Yep. My thought on this is that the video was first done with the answer being 12 (which is the correct answer because 1/2 is the same as 1 divided by 2), then redone a 2nd time where the 1/2 is re-interpreted as a single symbol replaceable by 0.5, and thus the answer is 48.
@@marscience7819 12 is not the correct answer. As I delineated in previous comments....the numerator is 18/1/2x4, and the denominator is 3. With that fraction as the numerator 18/1/2x4, well 18 is the numerator, and 1/2x4 is the denominator, for which that is a product. so 18/1/2x4=18/2, which equals 9. 9/3=3. Now the errors made in this video are assuming parenthesis where they aren't present, as that violates the definition of an implied multiplication operator. To realize 18/1/2x4 to equal 36, that would need to be written with parenthesis of (18/1/2)x4, which it is not. Secondly the dividing line is called the vinculum, which by definition values are grouped above the line and below the line. With this expression, 18 is above the line, and 1/2x4 is below the line. So the wrongful answer is in violation of the definition of the vinculum, as 1/2x4 is below the line, but is being broken up. Lastly there is a simple algebraic proof of a/bc=a/bx1/c, and not (a/b)c, as parenthesis cannot be assumed. Take 1/3 x 1/4. That equals 1/12th. But what this wrongful video states is that 1/3x4 is not 1/12th, but is rather being treated as (1/3)x4, when no parenthesis are present, and that would give a wrongful answer of 4/3.
You are clear as mud. You made an easy thing so complicated, that I was very tempted to zap you. I was raised on B.O.D.M.A.S. (brackets, of, division, multipllication, addition and subtraction) and it was treated me correctly. so no need to change it. All in all the most simple thing to do is to convert 1/2 into 0.5 and proceed from there.
Why transfer 1/2 to 0.5? There's no need for that.. At first you can cancel 18 in denominated by 3 in nominator. That gives you 6 / 1/2 * 4 which is the same as 6*2*4 and that equals 48
If you simply follow the rules, and don't add any of your own assumptions, the "1/2" can NOT be replaced by "0.5". The forward slash is defined to mean "divided by". So, if you see the symbol "1/2" BY ITSELF, nothing to it's left, then yes, it can be replaced by 0.5. BUT IT'S NOT BY ITSELF, it has something to the left of it that has to be done first by the rules. What you have done is added another assumption, which is in your head, but not part of the rules!!!
@@marscience7819 I had no problems converting 1/2 to .5.. which is simply 18/.5 which is 36 x 4, then divide by 3.. comes out perfectly to 48.. 1/2 does equate to .5 in this equation..
I'm 75, don't remember when I last sat for a math class. I got the answer in less than 10 seconds. Contemporary education is missing something if young folks can't figure this out.
One thing to understand is this problem has nothing whatsoever to do with arithmetic. It has to do with the rules to apply. With the rules defined, the answer can be either 12 or 48, where I lean toward 12 because there is no rule in PEDMAS that tells us to treat the symbol "1/2" as if it one thing. The commonsense thing is to treat 1/2 as 1 divided by 2, which then means the numerator must be 36 by PEDMAS. Let me say again, the problem with these kinds of arithmetic has nothing to do with arithmetic, it has to do with the rules to use. Try this: It's not exactly the same, but you should get the point. Consider these two sentences. "Let's eat grandma" and "Let's eat, grandma". It isn't the "young folk" that are the problem, it's the "old folk" that unnecessarily complicate this simple arithmetic problem. They do it on purpose to confuse the student because they have nothing better to do. They make the expression ambiguous. If the teacher wants the answer to be 48, then write it as (18 # (1/2) X 4)/3. I don't have a divide sign on my keyboard, so I use #. That expression is unambiguously 48. If you want to confuse the hell out of clean, unbiased young minds, then write it the way this teacher did. The way he wrote it should technically have the answer 12, but 48 might be acceptable with the additional rule that a symbol like 1/2 is to be treated as single symbol and not as "1 divided by 2".
Well, I'm 44 (not old, but not young either lol) and this entire sequence is completely beyond me so it's not just young individuals that struggle. I got 0.75 for an answer by trying to do this intuitively (at least my version of it) but then again, no math teacher could EVER figure out how I looked at things like this - so with neither party understanding ANYTHING that the other was talking about, math class got pretty interesting. I always lost though 😂
@@marscience7819 I know, I never got any of these right back when I was in school either - just illustrating how this is beyond simple for some, but confoundingly impossible for others 😵💫
@8:33 Why did the answers change from the original problem's answers here? 48 is no longer D here, which was super confusing. I had 48, but changed my PEMDAS around as 48 was not an answer given?? I got the problem correct initially (48) until I got to this phase of the review and changed my answer to B) 3 as I multiplied first .5 x 4 = 2 to 18/2 over 3 or 9/3 or 3.
@@Spitfireseven Likewise, 79 and found it simple, education today is to what it was. Try giving a cashier £12. 25 (to get rid of pockets full of shrapnel) when she asks for £6.75 and watch the reaction.
I used to get F’s bc I never showed my work. This was probably the easiest one in the 6-8 I’ve done so far. In my jr. and sr. High classes I would get poor marks because I never showed my work. I didn’t even know how I came to the right conclusion and honestly, couldn’t explain how I found the right answer! I even had to repeat 2 levels of math before I could even graduate bc no one knew or even understood what Aspergers was in 1991. Thank you so much for putting these problems out there. It feels SO AMAZING 🤩 😊 to answer your questions and know in the blink of an eye what the answer is. I hope you can make an impact on all of the others out there who were either wrongly diagnosed or not diagnosed at all. We are really smart and now grateful that someone else (you) can test us and we can show you what we can do and literally how fast we can do it!! I’d love to talk to you about your experiences with people with Aspergers and Autism (high functioning Autism)❤❤❤❤❤❤❤
Old school math teacher here. Purposely not using parentheses is like leaving verbs out of a sentence. No one will fill in the missing word the same way. Not to mention that the order of operations was taught differently. Just use the fricken parentheses. I did an exercise with the parents of one of my 4th graders. Gave them and a group of other adults ranging in age from 18 to 60 an math problem. ALL 6 adults got it wrong. The parents were at a BBQ and a little buzzed. The math problem caused major arguments and almost ended up in fist-a-cuffs. THIS BS IS WHY PEOPLE HATE MATH!!! It is more important to get the right answer.
The question of whether and where to put parentheses is a minor detail compared to the fundamental, inexcusable error of using two different symbols for division in the same expression. He needs to fix that before we can have a discussion about parentheses
@@gavindeane3670 100% agree! Making math miserable is not helping people learn math. There are 10 kinds of people who get that. 😉 (a little binary humor)
The correct way to interpret an expression is in the way that the person who wrote it intended and in this case it was intended to confuse. Sadly, some folk just enter such expressions into a calculator without any thought as to what was intended and of course the result is often wrong. Even more confusion arises with implied multiplication, for example, what is the value of 1/2𝝅f where f=10 ? This is a standard formula in electronics and it's intended to mean 1/(2πf) rather than (1/2)πf. But if you blindly follow BODMAS you'll end up with the wrong result.
Leaving aside the specific issue of implied multiplication after inline division, which isn't relevant to the video, if you enter an expression into a calculator then by definition the answer that comes out is the correct answer. If that is not the answer that the author intended, that is not the fault of the reader or the calculator. That is the author's fault.
@@gavindeane3670 Sadly, it's not quite that simple. I've watched a few videos on RUclips in which someone enters the same expression into two calculators and gets two different answers. So basically, blindly entering an expression into a calculator and claiming that the result that comes out is the correct answer is exactly NOT the right thing to do. The key is to think about the situation and interpret the expression accordingly.
@@RawFitChris No, I rejected algebraic calculators long ago and ONLY use RPN ones. They are the only ones that I trust. Algebraic calculators are ok for simple expressions, but as soon as you need to calculate square roots or trig functions, they vary in whether you need to put the operator before or after the number.
@@Chris-hf2sl That is a well known and well understood issue with implied multiplication after inline division. Different calculators do indeed give different answers in that specific case, but that's not relevant here.
ISO 80000-2 states you should not use an obelus for division, you should use a solidus. In its original use the obelus was used as a ratio. As a ratio 18 over .5 * 4 = 9 9/3 = 3
once you get rid of the pesky 'divided by one half' by changing it to x2 it is simple and the remaining operations can be in any order so the simplest solution is 36/3 =12 x4=48 final answer.
I can't tell you why. Between my sophomore and junior years in high school, I went to a "math camp" for six weeks at Rutgers University. I had a blast learning all kinds of math they never teach you in public school. Loved it!
Sorry, will have to disagree. There is no rule in PEDMAS that says to treat 1/2 differently than 1 # 2 (sorry, my keyboard does not have a divide symbol, so I use "#"). So the numerator might as well read 18 # 1 # 2 X 4 which gives 36 by PEDMAS. 36 then divided by 3 is 12. Given PEDMAS with no other rules, the answer is unambiguous. Both 12 and 48 would have to be accepted as correct. The way around this is to use parenthesis around the 1/2........18 # (1/2) X 4. Whether it matters or not, I do have a Ph.D. in physics.
About 50 years ago I made it through business calculus, with quadratics, along with stats and geography, and graduated with a Bachelor of Science degree in Business Administration/Economics. I am currently retired, but I do not remember anyone ever mentioning PEMDAS. Before you start mocking me, I developed a degenerative neuromuscular disease, which is advancing. Along with other mental exercises, I am following this program to hopefully slow some of my cognitive loss, and not to get frustrated so easily. I just don't remember problems being presented like this back a half century ago. There always seemed to be more structure to the process, which determined which step was to be taken first, and/or next, etc.
The main principle in PEMDAS - multiplication having higher precedence than addition - has been the way mathematical notation works for a few centuries now. Given the level you reached, the way you were writing mathematics undoubtedly relied on this principle. For example, I'm sure you would have written a quadratic as ax²+bx+c rather than a•x²+(b•x)+c But you were probably relying on this principle without even realising it. What seems to have changed more recently is explicitly teaching this principle in the context of simple arithmetic. That is widespread today but it seems to have been more patchy in the past.
@@gavindeane3670 I spoke with a life-long friend who has a PhD from Penn State. We grew up together and graduated from high school in the same class. He is known for starting the largest experiment on the effects of ozone gas on old grow forests in the world and National Geographic did a video on him and his work back in the 90s. He retired early due to a Pulmonary disease and since we are both disabled, we check in on each other from time to time. He had his share of different types of math and he also said that what he sees on RUclips today is completely different from the way he was educated. Again, this was 50 years ago. So, it's just not me and although I deal with a neurological disorder that has made life complicated, there are certain things that stay with me. My keyboard doesn't have the capabilities to show powers and long division lines, but the quadratic formula I remember (spelled out) was negative b plus or minus the square root of b squared minus 4ac, over 2a. It's been a long time, so that might be a bit off. The math I used in my career was very narrow in scope. Can you see where the difference in how the formulas are presented are confusing to someone who doesn't eat and sleep numbers? If you are a math teacher, it must be obvious, but as someone who had to take this class and although an A student, I concentrated on the applications geared towards the business world. Such as finding the break even point, and maximum efficiency level in manufacturing. You could see the vertex of the parabola when graphing it out. Again, please forgive the fog.
PEMDAS is a notational convention that was finalized about 400 years ago in order to minimize the need to use parentheses. I like to tell my students that it's an artifact of history and could have turned out differently. Therefore, it is "correct" by general agreement.
@@DeanNataro It may be old, but that is still not how math was taught for a very long time. No wonder why parents are not able to help their kids with homework. With parentheses you knew in an instant what had to be finished first. You would become efficient after using PEMDAS for a while, but I still see no need for a change. Quadratics looks totally different.
@@thinkcivil1627It was implicitly taught, in the way that mathematical expressions are written - particularly algebraic expressions. What's changed is that it is now widely taught explicitly, using the context of simple arithmetic.
If you key his formula exactly as written into a spreadsheet such as Excel (use / for the division sign): 18/1/2*4/3 = 36. To get his answer of 48, in Excel you would have to enter it as 18/(1/2)*4/3. Algebraic expressions in Excel never assume parenthesis, they must be entered. Anytime I see a formula without parenthesis, I assume it means no parenthesis.
@@captainjaybird You're correct in general, although in this particular case the parentheses around numerator and denominator don't make a difference. 18/1/2×4/3 will still give 12 without the parentheses. I don't know why the person you replied to says they got 36 in Excel. They would have got 12 for what they wrote.
This question is at the least ambiguous because the slash symbol / is short hand (an alternative) for the horizontal line when used write equations on a single line instead and so would imply everything before the slash is the numerator and everything after as the denominator. The use of both division symbols in the same equation only adds to further ambiguity as it implies there is a difference between the two; if not this, then what other differences would there be? The last item causing ambiguity is the spacing of the 1 / 2 which is close to the spacing of the other possibly indicating that 1/2 was really 1 / 2 which would add support for the use / as an alternative for the horizontal line spelled out above. Nice Work TabletClass this video definitely got some engagement, lol. 🤑
But if your saying that the slash is a division line then why isn't it read as "18 divided by 1" over "2x4" which no one here seems to be arguing for ..... It seems to me the 1/2 which is spaced as if it were a whole number does indicate that it is meant to be a fraction and not short hand notation for division)
A second question about the use of the fraction bar is that while treated as a vinculum the original examples given for the obelus was treating it as a vinculum.
Correct. What is shorthand is an Obelus. When first presented it was shown in examples as a vinculum with one major deference and that line length. What is above or below the line is determined by the line itself. The obelus essentially eliminated the length of the line.
I will reject the problem and make no attempt to solve it as it contains both ÷ and /. My guess is the 1/2 is intended to mean 0.5, not one divided bt two. If that is the case the fraction should be reformatted with the fraction bar horizontal. When the student has to guess what the teacher intends, the problem should be withdrawn.
The division sign and the slash sign both mean division so under his description of PEMDAS 18 should first be divided by 1, the answer then divided by 2 and that answer multiplied by 4, with that whole numerator divided by 3, equaling 12. PEMDAS didn't require us to do a slash division before a division-sign division, did it? Just for fun I prefer to solve the problem like this: [(18/1) / (2x4)] all divided by 3 which would be 0.75, but that wasn't one of the multiple-choice answers.
@@gcarapThe / symbol does not imply parentheses anywhere. It is the division operator, not a grouping symbol. There are no fractions in the numerator in this question. There are four numbers (18, 1, 2, and 4) and there are three operations (two divisions and a multiplication).
@@gcarapIn isolation we can represent fractions by writing things like 1/2 but that's not what it is. 1/2 is a number and a division operator and another number. And the division operator absolutely is not a grouping symbol. When it appears as part of a larger expression you cannot blindly assume that you can put parentheses around it. Whether you can do that or not depends entirely on the context. Think about why 1+3/4 is the same as 1+(3/4) but 3/4² is NOT the same as (3/4)².
@@gavindeane3670 No. If your intent is to express division, express it as division symbol (sorry, not on my keyboard LOL), If you use /, it is interptreted as a fraction formulaicly. So in that sense, the division sign and the / are NOT the same when used within formulas. And while his solution here was 100% correct, it would have helped if he mentioned the fraction as an implied P instead of stating there are no Ps. I suppose he assumed the solver already knew that the use of "/" is aleays interpreted as a fraction when part of an equation.
All you gotta do is change a rule slightly, (if that could be phrased like that) and you get a different answer. I'll never forget the new math about fifth grade in 1969. It's all so changable. There's no yelling, "Foul" and getting away with it!
I'm 66 and have struggled with math my whole life. But I also think math is fascinating. This problem has me flummaxed! When I see 18÷2, logically I think the answer is "9". Is there a way to explain (verbally) this conundrum? Thanks!
Any one else notice that the " correct" answer 48 at 6:17 of the vid is no longer there at 8:28 of the vid then the answer list dissapears at 9: 48 while he ' explains' the order of opetations...48 again reapears at 10 :58....this is a poor explaination of the order of operations and and would only confuse some one trying to learn this type of math
The big question is how would 'you' code it to a line in a computer software program, then run it to get the answer d) I would have to go ((18/(1/2))*4)/3
Interesting point. I wish my main computer was fixed, because I have a math parser that should handle that equation as written. Only you have to enclose the top half in parentheses. This would be a good test for it.
@@johnshaw6702 I am sure All the top half is enclosed in parenthesis as ( (18/(1/2)) * 4 ) /3 example start 1st, bracket, start 2nd bracket, 18 / start 3rd bracket, 1/2 end of 3rd & 2nd bracket *4 end of 1st bracket /3 On reflection I shall have written words "the minimum parenthesis or brackets needed to make it work for the correct answer", even so I sure I got it right first time.
@@ericr2646 You are probably correct, but I haven't even looked at my parser in over a decade. I wrote that code over 25 years ago for an equation graphing program. It had a few more tricks up it's sleeve than the average parser.
I was thinking the same.. knowing that multiplication and division are "weighted" the same in order of operations it seems like you'd just go in order.. Wasn't aware that 1/2 isn't the same as 1 divided by 2.
That is a very reasonable question. The author is trying to use ÷ and / to mean different things, but that is not standard and the notation in the question is sloppy. Your interpretation is completely reasonable.
@@bulldog6925No. 1/2 is a mathematical expression that EVALUATES to 0.5. At least, that's what 1/2 is in isolation. But it's not in isolation here. Context matters.
What many miss is how an obelus was originally used. Essentially all above over all below. ISO 80000-2 states not to use it for division. In Nordic countries it was used for subtraction. Before using order of operations one needs to use proper notation.
If you rigorously follow PEMDAS, the answer is twelve. If you treat 1/2 as an implied notation (much like 3x or f(x)), then 48. So, which dialect of math do you wish to speak?
As there is no sensible dialect of math that permits two different symbols for division in the same expression, the best answer to this is to take it back to the person who wrote it and tell them to write it properly.
No, the correct answer is 12. As any computer user can tell you, / and ÷ are identical, both denoting divide. If you want the second term to be 0.5, then write ½, not 1/2. Hence, the correct answer is 12, not 48. The equation should be evaluated as (18÷1÷2×4)÷3 = 12, NOT (18÷½×4)÷3 = 48.
@@RationalSaneThinker I think you are being irrational !! One would NOT use both division symbols in the same expression for both to mean "divide". Where both are used, the "'/" would always indicate a fraction, not an operator.
Exactly right. The / symbol literally is a division operator. The expression he's written evaluates to 12. In the video he's evaluating the expression he meant to write, not the expression he actually wrote. The correct way to write the numerator he's trying to write here, using inline notation, is 18/(1/2)×4
At 63, you made me dust off lots of old memories. But i did get the answers right. In fraction math. I just asked myself, how many half units are in 18. 36. The rest was elementary.,
This is not really about the mathematics itself, but about the system of notation and the ability to read it. If I read it the way the narrator does (and I did) I get his answer (and I did). But if someone reads it differently, I can't blame him.
@@lindakrzyz5512 12 is what it actually evaluates to. 48 would be if there were parentheses around the 1/2. 3 would be if there were parentheses around the 1/2×4.
@@martinglenn27As written, the only answer is 12. Well, the only real answer is to take it back to the person who wrote it and tell them to write it properly.
I reached the same conclusions as you. At first I thought 48 was wrong and came up with 12 but then I realized that fractions must inherently come with their own brackets when it comes to fractional divisors and the order of operations. If they did not, then dividing by a fraction would be impossible since the fraction would be split apart into two separate divisors. The quantity being divided (a) would be divided only by the numerator of the divisor fraction, not the whole fraction. This first result (call it 'b' as this is a new number) would next get divided by the denominator. Without the inherent brackets to prioritize fractional divisors as distinct numbers instead of mere parts of an expression, the fraction would get torn apart. The invert and multiply concept would not exist which would defy common sense. I thought the creator here was getting cute with the astonishingly rare mix of division sign and fractions within a single expression. I doubt this was his intention however as he makes no mention of this issue of fractional integrity under OOO manipulations. I believe the international interpretation of OOO does dictate fractions as distinct numerical values (meaning their a over b value is determined before anything else applies - aka inherent brackets)
@@joeblog2672 There is no such thing as inherent brackets around a division just because you want to think of it as a single fraction. If brackets are needed around the (1/2) they must be written. And anyway, even if they're was such a rule, why does the second division in the expression get to use the rule but the first division in the expression doesn't? Why does 1/2 get the brackets but 18÷1 doesn't? That would only make sense if ÷ meant something fundamentally different to /. It doesn't. They mean exactly the same thing. They are both just a division operator. The only difference is that ÷ is deprecated and should not be used. The proper inline symbol for division is /. So the numerator in this question should be written 18/1/2×4. Dividing by a fraction is not impossible. It's extremely easy. The best way to divide one fraction by another is to actually write fractions: 1 3 ---- / ---- 2 4 If you are writing inline instead of using a vertical layout then it is trivial (and essential) to add brackets: (1/2) / (3/4) The use of two different symbols for division in this question is indeed astonishingly rare - and thankfully so, because it is also astonishingly silly. There is absolutely no excuse for it.
It's not 18 divided by one half, it's 18 divided by 1 divided by 2. The divisions are applied left to right: 18 divided by 1 is 18, 18 divided by 2 is 9. 9 divided by 3 is 3 and 3 times 4 is 12. 18 divided by one half would have to be written 18 divided by 0.5
I think that since the obelus was used first to divide, it indicates to me that the solidus indicates a fraction. If that is the case the answer is 48.
I am a bit confused… always thought / was interchangeable with ÷ … making the the numerator: 18 ÷ 1 ÷ 2 x 4 I get the reciprocal but shouldn’t the 1/2 be in parentheses?
You're absolutely right. ÷ and / are just different symbols for division so as written the expression evaluates to 12. With parentheses around the (1/2) the answer changes to 48.
@@gavindeane3670 This is the comment I was looking for, both yours and the one you're replying to. One could argue that the use of the divided by sign in one place makes you assume a fraction in the other, but not necessarily. The parentheses absolutely should have been used to clarify as you mentioned. I would say that it is justified that you could say the answer is 12. Order of operations says left to right and a forward slash means divide, so you are correct.
In order for your answer (48) to be correct, you would need the 1/2 fraction in the numerator to be set off by parentheses. This would give you: 18 / .5 x 4 = 144. Without the parens around the 1/2 fraction, the PEMDAS rule would be 18 / 1 / 2 x 4 = 36. The correct answer is 12.
As written the fraction bar could be interpreted as a horizontal representation of a vinculum by its length which exist below the base. A vinculum has a automatic grouping meaning. That was also the original meaning of the obelus.
you're respond would imply that its equivalent to (18/1)/2*4 then all divided by 3, which is 36 and that's not an option. so it can be safe to presume that the properly implied equation is 18 / ([1/2] fraction notation=.5) * 4 all divided by 3 which is D)48
@@indifinity215 It's not about how easily we can guess what he might have meant to write compared to what he actually wrote. If this had been written by a child in primary school it would be forgivable. But it's not been written by a child. It's been written by someone who purports to be a mathematics teacher, and there is no excuse for him not writing it properly. The correct way to write the numerator he's trying to write, using inline notation, is 18/(1/2)×4
@@gavindeane3670 yes thats my interpretation because if they meant 18 ÷ 1 ÷ 2 x 4, they would have witten it with the ÷ instead of using the ÷ after the 18 and before the 1/2. so logically they inferred a fraction of 1/2 or 0.5... lol :p
The equation is misleading. You are verbally implying parenthesis around what you are referring to as a fraction.... However there are no parentheses in the equation.
Is not the slash (/) in the “½” the same as a divisor symbol? ½ .., same as ... 1 divisor symbol 2 ? (=0.5) … e.g., N= 18/1/2x4 … vs. … 18/(½)x4...vs ... Why did you consider the ½ (0.5) before the divisor immediately after the 18, just like you would with a parentheses around the ½? Maybe you consider the1/2 as a mini N/D equation, within the main N/D equation, that needs to be done first?
Yes, the / symbol is the division operator. In the video he is treating it as if he'd put parentheses around the 1/2. He's evaluating the expression he meant to write, not the expression he actually wrote.
What makes me wonder is how dividing 18 by 0.5 increases the value of 18 to 36. Usually, in my mind I interpret 18 divided by 1/2 as 18/2 = 9 Which is correct? Are we dividing by 2 or multiplying by 2?
No, the teacher is correct …. in the PEMDAS, the grouping “MD” is a performed left to right. e.g., you could say, “after I do all the parentheses and powers, I will do the Multipliers and Divisions in a left to right order as I read them. After all the multipliers and divisors are completed, I will move to the next group, the “Additions and Subtractions”. The Additions and Subtractions are also to performed in the Left to Right order (just like the M & D group), but it really will not make difference in the result at this point
Interesting when I did this in Excel I got 12. This is why whenever I write computer programs or do financial spreadsheets, I use parenthesis and this eliminates any misinterpretation.
Excel said 12 because 12 is the answer. As written, that's what this expression evaluates to. In the video he's solving it as if there were parentheses around the 1/2. But he didn't write those parentheses. He's solving the question he meant to write, not the question he actually wrote.
@@richardcarlin1332Completely agree. Another good tip to avoid confusion, relevant to the author if the video, is not to use two different symbols for division in the same expression.
In the UK the BODMAS mnemonic is used: “brackets over division before multiplication before subtraction”? Not PEMDAS which is not correct! Division before multiplication please!🧐☝
PEMDAS is just another name for BODMAS. They're the same thing. DM vs MD in the acronym doesn't make any difference. It's not division before multiplication in BODMAS and it's not multiplication before division in PEMDAS. It's a 4 step process not a 6 step process. The MD step in PEMDAS is identical to the DM step in BODMAS. You calculate all the multiplications and division with equal priority, reading left to right.
@@tuftyaurelius9062Obviously if you do multiplication before division vs division before multiplication you can get different answers for things. But as I already explained, PEMDAS does not tell you to do multiplication before division and BODMAS does not tell you to do division before multiplication. You do whichever appears first on the expression. When multiplication appears first, BODMAS and PEMDAS tell you to do the multiplication first. When division appears first, BODMAS and PEMDAS tells you to do the division first. Your mistake is that you are blindly following the sequence of letters in the acronym instead of following the rules that the acronym refers to. There are lots of variations of the acronym: BODMAS, PEMDAS, BIDMAS, BEDMAS, GEMDAS, PEMA, BOPS, BIPS, GEMS, etc... They all refer to the save calculation process. They all mean exactly the same thing. What you're doing is a common and understandable misconception. It's the reason why the 4 letter variations of the acronym exist.
8:40, hm..there's this deal with fractions that is the crux of this (and my error). this idea of how to handle fractions is not in PEMDAS...i dont memorize things like that, but thanks for showing me the 'fraction issue' . PEMDAS doesnt help with this problem.
GEMDAS addresses exactly that issue, with G for Groupings. It's exactly the same as PEMDAS except for recognising that parentheses are not the only grouping symbol in mathematical notation. The vinculum (the horizontal fraction bar) is a grouping symbol too. You need to evaluate the numerator expression that is grouped by that fraction bar, just as you would evaluate an expression grouped by parentheses.
You don't get to decide on a test how the problem is posed to you. So you have to deal with what is given. (which you did in your own way) Also, 0.5 IS a division. It is shorthand notation for 5/10 , which is the same value as 1/2 . So changing it to a decimal does not get rid of that division, it just puts it in a form that you are more comfortable with. But you'd likely get dinged in an algebra class if the teacher is anal about the methodology--decimals are sort of frowned upon in algebra 101 (usually).
When on an international forum you should use international standards which uses a solidus for division not an obelus. An obelus in Anglophone countries usually means division, however in Nordic countries can mean subtraction, in Russia grouping (original use was demonstrated as a vinculum). When you follow an obelus by numbers separated by a fraction bar (note it ends below the base line) indicates it isva fraction as the obelus already splits the expression.
@@perryfarmer3280 And different mathematical operators/notation is used all around the world. Which means that an "algebra book" in Chile will likely have different notation/symbols compared to a book in the USA or somewhere else. That's just the way it is. You go with the conventions of your home country. Insisting that everyone notate the same way is the same as insisting that everyone speak Esperanto. It might be a logical and noble cause, but it simply is not practical. The best thing to do is get used to the way it is done in your local setting or the setting that you wish to become a part of. This poster is simply giving it the way it would/could appear in any typical algebra book in the US or several other nations. So it is nothing out of the ordinary here, even though it may seem weird to you. There are just way too many math textbooks in way too many countries using way too many notations to hope everything will be consistent. Maybe someday, but right now... not so much.
While countries do use different symbols when dealing with them in an international community you use accepted standards. Once past about 5th grade you rarely if ever use an obelus. If you go by history on page 76 in the year 1659 the obelus was used like a vinculum. You use standards for everything for clarity. If you do not you crash into Mars or in my background you just cost yourself 20 million U.S. dollars because you used a comma for 1500 in international power sales.
@drewt1081 You're absolutely correct. I've taught math and have written tests. If the video wanted to denote 0.5, then it should've used ½, not 1/2. There is no reason why that handwritten equation couldn't have written ½. As any computer user knows, / and ÷ are identical, both meaning divide. As such, the equation is NOT (18÷½×4)÷3 = 48. Instead, it should be evaluated as (18÷1÷2×4)÷4 = (18÷2×4)÷4 = (9×4)÷4 = 36÷4 = 9. If the problem wanted the second term to be 0.5, then write ½, not 1/2. So the correct answer is 9.
Nope 48 is the answer. By using both the obelus and solidus it is obvious that the solidus represents a fraction. Only if solidus is used as the only operator should it be interpreted as divide, instead of a fraction.
When he wrote the problem down he should have put the fraction 1/2 in parentheses (1/2) if he wanted it to be worked the way he did it. The answer is 12.
The lack of parenthesis around the 1/2 could suggest it could be viewed as 18 divided by 1 divided by 2 times 4 on the top the answer divided by 3 = 12 Without the parenthesis 1/2 is not a number it’s a sequence of operations
No. He should have put the 18 and the1/2 in parentheses, that is (18 divided by 1/2). It is meaningless to put parentheses around a single number, because it does not tell us anything more than it is a number.
Giving division and multiplication the same precedence and going left to right leads to the answer 12. There's no parentheses around the one divided by two part.
We mustn't divide 1/2 in the first step! There are no brackets so calculations start from left to right. So 18/1/2 = 9 and the final answer is 12. Using this notation 1/2 is not the same as 0.5.
@joefergerson5243 Wrong, there are 36 halves. If you have 18 apples and you cut them in half, you get 36 pieces. You're not multiplying by 1/2, you are dividing by 1/2
1/2 is exactly the same as .5, the answer is 48! t took me less than 10 seconds to do that, then checked with my calculator, and, surprise! it also said 48!
This is a clear case of lazy, unclear notation in the original. Mixing Fractional notation beside a divide sign, Al in a numerator. The real lesson is to be more clear in how you present an equation. While I would evaluate this exactly this way, I would fear that the person composing it had a different thought.
I do not think that the problem is presented correctly. When you need to introduce BOMDAS or PEMDAS or any of these other rules - it means that the problem is shown as badly defined. This is where the use of Brackets or Multiple Brackets reduces the mistake of multiple interpretations - just as correct punctuation can reduce the mistake of incorrect English interpretations - incorrect as to what the writer intially wants to convey.
There's nothing wrong with the precedence rules in BODMAS/PEMDAS. They have endured for so long because they work. They make mathematical notation cleaner and more readable. The issue here is that the notation is garbage in the first place. He shouldn't really be using the ÷ symbol at all, and using two DIFFERENT division symbols in the same expression is inexcusable.
The equation itself is "wrong". There are several "correct" standards of operation rules when solving problems. I know three. The only rule for writing those equations is that there can be no ambiguity no matter which solution system you use. Engineers love standards. There's so many to choose from!
@@martinglenn27 The rest should never be trusted. This way lies madness - too many opportunities for error for no reason at all. Speak clearly, write expressions clearly? Just as there is street language, PEMDAS is street math.
PEMDAS isn't the issue here. The issue is the use of two different division symbols in the same expression. Using inline notation, the correct way to write the numerator that he wants here is 18/(1/2)×4
No it isn't. / is the correct symbol for division. He shouldn't even be using the ÷ symbol and he certainly shouldn't be mixing two different division symbols in the same expression. The expression as written in the question evaluates to 12. Using inline notation, to get the answer to be 48 he must write the numerator as 18/(1/2)×4 To get the answer 3 it would be 18/(1/2×4)
@@JimD-tn6bt Obviously in isolation 1/2 is the same as 0.5. But that doesn't mean that everywhere you see the text "1/2" as part of a larger expression you can simply replace it with 0.5 without considering context. If he wants the reader treat the 1/2 as a single entity like 0.5 then he must enclose the 1/2 in parentheses. That's what parentheses are for. It's literally the entire point of parentheses.
Nope. You're missing the other part of the equation - the spaces. If an equation is written using spaces between the numbers, 1/2 surrounded by spaces means one half. The right answer is 48. If the equation was presented with no spaces, or if 1/2 were presented as 1 / 2, then the answer would be 12.
@@jerryz2541 Spacing is not a symbol in mathematical notation!!! Whoever told you that, you need to stop listening to them because they don't know what they're talking about! The correct grouping symbol to communicate what he wanted to communicate is a set of parentheses. He failed to use the parentheses he needed, and as a result the expression does not say what he wanted it to say.
The problem is intentionally written to create a confusion point. Is the 1/2 a fraction? Or is the / a division symbol that follows the first division from left to right?
The / symbol is certainly a division operator. You could argue a different meaning for the ÷ symbol because the ÷ symbol is not formally part of mathematical notation. But it's hard to come up with a new definition of the ÷ symbol that leads to the answer 48 here. The notation he's written is just nonsense.
@@billywilliams3204No, it is divided by 2. The numerator evaluates as: 18/1 = 18, then 18/2 = 9, then 9×4 = 36 Then you divide the whole thing by 3 and get the answer 12.
@@billywilliams3204 Well... another clue is that it's a different division symbol. Most math texts I've seen would have written it with the 1 over a 2 to avoid confusion though.
@@greghoward1561In this video he uses careless, shoddy, improper notation. And he evaluates the expression he meant to write, not the expression he actually wrote. He's certainly very comprehensive in his explanations, but that means he should take even more care not to make the sort of errors he does here. His target audience is very likely to include people who wouldn't know any better and would have no chance of realising that the errors are even there.
@@greghoward1561The problem is written incorrectly for answer to be 48. As written problem should be solved as: 18 ÷1 (not divided by 1/2) = 18/2=9×4=36/3=12. The two different division signs should not have been used. If he wanted 18 to be divided by half he should have written problem as 18/.50x4/3. As a high school math teacher I would never give my students a math problem written as incorrectly as this one.
There might be some people who are getting 12 because they're incorrectly calculating 18 / ½ as 9 instead of 36. But there's also a bunch of people getting 12 because they recognise that the question does not actually ask us to divide 18 by ½. The question as written DOES evaluate to 12. There are no fractions in the numerator of this question. We are asked to divide 18 by 1, then divide the result of that by 2, then multiply the result of that by 4, then divide the result of all that by 3. To get 48, the author needed to write the numerator in the question as 18/(1/2)×4 Those parentheses are essential if he wants us to divide the 18 by the entire 1/2 instead of just dividing the 18 by the 1. A division operation does not get higher precedence than another division operation just because he happens to have used a different division symbol. There's no excuse for using two different division symbols in the same expression. In the video, he is answering the question he meant to write, not the question he actually wrote.
Uhh, uhh. Unless you write 0.5 you don't get to introduce two separate symbols for division. The ISO 80000-2 standard for mathematical notation recommends only the solidus / or "fraction bar" for division, or the "colon" : for ratios; it says that the ÷ sign "should not be used" for division. So it is either _(18/0.5*4)/3_ or: _(18/1/2*4)/3_ - and only the first one will render your solution.
That's a very fair question. These 6 letter acronyms are misleading. They create the impression that there is a hierarchy between multiplication and division, and a hierarchy between addition and subtraction. If you want to use an acronym for this stuff then the 4 letter acronyms like PEMA are better for exactly this reason.
That's because 12 is the answer. He's written an expression that evaluates to 12 and he's telling everyone it evaluates to 48. That's not great behaviour from someone who purports to be a teacher. It would have been easy for him to rewrite it properly so it did actually evaluate to 48.
@@jessejordache1869 No it isn't. The numerator would be 48 if the 18 was divided by the entire 1/2. But that would require brackets around the entire 1/2 and the author didn't write those brackets. What he should have written in the numerator is 18/(1/2)×4. Then the final answer would be 48.
@@gavindeane3670 You have to take the fraction as an atomic unit: if you divide 18 by 1, and then multiply 2 by 4, you're not using the same numbers that are written on the formula. True, .5 makes it simpler, but there's no sense where you can take 1/2 and have the 2 interact as a two, and not a half, unless you're deliberately playing around with reciprocals.
@@dazartingstall6680It's got nothing to do with whether calculators recognise fractions. The problem is that the author doesn't know how to write fractions. As you've shown, using inline division operators as the author has done, then the answer is not 48 unless you add some parentheses that are not in the question.
@@gavindeane3670 The brackets are for the calculator's benefit, not the reader's. 1/2, written as a separate term as it is in the video, is one half. Though I will admit that I'd prefer it if the video maker had used a horizontal fraction-bar.
@@dazartingstall6680 The calculator doesn't need you to do things for it's benefit. It is perfectly capable of evaluating the exclusion with or without the extra parentheses. The point is, the parentheses *change* the meaning of the expression - as the calculator demonstrates. The expression in the question does not evaluate to 48 unless and until parentheses are added around the 1/2. The 1/2 is *not* written as a separate term. That's the problem. Plainly that's what the author intended, but it's not what he wrote. For it to be a separate term it needs to be in parentheses. That's literally the entire point of parentheses. It's what they're for. Or better still, as you say, write it as a fraction: a horizontal line with the 1 above and the 2 below.
@@gavindeane3670 I agree in principle but I think you're maybe being a tad pedantic. While I'm not struck on the inline fraction symbol, it is common. And in this case is further clarified by its juxtaposition with the simple division sign, ÷. As to calculators, they typically have one division sign available, as opposed to the three variants (horizontal bar, ⁄ and ÷) available to a person calculating on paper. A fraction is a single term which needs to be rendered as a decimal (1/2 = 0.5) before a calculator can use it, so it needs to be given higher priority than what would, in this case be 18÷1. The only way we can force this is to bracket the fraction. Human beings don't need the brackets, because we can recognise and treat a fraction as a single term. Not everything needs to be machine-readable.
Unfortunately, the teacher is not right. He did not apply the sequence of operations right. The answer is as I indicated above 12. Where did he go wrong? He divided 18 by (1/2) He should have divided 18 by 1, then divide the result by 2. That is 9. Multiply 9 by 4 and divide the result by 3, you end up with 12, not 48. If it is not clear, I can explain it with some simplifications and reasoning.
I am good at math but that did not make sense at the beginning. who would ask a question like that? If you want (C. 12 ) to u be the correct answer how would write the same question when you want 18 × 50% × 4 /over 3 = 9 ×4 /3 = 36/3 = 12q
I'm not sure about this as I try to make the problem faster to solve. It appears as if I could change the fraction into a whole number of 2. So I would get 18x2=36x4=144. 144/3=48. Again, I'm not sure if this works in all cases as it just appears as if it works this time.
What he does in his verbal explanation is describe 1/2 as 'one half'. The accepted definition of the phrase 'one half' is one of two approximately equal parts of a divisible whole. Point 5 only applies to a divisible whole of one.
Not sure what you mean. "One half" is the name of the number ½. There's a question about whether the notation actually asks us to divide 18 by ½ anyway, but that's a separate issue.
Finally found your reply. The verbal explanation should had cleared the ambiguity but actually adds to it. Verbally one half by definition is one of two equal parts. One of two equal parts of 18 when spoken verbally would equal 9, which is one part of two. As writen however one half depending on what the slash actually represents would equal one of two equal parts of one which is point five. Multiplied by 18 and you have 36 halves. He also screws up the vinculum since the line length should represent what is the grouping.
The answer is 48 18 ÷ ½ × 4 --------- 3 Simplify the numerator. Apply PEMDAS from left to right: (18 ÷ ½) × 4 ---------- 3 Rewrite for clarity. Remember, division by a fraction is the same as multiplying by the inverse reciprocal (i.e., of the denominator). As such ½ becomes 2/1: 18 2 ( --- x -- ) × 4 1 1 ----------- 3 Simplify: 36 --- × 4 1 ------- 3 Simplify again: 36 × 4 ------ 3 Simplify again: 144 ---- 3 Solve: 48
Because changing the 1/2 into 0.5 is invalid unless you either put the 1/2 in parentheses, or change the meaning of at least one of the division symbols.
I disagree with the video. The second term should not be treated as ½ or 0.5. Instead / and ÷ are identical, and both are division, as any computer user knows. So the equation is NOT (18÷½×4)÷3 = 48. Instead, it should be evaluated as (18÷1÷2×4)÷4 = (18÷2×4)÷4 = (9×4)÷4 = 36÷4 = 9. If the problem wanted the second term to be 0.5, then write ½, not 1/2. So the correct answer is 9.
First let me say that I DO enjoy your posts- even when I get them wrong. Even when I question how you arrived at the result. (At 60yrs old mathematics was a little different, right?) Now, for me my answer was c) 12. This is a question of appearances. The "1/2" does not look like a fraction- it looks like, 1- then division symbol "/" - then 2. I suppose in my era fractions stood out more. I googled your numerator as you wrote it and they rewrote it as (18/(1/2))*4, which equals 144. There the fraction stands out! Oh, the good ol' days......
In my day it was BODMAS that was the order of operation. Brackets, Operation, Division, Multiplication, Addition, Subtraction...with the same rule as you described with D,M and A,S
48...now I'll read comments and watch video If placing a fraction IN a fraction...write it more clearly 1 over 2, not 1 slash 2. The 1 over 2, becomes a fraction within a fraction. It has to be reduced, in order to proceed.
I first hit the problem of operator precedence at age 11 in the 1st year of my secondary school. Despite being an infant maths genius in primary school, no teacher ever mentioned that multiplication had precedence over addition. Since then I've succeeded in maths and engineering and used many computer languages and it's always vital to understand operator precedence. But what this video highlights to me is that PEMDAS is a ridiculously terrible tool to help remember the expected order. E stands for Power and P doesn't! In fact P stands for Parenthesis, which is not an operator at all. Then the real killer: M comes before D in this supposed left-to-right ordering but we should treat Multiplication and Division as equal priority and perform left to right. Same with Addition and Subtraction. Utterly ridiculous, I'm sorry to say. DON'T TEACH KIDS WITH THIS TOOL!
I think you've hit the nail on the head there. The "M before D" and "A before S" misconception is the most obvious and visible issue with this stupid acronym. But I think that including parentheses in a topic called "order of operations", when parentheses are not an operator at all, actually causes more fundamental problems.
Why has no one noticed that he gave two different sets of answers @1:25[a) 18, b) 3, c) 12, d) 48] and @9:22 [a) 18, b) 3, c) 9, d) 12]?
I did notice that 🤔🤔🤔
There is only one correct answer, for which that is 3, and you should read my original comment providing 4 points of mathematical proof on that.
@@randylazer2894 WTF. We weren't even talking about which answer was right or wrong 🙄🙄🙄🙄
Yep. My thought on this is that the video was first done with the answer being 12 (which is the correct answer because 1/2 is the same as 1 divided by 2), then redone a 2nd time where the 1/2 is re-interpreted as a single symbol replaceable by 0.5, and thus the answer is 48.
@@marscience7819 12 is not the correct answer.
As I delineated in previous comments....the numerator is 18/1/2x4, and the denominator is 3.
With that fraction as the numerator 18/1/2x4, well 18 is the numerator, and 1/2x4 is the denominator, for which that is a product.
so 18/1/2x4=18/2, which equals 9. 9/3=3.
Now the errors made in this video are assuming parenthesis where they aren't present, as that violates the definition of an implied multiplication operator.
To realize 18/1/2x4 to equal 36, that would need to be written with parenthesis of (18/1/2)x4, which it is not.
Secondly the dividing line is called the vinculum, which by definition values are grouped above the line and below the line.
With this expression, 18 is above the line, and 1/2x4 is below the line.
So the wrongful answer is in violation of the definition of the vinculum, as 1/2x4 is below the line, but is being broken up.
Lastly there is a simple algebraic proof of a/bc=a/bx1/c, and not (a/b)c, as parenthesis cannot be assumed.
Take 1/3 x 1/4. That equals 1/12th. But what this wrongful video states is that 1/3x4 is not 1/12th, but is rather being treated as (1/3)x4, when no parenthesis are present, and that would give a wrongful answer of 4/3.
You are clear as mud. You made an easy thing so complicated, that I was very tempted to zap you. I was raised on B.O.D.M.A.S. (brackets, of, division, multipllication, addition and subtraction) and it was treated me correctly. so no need to change it. All in all the most simple thing to do is to convert 1/2 into 0.5 and proceed from there.
Why transfer 1/2 to 0.5? There's no need for that.. At first you can cancel 18 in denominated by 3 in nominator. That gives you 6 / 1/2 * 4 which is the same as 6*2*4 and that equals 48
If you simply follow the rules, and don't add any of your own assumptions, the "1/2" can NOT be replaced by "0.5". The forward slash is defined to mean "divided by". So, if you see the symbol "1/2" BY ITSELF, nothing to it's left, then yes, it can be replaced by 0.5. BUT IT'S NOT BY ITSELF, it has something to the left of it that has to be done first by the rules. What you have done is added another assumption, which is in your head, but not part of the rules!!!
@@marscience7819 I had no problems converting 1/2 to .5.. which is simply 18/.5 which is 36 x 4, then divide by 3.. comes out perfectly to 48.. 1/2 does equate to .5 in this equation..
I read your comment before the video, so I didn't watch it! I got 48...
@@karenshaw7807 so what do you get now?
I'm 75, don't remember when I last sat for a math class. I got the answer in less than 10 seconds. Contemporary education is missing something if young folks can't figure this out.
One thing to understand is this problem has nothing whatsoever to do with arithmetic. It has to do with the rules to apply. With the rules defined, the answer can be either 12 or 48, where I lean toward 12 because there is no rule in PEDMAS that tells us to treat the symbol "1/2" as if it one thing. The commonsense thing is to treat 1/2 as 1 divided by 2, which then means the numerator must be 36 by PEDMAS. Let me say again, the problem with these kinds of arithmetic has nothing to do with arithmetic, it has to do with the rules to use. Try this: It's not exactly the same, but you should get the point. Consider these two sentences. "Let's eat grandma" and "Let's eat, grandma". It isn't the "young folk" that are the problem, it's the "old folk" that unnecessarily complicate this simple arithmetic problem. They do it on purpose to confuse the student because they have nothing better to do. They make the expression ambiguous. If the teacher wants the answer to be 48, then write it as (18 # (1/2) X 4)/3. I don't have a divide sign on my keyboard, so I use #. That expression is unambiguously 48. If you want to confuse the hell out of clean, unbiased young minds, then write it the way this teacher did. The way he wrote it should technically have the answer 12, but 48 might be acceptable with the additional rule that a symbol like 1/2 is to be treated as single symbol and not as "1 divided by 2".
Well, I'm 44 (not old, but not young either lol) and this entire sequence is completely beyond me so it's not just young individuals that struggle. I got 0.75 for an answer by trying to do this intuitively (at least my version of it) but then again, no math teacher could EVER figure out how I looked at things like this - so with neither party understanding ANYTHING that the other was talking about, math class got pretty interesting. I always lost though 😂
@@squatch253 Definitely not 3/4
@@marscience7819 I know, I never got any of these right back when I was in school either - just illustrating how this is beyond simple for some, but confoundingly impossible for others 😵💫
@@marscience7819you don't get that 1/2 is meant as s fraction one half don't you?
@8:33 Why did the answers change from the original problem's answers here? 48 is no longer D here, which was super confusing. I had 48, but changed my PEMDAS around as 48 was not an answer given?? I got the problem correct initially (48) until I got to this phase of the review and changed my answer to B) 3 as I multiplied first .5 x 4 = 2 to 18/2 over 3 or 9/3 or 3.
I am in my late 70s with a high school education and did this in my mind in about 5 seconds, I wonder how many high school seniors now can do this?
69 and it took me 15 sec.
I bet the answer to your question is 0.
I incidently screwed this up so bad I couldn't even figure out how I got the answer.
@@Spitfireseven Likewise, 79 and found it simple, education today is to what it was. Try giving a cashier £12. 25 (to get rid of pockets full of shrapnel) when she asks for £6.75 and watch the reaction.
I used to get F’s bc I never showed my work. This was probably the easiest one in the 6-8 I’ve done so far. In my jr. and sr. High classes I would get poor marks because I never showed my work. I didn’t even know how I came to the right conclusion and honestly, couldn’t explain how I found the right answer! I even had to repeat 2 levels of math before I could even graduate bc no one knew or even understood what Aspergers was in 1991. Thank you so much for putting these problems out there. It feels SO AMAZING 🤩 😊 to answer your questions and know in the blink of an eye what the answer is. I hope you can make an impact on all of the others out there who were either wrongly diagnosed or not diagnosed at all. We are really smart and now grateful that someone else (you) can test us and we can show you what we can do and literally how fast we can do it!! I’d love to talk to you about your experiences with people with Aspergers and Autism (high functioning Autism)❤❤❤❤❤❤❤
Old school math teacher here. Purposely not using parentheses is like leaving verbs out of a sentence. No one will fill in the missing word the same way. Not to mention that the order of operations was taught differently. Just use the fricken parentheses. I did an exercise with the parents of one of my 4th graders. Gave them and a group of other adults ranging in age from 18 to 60 an math problem. ALL 6 adults got it wrong. The parents were at a BBQ and a little buzzed. The math problem caused major arguments and almost ended up in fist-a-cuffs. THIS BS IS WHY PEOPLE HATE MATH!!! It is more important to get the right answer.
The question of whether and where to put parentheses is a minor detail compared to the fundamental, inexcusable error of using two different symbols for division in the same expression.
He needs to fix that before we can have a discussion about parentheses
@@gavindeane3670 100% agree! Making math miserable is not helping people learn math. There are 10 kinds of people who get that. 😉 (a little binary humor)
Stop posting questions like this. No one would ever purposely write an ambitious equation to trip people up.
@@craigshaw8881 Yeah, they would.
The correct way to interpret an expression is in the way that the person who wrote it intended and in this case it was intended to confuse. Sadly, some folk just enter such expressions into a calculator without any thought as to what was intended and of course the result is often wrong. Even more confusion arises with implied multiplication, for example, what is the value of 1/2𝝅f where f=10 ? This is a standard formula in electronics and it's intended to mean 1/(2πf) rather than (1/2)πf. But if you blindly follow BODMAS you'll end up with the wrong result.
Leaving aside the specific issue of implied multiplication after inline division, which isn't relevant to the video, if you enter an expression into a calculator then by definition the answer that comes out is the correct answer.
If that is not the answer that the author intended, that is not the fault of the reader or the calculator. That is the author's fault.
@@gavindeane3670 Sadly, it's not quite that simple. I've watched a few videos on RUclips in which someone enters the same expression into two calculators and gets two different answers. So basically, blindly entering an expression into a calculator and claiming that the result that comes out is the correct answer is exactly NOT the right thing to do. The key is to think about the situation and interpret the expression accordingly.
You have to use an algebraic calculator.
@@RawFitChris No, I rejected algebraic calculators long ago and ONLY use RPN ones. They are the only ones that I trust. Algebraic calculators are ok for simple expressions, but as soon as you need to calculate square roots or trig functions, they vary in whether you need to put the operator before or after the number.
@@Chris-hf2sl That is a well known and well understood issue with implied multiplication after inline division. Different calculators do indeed give different answers in that specific case, but that's not relevant here.
ISO 80000-2 states you should not use an obelus for division, you should use a solidus. In its original use the obelus was used as a ratio.
As a ratio 18 over .5 * 4 = 9
9/3 = 3
Correct. I approve.
And your algebra text doesn't care what ISO 80000-2 states. You have to deal with the problem as it is posed in the book.
they both are identical and in mathematics you can use either. stop quoting printing standards for weights, measures, and units.
@@johng.1703 Absolutely correct. Math texts from basic arithmetic right on up through abstract algebra and real analysis use both symbols.
thank you for explaining, i was so confused by his answer cause i also found 9
once you get rid of the pesky 'divided by one half' by changing it to x2 it is simple and the remaining operations can be in any order so the simplest solution is 36/3 =12 x4=48 final answer.
Can you understand why some people dislike math so much? Math teachers are not always good communicators, especially to young people.
12
at least they are not teaching non-binary biology
3
He says WAY too much, causes confusion, and boredom.
I can't tell you why. Between my sophomore and junior years in high school, I went to a "math camp" for six weeks at Rutgers University. I had a blast learning all kinds of math they never teach you in public school. Loved it!
Sorry, will have to disagree. There is no rule in PEDMAS that says to treat 1/2 differently than 1 # 2 (sorry, my keyboard does not have a divide symbol, so I use "#"). So the numerator might as well read 18 # 1 # 2 X 4 which gives 36 by PEDMAS. 36 then divided by 3 is 12. Given PEDMAS with no other rules, the answer is unambiguous. Both 12 and 48 would have to be accepted as correct. The way around this is to use parenthesis around the 1/2........18 # (1/2) X 4. Whether it matters or not, I do have a Ph.D. in physics.
18*.5*4
I'm sure 1/2 in the numerator is atomic, so the parens around 1/2 are assumed.
@@jessejordache1869...there are no assumptions in math
@@jimbuxton2187 That's actually, literally false. They're called axioms. Come join us in the 19th century.
*PEMDAS
About 50 years ago I made it through business calculus, with quadratics, along with stats and geography, and graduated with a Bachelor of Science degree in Business Administration/Economics. I am currently retired, but I do not remember anyone ever mentioning PEMDAS. Before you start mocking me, I developed a degenerative neuromuscular disease, which is advancing. Along with other mental exercises, I am following this program to hopefully slow some of my cognitive loss, and not to get frustrated so easily. I just don't remember problems being presented like this back a half century ago. There always seemed to be more structure to the process, which determined which step was to be taken first, and/or next, etc.
The main principle in PEMDAS - multiplication having higher precedence than addition - has been the way mathematical notation works for a few centuries now. Given the level you reached, the way you were writing mathematics undoubtedly relied on this principle. For example, I'm sure you would have written a quadratic as
ax²+bx+c
rather than
a•x²+(b•x)+c
But you were probably relying on this principle without even realising it. What seems to have changed more recently is explicitly teaching this principle in the context of simple arithmetic. That is widespread today but it seems to have been more patchy in the past.
@@gavindeane3670 I spoke with a life-long friend who has a PhD from Penn State. We grew up together and graduated from high school in the same class. He is known for starting the largest experiment on the effects of ozone gas on old grow forests in the world and National Geographic did a video on him and his work back in the 90s. He retired early due to a Pulmonary disease and since we are both disabled, we check in on each other from time to time. He had his share of different types of math and he also said that what he sees on RUclips today is completely different from the way he was educated. Again, this was 50 years ago. So, it's just not me and although I deal with a neurological disorder that has made life complicated, there are certain things that stay with me. My keyboard doesn't have the capabilities to show powers and long division lines, but the quadratic formula I remember (spelled out) was negative b plus or minus the square root of b squared minus 4ac, over 2a. It's been a long time, so that might be a bit off. The math I used in my career was very narrow in scope. Can you see where the difference in how the formulas are presented are confusing to someone who doesn't eat and sleep numbers? If you are a math teacher, it must be obvious, but as someone who had to take this class and although an A student, I concentrated on the applications geared towards the business world. Such as finding the break even point, and maximum efficiency level in manufacturing. You could see the vertex of the parabola when graphing it out. Again, please forgive the fog.
PEMDAS is a notational convention that was finalized about 400 years ago in order to minimize the need to use parentheses. I like
to tell my students that it's an artifact of history and could have turned out differently. Therefore, it is "correct" by general
agreement.
@@DeanNataro It may be old, but that is still not how math was taught for a very long time. No wonder why parents are not able to help their kids with homework. With parentheses you knew in an instant what had to be finished first. You would become efficient after using PEMDAS for a while, but I still see no need for a change. Quadratics looks totally different.
@@thinkcivil1627It was implicitly taught, in the way that mathematical expressions are written - particularly algebraic expressions.
What's changed is that it is now widely taught explicitly, using the context of simple arithmetic.
If you key his formula exactly as written into a spreadsheet such as Excel (use / for the division sign): 18/1/2*4/3 = 36. To get his answer of 48, in Excel you would have to enter it as 18/(1/2)*4/3. Algebraic expressions in Excel never assume parenthesis, they must be entered. Anytime I see a formula without parenthesis, I assume it means no parenthesis.
It's not just Excel, it's any calculator.
Any calculator will tell you that (18/1/2×4)/3 is 12.
You have to treat the Numerator and Denominator as separate questions … e.g.. (N)/(D) … so Excel equation would be … (18/1/2*4)/(3) = 12
@@captainjaybird You're correct in general, although in this particular case the parentheses around numerator and denominator don't make a difference.
18/1/2×4/3 will still give 12 without the parentheses. I don't know why the person you replied to says they got 36 in Excel. They would have got 12 for what they wrote.
But, you did not enter it into the spreadsheet as written.
This question is at the least ambiguous because the slash symbol / is short hand (an alternative) for the horizontal line when used write equations on a single line instead and so would imply everything before the slash is the numerator and everything after as the denominator. The use of both division symbols in the same equation only adds to further ambiguity as it implies there is a difference between the two; if not this, then what other differences would there be? The last item causing ambiguity is the spacing of the 1 / 2 which is close to the spacing of the other possibly indicating that 1/2 was really 1 / 2 which would add support for the use / as an alternative for the horizontal line spelled out above.
Nice Work TabletClass this video definitely got some engagement, lol. 🤑
But if your saying that the slash is a division line then why isn't it read as "18 divided by 1" over "2x4" which no one here seems to be arguing for ..... It seems to me the 1/2 which is spaced as if it were a whole number does indicate that it is meant to be a fraction and not short hand notation for division)
Exactly!
A second question about the use of the fraction bar is that while treated as a vinculum the original examples given for the obelus was treating it as a vinculum.
Correct. What is shorthand is an Obelus. When first presented it was shown in examples as a vinculum with one major deference and that line length. What is above or below the line is determined by the line itself. The obelus essentially eliminated the length of the line.
I will reject the problem and make no attempt to solve it as it contains both ÷ and /. My guess is the 1/2 is intended to mean 0.5, not one divided bt two. If that is the case the fraction should be reformatted with the fraction bar horizontal. When the student has to guess what the teacher intends, the problem should be withdrawn.
Improperly formatted to create an argument.
i totally agree i hated math to some degree for that reason seems like they wanted to over complicate and make it a puzzle
@@louiskovach That's life, bub. Get used to it.
@@Jabberwalkie-zi5tuPretty much the same in each episode, set up to generate lame repetitive discussion about formatting.
absolutely correct @richardhole
The division sign and the slash sign both mean division so under his description of PEMDAS 18 should first be divided by 1, the answer then divided by 2 and that answer multiplied by 4, with that whole numerator divided by 3, equaling 12. PEMDAS didn't require us to do a slash division before a division-sign division, did it?
Just for fun I prefer to solve the problem like this: [(18/1) / (2x4)] all divided by 3 which would be 0.75, but that wasn't one of the multiple-choice answers.
Frractions are always done first so there are implied brackets around the 1/2
@@gcarapThe / symbol does not imply parentheses anywhere. It is the division operator, not a grouping symbol.
There are no fractions in the numerator in this question. There are four numbers (18, 1, 2, and 4) and there are three operations (two divisions and a multiplication).
@@gavindeane3670 the expression 1/2 is a fraction and thus auto-defaults to ( ).
@@gcarapIn isolation we can represent fractions by writing things like 1/2 but that's not what it is. 1/2 is a number and a division operator and another number. And the division operator absolutely is not a grouping symbol.
When it appears as part of a larger expression you cannot blindly assume that you can put parentheses around it. Whether you can do that or not depends entirely on the context.
Think about why 1+3/4 is the same as 1+(3/4) but 3/4² is NOT the same as (3/4)².
@@gavindeane3670 No. If your intent is to express division, express it as division symbol (sorry, not on my keyboard LOL), If you use /, it is interptreted as a fraction formulaicly. So in that sense, the division sign and the / are NOT the same when used within formulas. And while his solution here was 100% correct, it would have helped if he mentioned the fraction as an implied P instead of stating there are no Ps. I suppose he assumed the solver already knew that the use of "/" is aleays interpreted as a fraction when part of an equation.
8:27 Shows (d) is the correct answer of "12" (48 is not even an option at this timestamp)
18 / 1 / 2 * 4 / 3
18 / 2 * 4 / 3
9 * 4 / 3
36 / 3
12
All you gotta do is change a rule slightly, (if that could be phrased like that) and you get a different answer. I'll never forget the new math about fifth grade in 1969. It's all so changable. There's no yelling, "Foul" and getting away with it!
18/(1/2)*4/3
18*2*4/3
36*4/3
144/3
48
@robby1816 I got the same answer of 12. I thought you would divide 18 by 1\2 to get 9... Then multiply by 4....hmmm oh well...
I'm 66 and have struggled with math my whole life. But I also think math is fascinating. This problem has me flummaxed! When I see 18÷2, logically I think the answer is "9". Is there a way to explain (verbally) this conundrum? Thanks!
It's not 18 divided by 2, it's 18 divided by 1/2 which equals 18 * 2.
When dividing by a fraction, flip the fraction then multiply. :)
Any one else notice that the
" correct" answer 48 at 6:17 of the vid is no longer there at 8:28 of the vid then the answer list dissapears at 9: 48 while he ' explains' the order of opetations...48 again reapears at 10 :58....this is a poor explaination of the order of operations and and would only confuse some one trying to learn this type of math
The big question is how would 'you' code it to a line in a computer software program, then run it to get the answer d)
I would have to go ((18/(1/2))*4)/3
Interesting point. I wish my main computer was fixed, because I have a math parser that should handle that equation as written. Only you have to enclose the top half in parentheses.
This would be a good test for it.
@@johnshaw6702 I am sure All the top half is enclosed in parenthesis as ( (18/(1/2)) * 4 ) /3
example start 1st, bracket, start 2nd bracket, 18 / start 3rd bracket, 1/2 end of 3rd & 2nd bracket *4 end of 1st bracket /3
On reflection I shall have written words "the minimum parenthesis or brackets needed to make it work for the correct answer", even so I sure I got it right first time.
@@ericr2646 In VBA this works:
MsgBox (18 / (1 / 2) * 4) / 3
@@ericr2646 You are probably correct, but I haven't even looked at my parser in over a decade. I wrote that code over 25 years ago for an equation graphing program. It had a few more tricks up it's sleeve than the average parser.
Looks good, worked inside out, same number of left and right brackets.
This may sound extreme, but why is it 18 divided by 1/2 (18 / 1/2) and not (18 / 1) / 2?
1/2 is a position on the number line. You can not split that position with a symbol. Using decimal, 1/2 is .5
I was thinking the same.. knowing that multiplication and division are "weighted" the same in order of operations it seems like you'd just go in order.. Wasn't aware that 1/2 isn't the same as 1 divided by 2.
@@bulldog6925 makes sense especially when considering the decimal equivalent. Thank you.
That is a very reasonable question. The author is trying to use ÷ and / to mean different things, but that is not standard and the notation in the question is sloppy. Your interpretation is completely reasonable.
@@bulldog6925No. 1/2 is a mathematical expression that EVALUATES to 0.5.
At least, that's what 1/2 is in isolation. But it's not in isolation here. Context matters.
YES YES YES!!! Took about 45 seconds and did it in my head! 🎉🎉
What many miss is how an obelus was originally used. Essentially all above over all below. ISO 80000-2 states not to use it for division.
In Nordic countries it was used for subtraction. Before using order of operations one needs to use proper notation.
Grew up in the 70's and this was just simple math. I got it quickly.
If you rigorously follow PEMDAS, the answer is twelve. If you treat 1/2 as an implied notation (much like 3x or f(x)), then 48. So, which dialect of math do you wish to speak?
As there is no sensible dialect of math that permits two different symbols for division in the same expression, the best answer to this is to take it back to the person who wrote it and tell them to write it properly.
18 divided by 1/2. You have to change it to x, which is 18x 2, =36x4=144 divided by 3=48!
WHAAATTT!!! 144 divided by 3 = 48 FACTORIAL ‽‽‽ (Sorry, woke up in Smart Ass mode today. Gave you a Thumbs Up!))
When you said turn it to x I thought you’d jumped into algebra! Yes that’s what I did. Useful trick, and it works in algebra too
That's what I got.
No, the correct answer is 12. As any computer user can tell you, / and ÷ are identical, both denoting divide. If you want the second term to be 0.5, then write ½, not 1/2.
Hence, the correct answer is 12, not 48. The equation should be evaluated as (18÷1÷2×4)÷3 = 12, NOT (18÷½×4)÷3 = 48.
@@RationalSaneThinker I think you are being irrational !! One would NOT use both division symbols in the same expression for both to mean "divide". Where both are used, the "'/" would always indicate a fraction, not an operator.
You would be right if it said 0.5 instead of 1/2. But it doesn't and now you are wrong. 18/1 = 18, 18/2 = 9, 9*4 = 36, 36/3 = 12
Lol
Correct....12 is actually the right answer.
I agree
12 was the answer I got also.
3
What about interpreting the forward slash between 1 and 2 on the upper half as a division operator, instead of reading 1/2 as 0,5 ????
Exactly right. The / symbol literally is a division operator. The expression he's written evaluates to 12. In the video he's evaluating the expression he meant to write, not the expression he actually wrote.
The correct way to write the numerator he's trying to write here, using inline notation, is
18/(1/2)×4
So, do you ALWAYS change a division to multiplication in fractions?
At 63, you made me dust off lots of old memories. But i did get the answers right. In fraction math. I just asked myself, how many half units are in 18. 36. The rest was elementary.,
This is not really about the mathematics itself, but about the system of notation and the ability to read it. If I read it the way the narrator does (and I did) I get his answer (and I did). But if someone reads it differently, I can't blame him.
As in "eats shoots and leaves" or "nut screws washers and bolts" without commas
Read and figured it three different ways/times. Getting 12, 3 and finally 48.
@@lindakrzyz5512
12 is what it actually evaluates to.
48 would be if there were parentheses around the 1/2.
3 would be if there were parentheses around the 1/2×4.
The answer is either c)12, or d)48,
depending on whether you assume there are parenthesis around the "1/2" term.
Case 1, as written:
18 ÷ 1 / 2 • 4 ÷ 3 // 18 ÷ 1 = 18
18 / 2 • 4 ÷ 3 // 18 / 2 = 9
9 • 4 ÷ 3 // 9 • 4 = 36
36 ÷ 3 // 36 ÷ 3 = 12
36 ÷ 3 = 12, answer: c)12
Case 2:
18 ÷ (1/2) • 4 ÷ 3 // 18 ÷ (1/2) = 18 • (2/1) = 18 • (2) = 36
36 • 4 ÷ 3 // 36 • 4 = 144
144 ÷ 3 // 144 ÷ 3 = 48
144 ÷ 3 = 48, answer: d)48
So there ya-go, the answer is either c)12 or d)48, depending on how John is feeling today... how "tricky" he wants to be today...
£ $ € ฿ ± Σ Ω Π Δ µ ← ↑ → ↓ ^ √ ³√ ∞ * ≈ ≠ ≤ ≥ ÷ •
The answer is 48, and only 48.
@@martinglenn27As written, the only answer is 12.
Well, the only real answer is to take it back to the person who wrote it and tell them to write it properly.
I reached the same conclusions as you. At first I thought 48 was wrong and came up with 12 but then I realized that fractions must inherently come with their own brackets when it comes to fractional divisors and the order of operations. If they did not, then dividing by a fraction would be impossible since the fraction would be split apart into two separate divisors. The quantity being divided (a) would be divided only by the numerator of the divisor fraction, not the whole fraction. This first result (call it 'b' as this is a new number) would next get divided by the denominator.
Without the inherent brackets to prioritize fractional divisors as distinct numbers instead of mere parts of an expression, the fraction would get torn apart. The invert and multiply concept would not exist which would defy common sense.
I thought the creator here was getting cute with the astonishingly rare mix of division sign and fractions within a single expression. I doubt this was his intention however as he makes no mention of this issue of fractional integrity under OOO manipulations. I believe the international interpretation of OOO does dictate fractions as distinct numerical values (meaning their a over b value is determined before anything else applies - aka inherent brackets)
@@joeblog2672 There is no such thing as inherent brackets around a division just because you want to think of it as a single fraction. If brackets are needed around the (1/2) they must be written.
And anyway, even if they're was such a rule, why does the second division in the expression get to use the rule but the first division in the expression doesn't? Why does 1/2 get the brackets but 18÷1 doesn't? That would only make sense if ÷ meant something fundamentally different to /. It doesn't. They mean exactly the same thing. They are both just a division operator. The only difference is that ÷ is deprecated and should not be used. The proper inline symbol for division is /. So the numerator in this question should be written 18/1/2×4.
Dividing by a fraction is not impossible. It's extremely easy. The best way to divide one fraction by another is to actually write fractions:
1 3
---- / ----
2 4
If you are writing inline instead of using a vertical layout then it is trivial (and essential) to add brackets:
(1/2) / (3/4)
The use of two different symbols for division in this question is indeed astonishingly rare - and thankfully so, because it is also astonishingly silly. There is absolutely no excuse for it.
@@gavindeane3670 as written, the only answer is 48.
It's not 18 divided by one half, it's 18 divided by 1 divided by 2. The divisions are applied left to right: 18 divided by 1 is 18, 18 divided by 2 is 9. 9 divided by 3 is 3 and 3 times 4 is 12.
18 divided by one half would have to be written 18 divided by 0.5
Or written 18/(1/2)
I think that since the obelus was used first to divide, it indicates to me that the solidus indicates a fraction. If that is the case the answer is 48.
I am a bit confused… always thought / was interchangeable with ÷ … making the the numerator: 18 ÷ 1 ÷ 2 x 4
I get the reciprocal but shouldn’t the 1/2 be in parentheses?
You're absolutely right. ÷ and / are just different symbols for division so as written the expression evaluates to 12.
With parentheses around the (1/2) the answer changes to 48.
@@gavindeane3670 This is the comment I was looking for, both yours and the one you're replying to. One could argue that the use of the divided by sign in one place makes you assume a fraction in the other, but not necessarily. The parentheses absolutely should have been used to clarify as you mentioned. I would say that it is justified that you could say the answer is 12. Order of operations says left to right and a forward slash means divide, so you are correct.
Yep you are correct.
stupid questions get stupid answers.
Winner-Winner-Chicken-Dinner
18 ÷ 1/2 × 4
-------------------- = 48.
3
In order for your answer (48) to be correct, you would need the 1/2 fraction in the numerator to be set off by parentheses. This would give you: 18 / .5 x 4 = 144. Without the parens around the 1/2 fraction, the PEMDAS rule would be 18 / 1 / 2 x 4 = 36. The correct answer is 12.
48 is the correct answer. Solve the whole numerator. 18÷1/2 is the same as 18×2. This gives the numerator as (18×2×4)/3
Why does everyone insist on the () to make 18 divided by a fraction true?
That would violate a rule about two different symbols for division. Following standards this would then be 18/1/2*4/3
Yes ans is 12
As written the fraction bar could be interpreted as a horizontal representation of a vinculum by its length which exist below the base. A vinculum has a automatic grouping meaning. That was also the original meaning of the obelus.
Once I kicked in my math brain cells I got it in an instant.
You deserve the highest award available in the world for being such an excellent teacher. Accept my salute
So the Master can violate the order of P.E.M.D.A.S. but not the students. So that we always make mistakes.
You should have described a fraction with an implied parentheses, other wise you broke the PEMDES rule by dividing 1 by 2 before 18 divided by 1.
you're respond would imply that its equivalent to (18/1)/2*4 then all divided by 3, which is 36 and that's not an option. so it can be safe to presume that the properly implied equation is 18 / ([1/2] fraction notation=.5) * 4 all divided by 3 which is D)48
@@indifinity215(18/1)/2×4 then all divided by 3 is not 36. It's 12.
@@gavindeane3670 the notation 1/2 is so obviously one notation and meant to be representing 0.5.... but this is a moot arguement... IDK... LOL
@@indifinity215 It's not about how easily we can guess what he might have meant to write compared to what he actually wrote.
If this had been written by a child in primary school it would be forgivable. But it's not been written by a child. It's been written by someone who purports to be a mathematics teacher, and there is no excuse for him not writing it properly.
The correct way to write the numerator he's trying to write, using inline notation, is
18/(1/2)×4
@@gavindeane3670 yes thats my interpretation because if they meant 18 ÷ 1 ÷ 2 x 4, they would have witten it with the ÷ instead of using the ÷ after the 18 and before the 1/2. so logically they inferred a fraction of 1/2 or 0.5... lol :p
The equation is misleading. You are verbally implying parenthesis around what you are referring to as a fraction.... However there are no parentheses in the equation.
The problem was crafted by a slothful individual. Run away.
I agree, except that it is not an equation - it is an expression.
Is not the slash (/) in the “½” the same as a divisor symbol? ½ .., same as ... 1 divisor symbol 2 ? (=0.5) … e.g., N= 18/1/2x4 … vs. … 18/(½)x4...vs ... Why did you consider the ½ (0.5) before the divisor immediately after the 18, just like you would with a parentheses around the ½? Maybe you consider the1/2 as a mini N/D equation, within the main N/D equation, that needs to be done first?
Yes, the / symbol is the division operator.
In the video he is treating it as if he'd put parentheses around the 1/2. He's evaluating the expression he meant to write, not the expression he actually wrote.
What makes me wonder is how dividing 18 by 0.5 increases the value of 18 to 36. Usually, in my mind I interpret 18 divided by 1/2 as 18/2 = 9
Which is correct? Are we dividing by 2 or multiplying by 2?
Multiplier first 0.5X4 = 2 then first divider 18/2 = 9 then 2nd divider 9/3 = 3
I’m with you D before M but just didn’t know you could do either D or M, A or S first. Now I know
I also got 3.
No, the teacher is correct …. in the PEMDAS, the grouping “MD” is a performed left to right. e.g., you could say, “after I do all the parentheses and powers, I will do the Multipliers and Divisions in a left to right order as I read them. After all the multipliers and divisors are completed, I will move to the next group, the “Additions and Subtractions”. The Additions and Subtractions are also to performed in the Left to Right order (just like the M & D group), but it really will not make difference in the result at this point
Interesting when I did this in Excel I got 12. This is why whenever I write computer programs or do financial spreadsheets, I use parenthesis and this eliminates any misinterpretation.
Excel said 12 because 12 is the answer. As written, that's what this expression evaluates to.
In the video he's solving it as if there were parentheses around the 1/2. But he didn't write those parentheses.
He's solving the question he meant to write, not the question he actually wrote.
@@gavindeane3670 And this is why one should use parenthesis to avoid any confusion. My point precisely. 😀
@@richardcarlin1332Completely agree.
Another good tip to avoid confusion, relevant to the author if the video, is not to use two different symbols for division in the same expression.
You don’t need parentheses. All y’all need is to learn the priorities of math operators.
@@bugtracker152 That's the entire point. The video is treating the expression as if it had parentheses when it doesn't.
D 48
God bless my math teacher who told us that divided by half is basically x 2 I never forgot it.
In the UK the BODMAS mnemonic is used: “brackets over division before multiplication before subtraction”? Not PEMDAS which is not correct! Division before multiplication please!🧐☝
PEMDAS is just another name for BODMAS. They're the same thing.
DM vs MD in the acronym doesn't make any difference. It's not division before multiplication in BODMAS and it's not multiplication before division in PEMDAS.
It's a 4 step process not a 6 step process. The MD step in PEMDAS is identical to the DM step in BODMAS. You calculate all the multiplications and division with equal priority, reading left to right.
@@gavindeane3670 PEMDAS≠BODMAS! Look at the problem as set! If you did division before multiplication and vice verse you’ll get different answers!👆🙄🤣
@@tuftyaurelius9062Obviously if you do multiplication before division vs division before multiplication you can get different answers for things.
But as I already explained, PEMDAS does not tell you to do multiplication before division and BODMAS does not tell you to do division before multiplication.
You do whichever appears first on the expression. When multiplication appears first, BODMAS and PEMDAS tell you to do the multiplication first. When division appears first, BODMAS and PEMDAS tells you to do the division first.
Your mistake is that you are blindly following the sequence of letters in the acronym instead of following the rules that the acronym refers to.
There are lots of variations of the acronym: BODMAS, PEMDAS, BIDMAS, BEDMAS, GEMDAS, PEMA, BOPS, BIPS, GEMS, etc...
They all refer to the save calculation process. They all mean exactly the same thing.
What you're doing is a common and understandable misconception. It's the reason why the 4 letter variations of the acronym exist.
My Dear Aunt Sally; multiply, divide, add then subtract.
This is less maths and more 'did you catch the trick'?
18 ÷ 1/2 * 4 ÷ 3
18 * 2/1 * 4 ÷ 3
36 * 4 ÷ 3
144 ÷ 3 = 48
Therefore, the answer is d.
8:27 Shows (d) is the correct answer of "12" (48 is not an option at this timestamp)
18 / 1 / 2 * 4 / 3
18 / 2 * 4 / 3
9 * 4 / 3
36 / 3
12
Where would I ever use this ?
8:40, hm..there's this deal with fractions that is the crux of this (and my error). this idea of how to handle fractions is not in PEMDAS...i dont memorize things like that, but thanks for showing me the 'fraction issue' . PEMDAS doesnt help with this problem.
separating parts of the fractions makes a 'clean rule' like PEMDAS, inadequate
GEMDAS addresses exactly that issue, with G for Groupings. It's exactly the same as PEMDAS except for recognising that parentheses are not the only grouping symbol in mathematical notation.
The vinculum (the horizontal fraction bar) is a grouping symbol too. You need to evaluate the numerator expression that is grouped by that fraction bar, just as you would evaluate an expression grouped by parentheses.
The first thing I did was convert 1/2 to .5. Never use two different division symbols in the same equation, it's just stupid, and confusing.
You don't get to decide on a test how the problem is posed to you. So you have to deal with what is given. (which you did in your own way)
Also, 0.5 IS a division. It is shorthand notation for 5/10 , which is the same value as 1/2 . So changing it to a decimal does not get rid of that division, it just puts it in a form that you are more comfortable with. But you'd likely get dinged in an algebra class if the teacher is anal about the methodology--decimals are sort of frowned upon in algebra 101 (usually).
When on an international forum you should use international standards which uses a solidus for division not an obelus. An obelus in Anglophone countries usually means division, however in Nordic countries can mean subtraction, in Russia grouping (original use was demonstrated as a vinculum).
When you follow an obelus by numbers separated by a fraction bar (note it ends below the base line) indicates it isva fraction as the obelus already splits the expression.
@@perryfarmer3280 And different mathematical operators/notation is used all around the world. Which means that an "algebra book" in Chile will likely have different notation/symbols compared to a book in the USA or somewhere else. That's just the way it is. You go with the conventions of your home country. Insisting that everyone notate the same way is the same as insisting that everyone speak Esperanto. It might be a logical and noble cause, but it simply is not practical. The best thing to do is get used to the way it is done in your local setting or the setting that you wish to become a part of.
This poster is simply giving it the way it would/could appear in any typical algebra book in the US or several other nations. So it is nothing out of the ordinary here, even though it may seem weird to you. There are just way too many math textbooks in way too many countries using way too many notations to hope everything will be consistent. Maybe someday, but right now... not so much.
While countries do use different symbols when dealing with them in an international community you use accepted standards. Once past about 5th grade you rarely if ever use an obelus.
If you go by history on page 76 in the year 1659 the obelus was used like a vinculum. You use standards for everything for clarity. If you do not you crash into Mars or in my background you just cost yourself 20 million U.S. dollars because you used a comma for 1500 in international power sales.
@drewt1081 You're absolutely correct. I've taught math and have written tests. If the video wanted to denote 0.5, then it should've used ½, not 1/2. There is no reason why that handwritten equation couldn't have written ½. As any computer user knows, / and ÷ are identical, both meaning divide.
As such, the equation is NOT (18÷½×4)÷3 = 48. Instead, it should be evaluated as (18÷1÷2×4)÷4 = (18÷2×4)÷4 = (9×4)÷4 = 36÷4 = 9. If the problem wanted the second term to be 0.5, then write ½, not 1/2. So the correct answer is 9.
This is rubbish. The answer is 12. No. Nobody will sign up for your website.
Correct...12 is the answer
Nope 48 is the answer. By using both the obelus and solidus it is obvious that the solidus represents a fraction. Only if solidus is used as the only operator should it be interpreted as divide, instead of a fraction.
When he wrote the problem down he should have put the fraction 1/2 in parentheses (1/2) if he wanted it to be worked the way he did it. The answer is 12.
Yep. No parentheses, so left to right:
18/1=18
18/2=9
9x4=36
36/3=12
That's what I thought at first. Changed it to 3.
We're both wrong apparently.
The lack of parenthesis around the 1/2 could suggest it could be viewed as 18 divided by 1 divided by 2 times 4 on the top the answer divided by 3 = 12
Without the parenthesis 1/2 is not a number it’s a sequence of operations
@@jnesmld That was how I did it, and I'm 65!
No. He should have put the 18 and the1/2 in parentheses, that is (18 divided by 1/2). It is meaningless to put parentheses around a single number, because it does not tell us anything more than it is a number.
I love your style of teaching! Excellent! Thank you so very much!
I love these videos!!!! This helping me sharpen my skills. It’s been a long time. 😊
D 48
Division and multiplication have the same value. Simply go left to right.
Giving division and multiplication the same precedence and going left to right leads to the answer 12. There's no parentheses around the one divided by two part.
@@gavindeane3670exactly. beats me why anyone gets to a different result as if 1/2 were a standalone symbol representing (1/2)
Exactly, why is it so complicated?
We mustn't divide 1/2 in the first step! There are no brackets so calculations start from left to right. So 18/1/2 = 9 and the final answer is 12.
Using this notation 1/2 is not the same as 0.5.
Agreed
Old school I got that too 12 😅😅😅
@joefergerson5243 Wrong, there are 36 halves. If you have 18 apples and you cut them in half, you get 36 pieces. You're not multiplying by 1/2, you are dividing by 1/2
1/2 is exactly the same as .5, the answer is 48! t took me less than 10 seconds to do that, then checked with my calculator, and, surprise! it also said 48!
@@zicowilco60 Alas, wrong!
This is a clear case of lazy, unclear notation in the original. Mixing Fractional notation beside a divide sign, Al in a numerator.
The real lesson is to be more clear in how you present an equation.
While I would evaluate this exactly this way, I would fear that the person composing it had a different thought.
I do not think that the problem is presented correctly. When you need to introduce BOMDAS or PEMDAS or any of these other rules - it means that the problem is shown as badly defined. This is where the use of Brackets or Multiple Brackets reduces the mistake of multiple interpretations - just as correct punctuation can reduce the mistake of incorrect English interpretations - incorrect as to what the writer intially wants to convey.
There's nothing wrong with the precedence rules in BODMAS/PEMDAS. They have endured for so long because they work. They make mathematical notation cleaner and more readable.
The issue here is that the notation is garbage in the first place. He shouldn't really be using the ÷ symbol at all, and using two DIFFERENT division symbols in the same expression is inexcusable.
i wish you were my college math teacher. Oh, you are here on RUclips! Thanks You Are Awesome! I hope you are having a great life!
The equation itself is "wrong". There are several "correct" standards of operation rules when solving problems. I know three. The only rule for writing those equations is that there can be no ambiguity no matter which solution system you use.
Engineers love standards. There's so many to choose from!
Another example why PEMDAS should be entirely replaced by parentheses. Mathematics is not about a secret decoder ring.
The 'P' in PEMDAS means parentheses.
@@martinglenn27 The rest should never be trusted. This way lies madness - too many opportunities for error for no reason at all. Speak clearly, write expressions clearly? Just as there is street language, PEMDAS is street math.
@Pax.Alotin Ancients did not use PEMDAS or similar. (Masons is a whole different thing.) Tongue in cheek, I presume.
PEMDAS isn't the issue here. The issue is the use of two different division symbols in the same expression.
Using inline notation, the correct way to write the numerator that he wants here is
18/(1/2)×4
@gavindeane3670 no, the issue is in people not recognising a fraction when they see one.
The answer is 3. Because many will confuse this " / " simple to mean "devide" but it's actually a fraction equal to "0.5".
No it isn't. / is the correct symbol for division. He shouldn't even be using the ÷ symbol and he certainly shouldn't be mixing two different division symbols in the same expression.
The expression as written in the question evaluates to 12.
Using inline notation, to get the answer to be 48 he must write the numerator as
18/(1/2)×4
To get the answer 3 it would be
18/(1/2×4)
because it is .5, the correct answer is 48
@@JimD-tn6bt Obviously in isolation 1/2 is the same as 0.5. But that doesn't mean that everywhere you see the text "1/2" as part of a larger expression you can simply replace it with 0.5 without considering context.
If he wants the reader treat the 1/2 as a single entity like 0.5 then he must enclose the 1/2 in parentheses. That's what parentheses are for. It's literally the entire point of parentheses.
Nope. You're missing the other part of the equation - the spaces. If an equation is written using spaces between the numbers, 1/2 surrounded by spaces means one half. The right answer is 48. If the equation was presented with no spaces, or if 1/2 were presented as 1 / 2, then the answer would be 12.
@@jerryz2541 Spacing is not a symbol in mathematical notation!!!
Whoever told you that, you need to stop listening to them because they don't know what they're talking about!
The correct grouping symbol to communicate what he wanted to communicate is a set of parentheses. He failed to use the parentheses he needed, and as a result the expression does not say what he wanted it to say.
The problem is intentionally written to create a confusion point. Is the 1/2 a fraction? Or is the / a division symbol that follows the first division from left to right?
The / symbol is certainly a division operator. You could argue a different meaning for the ÷ symbol because the ÷ symbol is not formally part of mathematical notation. But it's hard to come up with a new definition of the ÷ symbol that leads to the answer 48 here.
The notation he's written is just nonsense.
Why two different symbols for the divide operator? No one writes math problems that way.
Another PEMDAS cream puff. Thanks Boss.
No parentheses so left to right… answer is unarguably 12. 18/1/2*4 all divided by 3. 12! Poorly written equation if 18 was meant to be divided by 1/2.
AMEN, the only clue is the heading says one half. There is no rule to do / before the first operator.
Divided by 1/2 , 1÷2=.5
Saying that divided by 1/2 not divided by 2
@@billywilliams3204No, it is divided by 2.
The numerator evaluates as:
18/1 = 18, then
18/2 = 9, then
9×4 = 36
Then you divide the whole thing by 3 and get the answer 12.
@@billywilliams3204 Well... another clue is that it's a different division symbol. Most math texts I've seen would have written it with the 1 over a 2 to avoid confusion though.
Exactly. He purposely obfuscated the equation in order to confuse.
While I love this channel, this video was not well communicated. I would not recommend this video to my students.
I think he purposely drags things out. You know...for the algorithms
Why, because you got it wrong? This guy explains very well and even the exceptions are explained.
@@greghoward1561In this video he uses careless, shoddy, improper notation. And he evaluates the expression he meant to write, not the expression he actually wrote.
He's certainly very comprehensive in his explanations, but that means he should take even more care not to make the sort of errors he does here. His target audience is very likely to include people who wouldn't know any better and would have no chance of realising that the errors are even there.
12
@@greghoward1561The problem is written incorrectly for answer to be 48. As written problem should be solved as: 18 ÷1 (not divided by 1/2) = 18/2=9×4=36/3=12. The two different division signs should not have been used. If he wanted 18 to be divided by half he should have written problem as 18/.50x4/3. As a high school math teacher I would never give my students a math problem written as incorrectly as this one.
I plugged the numbers into an excel spreadsheet. A1= 18/1/2*4/3 gives the value for A1 as 12 then I plugged A1=18/.5*4/3 and the value changes to 48.
That's correct. That's what any calculator will tell you.
The answer to the question he's written is 12.
got it 48 simple pemdas thanks for the fun
He is correct. Those who say it is 12 don’t know how to divide fractions.
There might be some people who are getting 12 because they're incorrectly calculating 18 / ½ as 9 instead of 36.
But there's also a bunch of people getting 12 because they recognise that the question does not actually ask us to divide 18 by ½. The question as written DOES evaluate to 12.
There are no fractions in the numerator of this question. We are asked to divide 18 by 1, then divide the result of that by 2, then multiply the result of that by 4, then divide the result of all that by 3.
To get 48, the author needed to write the numerator in the question as
18/(1/2)×4
Those parentheses are essential if he wants us to divide the 18 by the entire 1/2 instead of just dividing the 18 by the 1. A division operation does not get higher precedence than another division operation just because he happens to have used a different division symbol. There's no excuse for using two different division symbols in the same expression.
In the video, he is answering the question he meant to write, not the question he actually wrote.
And DON’T Care!
This problem is mixing +, /, and ____ to represent division, fraction (half) and fraction (third) respectively. This is ambiguously specified.
A vinculum is not a third fraction, it is a grouping symbol.
Uhh, uhh. Unless you write 0.5 you don't get to introduce two separate symbols for division. The ISO 80000-2 standard for mathematical notation recommends only the solidus / or "fraction bar" for division, or the "colon" : for ratios; it says that the ÷ sign "should not be used" for division. So it is either _(18/0.5*4)/3_ or: _(18/1/2*4)/3_ - and only the first one will render your solution.
He’s not. The 1/2 is a fraction…there are no spaces between the numbers and “/“.
If you do the division furst then what is the use of PEMDAS
That's a very fair question. These 6 letter acronyms are misleading. They create the impression that there is a hierarchy between multiplication and division, and a hierarchy between addition and subtraction.
If you want to use an acronym for this stuff then the 4 letter acronyms like PEMA are better for exactly this reason.
PEMDAS does not mean that multiply comes first. M&D have the same precedence and are processed left to right.
according to WolframAlpha the solution is the following: 18/1/2*4/3 = 12
That's because 12 is the answer.
He's written an expression that evaluates to 12 and he's telling everyone it evaluates to 48. That's not great behaviour from someone who purports to be a teacher.
It would have been easy for him to rewrite it properly so it did actually evaluate to 48.
@@gavindeane3670 If you go left to right and solve the numerator before the denominator, it's 48.
@@jessejordache1869
No it isn't. The numerator would be 48 if the 18 was divided by the entire 1/2. But that would require brackets around the entire 1/2 and the author didn't write those brackets.
What he should have written in the numerator is 18/(1/2)×4. Then the final answer would be 48.
@@gavindeane3670 or, instead of 1/2, he could have used 0.5
@@gavindeane3670 You have to take the fraction as an atomic unit: if you divide 18 by 1, and then multiply 2 by 4, you're not using the same numbers that are written on the formula.
True, .5 makes it simpler, but there's no sense where you can take 1/2 and have the 2 interact as a two, and not a half, unless you're deliberately playing around with reciprocals.
If you use a calculator you get 12 but if you divide 18 by the decimal value of 1/2 then you do get 48
Yeah, calculators don't recognise fractions. Try typing it in as 18÷(1÷2 )×4
@@dazartingstall6680It's got nothing to do with whether calculators recognise fractions. The problem is that the author doesn't know how to write fractions.
As you've shown, using inline division operators as the author has done, then the answer is not 48 unless you add some parentheses that are not in the question.
@@gavindeane3670 The brackets are for the calculator's benefit, not the reader's. 1/2, written as a separate term as it is in the video, is one half. Though I will admit that I'd prefer it if the video maker had used a horizontal fraction-bar.
@@dazartingstall6680 The calculator doesn't need you to do things for it's benefit. It is perfectly capable of evaluating the exclusion with or without the extra parentheses. The point is, the parentheses *change* the meaning of the expression - as the calculator demonstrates.
The expression in the question does not evaluate to 48 unless and until parentheses are added around the 1/2.
The 1/2 is *not* written as a separate term. That's the problem. Plainly that's what the author intended, but it's not what he wrote.
For it to be a separate term it needs to be in parentheses. That's literally the entire point of parentheses. It's what they're for.
Or better still, as you say, write it as a fraction: a horizontal line with the 1 above and the 2 below.
@@gavindeane3670 I agree in principle but I think you're maybe being a tad pedantic. While I'm not struck on the inline fraction symbol, it is common. And in this case is further clarified by its juxtaposition with the simple division sign, ÷.
As to calculators, they typically have one division sign available, as opposed to the three variants (horizontal bar, ⁄ and ÷) available to a person calculating on paper. A fraction is a single term which needs to be rendered as a decimal (1/2 = 0.5) before a calculator can use it, so it needs to be given higher priority than what would, in this case be 18÷1. The only way we can force this is to bracket the fraction.
Human beings don't need the brackets, because we can recognise and treat a fraction as a single term. Not everything needs to be machine-readable.
Unfortunately, the teacher is not right. He did not apply the sequence of operations right.
The answer is as I indicated above 12.
Where did he go wrong?
He divided 18 by (1/2)
He should have divided 18 by 1, then divide the result by 2. That is 9. Multiply 9 by 4 and divide the result by 3, you end up with 12, not 48.
If it is not clear, I can explain it with some simplifications and reasoning.
Incorrect. By using both the obelus and the solidus it is obvious the solidus indicates a fraction. Answer is 48.
Thank you for reminding me what I have forgotten. Cheers to you!
I am good at math but that did not make sense at the beginning. who would ask a question like that? If you want (C. 12 ) to u be the correct answer how would write the same question when you want 18 × 50% × 4 /over 3 = 9 ×4 /3 = 36/3 = 12q
If that's how he writes equations, I pity his students.
I'm not sure about this as I try to make the problem faster to solve. It appears as if I could change the fraction into a whole number of 2. So I would get 18x2=36x4=144. 144/3=48. Again, I'm not sure if this works in all cases as it just appears as if it works this time.
What he does in his verbal explanation is describe 1/2 as 'one half'.
The accepted definition of the phrase 'one half' is one of two approximately equal parts of a divisible whole. Point 5 only applies to a divisible whole of one.
Not sure what you mean. "One half" is the name of the number ½.
There's a question about whether the notation actually asks us to divide 18 by ½ anyway, but that's a separate issue.
Finally found your reply.
The verbal explanation should had cleared the ambiguity but actually adds to it.
Verbally one half by definition is one of two equal parts. One of two equal parts of 18 when spoken verbally would equal 9, which is one part of two. As writen however one half depending on what the slash actually represents would equal one of two equal parts of one which is point five. Multiplied by 18 and you have 36 halves.
He also screws up the vinculum since the line length should represent what is the grouping.
This makes no sense to me. Just the first step. How can you start with a number of 18, you are going to divide it and now it’s larger?
Because dividing any number by ½ doubles the value of the number.
1 half .50 to 50 into then devide into1800 =36 .is that wrong ?
The answer is 48
18 ÷ ½ × 4
---------
3
Simplify the numerator. Apply PEMDAS from left to right:
(18 ÷ ½) × 4
----------
3
Rewrite for clarity. Remember, division by a fraction is the same as multiplying by the inverse reciprocal (i.e., of the denominator). As such ½ becomes 2/1:
18 2
( --- x -- ) × 4
1 1
-----------
3
Simplify:
36
--- × 4
1
-------
3
Simplify again:
36 × 4
------
3
Simplify again:
144
----
3
Solve:
48
Why wouldn’t we just change 1/2 to .5 right of the bat? 18 divided by .5 =36, 36 x 4=144, 144/3=48
Because changing the 1/2 into 0.5 is invalid unless you either put the 1/2 in parentheses, or change the meaning of at least one of the division symbols.
The answer depends on top of division line phrasing. You can actually get 2 answers. B or C depending on how you phrase.
You can't get B. That would require parentheses around the 1/2×4. Unless you're going to say that ÷ isn't simply a division operator.
I disagree with the video. The second term should not be treated as ½ or 0.5. Instead / and ÷ are identical, and both are division, as any computer user knows. So the equation is NOT (18÷½×4)÷3 = 48. Instead, it should be evaluated as (18÷1÷2×4)÷4 = (18÷2×4)÷4 = (9×4)÷4 = 36÷4 = 9. If the problem wanted the second term to be 0.5, then write ½, not 1/2. So the correct answer is 9.
Correct, except for what I'm sure was just a typo. It's not 36/4 at the end. It's 36/3, giving 12.
First let me say that I DO enjoy your posts- even when I get them wrong. Even when I question how you arrived at the result. (At 60yrs old mathematics was a little different, right?) Now, for me my answer was c) 12. This is a question of appearances. The "1/2" does not look like a fraction- it looks like, 1- then division symbol "/" - then 2. I suppose in my era fractions stood out more. I googled your numerator as you wrote it and they rewrote it as
(18/(1/2))*4, which equals 144. There the fraction stands out! Oh, the good ol' days......
Yep. His numerator is incorrect to get the answer 48. As you've seen, it needs parentheses around the 1/2.
In my day it was BODMAS that was the order of operation.
Brackets, Operation, Division, Multiplication, Addition, Subtraction...with the same rule as you described with D,M and A,S
BODMAS is just another name for PEMDAS. They're the same thing. There are lots of variations of the acronym.
Ans D-48
Did anyone think about using ( ) around the dang part of the problem to be done first?
48...now I'll read comments and watch video If placing a fraction IN a fraction...write it more clearly 1 over 2, not 1 slash 2. The 1 over 2, becomes a fraction within a fraction. It has to be reduced, in order to proceed.
I first hit the problem of operator precedence at age 11 in the 1st year of my secondary school. Despite being an infant maths genius in primary school, no teacher ever mentioned that multiplication had precedence over addition. Since then I've succeeded in maths and engineering and used many computer languages and it's always vital to understand operator precedence. But what this video highlights to me is that PEMDAS is a ridiculously terrible tool to help remember the expected order. E stands for Power and P doesn't! In fact P stands for Parenthesis, which is not an operator at all. Then the real killer: M comes before D in this supposed left-to-right ordering but we should treat Multiplication and Division as equal priority and perform left to right. Same with Addition and Subtraction. Utterly ridiculous, I'm sorry to say. DON'T TEACH KIDS WITH THIS TOOL!
I think you've hit the nail on the head there. The "M before D" and "A before S" misconception is the most obvious and visible issue with this stupid acronym. But I think that including parentheses in a topic called "order of operations", when parentheses are not an operator at all, actually causes more fundamental problems.
Reminds me of math class where i would pay more attention to the music in my head than to the material.