If you key in this expression exactly as written on any Casio fx82 scientific calculator, the answer is 1/2. This is because 3(1 + 3) is algebraically like the single term 3y, or 12. Please get yourself a decent pen!
That's not the reason why. The reason why the calculator gives that answer is because it parses implied multiplication with higher priority than division. Casio put the user manuals for their calculators online - you can look up exactly how it works.
@@KeithAllen-pg8ep Yes. Your explanation was misconceived. 3(1+3) is like 3y, but 3(1+3) and 3y are not like 12. To see the difference, just think about squaring them. You can square 12 by writing 12², but you cannot square 3y by writing 3y² and you cannot square 3(1+3) by writing 3(1+3)². If you want to square the entire 3y then you need to group the 3 and the y together with a set of parentheses, as (3y)², because the 3 and the y are separate things. Yet if you want to add these things to 1 you don't need any parentheses. You can add 3y to 1 by writing 1+3y just as you can add 12 to 1 by writing 1+12. When you want to operate on the entire 3y, what determines when the 3y needs to be placed inside a set of parentheses and when it doesn't? The answer is precedence. If someone isn't talking about precedence when they explain their interpretation of 6/3(1+3), it shows that they haven't properly understood what's going on.
Implicitly connected GROUPS of factors and coefficients include the implied grouping relationship as well as the implied multiplication. So 3(1+3)≡[3×(1+3)]=12 6÷12=1/2 Distance traveled divided by circumference is equal to revolutions regardless of which formula for circumference you choose. D÷2πr≡D÷(2πr)≡D÷[πd] So 6÷3(1+3)≡6÷[3×(1+3)]= 6÷12=1/2
@yiutungwong315 I'm happy that we agree. You will get a strong argument from a lot of people that this somehow does not apply to 1/2a however. Though when one replaces the 'a' unknown with a numerical value, say 4, one gets 1/2(4)=0.5(4)=2 Which damages that argument.
Nope. First resolve inside the parentheses, if it resolves to a number you can remove the parentheses and make it a multiply like this 6÷2*4. Then go left to right. If there are variables with the parentheses you resolve as far as you can, then go outside and process left to right so 6÷2(a+b)→3(a+b) then you can distribute to 3a+3b.
@@petersearls4443 I disagree, you don't simply resolve the parentheses by performing the arithmetic within them - they are bound to the number/variable which sits immediately outside. This is how we perform multiplication over addition.
@@PenndennisHe said first to resolve INSIDE the parentheses, not resolve the parentheses. There is no such thing as "resolving the parentheses". That doesn't mean anything.
It's 1/2. It's never about old or new interpretaion of PEMDAS. The parenthesis MUST remain intact after performing the operation on whatever is inside it. You downgraded it to Multiplication which is a no-no, i.e. = 6÷3(4) = 6÷12 as parenthesis comes first. Algebraically, a(b+c) = ab + ac always, regardless of what is in front. Math is an exact international language interpreted the same way in every country. It does not change with time and has no ambivalence. Your posting can be very damaging to Math learners.
this is how I see it too. And there really is not any other way. Parenthesis still remain after the addition 1+3 .. only way to get rid of parenthesis is doing the multiplication 3(4), generating the 12 under the devicion mark. So, parenthesis all the way first!
"The parenthesis MUST remain intact after performing the operation on whatever is inside it." Here is a simple counter-example showing that there is no such rule in math: 6 - (3 + 2) 6 - 5 1 The parentheses are not needed after performing the operation inside them, and therefore can immediately be dropped. "You downgraded it to Multiplication which is a no-no, ..." It already was multiplication. 3(4) is an expression that means multiply 3 and 4. The parentheses in 3(4) serve no other purpose. "Math is an exact international language interpreted the same way in every country. It does not change with time and has no ambivalence." A wonderful ideal that is not met in practice. For example, in Australia they teach a concept called "pronumeral" which as far as I can tell is used in little, if any, of the rest of the world. And math notation (its language) most certainly has changed over time. Look up the differences between how Leibniz and Newton notated calculus, that they independently invented. Or download a copy of the book, Cajori_Florian_A_History_of_Mathematical_Notations.
answer is 1/2 because u cant remove the bracket (1+3) whenever u want to, the 3 behind the brackets stop it from opening so it becomes 3(4) therefore parenthesis still exists so we have to do it before the division so it becomes 6/12 which gives us 1/2 :)
The difference between the two answers has got absolutely nothing to do with parentheses. You don't have to "do the parentheses". There's no such thing as "doing the parentheses". That doesn't mean anything. The only things you can do here are mathematical operations. In 6/3(4) there are two mathematical operations: one division and one multiplication. The answer you get depends on which of those operations you do first.
@@gavindeane3670 Incredibly, amongst the UA-cam discussions I have seen two people say that 3(4) is not multiplication. As in, "No multiply sign, no multiplication. Simple really."
@@donmacqueen it's a product, not multiplication. If you insert an operator into the middle of a product and then apply the order of operations you get the wrong answer. x² is also multiplication, but it's also not, and if you insert an operator you can change an expression from 1/x² to 1/x*x. PEMDAS tells you to resolve the exponent first, but it does not tell you to resolve implicit multiplication first, which is why people get the wrong answer when they use it. The correct order of operations to apply to this expression is PEJMDAS.
@@gavindeane3670 the P in PEJMDAS says you need to do the parentheses first. It's the J that's important here though, because Juxtaposition tells you that the implied multiplication has to be done before any multiplication operators.
You have not accounted for the property that provides for distributing the multiplication over the addition. You have assumed that when you add the numbers inside the parentheses that the brackets disappear and therefore, we then evaluate the multiplication/division as they appear from left to right. The correct answer is 1/2. The parentheses and the number 3 outside are bound together. 6÷3(1+3) and 6÷3(4) are identical. You are evaluating 6÷3 multiplied by (1+3). That is not what the notation demands.
It's got absolutely nothing to do with distribution. Distribution is irrelevant. You can both answers using distribution. The difference between the two answers is entirely about whether you parse implied multiplication with higher precedence than division. Of course it's the same as 6/3(4). The issue is whether to parse that as 6 ------ 3(4) or 6 ---- (4) 3
@@gavindeane3670 Exactly so. The distributive property describes a relationship between multiplication and addition. It does not include a requirement that it be must always be used.
From the given problem, 3(1+3) is a term which represents a certain number and can be simplified as 12 when the parentheses is taken out. In this case, 6/3(1+3)= 6/12=1/2.
@@diegoalexhidalgo6588 if 3(1+3) were a stand alone operation you would be correct. But once the inside of the parentheses is resolved you return to the outside and go left to right performing multiply or divide as encountered. So 6÷3(1+3)→6÷3(4) now you have to first resolve the 6 divided by 3 prior to the multiplication, observing the order of operations.
@@NoTimeForCheats-pg2lu try most modern calculators, online calculators and math solvers, software and Ai. It will be handled like I said, it may not be the correct approach according to mathematicians, but in the real world that is what you get. I went to MIT’s website to see how they handle juxtaposition to parentheses. Acknowledging that mathematicians would not parenthesize only numbers. But for an expression like 6÷2(1+2), to make sure that software would handle it properly you see them writing it like this. 6÷(2(1+2)).
@@petersearls4443 Just Bless your heart. You say the coefficient "of the parenthesis" is not "of the parenthesis" Just listen to yourself dear.. Maybe we should call it the coefficient not of the parenthesis. LOL
The answer is 1/2. The parenthesis comes first solving what is inside and related to it. After solving what is inside you get the expression 3(4). The moment you change that to X, then you are still solving the parenthesis and you must continue to the end of solving the (), you cannot stop midway and jump over to another sign in the equation, in this case ÷ sign. 3 x N is not same expression, logically as 3(N), even though, they are arithmetical equal.
3×N is exactly equivalent to 3(N). There is no such thing as "related to the parentheses". That is completely misconceived. The difference between the two answers here has got absolutely nothing to do with parentheses. It's entirely about whether you parse implied multiplication with higher precedence than division.
@@gavindeane3670 Give an answer and explain it. We don't need some failed math student to tell us we're wrong. My degree in math came from growing up in the '60s and ' 70s. Flash Cards and multiplication tables. Rote memorization, PEDMAS, and being allowed and encouraged to think for yourself. You kids today are so screwed...
@@johnleeson6946 The answer is ½ if you parse the implied multiplication with higher precedence than division and 8 if you don't. It has got absolutely nothing to do with parentheses. You can see why it's got nothing to do with parentheses by recognising that the expression is of the form a/bc. Different people have different ideas on the question whether an expression of the form a/bc should be interpreted as a ---- bc or a ---- c b but it is obviously preposterous to suggest that the answer to that question would depend on whether c happens to be a term in parentheses.
@@gavindeane3670 Good job using a whole bunch of nothing to try to explain your wrong answer to those that think you are correct. You are wrong. Just admit it. I admit you're wrong. You should too.
All this proves is poor semantics/nomenclature. Pemdas does not include 'left to right', so pure pemdas is 1/2. And 'correct' is misleading because that's like saying English is correct, French is not. Consider 3x when x = 4. What is the value of that? 12. But what is 6 divided by 3x which can be rewritten 6 divided by 3 multiplied by x. According to the author, it's 8. But what if we write it 6 / 3x? Then it's 1/2. And if we consider 3x as a term in an equation, then it's value should depend only on x and not on any other terms. Thus 3x = 12 and 6 / 3x = 1/2. But by the author's logic, 6 ~ (divided by) 3x = (6/3) * x which can be rewritten as 6 * x/3 so that 6 ~ 3x = 6 * x/3 so that 1/3x = x/3, aka x/3 = x squared / 3, an absurdity. Introducing left-to-right destroys the whole point of pemdas. Disturbingly, Excel also mixes left-to-right and pemdas from another channel's example. The final point would be that when channels post '97% got it wrong' what they should say is that the paradigm designers got it wrong. Maths is a language. If 97% say a tree has roots and leaves and 3% say a tree has wheels and an engine, then the common usage should dominate. The not-so-hidden flaw in introducing left-to-right is that it precisely contradicts the pemdas protocol.
He hits it with fairy dust and the distribution magically becomes an implied multiplication. Then he applies Unicorn piss and splits one term into two terms and gets 8 for an answer. Awesome
Save your dust and piss and enter this into Ai. “Is 3*(1+3) the same as 3(1+3)”, yes is the answer and the result is 8. The problem is that the value outside of the parentheses needs to be resolved prior to the distribution. 6÷3(1+3)→2(1+3)→2+6=8.
@@petersearls4443 proves you don't want to rely on calculators for the answer. Not only can you buy ones that give different answers, you can get them with a switch to give either answer. So your stance is that the coefficient "of the parenthesis" is not part "of the parenthesis". Please review basic factoring.
@@petersearls4443 so you believe that 6/2 is a not one term divided by another? Do you believe you should start each equation from left to right. Do you believe the 2 is stuck to the divisor? Do you not understand that the coefficient of the parenthesis is part of the parenthesis. THAT IT BELONGS TO THE PREVIOUS TERM. LMAO
@@Of_UnCommon_Sense once you resolve the value inside the parentheses you then go outside the parentheses and resolves the expression up to the coefficient using multiply and divide left to right. If you have the expression 1+3(1+3) then yes you would multiply the 3 times 4=12 then 1+12=13. But if you have a divide operation before the coefficient then that must be resolved prior to applying the coefficient to the value inside the parentheses. 6÷3(1+3)→2(1+3)=8.
@@mikemassey7403 juxtaposed symbols are resolved before the multiplication operator. He got it right; what they teach in school is not the whole story.
One cannot arbitrarily place a multiplication symbol between the 3 and the left parentheses. It is understood that 3 is a “FACTOR” of each of the numbers inside. For what other reason would the 3 be written outside the () without a multiplication symbol?
"It is understood that 3 is a “FACTOR” of each of the numbers inside. For what other reason would the 3 be written outside the () without a multiplication symbol?" No fancy reason is needed. Leaving out a multiplication sign in certain situations is a common and widespread convention that makes notation clearer and easier to read. For example, people commonly write (x+1)(x-1) = x^2 - 1 without considering x+1 to be a factor of x or -1. More specifically, there is a convention to the effect that when the operation next to () is multiplication, the multiplication sign can optionally be omitted.
@@johnferguson2728 "What notation do you use to show that 3 is a factor of the contents of the parentheses?" Why does anyone need for a notation for that? For example, when students are learning about factorizing, they might get asked, "What are the prime factors of 12?" The answer, of course, is "2 and 3 are the prime factors of 12". I don't recall any special notation that is used to indicate that 2 and 3 are factors of 12. For that matter, the numbers inside the parentheses are 1 and 3. 3 is not a factor of 1. That is, 3 is *not* a factor of the contents of the parentheses, not a factor of each of the numbers inside them. Now, it is true that 3(1+3) is a factorization of (3+9). So, if we had started with 6/(3+9) and wanted to calculate its value, we could, if we wanted, start by factorizing (3+9). There would be no point in doing so, because the simplest way to calculate 6/(3+9) is to first add, resulting in 6/12, which is of course equal to 1/2. But let's try starting by factorizing (3+9) into 3(1+3). In so doing, we would first have to notice that the whole of (3+9) is *_for sure_* in the denominator. We would then have to write the next step so that the factorized version is also *_for sure_* in the denominator. We would do this by writing 6/(3(1+3)). Without the extra parentheses, it's not *_for sure_*. (_Some people think it is for sure, but lots of people disagree, so it's not actually for sure. There is no universally agreed-upon standard that makes if for sure._) And of course this way of calculating 6/(3+9) would certainly be more complicated. However, that's all irrelevant, because we didn't start with 6/(3+9).
@@johnferguson2728 I thought I replied already but I don't see it. Sorry if I'm repeating myself. Answer is: I don't, because there is no need for a notation that shows 3 is a factor of the contents of the parentheses. (And actually, 3 is not a factor of 1, so 3 isn't a factor of "each of the numbers inside". You were probably thinking that 3(1+3) is a factorized version of (3+9). By itself, it is. But we didn't start with 6/(3+9), so it's not relevant.)
@@johnferguson2728What form of notation do you use to show that the 3 is a factor of the contents of the parentheses? You enclose the entire 3(1+3) in its own set of parentheses. That's what parentheses are for. That's literally the entire point of parentheses.
That "older usage" is still in use. You can't use PEMDAS for this expression because it contains juxtaposition, so you need PEJMDAS instead, and the implicit multiplication via juxtaposition comes before the division. This is not old, every mathematician does it today.
Failure. If you can resolve inside the parentheses to a number then the parens can be removed and make it a multiplication operation. 6÷3(1+3)→6÷3(4)→6÷3*4=2*4=8. Order of Operations clearly states that you resolve inside the parentheses. Juxtaposition typically refers to numbers juxtaposed to variables like 2X. 3( is exactly the same as 3*(. If you don’t believe me. Enter the expression into Ai.
@@petersearls4443 it's already multiplication, you don't need to make it into that. Typically juxtaposition is between numbers and variables, but this is not typical. AI is not the definitive source, mathematicians are. You will not find any example in mathematics journals where juxtaposition does not take a higher precedence than division.
@@shaunpatrick8345 my mathematician friend is the one who explained this to me. So you can see why it is confusing. He wrote software included in Galileo so I presume he knows what he is talking about. And no it wasn’t the section of code that screwed up the meters and feet.
@@petersearls4443 he doesn't know what he's talking about. The definitive video on the subject is by The How And Why Of Mathematics where she shows examples from mathematics and engineering papers, and the AMS style guide, and explains that PEMDAS is a failed attempt by American teachers to explain the order mathematicians use. If your friend can find an example from mathematics where juxtaposition is not given higher priority, he will have disproved her.
@@shaunpatrick8345 I went to her UA-cam channel the how and why of mathematics and watched her video 6÷2(1+2) PEMDAS is a lie. . In there she says the Order of Operations if dealing with ab÷cd would misinterpret it as a*b divided by c and then that result times d. Which I agree would be a mistake. Here is where it gets confusing again. Because the same Ai that would handle 6÷2(1+2) as 6÷2*3=9 says that if you have ab÷cd you multiply a *b then c * d and divide a*b by c*d. So it interprets it properly when variables are involved. So you are saying it is wrong when only numbers are involved but correct when variables are involved? Really?
1/2 is the correct answer pleaseee , because 3 is multiplied by (1+3) first, not 6:3 multiplied by (1+3). If the answer is 8, the problem should be shown like this = (6:3)(1+3) ....not all math videos give the right ways, answers & solutions.
You're absolutely right that you get the answer 8 it needs to be written (6/3)(1+3). And to get the answer 0.5 it needs to be written 6/(3(1+3)). The entire point of the expression in the video is that it can be read both ways.
@@gavindeane3670 You missed class when they taught basic factoring. Since the 3 is the coefficient "of the parenthesis" it belongs "to the parenthesis" and the extra outside parenthesis are indeed implied. Your teacher told the rest of the class that the 3 was stuck to the parenthesis. Does that ring a bell ? (3(1+3)) and 3(1+3) are exactly the same. The entire point of the video was to cause dissension and argument. It is truly amazing how people argue so feverently when they haven't got a clue.
@@Of_UnCommon_Sense Don't worry. I understand this stuff completely. It's not complicated, but it is widely misunderstood. For some reason, a lot of people struggle with the idea that notation can be ambiguous. Almost everybody makes the same mistake with this meme, which is to believe that their preferred interpretation is the only correct interpretation. They don't all agree on what that single correct interpretation actually is, but ultimately they're all making the same mistake. Many people then try and concoct some mathematical proof for why their interpretation is correct, even though this is not an issue capable of proof either way. I haven't missed anything about factoring. The first thing to say about factoring is that it's irrelevant here. We are not given the expression 6/(3+9) and asked to take out the factor of 3 from the (3+9). We are just given the expression 6/3(1+3). There's no basis for assuming that that expression necessarily started out as 6/(3+9). Let's just consider 3+9 in isolation for a moment. Yes, of course you can factor out the 3 from that. No, my teachers did not say things like the 3 outside was then "stuck to the parentheses" or that there was now some implicit set of parentheses outside the 3 and the (1+3), because my teachers were not incompetent fools. If somebody has told you things like that then you need to stop listening to them because they don't know what they're talking about. In fact, thinking about factoring is a good way to illustrate the logic of the 6/3(1+3) = 8 interpretation. If we consider 3+9 in isolation again, we can factor out the 3 to get 3×(1+3) and it obviously makes no difference if we elide the multiplication symbol and write it as 3(1+3). The choice to use implied or explicit notation for the multiplication there is purely a matter of personal preference. The argument then is that implied vs explicit multiplication is ALWAYS just a matter of personal preference. It shouldn't be a way to completely change the meaning. When you factor out the 3 in 6/(3+9), if you write it with an explicit multiplication operator you have to add an extra set of parentheses, as 6/(3×(1+3)) so an extra set of parentheses should be required if you happen to choose to use implied multiplication instead, as 6/(3(4)) In other words, since 6/3×(1+3) does not equal 6/(3+9), then 6/3(1+3) should not equal 6/(3+9) either. There is obvious logic there, and that argument is certainly not without merit. The counter argument of course is that something like 1/2π would have to mean 0.5×π, but the world is full of mathematicians and scientists and engineers who would naturally interpret 1/2π as 1 --- 2π not 0.5×π. Ultimately, such notation is ambiguous - that is the entire point of this meme. It's a well known, well understood, and very simple issue. Mathematicians will tell you it's ambiguous. Different calculators give different answers. And the international standard for mathematical notation simply disallows this syntax. Many people will argue to the death that their preferred interpretation is the only correct interpretation, but that's ultimately futile. (As an aside, an example like 1/2π illustrates how this issue is entirely about implied multiplication and has got absolutely nothing to do with parentheses)
@@gavindeane3670 despite your novella this equation is not some unusual made up equation. It is something seen all the time. It is laughable that you would think it unique. You have a trolley pushed by a measured force of 6.06 =F the mass of the trolley is measured at 2 and a measured at 4 is a mass placed on the trolley. The mass measurement device is off by 1%. So now the correction factor is. 1.O1 Now mass is M = 1.01(2+4). So now the acceleration is; A= F/M A = 6.06 / 1.01(2+4) Now we measure the acceleration. Can it be both 1 and also 36.
@@Of_UnCommon_Sense Indeed it is seen all the time. It does the rounds regularly on the internet because it makes great clickbait. It's not a properly formed mathematical expression. It's just a silly internet joke. It is, as I said, a well known and well understood issue. The best advice is: don't write like this. In the real world it's largely a non-issue because those of us who use mathematics to actually do things generally write division in a vertical layout, with numerator over denominator, not using inline operators.
How do you get -1 ? 8 should be acceptable. If you want 1/12, the use an additional set of parentheses. Ramming PEMDAS down students throats is not a good practice; teaching proper notional practices to prevent ambiguity and confusion is a better practice.
Complete rubbish. This is not math. Pemdas is not necessary. Just write the expression properly in the first place. Write (6/3)(1+3) or 6/((3(1+3)). No wonder kids are put off math.
That's not written in a way people who were not taught parentheses can understand. The expression in question is written in a way that people who learned mathematics can understand; the problem is that the person who made the video and most of the commenters didn't learn it.
What do you mean "not taught parentheses/brackets?" B in BOMDAS stands for brackets/parentheses. They are used in these expressions, but people don't understand them???
@@RobertCanova-sn4sh you imply that the expression has not been written properly, but it actually has. Had you learned what juxtaposition means you would be able to parse the expression, whereas the version you suggest can only be parsed by people who learned what parentheses mean. The issue is not in how the expression is written, it is whether people understand it. However it is written, even in the manner you suggest, there will be people who don't know how to resolve it. If people were presented with an expression containing calculus, it would be absurd for them to demand all such expressions be written in a way a 5th-grader can understand, and the same goes for this one.
a) You talk way too much b) You talk way too fast c) You talk a lot but are not clear d) Your singsong voice is annoying e) This video is far too long to convey a fairly simple concept
Nope! 3(1+3) is implied multiplication! You cannot magically change the symbology to explicit multiplication after doing the addition. The rule for implied multiplication changes the precedence such that after work inside the parentheses is done then the multiplication that is implied is done. Casio's website gives a good explanation of the rule. If you write the original problem using explicit multiplication, 3*(1+3), then you would get the answer you are presenting. The underlying reason for all this has to do with how computer algorithms and hardware have to parse input lines. I will add a caution to math students when using calculators to work problems such as this: not all calculator manufacturers have incorporated the implied multiplication rule. TI, for example has not. Some computer software, like Matlab and Maxima, will give a syntax error if the user tries implied multiplication notation.
The answer is the same both times: 1/2. The difference comes when you use the proper or improper order of operations. The proper one for an expression containing juxtaposition, like this one, is PEJMDAS.
That's not true. The answer is half and not 8. How did you remove the bracket between 3 and 4?. How did you bring the multiplication sign between 3 and 4 ? You took away the brackets and put multiplication. This is where you errorerd. You needed to multiply the 3 and 4 in brackets to take take out the brackets. Dont mislead people.
That's what it means when two terms are written next to each other like the 3 and the 4 here. It means multiplication. Obviously in isolation 3(4) and 3×4 mean exactly the same thing. So the question is, why shouldn't 3(4) mean 3×4 when it happens to be part of a larger expression?
@@gavindeane3670 Indeed! Some people think 3(4) means 3*4 and others think it means (3*4), when it happens to be part of a larger expression. And it may not matter, depending on the larger expression. For example, it doesn't matter if the larger expression is 12*3(4). But it does matter for 12/3(4).
@@gavindeane3670 Even the the number of terms inside are reduced to only one it is still a distribution. The multiplication still occurs within the parenthesis. (3*1+3*3)=(3+9)=(12)=12 The parenthesis has a value of 12 no matter what form we write it in. This is two multiplications and one addition. The smarter way is one multiplication and one addition. Here is how. (3*1+3*3)=(3+9)=(12)=12 Remove the common factor; 3(1+3) The only way to return the 3 to the inside of the parenthesis for evaluation is distribution. Distribute; 3(1+3)=(3+9)=(12)=12 [two multiplications required] Combine terms then distribute. 3(4)=(3*4)=(12)=12 [one multiplication required] 3(4) is still 12 by implied multiplication. It is a single term, while 3*4 is two terms. 6 / 3 * 4 is different from 6 / (3*4) Any time you have a set of parenthesis with a coefficient it is a distribution. Therefore a single value, parenthesis are implied.
@@Of_UnCommon_Sense It is not distribution when there is a single term in the parentheses! Who told you that??? The fundamental nature of distributivity is that it is a property that one type of mathematical operation has OVER ANOTHER TYPE OF MATHEMATICAL OPERATION. When we talk about distribution here, what we're using is the distributive property of multiplication over addition. That's its proper mathematical name. If there's no addition inside the parentheses then by definition we are not distributing. 3(4) is not a single term. It's trivially easy to see why that's wrong. Just think about how you would square 3(4). If it was a single term then you could simply write 3(4)². But as I'm sure you know, if you write 3(4)² the squaring applies only to the 4. If you want to square the entire 3(4) then you must put the entire 3(4) in a set of parentheses, as (3(4))². The 3 and the 4 need to be placed inside a grouping symbol precisely BECAUSE they are not grouped by the implied multiplication notation. They are separate things.
@@donmacqueen Some people do think that 3(4) means (3×4) as part of a larger expression, but those people are incorrect. Just consider the expression 3(4)². That certainly does not mean (3×4)². People who actually understand this stuff know that the issue is about the precedence you give to implied multiplication. It is a common convention to parse implied multiplication with higher precedence than division (but absolutely not higher precedence than exponentiation). That's how you actually get 6/3(4) = 6/12 = 0.5. The problem comes when people try and argue that that's the ONLY way it can be parsed.
It's got nothing to do with parentheses. Parentheses literally cannot have precedence. Precedence is a concept that relates to mathematical operations and "parentheses" is not an operation. What you did was to give the multiplication higher precedence than the division.
There should not be any argument because of the implied operator only operates on the parentheses, meaning the 3 cannot be separated from the parentheses, its one term and must be simplified. It’s not 6/3*(1 + 3) which would be a fixed operator, meaning the 3 does not operate on the parentheses. Writing equations has rules just like solving equations. And give up on PEMDAS, it’s long overdue to throw it out because it is flawed in too many way to count!
@@michaelcoll433 they are not rules you can follow when the expression contains implicit multiplication, unless you are happy with the wrong answer. PEJMDAS is a more complete set of rules which do work.
You're wrong because once the expression(s) within the parenthesis/parentheses are solved the parenthesis/parentheses seized to exist. I refer you to your Math's teacher, please.
6 : (1 + 3) = 6 : 3x4 = 6 : 12 = 1:2 Los factores de un producto, NO SE PUEDEN SEPARAR. Expliquen esto: Si 6 : 3x4 = 2x4 = 8, siendo 3x4 igual que 4x3, 6 : 4x3, también debe ser 8. Compruébenlo.
One half
Its 8
6÷3(1+3)= 1/2
Definitely 1/2 (one half).
You might have me drive the rocket ship so we can get back.
Basic mathematic
First simplify parentheses
1+3 = 4
Divide 6÷ 3 = 2
2(4) 2 • 4 or 2× 4
= 8
If you key in this expression exactly as written on any Casio fx82 scientific calculator, the answer is 1/2. This is because 3(1 + 3) is algebraically like the single term 3y, or 12. Please get yourself a decent pen!
That's not the reason why. The reason why the calculator gives that answer is because it parses implied multiplication with higher priority than division. Casio put the user manuals for their calculators online - you can look up exactly how it works.
@@gavindeane3670 Is that *really* any different to what I said?
@@KeithAllen-pg8ep Yes. Your explanation was misconceived. 3(1+3) is like 3y, but 3(1+3) and 3y are not like 12.
To see the difference, just think about squaring them. You can square 12 by writing 12², but you cannot square 3y by writing 3y² and you cannot square 3(1+3) by writing 3(1+3)².
If you want to square the entire 3y then you need to group the 3 and the y together with a set of parentheses, as (3y)², because the 3 and the y are separate things.
Yet if you want to add these things to 1 you don't need any parentheses. You can add 3y to 1 by writing 1+3y just as you can add 12 to 1 by writing 1+12.
When you want to operate on the entire 3y, what determines when the 3y needs to be placed inside a set of parentheses and when it doesn't? The answer is precedence.
If someone isn't talking about precedence when they explain their interpretation of 6/3(1+3), it shows that they haven't properly understood what's going on.
@@gavindeane3670 Pedant.
6/3x(1+3)
2x4
8
Implicitly connected GROUPS of factors and coefficients include the implied grouping relationship as well as the implied multiplication. So 3(1+3)≡[3×(1+3)]=12
6÷12=1/2
Distance traveled divided by circumference is equal to revolutions regardless of which formula for circumference you choose.
D÷2πr≡D÷(2πr)≡D÷[πd]
So
6÷3(1+3)≡6÷[3×(1+3)]=
6÷12=1/2
I got it....... Also free Palestine and the whole world from the protocols of the elders of zion.
@@Vibe77Guy
1/2π = 0.5π
1÷2π = 1 ÷ (2π)
@yiutungwong315
I'm happy that we agree.
You will get a strong argument from a lot of people that this somehow does not apply to 1/2a however.
Though when one replaces the 'a' unknown with a numerical value, say 4, one gets
1/2(4)=0.5(4)=2
Which damages that argument.
B
@@jasonseidel3784
So long as you can deal with square kilowatts.
Sequence is well defined. Addition, subtraction, multiplication and finally division. Answer is 1/2
Nope. First resolve inside the parentheses, if it resolves to a number you can remove the parentheses and make it a multiply like this 6÷2*4. Then go left to right. If there are variables with the parentheses you resolve as far as you can, then go outside and process left to right so 6÷2(a+b)→3(a+b) then you can distribute to 3a+3b.
PEMDAS it's B 8
@@petersearls4443 I disagree, you don't simply resolve the parentheses by performing the arithmetic within them - they are bound to the number/variable which sits immediately outside. This is how we perform multiplication over addition.
@@PenndennisHe said first to resolve INSIDE the parentheses, not resolve the parentheses.
There is no such thing as "resolving the parentheses". That doesn't mean anything.
1/2 is the correct answer. I'm ready to challenge anyone.
B 8 easy peasy!
2x4=8(b)
Such a long and complicated 'solution' to this relatively simple problem! If I had been taught like this I would have quickly lost interest in math.
I agree, I still don't understand.
It's 1/2.
It's never about old or new interpretaion of PEMDAS.
The parenthesis MUST remain intact after performing the operation on whatever is inside it.
You downgraded it to Multiplication which is a no-no, i.e.
= 6÷3(4) = 6÷12 as parenthesis comes first.
Algebraically, a(b+c) = ab + ac always, regardless of what is in front.
Math is an exact international language interpreted the same way in every country. It does not change with time and has no ambivalence.
Your posting can be very damaging to Math learners.
this is how I see it too. And there really is not any other way. Parenthesis still remain after the addition 1+3 .. only way to get rid of parenthesis is doing the multiplication 3(4), generating the 12 under the devicion mark. So, parenthesis all the way first!
Do it on a calculator
@@petercrane8216 Don't trust calculator esp free apps on internet. An engineering maths calculator will give you the right answer
@@petercrane8216 Do it on an engineering maths calculator, not an app from internet
"The parenthesis MUST remain intact after performing the operation on whatever is inside it."
Here is a simple counter-example showing that there is no such rule in math:
6 - (3 + 2)
6 - 5
1
The parentheses are not needed after performing the operation inside them, and therefore can immediately be dropped.
"You downgraded it to Multiplication which is a no-no, ..."
It already was multiplication. 3(4) is an expression that means multiply 3 and 4. The parentheses in 3(4) serve no other purpose.
"Math is an exact international language interpreted the same way in every country. It does not change with time and has no ambivalence."
A wonderful ideal that is not met in practice. For example, in Australia they teach a concept called "pronumeral" which as far as I can tell is used in little, if any, of the rest of the world. And math notation (its language) most certainly has changed over time. Look up the differences between how Leibniz and Newton notated calculus, that they independently invented. Or download a copy of the book, Cajori_Florian_A_History_of_Mathematical_Notations.
The answer is by which is 8 ie 1+3=4
6÷3=2 therefore 4*2=8
B
Skip a bit, Brother Maynard!
The Holy Hand Grenade of Antioch is ready.
Please change your Pen
answer is 1/2 because u cant remove the bracket (1+3) whenever u want to, the 3 behind the brackets stop it from opening so it becomes 3(4) therefore parenthesis still exists so we have to do it before the division so it becomes 6/12 which gives us 1/2 :)
The difference between the two answers has got absolutely nothing to do with parentheses.
You don't have to "do the parentheses". There's no such thing as "doing the parentheses". That doesn't mean anything. The only things you can do here are mathematical operations.
In 6/3(4) there are two mathematical operations: one division and one multiplication. The answer you get depends on which of those operations you do first.
@@gavindeane3670 Incredibly, amongst the UA-cam discussions I have seen two people say that 3(4) is not multiplication. As in, "No multiply sign, no multiplication. Simple really."
@@donmacqueen it's a product, not multiplication. If you insert an operator into the middle of a product and then apply the order of operations you get the wrong answer. x² is also multiplication, but it's also not, and if you insert an operator you can change an expression from 1/x² to 1/x*x. PEMDAS tells you to resolve the exponent first, but it does not tell you to resolve implicit multiplication first, which is why people get the wrong answer when they use it. The correct order of operations to apply to this expression is PEJMDAS.
@@gavindeane3670 the P in PEJMDAS says you need to do the parentheses first. It's the J that's important here though, because Juxtaposition tells you that the implied multiplication has to be done before any multiplication operators.
You have not accounted for the property that provides for distributing the multiplication over the addition. You have assumed that when you add the numbers inside the parentheses that the brackets disappear and therefore, we then evaluate the multiplication/division as they appear from left to right. The correct answer is 1/2. The parentheses and the number 3 outside are bound together. 6÷3(1+3) and 6÷3(4) are identical. You are evaluating 6÷3 multiplied by (1+3). That is not what the notation demands.
It's got absolutely nothing to do with distribution. Distribution is irrelevant. You can both answers using distribution.
The difference between the two answers is entirely about whether you parse implied multiplication with higher precedence than division.
Of course it's the same as 6/3(4). The issue is whether to parse that as
6
------
3(4)
or
6
---- (4)
3
@@gavindeane3670 Exactly so.
The distributive property describes a relationship between multiplication and addition. It does not include a requirement that it be must always be used.
that's all neat and all, what's the practical application of this?
From the given problem, 3(1+3) is a term which represents a certain number and can be simplified as 12 when the parentheses is taken out. In this case, 6/3(1+3)= 6/12=1/2.
@@diegoalexhidalgo6588 if 3(1+3) were a stand alone operation you would be correct. But once the inside of the parentheses is resolved you return to the outside and go left to right performing multiply or divide as encountered. So 6÷3(1+3)→6÷3(4) now you have to first resolve the 6 divided by 3 prior to the multiplication, observing the order of operations.
@@petersearls4443 utter nonsense
@@NoTimeForCheats-pg2lu try most modern calculators, online calculators and math solvers, software and Ai. It will be handled like I said, it may not be the correct approach according to mathematicians, but in the real world that is what you get. I went to MIT’s website to see how they handle juxtaposition to parentheses.
Acknowledging that mathematicians would not parenthesize only numbers. But for an expression like 6÷2(1+2), to make sure that software would handle it properly you see them writing it like this. 6÷(2(1+2)).
@@petersearls4443 Just Bless your heart. You say the coefficient "of the parenthesis" is not "of the parenthesis" Just listen to yourself dear.. Maybe we should call it the coefficient not of the parenthesis. LOL
@@Of_UnCommon_Sense uphill battle in the real world on your part.
Doh!! He needs to do harder problems in his vids.
8
The answer is 1/2. The parenthesis comes first solving what is inside and related to it. After solving what is inside you get the expression 3(4). The moment you change that to X, then you are still solving the parenthesis and you must continue to the end of solving the (), you cannot stop midway and jump over to another sign in the equation, in this case ÷ sign. 3 x N is not same expression, logically as 3(N), even though, they are arithmetical equal.
Uh... WRONG!!!!
3×N is exactly equivalent to 3(N).
There is no such thing as "related to the parentheses". That is completely misconceived.
The difference between the two answers here has got absolutely nothing to do with parentheses. It's entirely about whether you parse implied multiplication with higher precedence than division.
@@gavindeane3670 Give an answer and explain it. We don't need some failed math student to tell us we're wrong.
My degree in math came from growing up in the '60s and ' 70s. Flash Cards and multiplication tables. Rote memorization, PEDMAS, and being allowed and encouraged to think for yourself.
You kids today are so screwed...
@@johnleeson6946 The answer is ½ if you parse the implied multiplication with higher precedence than division and 8 if you don't.
It has got absolutely nothing to do with parentheses.
You can see why it's got nothing to do with parentheses by recognising that the expression is of the form a/bc. Different people have different ideas on the question whether an expression of the form a/bc should be interpreted as
a
----
bc
or
a
---- c
b
but it is obviously preposterous to suggest that the answer to that question would depend on whether c happens to be a term in parentheses.
@@gavindeane3670 Good job using a whole bunch of nothing to try to explain your wrong answer to those that think you are correct.
You are wrong. Just admit it. I admit you're wrong. You should too.
1/2is the correct answer
8. Quicker, Apu!
All this proves is poor semantics/nomenclature. Pemdas does not include 'left to right', so pure pemdas is 1/2. And 'correct' is misleading because that's like saying English is correct, French is not. Consider 3x when x = 4. What is the value of that? 12. But what is 6 divided by 3x which can be rewritten 6 divided by 3 multiplied by x. According to the author, it's 8. But what if we write it 6 / 3x? Then it's 1/2. And if we consider 3x as a term in an equation, then it's value should depend only on x and not on any other terms. Thus 3x = 12 and 6 / 3x = 1/2. But by the author's logic, 6 ~ (divided by) 3x = (6/3) * x which can be rewritten as 6 * x/3 so that 6 ~ 3x = 6 * x/3 so that 1/3x = x/3, aka x/3 = x squared / 3, an absurdity. Introducing left-to-right destroys the whole point of pemdas. Disturbingly, Excel also mixes left-to-right and pemdas from another channel's example. The final point would be that when channels post '97% got it wrong' what they should say is that the paradigm designers got it wrong. Maths is a language. If 97% say a tree has roots and leaves and 3% say a tree has wheels and an engine, then the common usage should dominate. The not-so-hidden flaw in introducing left-to-right is that it precisely contradicts the pemdas protocol.
Have you stopped making videos?
b) 8
6÷3=2×(1+3)4=8
Who is Brian Logic? Maybe he is a guy who follows PEMDAS to solve math?
C
3 isn't a factor here.
8.
He hits it with fairy dust and the distribution magically becomes an implied multiplication. Then he applies Unicorn piss and splits one term into two terms and gets 8 for an answer. Awesome
Save your dust and piss and enter this into Ai. “Is 3*(1+3) the same as 3(1+3)”, yes is the answer and the result is 8. The problem is that the value outside of the parentheses needs to be resolved prior to the distribution. 6÷3(1+3)→2(1+3)→2+6=8.
@@petersearls4443 proves you don't want to rely on calculators for the answer. Not only can you buy ones that give different answers, you can get them with a switch to give either answer. So your stance is that the coefficient "of the parenthesis" is not part "of the parenthesis". Please review basic factoring.
@@petersearls4443 so you believe that 6/2 is a not one term divided by another? Do you believe you should start each equation from left to right. Do you believe the 2 is stuck to the divisor? Do you not understand that the coefficient of the parenthesis is part of the parenthesis. THAT IT BELONGS TO THE PREVIOUS TERM. LMAO
@@Of_UnCommon_Sense once you resolve the value inside the parentheses you then go outside the parentheses and resolves the expression up to the coefficient using multiply and divide left to right. If you have the expression 1+3(1+3) then yes you would multiply the 3 times 4=12 then 1+12=13. But if you have a divide operation before the coefficient then that must be resolved prior to applying the coefficient to the value inside the parentheses. 6÷3(1+3)→2(1+3)=8.
@@Of_UnCommon_Sense do you believe that what is true in simple arithmetic is also true in advanced mathematics?
Brackets are first 1+3=4. Always left to right. 6÷3=2. 2×4=8. Pretty basic math.
You still have to work the parenthesis. 3(1+3) =3(4)=12, 6÷12=2 or 1/2
Can't be that basic as you're wrong 😂😂😂
If you got 1/2 instead of 8 please don't apply to build my mansion.
@@browniegay9130You don't still have to "work the parentheses". That phrase doesn't mean anything.
@@mikemassey7403 juxtaposed symbols are resolved before the multiplication operator. He got it right; what they teach in school is not the whole story.
8 is my answer
6 ÷3 (1 + 3) = (2)(4)= 8
1/2.
c) 1/2
I did this in 10 seconds. Lol
Because *before
First....finish inside the brackets....1 + 3 equal 4.
Then 6 divided by 3, equal 2.
Proceed with 2 times 4, that's equal 8.
There is no multiplication operator. When you insert one you change the expression - the product of 3 and (1+3) has to be resolved as a single term.
Did you graduate elementary school? I don’t think so
b
Answer is 1/2.
B 8
0.5
One cannot arbitrarily place a multiplication symbol between the 3 and the left parentheses. It is understood that 3 is a “FACTOR” of each of the numbers inside. For what other reason would the 3 be written outside the () without a multiplication symbol?
"It is understood that 3 is a “FACTOR” of each of the numbers inside. For what other reason would the 3 be written outside the () without a multiplication symbol?"
No fancy reason is needed. Leaving out a multiplication sign in certain situations is a common and widespread convention that makes notation clearer and easier to read. For example, people commonly write (x+1)(x-1) = x^2 - 1 without considering x+1 to be a factor of x or -1. More specifically, there is a convention to the effect that when the operation next to () is multiplication, the multiplication sign can optionally be omitted.
@@donmacqueen What notation do you use to show that 3 is a factor of the contents of the parentheses?
@@johnferguson2728 "What notation do you use to show that 3 is a factor of the contents of the parentheses?"
Why does anyone need for a notation for that? For example, when students are learning about factorizing, they might get asked, "What are the prime factors of 12?" The answer, of course, is "2 and 3 are the prime factors of 12". I don't recall any special notation that is used to indicate that 2 and 3 are factors of 12.
For that matter, the numbers inside the parentheses are 1 and 3. 3 is not a factor of 1. That is, 3 is *not* a factor of the contents of the parentheses, not a factor of each of the numbers inside them.
Now, it is true that 3(1+3) is a factorization of (3+9). So, if we had started with 6/(3+9) and wanted to calculate its value, we could, if we wanted, start by factorizing (3+9). There would be no point in doing so, because the simplest way to calculate 6/(3+9) is to first add, resulting in 6/12, which is of course equal to 1/2.
But let's try starting by factorizing (3+9) into 3(1+3). In so doing, we would first have to notice that the whole of (3+9) is *_for sure_* in the denominator. We would then have to write the next step so that the factorized version is also *_for sure_* in the denominator. We would do this by writing 6/(3(1+3)). Without the extra parentheses, it's not *_for sure_*. (_Some people think it is for sure, but lots of people disagree, so it's not actually for sure. There is no universally agreed-upon standard that makes if for sure._) And of course this way of calculating 6/(3+9) would certainly be more complicated.
However, that's all irrelevant, because we didn't start with 6/(3+9).
@@johnferguson2728 I thought I replied already but I don't see it. Sorry if I'm repeating myself. Answer is:
I don't, because there is no need for a notation that shows 3 is a factor of the contents of the parentheses.
(And actually, 3 is not a factor of 1, so 3 isn't a factor of "each of the numbers inside". You were probably thinking that 3(1+3) is a factorized version of (3+9). By itself, it is. But we didn't start with 6/(3+9), so it's not relevant.)
@@johnferguson2728What form of notation do you use to show that the 3 is a factor of the contents of the parentheses? You enclose the entire 3(1+3) in its own set of parentheses. That's what parentheses are for. That's literally the entire point of parentheses.
0.5
Your math is excellent, but not your spelling. Brain, not Brian please. Brian is a man’s name.
Answer is 8 . Not 1/2 .
No -C is answer
1/2
That "older usage" is still in use. You can't use PEMDAS for this expression because it contains juxtaposition, so you need PEJMDAS instead, and the implicit multiplication via juxtaposition comes before the division. This is not old, every mathematician does it today.
Failure. If you can resolve inside the parentheses to a number then the parens can be removed and make it a multiplication operation.
6÷3(1+3)→6÷3(4)→6÷3*4=2*4=8. Order of Operations clearly states that you resolve inside the parentheses. Juxtaposition typically refers to numbers juxtaposed to variables like 2X. 3( is exactly the same as 3*(. If you don’t believe me. Enter the expression into Ai.
@@petersearls4443 it's already multiplication, you don't need to make it into that. Typically juxtaposition is between numbers and variables, but this is not typical. AI is not the definitive source, mathematicians are. You will not find any example in mathematics journals where juxtaposition does not take a higher precedence than division.
@@shaunpatrick8345 my mathematician friend is the one who explained this to me. So you can see why it is confusing. He wrote software included in
Galileo so I presume he knows what he is talking about. And no it wasn’t the section of code that screwed up the meters and feet.
@@petersearls4443 he doesn't know what he's talking about. The definitive video on the subject is by The How And Why Of Mathematics where she shows examples from mathematics and engineering papers, and the AMS style guide, and explains that PEMDAS is a failed attempt by American teachers to explain the order mathematicians use. If your friend can find an example from mathematics where juxtaposition is not given higher priority, he will have disproved her.
@@shaunpatrick8345 I went to her UA-cam channel the how and why of mathematics and watched her video 6÷2(1+2) PEMDAS is a lie. . In there she says the Order of Operations if dealing with ab÷cd would misinterpret it as a*b divided by c and then that result times d. Which I agree would be a mistake. Here is where it gets confusing again. Because the same Ai that would handle 6÷2(1+2) as 6÷2*3=9 says that if you have ab÷cd you multiply a *b then c * d and divide a*b by c*d. So it interprets it properly when variables are involved. So you are saying it is wrong when only numbers are involved but correct when variables are involved? Really?
2@4=8
b)8
How old are you? Cause it looks like you didn’t graduate elementary school
I think its 8
6 :3 ( 4 ) = 2(4) = 8 ( b )
Get a better narrator. My first language wasn't Apuliainanium...
Brasil
Wrong the right answer is:1/2
I got it....... Also free Palestine and the whole world from the protocols of the elders of zion.
1/2 is the correct answer pleaseee , because 3 is multiplied by (1+3) first, not 6:3 multiplied by (1+3). If the answer is 8, the problem should be shown like this = (6:3)(1+3) ....not all math videos give the right ways, answers & solutions.
You're absolutely right that you get the answer 8 it needs to be written (6/3)(1+3).
And to get the answer 0.5 it needs to be written 6/(3(1+3)).
The entire point of the expression in the video is that it can be read both ways.
@@gavindeane3670 You missed class when they taught basic factoring. Since the 3 is the coefficient "of the parenthesis" it belongs "to the parenthesis" and the extra outside parenthesis are indeed implied. Your teacher told the rest of the class that the 3 was stuck to the parenthesis. Does that ring a bell ?
(3(1+3)) and 3(1+3) are exactly the same.
The entire point of the video was to cause dissension and argument.
It is truly amazing how people argue so feverently when they haven't got a clue.
@@Of_UnCommon_Sense Don't worry. I understand this stuff completely. It's not complicated, but it is widely misunderstood. For some reason, a lot of people struggle with the idea that notation can be ambiguous.
Almost everybody makes the same mistake with this meme, which is to believe that their preferred interpretation is the only correct interpretation. They don't all agree on what that single correct interpretation actually is, but ultimately they're all making the same mistake. Many people then try and concoct some mathematical proof for why their interpretation is correct, even though this is not an issue capable of proof either way.
I haven't missed anything about factoring. The first thing to say about factoring is that it's irrelevant here. We are not given the expression 6/(3+9) and asked to take out the factor of 3 from the (3+9). We are just given the expression 6/3(1+3). There's no basis for assuming that that expression necessarily started out as 6/(3+9).
Let's just consider 3+9 in isolation for a moment. Yes, of course you can factor out the 3 from that. No, my teachers did not say things like the 3 outside was then "stuck to the parentheses" or that there was now some implicit set of parentheses outside the 3 and the (1+3), because my teachers were not incompetent fools. If somebody has told you things like that then you need to stop listening to them because they don't know what they're talking about.
In fact, thinking about factoring is a good way to illustrate the logic of the 6/3(1+3) = 8 interpretation. If we consider 3+9 in isolation again, we can factor out the 3 to get 3×(1+3) and it obviously makes no difference if we elide the multiplication symbol and write it as 3(1+3). The choice to use implied or explicit notation for the multiplication there is purely a matter of personal preference.
The argument then is that implied vs explicit multiplication is ALWAYS just a matter of personal preference. It shouldn't be a way to completely change the meaning. When you factor out the 3 in 6/(3+9), if you write it with an explicit multiplication operator you have to add an extra set of parentheses, as
6/(3×(1+3))
so an extra set of parentheses should be required if you happen to choose to use implied multiplication instead, as
6/(3(4))
In other words, since 6/3×(1+3) does not equal 6/(3+9), then 6/3(1+3) should not equal 6/(3+9) either.
There is obvious logic there, and that argument is certainly not without merit. The counter argument of course is that something like 1/2π would have to mean 0.5×π, but the world is full of mathematicians and scientists and engineers who would naturally interpret 1/2π as
1
---
2π
not 0.5×π.
Ultimately, such notation is ambiguous - that is the entire point of this meme. It's a well known, well understood, and very simple issue. Mathematicians will tell you it's ambiguous. Different calculators give different answers. And the international standard for mathematical notation simply disallows this syntax. Many people will argue to the death that their preferred interpretation is the only correct interpretation, but that's ultimately futile.
(As an aside, an example like 1/2π illustrates how this issue is entirely about implied multiplication and has got absolutely nothing to do with parentheses)
@@gavindeane3670 despite your novella this equation is not some unusual made up equation. It is something seen all the time. It is laughable that you would think it unique.
You have a trolley pushed by a measured force of 6.06 =F the mass of the trolley is measured at 2 and a measured at 4 is a mass placed on the trolley. The mass measurement device is off by 1%. So now the correction factor is. 1.O1
Now mass is M = 1.01(2+4). So now the acceleration is; A= F/M
A = 6.06 / 1.01(2+4)
Now we measure the acceleration. Can it be both 1 and also 36.
@@Of_UnCommon_Sense Indeed it is seen all the time. It does the rounds regularly on the internet because it makes great clickbait.
It's not a properly formed mathematical expression. It's just a silly internet joke. It is, as I said, a well known and well understood issue.
The best advice is: don't write like this. In the real world it's largely a non-issue because those of us who use mathematics to actually do things generally write division in a vertical layout, with numerator over denominator, not using inline operators.
How do you get -1 ?
8 should be acceptable.
If you want 1/12, the use an additional set of parentheses.
Ramming PEMDAS down students throats is not a good practice; teaching proper notional practices to prevent ambiguity and confusion is a better practice.
Complete rubbish. This is not math. Pemdas is not necessary. Just write the expression properly in the first place. Write (6/3)(1+3) or 6/((3(1+3)). No wonder kids are put off math.
That's not written in a way people who were not taught parentheses can understand. The expression in question is written in a way that people who learned mathematics can understand; the problem is that the person who made the video and most of the commenters didn't learn it.
@shaunpatrick8345 I guess my point is that kids at school should be taught parentheses to avoid the use of PEMDAS.
@shaunpatrick8345 can you clarify your post, please? I don't think I can follow everything that you are trying to say...
What do you mean "not taught parentheses/brackets?" B in BOMDAS stands for brackets/parentheses. They are used in these expressions, but people don't understand them???
@@RobertCanova-sn4sh you imply that the expression has not been written properly, but it actually has. Had you learned what juxtaposition means you would be able to parse the expression, whereas the version you suggest can only be parsed by people who learned what parentheses mean. The issue is not in how the expression is written, it is whether people understand it. However it is written, even in the manner you suggest, there will be people who don't know how to resolve it. If people were presented with an expression containing calculus, it would be absurd for them to demand all such expressions be written in a way a 5th-grader can understand, and the same goes for this one.
You over complicate and get it wrong. It is still 8
a) You talk way too much
b) You talk way too fast
c) You talk a lot but are not clear
d) Your singsong voice is annoying
e) This video is far too long to convey a fairly simple concept
Concur 👍
11
It´s 1/2, I guarantee it!
Yes it's 8.
I can see why 97% of people get it wrong by reading the comments!😂
Nope! 3(1+3) is implied multiplication! You cannot magically change the symbology to explicit multiplication after doing the addition. The rule for implied multiplication changes the precedence such that after work inside the parentheses is done then the multiplication that is implied is done. Casio's website gives a good explanation of the rule. If you write the original problem using explicit multiplication, 3*(1+3), then you would get the answer you are presenting. The underlying reason for all this has to do with how computer algorithms and hardware have to parse input lines. I will add a caution to math students when using calculators to work problems such as this: not all calculator manufacturers have incorporated the implied multiplication rule. TI, for example has not. Some computer software, like Matlab and Maxima, will give a syntax error if the user tries implied multiplication notation.
BS - you do not know what you are talking about. Go learn. Start again.
When you use ÷ the Answer is 1/2
When you use / the Answer is 8
The answer is the same both times: 1/2. The difference comes when you use the proper or improper order of operations. The proper one for an expression containing juxtaposition, like this one, is PEJMDAS.
@@shaunpatrick8345put the expression into Ai 2 times, once using the obelus and once using the soledus both will return 8.
6 : 3(1+3)=
6 : 12 = 0,5
6÷2(1+3)
Parentheses first
Divide
Multiply
That's not true. The answer is half and not 8. How did you remove the bracket between 3 and 4?. How did you bring the multiplication sign between 3 and 4 ? You took away the brackets and put multiplication. This is where you errorerd. You needed to multiply the 3 and 4 in brackets to take take out the brackets. Dont mislead people.
That's what it means when two terms are written next to each other like the 3 and the 4 here. It means multiplication.
Obviously in isolation 3(4) and 3×4 mean exactly the same thing. So the question is, why shouldn't 3(4) mean 3×4 when it happens to be part of a larger expression?
@@gavindeane3670 Indeed! Some people think 3(4) means 3*4 and others think it means (3*4), when it happens to be part of a larger expression.
And it may not matter, depending on the larger expression. For example, it doesn't matter if the larger expression is 12*3(4). But it does matter for 12/3(4).
@@gavindeane3670 Even the the number of terms inside are reduced to only one it is still a distribution. The multiplication still occurs within the parenthesis.
(3*1+3*3)=(3+9)=(12)=12 The parenthesis has a value of 12 no matter what form we write it in.
This is two multiplications and one addition. The smarter way is one multiplication and one addition.
Here is how.
(3*1+3*3)=(3+9)=(12)=12
Remove the common factor;
3(1+3)
The only way to return the 3 to the inside of the parenthesis for evaluation is distribution.
Distribute;
3(1+3)=(3+9)=(12)=12
[two multiplications required]
Combine terms then distribute.
3(4)=(3*4)=(12)=12
[one multiplication required]
3(4) is still 12 by implied multiplication. It is a single term, while 3*4 is two terms.
6 / 3 * 4 is different from 6 / (3*4)
Any time you have a set of parenthesis with a coefficient it is a distribution. Therefore a single value, parenthesis are implied.
@@Of_UnCommon_Sense It is not distribution when there is a single term in the parentheses! Who told you that???
The fundamental nature of distributivity is that it is a property that one type of mathematical operation has OVER ANOTHER TYPE OF MATHEMATICAL OPERATION.
When we talk about distribution here, what we're using is the distributive property of multiplication over addition. That's its proper mathematical name. If there's no addition inside the parentheses then by definition we are not distributing.
3(4) is not a single term. It's trivially easy to see why that's wrong. Just think about how you would square 3(4). If it was a single term then you could simply write 3(4)². But as I'm sure you know, if you write 3(4)² the squaring applies only to the 4. If you want to square the entire 3(4) then you must put the entire 3(4) in a set of parentheses, as (3(4))². The 3 and the 4 need to be placed inside a grouping symbol precisely BECAUSE they are not grouped by the implied multiplication notation. They are separate things.
@@donmacqueen Some people do think that 3(4) means (3×4) as part of a larger expression, but those people are incorrect. Just consider the expression 3(4)². That certainly does not mean (3×4)².
People who actually understand this stuff know that the issue is about the precedence you give to implied multiplication. It is a common convention to parse implied multiplication with higher precedence than division (but absolutely not higher precedence than exponentiation). That's how you actually get 6/3(4) = 6/12 = 0.5.
The problem comes when people try and argue that that's the ONLY way it can be parsed.
B)8
Using PEMDAS, the answer is 8.
But the expression contains juxtaposition, so PEMDAS will get the wrong answer. Use PEJMDAS, the answer is 1/2.
2x4=8
The ans is 1/2
The answer is 1/2. If 97% failed this then I start to believe we didn’t get to the moon!…😂
Answer is 8(b).
@@RamDas-eo3ol Hi you right I must have mistaken with another answer, (brackets first and time the previous 8)
Somebody got bumped off before it lifted off!
@@mikemassey7403
3 it can be a factor as well because the brackets are always first. Last minute too scared to join the club, cheers 🙂
@@mikemassey7403
Brackets got precedence,
always in any form. 1/2. Last minute scared to join the club before take off. 😊Cheers
Ans=6÷3(1+3)=6÷3×4=2×4=8.
Si 6:3x4 = 8, 6:4x3, también debe dar 8. Pero no.... Porque el método empleado, es erróneo.
The answer is 1/2 because parenthesis has presidency. ( 3×1 + 3x3) r= 12
It's got nothing to do with parentheses. Parentheses literally cannot have precedence. Precedence is a concept that relates to mathematical operations and "parentheses" is not an operation.
What you did was to give the multiplication higher precedence than the division.
@@gavindeane3670 the P in PEJMDAS gives the precedence. Despite getting the wrong answer, at least the video maker got that right.
Ans is 1/2
2×4=8
6 ÷ 3 ( 1 + 3) =?
6÷ 3 x 4 =?
2 x 4 = 8
6÷3(1+3)=
6÷3× 4 6÷3=2 × 4= 8
It 8
There should not be any argument because of the implied operator only operates on the parentheses, meaning the 3 cannot be separated from the parentheses, its one term and must be simplified. It’s not 6/3*(1 + 3) which would be a fixed operator, meaning the 3 does not operate on the parentheses.
Writing equations has rules just like solving equations.
And give up on PEMDAS, it’s long overdue to throw it out because it is flawed in too many way to count!
Nope. They are rules. Arbitrary, perhaps, but the rules nonetheless. As such the answer is 8
@@michaelcoll433
Try to say it stronger next time and I still will be right!
@@michaelcoll433
ua-cam.com/video/4x-BcYCiKCk/v-deo.htmlfeature=shared
@@michaelcoll433 they are not rules you can follow when the expression contains implicit multiplication, unless you are happy with the wrong answer. PEJMDAS is a more complete set of rules which do work.
Wrong wrong wrong the right answer is 1/2
You're wrong because once the expression(s) within the parenthesis/parentheses are solved the parenthesis/parentheses seized to exist. I refer you to your Math's teacher, please.
6 ÷ 3 = 2 × 4 = 8 is the answer
6 : (1 + 3) = 6 : 3x4 = 6 : 12 = 1:2 Los factores de un producto, NO SE PUEDEN SEPARAR. Expliquen esto:
Si 6 : 3x4 = 2x4 = 8, siendo 3x4 igual que 4x3, 6 : 4x3, también debe ser 8. Compruébenlo.
8 is the answer
The answer is 8-b.
B8
The answer is 8.
Ans 1/2
Ans is 8
The answer is8
C=1/2
12 is rezult
I got it....... Also free Palestine and the whole world from the protocols of the elders of zion.