You are awesome!!!

@cynthiastogden7000

3 жыл бұрын

Ditto. Great isn't it!

Order of operations is just a way to guess at what to do when someone writes an expression poorly. Be clear when you write.

@russelltan161

2 жыл бұрын

Correct is you/ gob jood

@frocat5163

2 жыл бұрын

Exactly. The whole reason we're taught order of operations is in case some jackass writes an expression like the one in the video. It's amazing to me how many people are so bent on disagreeing about it.

@martinfidel7086

2 жыл бұрын

@@frocat5163 ok I understand what you are saying but the cornerstone to my math is BODMAS, how else can you do it ?

@GanonTEK

2 жыл бұрын

If an expression is badly written the order of operations can't fix it. How could it? The question needs to be written properly by the person who wrote it. That's the only way the ambiguity can be resolved. It's like writing Sin60/2. It's terrible notation and is ambiguous as a result. No order of operations will fix this. Only appropriate brackets will. E.g. Sin(60/2) or (Sin60)/2 The order of operations is a tool to simplify and cannot fix anything.

@thirdyearronin

2 жыл бұрын

PEMDAS itself is a poorly taught and explained acronym... M does not come before D and A does not come before S.. M is equal to D and A is equal to S, so you calculate them from left to right in the order they appear.. PEMDAS should be taught as P, E, M or D, A or S

Part of the issue is whether one considers the number parked outside the parentheses to be a common factor of the terms within the parentheses, or just another number in the sequence. I was taught that the number just outside the parentheses (in this case 5) is a part of the terms inside the parentheses ((a-b), with in this case a=7, b=5) unless separated by a multiplication sign. So (5a-5b) is the same as 5(a-b), but not the same as 5*(a-b). This would lead to a result of 6, which I would consider to be the proper result. Also, look at the division sign itself. The top dot is the stuff to the left, the bottom dot is the stuff to the right. Which would also yield 6. I learned back in the 1980s and 90s that you have to interpret equations for computers and calculators to get the proper results. So I would input the above equation as =60/(5(7-5)) when using a calculator or computer. Which would again yield 6.

@Cdaragorn

10 ай бұрын

It's honestly feeling like a bunch of people were the subject of teachers trying bad ideas in an attempt to make things easier. That's not what "common factor" means at all. And as someone has already pointed out having the * explicitly changes absolutely nothing. It wouldn't make sense to have it change anything.

@trickortrump3292

10 ай бұрын

“So I would input the above equation as 60/[5(7-5)].” You completely changed the equation the way you wrote it. You can’t just add an extra set of brackets in the middle of the equation. Had it been presented in that form, then yes, the answer would be 6. People are getting confused with what “brackets first” actually means. They think if they see brackets, that means everything touching the brackets gets done first. Brackets first means you solve the inside of the brackets first. Once you do that, the brackets part is done. 5(2) is 5X2 is 5*2. It doesn’t matter what form you use, they’re all the same thing. Since it’s now just a straight up multiplication and division equation because the brackets have been solved, you move from left to right. And the above commenter is correct that 5(a-b) is the exact same thing as 5*(a-b) is the exact same thing as 5a-5b. If a=4 and b=2 5(4-2)= 5(2) 5(2)=10 Also 5*4-5*2=20-10 20-10=10

@matthewwahl3058

10 ай бұрын

I put this in a calculator on a computer and it came out 24 so you're wrong

@mohasat01

10 ай бұрын

Kudos! The expression on the RHS must be evaluated first before the division. What the RHS says is that there is a common factor of 5 and so the full expression on the RHS is 5(7-5) = 35-25 =10. And so the answer is 6. I don't care what Google says!

@Cdaragorn

10 ай бұрын

​@@mohasat01 You also don't care how math works. That's not what a common factor is. And even if it were common factors is just an interesting fact of the numbers and has nothing to do with how or when you evaluate them. Per order of operations 60 / 5 must be evaluated before 5 * (7-5) because multiplication and division are to be evaluated left to right.

All of these type example are due to someone writing mathematical statements in the most confusing way; in REAL mathematics, physics and computer programming we choose the write mathematical statements so as to prevent confusion. These example-makers lift a few excerpts from journal (or written text) articles where one is forced to use only a single line of text space; however most likely elsewhere equations are presented in an correct format.

I was helping my 13 year old with his math homework 15 years ago and learned something that I was never taught in school. Not even in College. "Please Excuse My Dear Aunt Sally".

@waynebennett7839

3 жыл бұрын

My 7th grade math teacher used her name in it: "Pretty Please, Mrs. Dovers Always Says".

@aligator7181

3 жыл бұрын

try to apply it to : 3*47-1/4398473+10-8/33 without parenthesis

@Chris_5318

3 жыл бұрын

@@aligator7181 That's (3*47)-(1/4398473)+(10)-(8/33) = 150 + (25/33) = 150.7575757575 . . . Most/all decent calculators will get that without using ( )s

@haroldprice1030

3 жыл бұрын

@@Chris_5318 Yes, but the trick is to get the order right. I have never used an expensive scientific calculator, I am assuming they probably sort out the order automatically?

@Chris_5318

3 жыл бұрын

@@haroldprice1030 Different, but almost identical, models from the same manufacture can give 6 or 24. The correct answer is the one found by using the same convention that the author used. We have not bee given tha info. However, the author would have to be crazy if he was expecting anyone to get 24.

If I owe you, my calculation is 6. If you owe me my calculation is 24.

@thetruth3828

3 жыл бұрын

Yeah its 6. Isnt it?? I dont want to watch the whole thing. It should be 6.

@onlythetruth883

3 жыл бұрын

@@thetruth3828 Must be a quadratic, because the claim is, if you are old school it's 6. But if you are new school it's 24. Don't know how it can be either or either, as there must be an intended definite outcome.

@patscott6365

3 жыл бұрын

Good answer! Ha ha!

@waynebrehaut7183

3 жыл бұрын

@@onlythetruth883 You clearly don't know what a quadratic is--but without knowing what you're doing or saying you've accidentally hit on the problem with many of the arguments in this thread: the given task is to evaluate a simple ARITHMETIC EXPRESSION using the generally-accepted rules for doing that. Attempting to translate it to an ALGEBRAIC EXPRESSION and applying rules useful there, then translati9ng back to do the arithmetic, does not work. If it involves just numbers and arithmetic operators and brackets, so one could evaluate it on a calculator or calculator app, then use the usual rules for evaluating arithmetic expressions and don't try to remember your high-school algebra and misuse that very foggy recollection to confuse yourself and others.

@onlythetruth883

3 жыл бұрын

@@waynebrehaut7183 Of course I was being sarcastic when I said must be a quadratic. And you did get the point-->. There is no point until the rules are firmly established.

The correct ways to phrase the questions (depending on what you want to ask) would be: 60/[5(7-5)] for which the answer is 6. Or (60/5)(7-5) for which the answer is 24. The question as originally phrased makes no sense. The division sign is never used beyond grade school nowadays (it is not there even in a computer keyboard), but it was there in the question but without the multiplication sign. It was not only confusing but sloppy. One set of parentheses would have eliminated all ambiguity. Assuming the question was originally an algebra question for which you then substitute in the actual numbers, then "6" as the answer actually makes more sense.

@DS-lp5xt

29 күн бұрын

the division symbol is above the "8" on the numerical side of my computer keyboard... I do however agree

When was PEMDAS implemented in Mathematics? Would the result not be; 60 divided by the result of everything following the division sign, meaning 6 would be the answer?

I remember being taught that parenthesis was calculated first, multiplication came next, then division, then addition & lastly subtraction. This gave me 6.

@scottreed991

3 жыл бұрын

I graduated from high school in 1987 and that's the way I was taught. The answer would be 6. Peace.

@mk_rexx

3 жыл бұрын

That's what they taught for most in our country's basic education too, literal PEMDAS in strict order (as the letters). Only in college that both math and computer science professors agree on the real correct method. I'm mildly infuriated that they always teach children outdated or plainly wrong things like this (the four taste regions also comes to mind, so wrong)

@davidevans8858

3 жыл бұрын

BODMAS????

@jerigeldenhuys7859

3 жыл бұрын

@@davidevans8858 B-Braces/Brackets, O-Orders

@curtmacquarrie

3 жыл бұрын

@@mk_rexx well, pemdas (or pedmas as I know it) isnt wrong though. But the order of division or multiplication doesnt matter, and the order of addition and subtraction doesnt matter, as in both cases they are effectively the same operation. So everything in brackets first. Then all multiplication and division. Then all addition and subtraction.

Based on the education I received in the USSR in the 1980's the answer is 6.

@themotivator373

3 жыл бұрын

I guess we now know why your economy and government crumbled when someone over there found MTV.

@kurtfrancis4621

3 жыл бұрын

Your teaching was correct and equivalent to the teaching in the US in the 1970s, which is when I did my primary education.

@Borvo1

3 жыл бұрын

Yes, and 6 is the correct answer worldwide. Let me summarize the positions as I see them: > for folks who are followers of the PEMDAS philosophy and believe such things as x/3x is equal to x squared divided by 3 the answer is 24. > for folks like me who believe that PEMDAS is BS and screwing up the teaching of math in America and believe in such things as x/3x = 1/3 the answer is 6. Now I do recognize that this is America and one is free to choose, but from my viewpoint it does appear that the PEMDAS philosophy falls into the category of metaphysics; - - - you know, that abstract theory with no basis in reality.

@JerryDLux

3 жыл бұрын

@@Borvo1 its A/BC = AB/C? True or False?

So when you say "modern" what time frame does this refer to? I feel like I was taught the left-by-right order, so I'm wondering when this changed. I'm not that old, so I can't figure out if I was taught incorrectly or has it changed since I was in school?

@MrGreensweightHist

9 ай бұрын

Left to right is correct. This rule is over 500 years old. Three is a myth it was different in the "old days" This myth is spread by people who learned it wrong, but assume everyone in their generation was learning it the same way they did

So how do you work around the fact 5(7-5)=5x7-5x5?

My Sharp EL-520W gives an answer of 6 for the expression "60÷5(7-5)", while it gives an answer of 24 for the expression "60÷5×(7-5)". This is also the way I was taught it in school. Implied multiplication with no operation symbol as in expressions like "xy or 3(5)" takes precedence over division indicated by the ÷ sign, while multiplication indicated with a × symbol has the same precedence as ÷, evaluated left to right. I didn't even realize this was controversial till I saw this mentioned in some of your videos. When did this other convention become popular?

@chinareds54

5 жыл бұрын

Exactly. No one in their right mind would evaluate 1/xy as y/x.

@rmsgrey

5 жыл бұрын

I'm not sure it's the convention becoming popular so much as a simplified set of rules being widely taught in some places.

@zeldajerk

5 жыл бұрын

Goodness, you're right. The syntax changes depending on whether you use / or ÷

@isyourdady7549

5 жыл бұрын

Same. My first answer is 6 cause the first thing I do is multiple 5*(7-5) wich is be come (35-25) and decrease the number at parenthesis, so it will be 60÷10 and is 6. Sorry for my bad grammar...

@angelaflierman

5 жыл бұрын

Same for me on Sharp EL-531W

Math and CS teacher here. I think everyone misses the most important part here: spacing. A common practice in CS is to use spaces to display precedence, so for example you would write a*b + c*d. It helps readability and can be really usefull for less known operators precedences like and/or. And also not all languages follow the exact same precedence rules, especially for bitwise operators. So in the ambiguous expression shown here, the modern precedence rules would give 24 but the spacing indicates that it's actually 6. For the same reason, when I see 1 / 2x, I tend to understand it as 1 / (2x).

@ChespiritoChavo322

2 жыл бұрын

you can add all the spaces you want. The result is still 24.. 60 / 5 (7-5) = 60 * 1/5 * (7-5)

@pierreardouin6441

2 жыл бұрын

@@ChespiritoChavo322 There's no "the result is ...", it's all about conventions. Don't take conventions as rules written in marble, they change over time, they change from a country to another, from a book to another, from a calculator to another, etc. We don't know the context of this expression, maybe it's from an old book for example, so we cannot know for sure that modern precedence rules apply. But the spacing clearly shows the intention, and that's something we can rely on.

@ChespiritoChavo322

2 жыл бұрын

@@pierreardouin6441 i didn't follow any rule. Just used the formal definition of division.

@GanonTEK

2 жыл бұрын

@@ChespiritoChavo322 There is no agreed upon convention on whether multiplication by juxtaposition implies grouping or not. That's what's causing the different answers. Division is used in either case.

@Kirke182

2 жыл бұрын

Why in the hell would you put parentheses around 2x when it did not have parentheses to begin with???? Spacing or no spacing, the answer is 24.

As a computer scientist I have worked quite some times with machine interpretation of such expressions. Therefore I can see both sides, since the rules I often implement are modifiable - and in more abstract math, the operators are defineable almost as you please. However, left-to-right associativity on same precedence operators (multiplication and division above addition and subtraction) is probably seen as the norm.

@Cdaragorn

10 ай бұрын

It's not just a norm. It's the strict rule. If it wasn't it would literally be impossible write mathematical equations because you couldn't guarantee everyone would get the same answers out of them.

@MrGreensweightHist

9 ай бұрын

If the computer is not doing left-to-right associativity on same precedence operators, then the computer is programmed wrong.

@xian8531

9 ай бұрын

@@MrGreensweightHist Then all programming languages (100+) I know of are wrong... My guess is that those guys having made the programming languages actually studied precedence rules a bit.

@MrGreensweightHist

9 ай бұрын

@@xian8531 "Then all programming languages (100+) I know of are wrong" Or you don't understand them as well as you think.

@harrymatabal8448

6 ай бұрын

60÷5(2). Why so much of fuss. Some are multiply 2and 5. They don't seem to understand it is 60×2÷5. My simple method is 60×1/5 ×2. I am not a mathematician or a rocket scientist but I am merely applying mathematical rules. Whichever way you look at the answer is 24. If that's not simple then stop the world rotating for 1 sec so that I can jump of

As written, for me, the correct answer is 6 because there is no "x" between 5 and (7-5). To get 24, it should be written 60÷5x(7-5).

@NightfallShadow

27 күн бұрын

as written the answer is 24. Left to right. Once you complete one calculation you start from the beginning every single time. It doesn't matter what the Order of operations are. The moment you start left to right and run out of P, you start from the beginning again and go right until you no longer have E and then treat M and D as well as A and S as the same regardless of what order they are in.

÷ is terrible notation

@timoriusmaximus

5 жыл бұрын

True. I learned in 5th class to use fractions and no terrible Division Symbol ...

@blue_tetris

5 жыл бұрын

And no one genuine has used the obelus symbol in the same expression as parenthetical multiplication. It just isn't done, except during these social media "math experiments" that offer no insight into how mathematics works. If anything, these problems just confuse math students (particularly young or inexperienced ones) trying to figure out order-of-operations rules in a realistic setting.

@Poldovico

5 жыл бұрын

inline division signs deserve a painful death.

@blue_tetris

5 жыл бұрын

Not to mention that the ISO for mathematical notation has (for quite some time) said that the obelus should never be used for division. Math classes and mathematical exercises are not supposed to use the symbol, so teaching it is only a way to confuse younger students.

@jimmyjohn8008

5 жыл бұрын

So ÷ =! /... plus I hated it because it sometimes looks like a minus sign if your dots are too small or a plus sign if your dots are too big

This shows that I am getting old, I came up with the answer of 6

@RS-fg5mf

3 жыл бұрын

One can get forgetful with age but plenty of young people fail to get the correct answer as well. The correct answer is 24

@RS-fg5mf

3 жыл бұрын

@Michael Stocker WRONG. There is absolutely nothing wrong with this expression except for the ignorance people have about parenthetical implicit multiplication.... The only correct answer when you actually understand and apply the Order of Operations and the various properties and axioms of math correctly is 24

@ronhan9

3 жыл бұрын

sorry for not knowing all the correct english terms So do I the paranthesis is broken down for easy of handeling and shopuld be multiplied as it stated 5(7-5) -> (35-25), of the five should be diveded down to a 1 by devidind all groups by 5 to clear it out (60 / 5(7-4) -> (60/5)/((5(7-5))/5 ---> 12/(1(7-5) --.> 12/(2) The 5(7-5) is a part of the paranthese operations and even in pedmas paranthese has priority

@Slw1111

3 жыл бұрын

@@RS-fg5mf This has nothing to do with being forgetful and everything to do with what method an individual is taught on precedence.

@RS-fg5mf

3 жыл бұрын

@@ronhan9 Wrong... 60/5(7-5) does NOT equal 60/(35-25) Easy handling is to simplify what is inside the parentheses. 5(2) is not a parenthetical priority and is exactly the same as 5×2... The TERM 60/5 is to be multiplied by the value of the parentheses 2 and the only correct answer is 24

Just curious why does the linear equation proof work if math is read like this, another way you can interpret 6 is if you 60 ÷ 5(7-5) 60 ÷ (35 - 25) 60 ÷ 10 6 Why does the proof for linear equation allow it to work if it is an exponent in the parentheses but not the case if there is no number in the parentheses?

@ArchimedesTheLegend

7 ай бұрын

You're assuming that the 5 is part of the brackets. This is the most common definition when doing higher level maths, but some consider it incorrect. If you don't consider the 5 as part of the brackets, than you need to remember that the division only belongs to the 5. So you could rewrite is as: 60*1/5*(7-5) =60*(7/5-1) =12*7-60 =24 If you consider the 5 as part of the bracket, you'll get: 60*1/(5(7-5)) =60*1/10 =6

When I enter this equation into the iOS calculator (in scientific mode, with parenthesis and ÷) I get 30 and I can’t find a reason for that! When and why did the 1917 historical usage of PEMDAS/BODMAS change?

Ok, I figured out.the equation… It’s (9min video)+(wrong answer)+(huge comments engagement)+(3,000,000 views) = $6000

@grape512

3 жыл бұрын

You have the winning answer

@supplanterjim

3 жыл бұрын

The guy even _said_ at the beginning of the video why he was making it. Cha-ching!

@sandragrant327

3 жыл бұрын

Good for him and I am glad that he is uncovering something that is making us say 🤔

@audiomaker1

3 жыл бұрын

@@sandragrant327 I agree, it’s quite an undertaking to make math controversial

@BradleyStBonnett

3 жыл бұрын

Yep, telling people that 5(2) is (5+5) .. first order operation or 5(2) is a scalar .. second order operation, wouldn't have given him my 2 cents.

Why would you use a calculator as the way to measure what interpretation to use. A calculator is just a computer and a computer only does what a human programmed it to do.

@terrythompson9091

3 жыл бұрын

Read my comment above....I think you will agree with me...

@L8rCloud

3 жыл бұрын

Because a calculator follows rules laid out by its human programmers instead of the unqualified presumptions of youtubers

@lizoliver4407

3 жыл бұрын

Why would you use a calculator for such a simple task? However when my daughter was 13 in 1989 I bought 13 candles at the local stationery shop. I gave the girl 13pence but she said I'd better check its correct & rang up 1penny 13 times. No it was an old till not computerised connected to stock control. She then said "Yes you are right 13 pence" & put out her hand for the money.

@Boogaboioringale

3 жыл бұрын

We couldn’t even use calculators in high school (they weren’t available in grade school) in an effort to prevent the inevitable, the DDOA (the dumbing down of America).

@workless4681

3 жыл бұрын

but computers are programmed to do math same way as us...7-5=2. 60/5=12. 12/2=6. In that order.

I’m not sure if I did it correctly, but on iPhone calculator 60:5(7-5) in exact order came up with 30. ??? Anybody can explain to me? Thanx

@GanonTEK

10 ай бұрын

It probably can't handle implicit notation or something. Like that. Looks like it just did 5×7-5 = 35-5 = 30. If you type 8:2(2+2) instead does it give 6?

As per pemdas rule bracket is to be removed before division so 5 (2) is done first to make it 10 and then 60 /10= 6, please explain

I was taught In school to do it the “historical way” because it’s still in parentheses so you multiply it first

@kevinsanderson4112

4 жыл бұрын

vikpun XD thats not how it works. You do whats IN the parenthese first not mulitplying or dividing the parenthesis

@jmanwild87

4 жыл бұрын

@@kevinsanderson4112 as written i would think the 5 was factored out 60/((5× 7) -(5×5))i know some teachers who teach it this way and my calc class was like that so my immediate thought was 60/10 =6

@kayiufong6290

4 жыл бұрын

@@jmanwild87 Your expression correct and that is the way I learn maths. How 24 become the unambiguous answer.

@user-uc6zg5oj3g

4 жыл бұрын

right????

@Edward4187

4 жыл бұрын

I also came to the historical way, although I think part of it for me was how I viewed the question. I saw it similar to 60/5x where x is (7-5) being 2.

You said : The "MODERN" interpretation. A lot of people, including myself, have been taught the one that gives 6 for result. I love math and was always at the top of my class. 24 would never have been the answer.

@GrumpyGrebo

3 жыл бұрын

6 is absolutely the correct answer. 24 is result of a different equation. The video is wrong.

@mercurywoodrose

3 жыл бұрын

i think my math training also results in 6. so we just changed the definitions. no right or wrong.

@rosemarylutcavage9629

3 жыл бұрын

ABSOLUTELY......me too !!!

@GrumpyGrebo

3 жыл бұрын

The issue is that the video author doesn't understand BODMAS correctly... "brackets" means you grab the brackets first and solve them themselves using BODMAS. So 60/5(7-5) the bracketed term is 5(7-5) which expands to 35-25 which makes 10. 60/10 = 6. Now, if you add a multiplication sign then it changes the precedence because you are actually changing the equation significantly. 5 * (7-5) the bracketed term becomes only (7-5) which is of course 2. A deliberate nuance used to create a video I think. Fair play.

@bagman817

3 жыл бұрын

You were taught incorrectly.

One way that was taught to calculate expressions like 5(7-5) is to multiply the value outside of the parentheses by each of the values within. If it were an algebraic expression like 5(a-7), no one would argue that it work out to (5a-25). Right? So, 5(7-5) turns into (35-25). Still within parentheses. That then calculates to 10. Then the rest of it becomes 60 divided by 10 which equals 6.

@THall-vi8cp

10 ай бұрын

Depends. Some people apply the idea that there is implied multiplication or multiplication by juxtaposition. That would result in the solution being 6. Others do what you did, which is called the Distributive Property, and that also gives 6. I find PEMDAS/BODMAS counterintuitive. For example, parentheses are a grouping symbol, and multiplication is often explained as "X groups of Y". From that angle, if we apply the problem to something real, such as money, we see the issue. $60 divided among 5 groups of 2 people (because 7-5=2). How much money does each person receive? Not $24.

@MrGreensweightHist

9 ай бұрын

" If it were an algebraic expression like 5(a-7), no one would argue that it work out to (5a-25). Right? " Correct, but it isn't 5(a-7) It is more like 60/5(a-7) Which is 12(a-7) And works out to 12a-84 Though keeping with the original problem you should have used 60/5(7-a) instead of reversing the minuend and the subtrahend 7-5 and 5-7 are two very different things. So 60/5(7-a) 12(7-a) 84-12a For the actual equivalent of 60/5(7-5)

Looking at the bigger picture, how does this works in practice where a correct answer is required or is it purely theoretical?

"Why would they change Math?? Math is Math!!!" Well said Bob/Mr. Incredible , well said

@sbeckstead

3 жыл бұрын

Math did not change in this case. Writing and glyph interpretation changed.

@gregpeterson7946

3 жыл бұрын

Oh Contraire, math must now be expected to include critical race theory.

@chriba6815

3 жыл бұрын

Math developed from the human ability to conceptualize, there is no inherent law of nature behind math.

@yvonnekeegan573

3 жыл бұрын

I read a while ago that it was 4% of Mathematicians who use it this way. The rest of the population didn't. Probably someone in a wee office somewhere decided.

@newinformation1942

3 жыл бұрын

Not in "1984"... "He" is "she" and "She" is "He"... or whatever they say it is...

I was always taught that anything that touches the parentheses / brackets was next after evaluating what was inside the parentheses/ brackets.

@raymondtan2415

4 жыл бұрын

That's how I was taught to calculate too and I absolutely stand by it even if the rocket crashes. :-P

@starlordz6111

4 жыл бұрын

Anything touching them simply implies multiplication if they wanted it to be the 5*2 first then they should have done this 60*(5(7-5))

@davemiller6055

3 жыл бұрын

@@starlordz6111 True.

@starlordz6111

3 жыл бұрын

@Chris Travers when I typed it into my ti-83 I got 24. And that was after I solved it without a calculator. Anything touching but not in parenthesis only means multiplication nothing else.

@douggwyn9656

3 жыл бұрын

In "60 ÷ 5(2)", the bracket "(2)" has higher precedence than " ÷ ".

See, if you tried this in Desmos for example which you input division as fraction as they should be, then you will receive an answer of 6 since division has a grouping element of its own

What will answer it is a real life practical application. Which one keeps a bridge standing, so to speak. Can you decide it witha physical model?

That's why we use fractions instead of the division symbol

@PowerIsReal

5 жыл бұрын

I agree. It completely avoids the issue

@neverforgettodofacepulls782

5 жыл бұрын

That division symbol is called an obelus. Just fyi.

@Ok-th2gd

5 жыл бұрын

? Thats division still.

@bleach4038

5 жыл бұрын

@@Ok-th2gd of course it's division, but using the fraction instead of the obelus it eliminates confusion like from this problem

@futuriser367

5 жыл бұрын

@@Ok-th2gd 60÷5(7-5) can be changed to 60/5(7-5). From that 60 is the numerator and 5(7-5) is the denominator. 5(7-5) becomes 5(2) = 10 so 60/5(7-5) changes to 60/10 which is 6.

I got 6, whenever I see a ➗ I automatically turn that in a fraction /. So I simplify the top and the bottom independently before finishing the division.

@RS-fg5mf

3 жыл бұрын

You failed to turn it into the correct fraction. 60 -------(7-5) ÷ 60÷5(7-5)= 24 5 60 ---------- = 60÷(5(7-5))= 6 5(7-5)

@KrogTharr

3 жыл бұрын

@@RS-fg5mf that was exactly what I did! Thank you for explaining!

@RS-fg5mf

3 жыл бұрын

@@KrogTharr so you understand now that the correct answer is 24, right?

@grigturcescu6190

3 жыл бұрын

and that's why you never use ➗ after the 4 grade... except when you want to make a semi trap video. Math is supposed to be clear, not interpreted. If you would have seen the correct fraction you whould have given the correct answer. It's not a matter of age, they just made this purposefully confusing. You won't find an engineer use this kind of writing.

@RS-fg5mf

3 жыл бұрын

@@grigturcescu6190 what this demonstrates is that people can't follow a few simple rules and that they need to be hand held all the way to the correct answer... When you actually understand and apply the Order of Operations and the various properties and axioms of math you get the ONLY correct answer 9 It doesn't help that on average 70% of adults incorrectly believe that 5+2×10=70.... You have people under educated who fail to understand the Order of Operations AND yoy have people who are over educated and try to make more out of a basic 4th grade arithmetic expression than it is...

I had a question about the order. In your example you said apply PEDMAS to solve so (7-2) would be solved first. Once that is done wouldnt the problem look like this? 60/5(2)? Why do you ignore the parenthesis that is still there? I am super curious. My answer was 6 because I assumed you needed to solve all parenthesis first before moving on.

@MrGreensweightHist

9 ай бұрын

"Why do you ignore the parenthesis that is still there? " In absence of another operator () simply count as * You can go.... 60/5(7-5) 60/5(2) and just remember the () are multiplication. or you can change 60/5(2) to 60/5*2 if leaving them there bothers you. Once everything INSIDE the () are done, they are no longer needed.

@garrettguitar

3 ай бұрын

You're somewhat correct although not for the reason you cited. In advanced math, any term where the operator is omitted is a singular term (e.g. 2x is singular, 5(x-y) is singular). In this case, 5(7-5) is singular and must be calculated first because of the parenthesis. Now, had it been written as: 5 x (7-5), it would be two separate terms where only the (7-5) would be calculated first, and then everything else is calculated from left to right.

The left to right for same precedence is the most common thing people forget about or don't know with order of operations.

Now we understand why Mr. Incredible was so frustrated in the Incredibles 2 “Math is math!”

@9crutnacker985

3 жыл бұрын

No. Math is Maths.

@jasonsturm893

3 жыл бұрын

I think that was a joke about common core math.

The expression typed into my Casio calculator exactly as shown returns the result 6. Which is exactly what I calculated as I was always taught that if there was no operator between a number and an expression in parentheses, then they were linked and to be calculated together. I.e. 5(7-5) = 10

@Harmonic14

3 жыл бұрын

Old Casio calculators do not handle the order of operations correctly.

@matts1166

3 жыл бұрын

@@Harmonic14 My TI-85 also states 6. I was always of the school of thought that when in doubt, use more parenthesis.

@timburke4837

3 жыл бұрын

Exactly so. And his sentence is not ambiguous. The verb saw separates the subject (I) from the direct object (man) and any modifiers of the object (binoculars). So if you wanted to say you saw the man by using binoculars, the binoculars would have to modify the verb saw.

@wacholder5690

3 жыл бұрын

So did I. And it confirmed my "old fashioned way" to interpret that unclear calculation. It is from 1981.

@richardpaulhall

3 жыл бұрын

@@wacholder5690 The order of operations has the answer 24.

Why would there be a special rule for division but not addition or subtraction or multiplication?

So is this BODMAS rule universal or just like one of those metric vs imperial things?

Scientific calculators (Casio & Sharp) give answer *6.* The rest answer 24. Pick your side.

@RS-fg5mf

5 жыл бұрын

And even half of Casio calculators give the correct answer 24

@rrsharizam

5 жыл бұрын

@@RS-fg5mf I test it on fx-570EX What do you use?

@RS-fg5mf

5 жыл бұрын

@@rrsharizam I don't use a CASIO calculator I use Wolfram Alpha a math engine and I dbl check with Mathway another math engine and if the two don't agree I find out why. But for basic arithmetic I only use them to validate my answer not to give me the answer... CASIO fx-82es will give 24 CASIO fx-570es will give 24 CASIO fx-50fh will give 24 CASIO fx-991es will give 24 CASIO fx-570ms will give 24 My response to anyone who says the answer is 6 is to evaluate 60a(7-5)=24......a =? Well a= 0.2 or 1/5 and the divisional reciprocal of 60*(1/5) is 60÷5 Soooo 60*(1/5)(7-5)=60÷5(7-5)=24

@rrsharizam

5 жыл бұрын

@@RS-fg5mf "will give" ??? So, you don't even use Casio, yet you say it will answer 24? I don't care whether the answer is 6 or 24. I just wanna say that Casio & Sharp answer 6. That's all

@RS-fg5mf

5 жыл бұрын

@@rrsharizam I have a pic of these model CASIOS giving the answet 9 to the expression 6÷2(1+2) So if it will give 9 to that expression it will give 24 to this expression....

This is interesting and the reason for the change is that in the old interpretation the division symbol was actually a fraction symbol. The point above the bar represented all of the equation to the left and the point below the bar represented all of the equation to the right. Now however the division symbol is simply that, a symbol to divide the order of operations to the left by the order of operations to the right. It's somewhat akin to English changing from archaic to modern English. The meaning of words has changed and if you keep up with the current meaning, you will understand what is being said. For example, If I said, your room is in shambles. Currently that would mean your room is a mess, however it would have meant that your room is in a meat market. What fun.

@RS-fg5mf

2 жыл бұрын

Prior to 1917 SOME text book printing companies pushed the use of the obelus in a manner similar to the vinculum because the vinculum took up too much vertical page space, was difficult to type set and more costly to print with the printing methods at that time. However, this was in direct conflict with the Order of Operations and the various properties and axioms of math that were established in the early 1600's when Algebraic notation was being developed in order to eliminate ambiguity and to minimize the unnecessary and excessive use of parentheses. So the ERROR was corrected post 1917... This was an ERROR brought about by the text book printing industry in regards to the misuse of the obelus. This is not why most people evaluate this expression incorrectly. They get the wrong answer 6 because they incorrectly believe that parenthetical implicit multiplication has priority over division.

@SmashingCapital

2 жыл бұрын

Im not sure if y'all do it too but here in italy we use : without the fraction symbol

@BeerIndependence4All

2 жыл бұрын

I'm 59 years old, for what it's worth. I was taught the fractional representation method in school and it still makes sense to me. Draw a line and solve for the numerator, then the denominator, then divide. That is how it was done then. If it is incorrect then how did we ever get to the Moon? LOL

@SmashingCapital

2 жыл бұрын

@@BeerIndependence4All fractions and divisions are 2 different things

@jamesrobbins26

2 жыл бұрын

@@SmashingCapital how?

5(2) counts the same as (2) ex x. the modern method generates 60/5x1(7-5) . the main problem with the modern method is the improper disposing of (). as soon as you make it 5x1() your disposing it the same as 5() without changing the number inside. no matter what () must be removed before proceeding even if exponents or multiplication takes place. this was know as completing operations between signs in the 90's. an example would be 2 x abc= vs. 2 x a x b x c . abc is a complete expression of 1 number to mutipply 2 by. no it may turn out a shortcut is it's all multiplied together so order doesn't mean much. but only if the shortcut doesn't ater the answer. in this case the shortcut 5x1(2) alters the correct answer so you have to follow the 5(2) = 10. since rewriteing 5(2) as 5x1(2) allows the interpation 60/5 x2 this is a basic half step to proper order of exponents and such. probably one of the most disturbing parts of teaching maths in a system

But why? What about the process that was used to get 24 proves that it the correct way? I got 24 but I want to understand why.

@chonzen1764

10 ай бұрын

Calculators he says. Prior to the early 1990s all calculators would have said 6. When the TI-82 showed up math teachers couldn't explain to their students why 60/5(7-4) = 6 and 60/ 5X(7-4) = 24 on TI-82s. Teachers complained to TI and TI agreed to do it incorreclty because there were far more high school kids and teachers than STEM professionals.

I prefer the ”special rule” version from 1917 I like writing my division as a fraction. That way there is no doubt as to what is numerator and denominator. The special rule seems to follow this process.

@KeitelDOG

4 жыл бұрын

I you use Google KZread to post this then you should stick to Google way of evaluating math expression. Google is the best guide.

@arttukettunen5757

4 жыл бұрын

You can just write it as a fraction and not division

@chengshengway

4 жыл бұрын

i dont get why the separate division and fraction, isn't 1 over 2 0.5? Isn't 1 divided by 2 0.5? Then why are they so FKN different when they are the SAME?!

@tianyilu3373

4 жыл бұрын

true, that's why don't use parentheses for multiplication in these situations, use * or the dot instead

@kmbbmj5857

4 жыл бұрын

@Anika Anjum That's why writing everything on a single line is ambiguous. The school I was taught is the division is a grouping operator so that everything to the right of it comes under the operator IE in the denominator. You were taught in a different school of thought. These different schools of thought are why equations need to be clearly written out.

I've used HP calculators with Reverse Polish notation from the start when they hit the market! In that system you start calculating the content of parenthesis and then go outward. With this logic, the result is definitely 6. During the whole time of my physics studies (that means dozens of textbooks in physics and applied mathematics), I haven't found a single case being confronted with any ambiguity of a mathematical term!!! If someone gives me such an ambiguous expression to calculate, I simply refuse to calculate! I will tell him to study mathematical semantics first! (This has already happened)

@nickg8424

3 жыл бұрын

yeah, but our text books were kick ass. notated,indexed and bibliographied with special symbols etc.

@harlancarraher3526

2 жыл бұрын

RPN rules! The answer for us is 6.

@brucebarber4104

2 жыл бұрын

I memorized times tables in the mid 60's; PEMDAS wasn't a thing when I went to school; I never took physics or calculus, only went as far as trig; the answer I got is 6.

@my3dviews

2 жыл бұрын

I went to school in the 70s and 80s. Was always taught the method that gives the answer 6.

@frankwijnans444

2 жыл бұрын

According to this 12x÷6x = 2x² You don't see that often... (I would go for the ambiguous)

I used to do it the old way but I kept getting it wrong. Thank you for this.

PEMDAS- order of operations, parentheses first, than exponents, than multiplication or division, lastly add or subtract. Still remember that acronym from elementary school Answer is 6

I'm not even that old and I was thought by all my math teachers that you would solve the multiplication next to parenthesis first regardless of from left to right, so I came up with 6. Blame my math teachers.

@9Geeple

3 жыл бұрын

So I went directly to comments -> and found Alpharex Rex! You are my kinda guy 🙋 Saved me from even Watching the video. Clearly we made it this far in life, paying bills, so there must be Alternative Math that also works 😉

@stephenbeesley5918

3 жыл бұрын

Me also

@citizenclown

3 жыл бұрын

I am right there with you. I remember doing parens by distributing the 5 to multiply it by the numbers in the parens, so 35-25=10, so 60/10 was 6.

@billjohnson2709

3 жыл бұрын

Me too. I was taught that 5(2) was a single term and should be simplified. Changing math rules is self destructive.

@kenmorley2339

3 жыл бұрын

I made it 6 too .

I'm not going to rely on a calculator's "judgement" on what is ambiguous. The calculator is merely following rules programmed by a human that could have interpreted an ambiguous statement one way or another.

@BypassOne

3 жыл бұрын

There's nothing ambiguous there. It's plain and simple, unless you were born in 1910 or something. Rules change, so people need to adapt and forget the old ones.

@wildasiandude432

3 жыл бұрын

Flat earther

@percyfaith11

3 жыл бұрын

@@BypassOne I agree the problem is not ambiguous but I'm merely pointing out that a calculator result is not proof of the answer to the problem but merely the result of human programming, which is not infallible.

@percyfaith11

3 жыл бұрын

@@wildasiandude432 Recognizing the fallibility of humans and technology is not the same as Luddism.

@BypassOne

3 жыл бұрын

@@percyfaith11 Human programming that is based on mathematical rules. Calculators were invented to easen and speed up calculations, exactly because people tend to forget them. So, believe me, the expression is not ambiguous just because YOU forgot the rules.

On a FX-100AU you get two different answers dependent on the way the statement is written: 60÷5(7-5) =6 therefore 60/(5(7-5))=6 or 60÷5x(7-5)=24 therefore 60/5x(7-5). In this case the multiplier between the 5 and the bracket is the key. Therefore what is the correct way of writing the statement? To me 60÷5(7-5) =6 is correct because 5 and (7-5) are actually (5(7-5)). Happy to be corrected.

@garrettguitar

3 ай бұрын

You have it correct. Most of us who did science / engineering / high-level math will interpret 5(7-5) to be a singular expression (just like 5x is a singular expression) because that is how the rule goes. If the integer is right next to the parenthesis with no operator symbol in between, it is considered to be a singular expression; therefore, 5(7-5) == (5(7-5)). I know science / engineering students who are still being taught this rule right now today.

I now think I understand the 2 dots and lines notation. It looks like it means to put the sides into a fraction. I did not observe this until I saw the video.

"It used to be 6, but now it's 24." No!

@vercimalle_0515

3 жыл бұрын

lol 😂

@Slowburn726

3 жыл бұрын

The correct answer is 6. Multiplication is done before division.

@briant7265

3 жыл бұрын

@@Slowburn726 Multiplication and division are the same level. Addition and subtraction are the same level. The mnemonic should really be PE(MD)(AS).

@Amblin80s

3 жыл бұрын

@@briant7265 I think you mean PEM/D(A-S)

@briant7265

3 жыл бұрын

@@Amblin80s PƏM/D(A-S). Stacked exponents are evaluated right to left. x^y^z = x^(y^z).

I have always struggled with maths having left school at age 14 but I am passionate in trying to figure out any maths problem. Don't often get the correct answer but I enjoy trying. Thanks for the exercise. Blessings.

@UTU49

3 жыл бұрын

There's disagreement on this answer because the notation is very sloppy. If you are uncertain about this particular math question, you might actually be better at math than you think. Your math might be very good when the notation is clear.

@joc8092

3 жыл бұрын

Maureen Mallett.....it's math. No plural

@MrGreensweightHist

3 жыл бұрын

@@joc8092 Depends on where you live. In England, it is pronounced Maths plural.

@joc8092

3 жыл бұрын

@@MrGreensweightHist k, I stand corrected

@MrGreensweightHist

3 жыл бұрын

@@joc8092 I only know from watching Doctor who, and thinking, "That sounds so bizarre" until i got used to it :D

The answer is 24. 60/5*2 = 12*2 = 24. Multiplication and division have the same priority, so when no parentheses are present, perform the operations as they are encountered from left to right.

@dannyvaneker9595

6 ай бұрын

wrong

Well, I would have thought 6, but I didn't know the rules had changed. I would love to know how this came about.

@williamaungleyraud

10 ай бұрын

Probably for the same reason why grammar gets more simplified every so many years because new kids are judged to be struggling and grades are falling so we gotta make it easy for them (sarcasm) I remember ordering a custom sandwich at Sprouts market, they usually have a paper chart with the ingredients to be marked out, but that day they run out of it, so there were blank sheets instead. I've learned cursive writing back in school, mind you that I graduated high school in 2009, but I acknowledge that my handwriting isn't the best, so I warned the young man behind the counter that if he didn't understand any of my "chicken scratch" I could read it out to him. He looked well on his late 20's if not early 30's, then he told me don't worry I've got this. Within seconds he started making an intestinal face and proceeded to say sorry he couldn't read it. And I told him, sure which one can't you read? He told me, all of it. So another young man, from behind him said, hang on in there, I know this stuff, that's cursive sh*t, I've learned this stuff in college. I didn't know if he was sincere or joking, but it was the real deal. For me I started crusive writing in the 1st grade all the way up to high school. These kids learn typing instead of handwriting, while they can poorly write in print type either. Then the government added 1 extra year of high school because kids didn't have enough time to learn. What's next changing the minimum passing grade to D? Soon kids will be getting celebration parties for D+. (more sarcasm)

@ashleyivena

7 ай бұрын

Exactly

according to my 1989 public USA education the answer is 6. 60÷5(7-5) = 60÷5(2) = And here is where the fight begins. Technically, according to the 1989 USA public education I received, the PARENTHESES still exist that this point, and therefore has to be resolved first by Order of Operations 60÷10 = 6 Parentheses (inside first, then anything dealing with the Parentheses), Exponent, multiply/divide, add/subtract. Even the distribution rule give the same answer 60÷5(7-5) = 60÷(35-25) = 60÷10 = 6

@RS-fg5mf

5 жыл бұрын

Your memory must be faulty or you had a bad teacher... I have at least 5 different math books from 1907 to the present and they all state the same thing... You evaluate what's (WITHIN) the grouping symbol not outside. And ALL multiplication and division can be evaluated equally from left to right..... When there are no (OPERATIONS INSIDE) the brackets/parentheses left to evaluate you can remove the parentheses and replace with an explicit multiplication sign or leave them to represent implicit multiplication and nothing more.... When you have a single value inside the parentheses that step is done... (7-5) is a parenthetical priority 5(2) is NOT a parenthetical priority and is exactly the same as 5*2 As for distribution, the whole point of distribution is to eliminate the need for parentheses by pulling what's inside to the outside not the other way around... Distribution requires that you multiply all the terms inside the parentheses with the TERM outside the parentheses. Terms are seoerated by addition and subtraction....60÷5 is one term to be multiplied by the two terms 7 and 5 60÷5(7-5)= 60÷5*7-60÷5*5= 12*7-12*5= 84-60= 24 60÷(5 (7-5))= 60÷(5*7-5*5)= 60÷(35-25)= 60÷10= 6 2+3+4+5 is 4 terms 10-9-8-7 is 4 terms 10÷2×6÷3 is 1 term 10÷2+5×3 is 2 terms I hope that helps you understand better....

@ComputerGarageLLC

5 жыл бұрын

Richard S Again, that is how I was taught and I noted when and the type of education. That's why I explained it the way I did. It was so everyone can see 1) the logic I used because 2) it was the logic I was taught by educators 3.) using math books they provided. So, with the correct answer being 24, you now have to ask the question; why are so many people like myself getting the answer 6? Because we were educated wrong!

@RS-fg5mf

5 жыл бұрын

@@ComputerGarageLLC unfortunately a lot of people swear that they were never taught to multiply and divide before they add and subtract. Are we to believe this as well?LOL I graduated in 1985 and was not taught in that manner. I have never seen a math book that supports your argument. I would be very interested in seeing a math book that supports your argument? It is very concerning that so many people do get this wrong considering that the order of operations supports 24 as well as the commutative property and distributive property support 24 and the multiplicative inverse of division supports 24 as well as the majority of online math engines and scientific calculators support 24. I guess this just goes to show that most people don't have to use math other than basic addition and subtraction on a regular basis. Thank you for your input. Have a great day

@ComputerGarageLLC

5 жыл бұрын

You are free to not believe me. That is your choice. But it was how I was taught through the public education system. Clearly I was taught wrong, and it appears that many others were taught wrong too. we, those who are wrong, are a reflection of what we were taught. And you are correct. a majority of people never use more than adding and subtracting most of their lives. Perfect example. Today a shirt cost $11.99, but tomorrow that shirt is on sale for 25% off. How much will you save by purchasing the shirt tomorrow? The answer that most people will give you......25%. Another example I use. Mary has $10, but she need 2 gallons of milk @ $1.98/gallon and at least $5 in fuel. Does Mary have enough money. Doesnt matter, as mary will go buy the 2 gallons of milks at the gas station, and tell the clerk to put the rest in fuel. So now, most of us never use more than very basic math most of our life. And you have a wonderful day also.

@groszak1

5 жыл бұрын

that's probably faulty education as Richard S said. 5(2) is a multiplication, and you can't split 60÷5 in half with distribution of lower priority.

The problem is for those bound to their calculator: If you have a TI you get 24 If you have Casio you get 6

@dakotayupyupyup8377

4 жыл бұрын

If you use proper math, it’s 24 If you want to use bad math, you could get any answer you want

@achyuththouta6957

4 жыл бұрын

@@dakotayupyupyup8377 The correct answer is 6. The problem is that you people always follow rules blindly. Do you even know or understand why we use order of operations? It's not about rules dictating us what to do. It's about solving a whole term first and then going to solve the next term. Once you have all terms you add and subtract. You all should go back to school and learn what maths is all about. The answer is 6 irrespective of how you look at it 5(7-2) is a single term which needs to be solved first. It doesn't matter what's before that . The answer is 6.

@comradeofthebalance3147

4 жыл бұрын

Achyuth Thouta Your method is also following a ‘rule’. So I don’t think you can just tell us off for just following rules.

@Justowner

4 жыл бұрын

@@comradeofthebalance3147 PEMDAS is convention, not a rule. It works that way because we decided it looked nice. 5(7-2) being a single term is a rule because algebra doesn't work without it.

@achyuththouta6957

4 жыл бұрын

@@comradeofthebalance3147 You misunderstand it. We have to logically analyse a problem and see the calculations that we have to do. We calculate from left to right and multiplication and division is always performed first so if we have to multiply or divide first in our problem , we don't have to put in paranthesis. But if we want to add or subtract before we multiply or divide , we put it in paranthesis. That's why we use paranthesis in the first place. So it's not the rules asking us what to do but we ourselves are defining the rules to suit our logic. This is Maths. It's not history or something where you just remember the facts and you become an expert. We analyse problems and we write these equations ourselves in real life so we know exactly what we want. It's not the other way around. Nature doesn't give us equations. We form equations by observing nature. So if the problem creates a controversy, it's a useless controversy and the problem itself is ambiguous. The person who put this problem should indicate what he exactly wants because it's simply not clear.

With new math, does this extend to physics and chemistry calculations?

@Philsh12

10 ай бұрын

I get the change on an algebra side, but this would drastically change say distance/velocity/acceleration equations and completely ruin that system? It’s been a while since I’ve been in school…

I got the right answer of 24, but I did the operation wrong. I went division first, then what’s in the parentheses, and multiplied last. But I don’t think in this case that it matters bc you’ll get the same answer if you go division first, then (), multiply, then add or subtract.

@MrGreensweightHist

9 ай бұрын

If one knows math well enough, they can play around with the rules a bit and get to the same place, as you did. The people getting 6, however, do not know the rules well enough to do that, but are trying it anyway

It's surprising how some modern calculators like CASIO, which are recommended by math teachers, also give 6 as the answer! (tested with models fx-82ES PLUS and fx-82SPXII Iberia)

@MindYourDecisions

5 жыл бұрын

Thanks for the info! CASIO's calculators were a thing for 6÷2(1+2) as well. I found one video, for example, that shows 9 on one calculator (fx-50FH) and 1 on another (fx-3650P), both which are marked in the video as "H.K.E.A.A. approved" (Hong Kong examinations and assessment authority). kzread.info/dash/bejne/e4yJpMepptzSgco.html I would love to speak to someone at CASIO about this--would make for a great video!

@antaresmaelstrom5365

5 жыл бұрын

SHARP Scientific Calculator EL-531LH , gives 6 as well

@daniellewandowski6945

5 жыл бұрын

The calculators tend to put in a bracket (in this case before the 5 and at the end) before displaying the result.

@Wizzielvl9

5 жыл бұрын

it is something called syntax. it is not as much math as it is programming. it is the programming of how to READ math in a single line. LIKE A TRANSLATOR FOR THE CALCULATOR.(it works in binary data) you do not.

@phasm42

5 жыл бұрын

When writing an expression parser, you may want to capture the intent of the user input. As I mentioned in another comment, the expression 1/2a is most likely meant to be interpreted as 1/(2*a), not (1/2)*a. The intent is generally to raise the precedence of implied multiplication above that of explicit division.

6 when I graduated but wth, nothing makes sense anymore.

@8ofwands300

3 жыл бұрын

Yep. I thought this was easy. 6. Then I read comments. 😵😵

@towmlvb3423

3 жыл бұрын

WHAT??? You GRADUATED and you got that wrong? Get a refund for all you spent to get that graduation. U woz robd...

@tekknow-9419

3 жыл бұрын

The thing that I don't understand that they're doing in the "modern" interpretation of this problem is that they are just dropping the parentheses after calculating (7-5), so 5(2) becomes just a regular multiplication, not a parentheses calculation now?

@smoydoyz

3 жыл бұрын

Or everyone else got it wrong. Wouldnt be the first time 😘

@solidpas761

3 жыл бұрын

@@towmlvb3423 5(7-5) is like a single sentence therefore the answer is 6. If it was written like 60/5*(7-5) then that will be different. Like seriously is it that hard to understand that the way u write it will determine the answer?

To me 6 is correct because you can write that equation 60 over 5(7-5) to get 24 you would need parenthesis around the 6 divided by 5 to show you work it out first. After all that is what parenthesis are for. You have them use them.

The order of operation jeft to right is the result of the limitations and acceptance of calculators with a reluctance to using notes to set up order of operation as was defined by the strength of an operation symbol. Those people are line up in whether you type with your fingers or thumbs and verbally as the difference of "Well yeah" or "Wull yea-uh".

If written as a fraction, and expand the brackets you get 60/35-25, which is also equal to 6. I’m surprised that this method wasn’t mentioned.

@GanonTEK

2 жыл бұрын

It wasn't mentioned as over in America they seem to teach that multiplication by juxtaposition does not imply grouping so to them this is generally the taught method. You also need a bracket there with what you wrote: 60/(35-25) and 60/35-25 are not the same answer when written on one line. However, it seems that multiplication by juxtaposition, ab or a(b) etc., may impliy grouping though, or it may not, so the notation is ambiguous making both answers valid. It depends on context (academic or programming). Modern international standards, ISO-80000-1, mention that brackets are required to remove ambiguity if you use division on one line with multiplication or division directly after it. The American Mathematical Society's official spokesperson literally says "the way it's written, it's ambiguous" even though they use the explicit interpretation. Wolfram Alpha's Solidus article mentions this ambiguity also. Microsoft Math gives both answers. Many calculators, even from the same manufacturer, don't agree on how to interpret multiplication by juxtaposition. No consensus. Entry 242 in Florian Cajori's book "A History of Mathematical Notation (1928)" (page 274) "If an arithmetic or algebraic term contains both ÷ and ×, there is at present no agreement as to which sign shall be used first..." It then goes on to say that brackets should be used to "avoid ambiguity in such cases" "The American Mathematical Monthly, Vol 24, No. 2 pp 93-95" mentions there was multiplication by juxtaposition ambiguity even in 1917 (and not the ÷ issue) "Common Core Math For Parents For Dummies" p109-110 addresses this problem, states it is ambiguous and says, "shame on that person for writing an ambiguous expression". "Twenty Years Before the Blackboard" (1998) p115 footnote says "note that implied multiplication is done before division". "Research on technology and teaching and learning of Mathematics: Volume 2: Cases and Perspectives" (2008) p335 mentions about implicit and explicit multiplication and the different interpretations they cause. Other credible sources are: - The PEMDAS Paradox (a paper by a PhD student on this ambiguity) - The Failure of PEMDAS (the writer has a PhD in maths) - Harvard Math Ambiguity (Cajori's book above is talked about here) - Berkeley Arithmetic Operations Ambiguity - PopularMechanics Viral Ambiguity (AMS's statement is here) - Slate Maths Ambiguity - Education Week Maths Ambiguity - The Math Doctors - Implicit Multiplication - YSU Viral Question (Highly decorated maths professor says it's ambiguous) - hmmdaily viral maths (Another maths professor says it's ambiguous) The volume of evidence highly suggests it's ambiguous.

@richardl6751

Жыл бұрын

But now you must follow the order of operations. 60/35=1.7143 then subtract 25 giving -23.2857.

@BabySuzuna

11 ай бұрын

That is because they dont actually solve the equation, they input it into a calculator from left to right without any thought to how calculators operate. this gives them an answer of 24 which they then seek ways to justify the answer given by the calculator solving 60/5*1(7-5)=x instead of solving 60/5(7-5)=x.

@Potencyfunction

11 ай бұрын

That correct.

@ChrisW228

11 ай бұрын

@@BabySuzunaTechnically, solving left to right would still equal 24. 60/5=12. So 12(7-5) is distributed as 12*7=84 minus 12*5=60. 84-60=24.

If KZread recommended this to you, it knows too much about you.

@Npc2thousand

3 жыл бұрын

Probably

@calamar1e320

3 жыл бұрын

I mean, not necessarily. I never answer these questions because I know they're made to start arguments

@NeoiconMintNet

3 жыл бұрын

The list of people with the wrong answer will help scammers rip these people off.

@Mericlen

3 жыл бұрын

I feel called out.

@flagmichael

3 жыл бұрын

I sometimes refer to myself as a recovering math head (I aced the math ACT test and was second in my high school in the MAA competition at the age of 16) but I am not recovering all that well. When I see this mistake being shown as the correct answer I cringe. Evaluate the numerator, evaluate the denominator, then divide.

See, when you get to "60 / 5(2)", to my mind, the 5(2) is an outer parenthesis+bracket expression (which should be evaluated after the inner parentheses+bracket) and should be evaluated before the typical multiplication+division. I was taught pre-PEMDAS, however, but I think that approach clarifies a lot of these "ambiguous" problems.

@trickortrump3292

10 ай бұрын

No in that case it would be [5(7-5)]. That’s where you would use inner brackets and then outer and that’s where you’d multiply by 5 before moving left to right from the beginning. In this case there are no outer brackets so once you’ve solved what’s inside of them, you move left to right from the beginning. 5(2) is the same as 5X2.

@Cdaragorn

10 ай бұрын

PEMDAS has been around for centuries, modern PEMDAS has been around for more than a century (as the video showed), so no you weren't taught pre-PEMDAS. You were just unfortunately taught wrong.

@smanzoli

10 ай бұрын

PEMDAS is not used by mathematicians, physicists or engineers: kzread.info/dash/bejne/noB3psWaZse_oKQ.htmlsi=Rzfnvk4hUtqL6ZVq

@DeirdreSM

10 ай бұрын

@@trickortrump3292 This is why I get dinged when I write essays in school - I genuinely use *too* many parentheses and think parenthetically. Not so much that I'm particularly proficient in LISP, though.

@MrHobo71

10 ай бұрын

@@trickortrump3292 No, the outer brackets are implied and aren't necessary. 5 is the coefficient of 2, so 5x2 must be done first.

The reason I came up with 6 was the fact I was taught that the order of operations was in the actual order of the letters. Parenthesis first then exponents, Math then Division, Addition then subtraction. VERY EYE-OPENING AND EDUCATIONAL. GREAT VIDEO!!!

@kentkyomen8812

3 жыл бұрын

That is how I also learned it. I was taught to remember - (P)lease (E)xcuse (M)y (D)ear (A)unt (S)ally. (P)arenthesis, (E)xponents, (M)ultiplication, (D)ivision, (A)ddition, and (S)ubtraction. Please note...I went to a public school. LOL!

@kayleemagoffin9573

3 жыл бұрын

Although it wasn't mentioned in the video, the reason multiplication/division are not given a specific importance is because they are the same operation, so you perform them in the order as written. Division is really just multiplying by a fraction. Ex: 60÷5 = 60 x (1/5). The same holds true for addition/subtraction. Subtraction is really just adding a negative number. Ex: 23 - 8 = 23 + (-8) If you change all division operations to the equivalent multiplication operation, and then multiply straight across, you would see the answer will always be 24 to the equation presented in this video.

@Paul-yb8pf

3 жыл бұрын

No you’re right it’s 6, cause multiplication is before division. The creator is just trying to cause division

@pa4765

3 жыл бұрын

Y'all learned wrong or were taught wrong. The correct translation of the acronym is "...Multiplication AND Division..." (equal rank performed left to right), "...Addition AND Subtraction.. " (equal rank performed left to right).

@rob-8928

Жыл бұрын

@@Paul-yb8pf no. Multiplication and division are equal. You solve left to right.

The problem is in the “modern interpretation”. How do we justify changing math when it completely changes the answer? It makes no sense to me at all.

@rammer561

3 жыл бұрын

@Judy Cherry Yes but when you are dealing with modern Neo Marxism like we are now there never is any correct answer. You know in their warped minds 2+2 can equal 5. Every thing is fluid, You know like the Genders are. God help us if we don't take the World back from the Satanic Globalists.

@GanonTEK

3 жыл бұрын

All that changed was notation not the rules of maths themselves which is what a lot of people think is changing. It's like using Sin²x to mean (Sinx)² or using Roman numerals, MCMXIX, instead of Arabic numerals, 1919. Both are valid notations and using one over another doesn't break any rules or axioms etc. The problem with the question here is it isn't written to modern international standards, the ISOs. If it was written properly then everyone would agree on just 6 or just 24.

@bingcherry2008

3 жыл бұрын

@@GanonTEK I hear you, but in the end, there should only be one correct answer, not two. Math used to always be an absolute. My answer is, and was, 6.

@GanonTEK

3 жыл бұрын

@@bingcherry2008 Oh there should be just 1 answer. You are right about what. What about the question 16/8/2? Or "What is 10 divided by 5 multiplied by 2?". They are ambiguous also, just like the one in the video, without more information to clarify what the person writing it meant by what they wrote. If someone was writing an academic paper and wrote 60÷5(2) they mean 6. If a programmer wrote a book on how to learn Python and wrote 60÷5(2) for an example they mean 24. The issue is the notation is ambiguous now. That's why we have international standards, to bridge the gap. With 60÷(5(2)) everyone agrees on 6. With 60÷5×(2) everyone agrees on 24. One of those is what the person writing the question meant but we will never know which. Until we do, both are valid.

@garymartin9777

3 жыл бұрын

See my reply from 5 months ago. Look above. All is explained.

My casio fx-991EX calculator gives the answer '6', as it should do I might add. It correctly interprets impicit multiplication with parenthesis and it understands that x÷y ≡ x/y, as it obviously is.

As a physicist. I went with 6.

I’m 53 years old and calculated 24 as the answer due to the way I was taught mathematics at school.

@dakotayupyupyup8377

3 жыл бұрын

You calculated correctly. For some reason these kids are wanting to do the multiplication on the right before the division on the left, madmen all of them. It’s easy to see that if you take 60 / 5 (7-5) you start with the parenthesis 60 / 5 (2) So you have 60 / 5 x 2 If you do math incorrectly and do the multiplication on the right first, you get a sum of 6, but anyone who passed 5th grade math knows you go from left to right 12 x 2 is the final product before solution

@dianawhatley6607

3 жыл бұрын

Same here Im 56.

@zakiranderson722

3 жыл бұрын

Same here ans is 24. I'm 42 btw

@dwightsmith4641

3 жыл бұрын

I’m 58. I get 24.

@catfishcave379

3 жыл бұрын

I’m 55... I got 24

Early on after scientific calculators became popular in doing this type of equation, math teachers told us not to use a calculator because it would give the wrong answer. When learning how to solve complex equations written in fraction form, the math teachers taught us to do the math above and below the line separately, then do the division. Engineers and physicists will use the old school method, which is called juxtaposition. This method accounts for the equation written in fraction form. The divided sign or a "/" use in the equation is just syntax. It replaces the horizontal line in fraction form. When written in one line using the arithmetic symbols and parentheses, some of these symbols are implied. So, when converting an equation from fraction to line form if the person writing the equation doesn't include a parentheses or bracket after the division symbol according the to PEDMAS, it changes the equation and the answer given. However, the rule for converting the equation from the signal line expression is to put everything left of the division symbols in the numerator and everything right of the division symbol in the numerator. This indicates that there is an implied bracket, or parentheses, in the equation. Which method really is correct? Having worked in the engineering field where my calculations had to have the correct answer to make what we were designing to work, I used the juxtaposition method and always got the correct answer. When using a calculator, I inserted the implied parentheses in the calculation. It is my opinion that in order of operations, multiplication should take presidence over division. I challenge a math teacher to prove which is the correct method to use on an ambiguous written equation.

@AliciaGuitar

10 ай бұрын

I was on the math team in school and was taught that either side of the / was implied parenthesis and the ÷ was not used at all. That was in the 90s so my memory might be wrong now, but i think you are right.

@blechtic

10 ай бұрын

I don't remember being taught that and would argue against it, because then you get to pretty iffy territory. That seems like a special, jargon-like usage convention: If everything is always of that form in some field, it makes sense to omit superfluous parentheses for readability, but it is problematic for general usage. Of course, a lot of it is *visual:* Are you using/imagining a large slash extending a character height above and below the rest of the expression with room around it or a small one packed tightly in one of multiple separated addition terms? To me, however, it is obvious that you can't just break an expression at a point, where there is no operator to break at (that matches the implied operation) for the sake of binding a part of that grouping to some another operator (with the same or lower preference). If you do that, you are just willy-nilly chopping the term in half at a completely unmarked place. The purpose of notation isn't to mislead. I've used examples of 3x/xy and xy/3x elsewhere.

@Cdaragorn

10 ай бұрын

The minute you start "implying" something that isn't there in math you're wrong. We could certainly have decided that multiplication has some precedence over division, but that would require us to change how we write our equations. That's the point of all of this. The rules have to be fixed in order to do math at all. In theory we could make order of operations anything we wanted to. What we choose dictates how we construct the equations though. And some ways make creating equations much more complicated than others. The simple fact is there is nothing ambiguous about this equation. You just can't invent things that aren't from the established rules for how math is to be evaluated and then complain when you get a different answer than the one the writer of the equation wrote it to produce.

@keenanvanaalst9865

10 ай бұрын

@@Cdaragorn huh? we were taught that multply goes before division and what ever number is outside of the brackets it getting multplied by the inside number then division comes. you cant just change math and thing youre going to get the right result.

@Cdaragorn

10 ай бұрын

@@keenanvanaalst9865 My entire comment was explaining why you can't just change math so you're right. The problem is multiply doesn't go before divide and it hasn't for more than 100 years. Multiply and divide are equal in the order of operations. You do them together. I'm sorry if you were taught wrong. Seems like a lot of people were given that misconception.

Hmm, if you use a stack parsed Reverse Polish Notation (RPN) calculator such as an HP-41C from my uni days late 1970's the answer comes out as 6 - eek ! ie sequence of operation (mostly, please correct me if error) is: Press 60 then Enter then 5 then Enter then 7 then Enter then 5 Press Minus ( ie 7-5) gives 2 with the first 5 entered above the 2 then times gives 10 ie the 2 at bottom of stack is multiplied by the item above which was a 5 then divide gives 6 ie the final result. So then what does this tell us about RPN stack based evaluations, which appears as start at right the go back to left, so did Hewlett Packard interpret differently - did they do a Boo Boo - heck lots of people used RPN in late 1970's across many universities USA, Australia, UK etc where HP-41C's and others were so very common - fark - nightmares ! How many recall that, comments please - this is Math - it should be preeminently substantive yet appears to have flaws of such as basic type - Yikes ! On reflection the writer of the equation is to blame - squarely they were NOT explicit and thus its their fault for NOT using brackets to avoid confusion - ie failure of the writer ! Maybe is this one reason maybe, of why the russian south pole moon lander crashed - WoW !

2:35 suggest re-writing as 60 / 5 * 2. The 5(2) = 5*2 Also some people read "multiplication - division" and forget about same precedence = so read left to right.

The correct answer is to use proper consistent notation. You want the answer to be 24? 60 / 5 * (7-5) 60 / 5 * 2 12 * 2 24 You want the answer 6? 60 / (5 * (7-5)) 60 / (5 * 2) 60 / 10 6

@stammina6338

5 жыл бұрын

Exactly. Notation is key

@thairorecordsamv1040

5 жыл бұрын

24 not 12 but yes ^^

@Icewind007

5 жыл бұрын

@@thairorecordsamv1040 lol yes. Ill fix that

@peckapuder

5 жыл бұрын

So, everything you've written is correct but I'd like to add: 5*(7-5) vs 5(7-5) There isn't a clear-cut difference but I'd lite to think that the latter represents factorization whilst the other is normal multiplication. If this was the case 6 would be the correct answer. Considering how unclear the notation is you wouldn't know the difference but this would simplify your second calculation.

@thereaction18

5 жыл бұрын

@@peckapuder The multiplication sign separates terms in the expression. The coefficient is part of the term. Order of operations applies to each separate term in the expression. What people are calling "implied multiplication" is simply using the number as a coefficient of the parenthetical expression as a term within the complete expression.

If that was rewritten as a fraction it would be 60/(5(7-5)), not (60/5)(7-5).

@ajeancongdon3948

3 жыл бұрын

Inside brackets first was my first clue. Because it was not my money that the problem is about, I didn't have 50%-100% interest to solve it.

@thomasmaughan4798

3 жыл бұрын

Wolfram re-writes it as 60/5 as a fraction, times (7-5). 24.

@garymartin9777

3 жыл бұрын

It IS written as a fraction. The rub comes in grouping what's in the denominator. The form 5(2) is really 5x2 which is not priority bound by PEMDAS. You are using parentheses to disambiguate to your preference. If you don't do that and evaluate by PEMDAS you get 24.

@cameraredeye3115

3 жыл бұрын

@@garymartin9777 That's not necessarily true. Remember in PEMDAS, multiplication comes _before_ division in order of precedence (M before D). So it's 60 over 5(7-5) = 60/10 = 6. Notice I did parentheses, THEN multiplication, THEN division. That's how it should always work. What the video got wrong is that they interpreted M and D to be on the same precedence level. They are not. M is above D, and that's why it's 6.

@anjhindul

3 жыл бұрын

You are not correct, it would be (60/5) would be the fraction with a *2 after, just as it is written. Don't try to change the equation please. Multiplication and division have the SAME priority, so whichever comes first is first.

When I punch into calculator, I get 6, but if I use the fraction button first I get 24. Because this really asks, "What is the product of the quotient of 60/5 and (7-5)

But the guidance says to do Multiplication before Division (as well as Addition before Subtraction) as suggested by the acronym PEMDAS

"Tortured enough, figures will admit to anything" - Ronald H. Coase

I remember being taught that when there is an “understood” multiplication because no “x” sign is there, then this calculation would be done before the preceding division sign. The 5 and the solution to the calculation in the parentheses are linked together, like the expression 5y are linked. If y=2, then 5y=10. Then divide what is on the other side of the division sign by 10. If they wanted me to do the division before the multiplication, they would have used a multiplication symbol in place between the 5 and the parentheses.

@vondalironfist5753

11 ай бұрын

I wasn’t taught this but I’ve always followed it as it seems more intuitive

@BabySuzuna

11 ай бұрын

correct because the 5 is the coefficient of the parentheses. whenever you have a parentheses, you have a coefficient, and whenever you have a coefficient, you have to utilize the distributive property.

@purplestar1545

11 ай бұрын

Ditto. No times sign between the 5 and the 2, just parentheses, was to be calculated first with how I was taught. I see it both ways but unless the order of operations changed in the last 25 years and it was not made public knowledge, then my math teachers would tell me I’m wrong to give 24 as the answer.

@ayokay123

11 ай бұрын

I'm old school (65) and we were taught the same thing. 6

@battletude

11 ай бұрын

agreed

so if lives are risk on these calculations it should be correct not a debate. A division makes it a fraction not a order of operation?

I solved that as soon as I looked at it. What's the issue?

Groucho Marx - "One morning I shot an elephant in my pajamas. How he got in my pajamas, I don't know."

@onlythetruth883

3 жыл бұрын

autophyte, Do you think, he possibly bored through with his erect trunk. And did it, sorry, did he survive?

@NatandGeorge

3 жыл бұрын

@@onlythetruth883 who? the elephant or Groucho?

@onlythetruth883

3 жыл бұрын

@@NatandGeorge Unfortunately it seems as if they are one and the same. That's why I was wondering about its fate. Sorry, his fate.

@lightningmacqueen4097

3 жыл бұрын

Fun fact, all of the Marx brothers loved go to Alabama to shoot elephants for their tusks! Why Alabama, you ask? Cuz everyone know that in Alabama, the Tuscaloosa.

@autophyte

3 жыл бұрын

@@lightningmacqueen4097 Boom -tsssshhhh

Me: when will I use this in real life Math teacher: 13 years later on KZread

@tk-xc2wg

3 жыл бұрын

BRILLIAN

@RajaBabu-oe4be

3 жыл бұрын

All the math we have is not meant for real life. It exercises and trains your brain to make it sharp so that your brain works instantaneously and perfectly to find a solution to your real life problems and also to help in your decision making..!!!!

@Emwest84

3 жыл бұрын

😂

@cindys2995

3 жыл бұрын

LOL!

@cindys2995

3 жыл бұрын

@@RajaBabu-oe4be This was a JOKE......relax.....

Can somebody refresh me on the "Order of Operation" I got 24 but I forgot all the rules

How would you solve 60/5y if y=2 ? 60/5*2 = 24 or 6 ? How would you solve 60/5y if y=7-5 ? 60/5(7-5) = 60/5*2 I would treat 5y as one entity Therefore 60/(5(y)) or 60/(5(7-5)) = 6

The main culprits are PEMDAS and single-line equations In my teaching career, I avoided these as much as possible, and included them only enough to familiarize my students with them.

@mikep490

11 ай бұрын

Yep. PEMDAS has been the standard for over 100 years. My teacher was a math nerd. In the 60's he showed the class a book from his collection of inaccurate text books. IIRC it was reprinted in the late 20's and, presumably, used in HS for years afterwards. (Did I mention he was a nerd?) FF to the 1990s and my son's HS was teaching math using a calculator and a decade later my co-worker's advanced studies daughter was using a different method than what I'd been taught in HS. It's weird to me how, what seemed to be fixed in stone, isn't. He had to, basically, relearn math to teach a 5th grade student.

@MrGreensweightHist

9 ай бұрын

Nothing wrong with PEMDAS.