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.

@marscience7819

Ай бұрын

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".

@squatch253

Ай бұрын

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

Ай бұрын

@@squatch253 Definitely not 3/4

@squatch253

Ай бұрын

@@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 😵‍💫

@grokranfan8578

Ай бұрын

​@@marscience7819you don't get that 1/2 is meant as s fraction one half don't you?

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.

@grokranfan8578

Ай бұрын

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

@marscience7819

Ай бұрын

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!!!

@LivelysReport

Ай бұрын

@@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..

@karenshaw7807

Ай бұрын

I read your comment before the video, so I didn't watch it! I got 48...

@marscience7819

Ай бұрын

@@karenshaw7807 so what do you get now?

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.

@Jabberwalkie-zi5tu

Ай бұрын

Improperly formatted to create an argument.

@louiskovach

Ай бұрын

i totally agree i hated math to some degree for that reason seems like they wanted to over complicate and make it a puzzle

@davedonkers4843

Ай бұрын

@@louiskovach That's life, bub. Get used to it.

@TheHsan22

Ай бұрын

​@@Jabberwalkie-zi5tuPretty much the same in each episode, set up to generate lame repetitive discussion about formatting.

@marscience7819

Ай бұрын

absolutely correct @richardhole

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)❤❤❤❤❤❤❤

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?

@jamesadair7085

22 күн бұрын

69 and it took me 15 sec.

Can you understand why some people dislike math so much? Math teachers are not always good communicators, especially to young people.

@zanelemasimula5174

Ай бұрын

12

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

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]?

@bazkeen

2 ай бұрын

I did notice that 🤔🤔🤔

@randylazer2894

2 ай бұрын

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.

@bazkeen

2 ай бұрын

@@randylazer2894 WTF. We weren't even talking about which answer was right or wrong 🙄🙄🙄🙄

@marscience7819

Ай бұрын

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.

@randylazer2894

Ай бұрын

@@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 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

@timmurphy3609

4 күн бұрын

Lol

@9999deoxys

2 күн бұрын

Correct....12 is actually the right answer.

@thor3120

Күн бұрын

I agree

My Dear Aunt Sally; multiply, divide, add then subtract.

You are a fabulous teacher. When I was in school I always detested math but watching your channel makes me like it. You make learning math a joy, like a fun puzzle to be solved. Thank you so much for this.

This problem is mixing +, /, and ____ to represent division, fraction (half) and fraction (third) respectively. This is ambiguously specified.

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.

@indifinity215

2 күн бұрын

you're respong wopould imply that its equivalent to (18/1)/2*4 then all divided by 3, which is 36 and thats not an option. so it canm be safe top presume that the propperly implied equation is 18 / ([1/2] fraction notation=.5) * 4 all divided by 3 which is D)48

This is less maths and more 'did you catch the trick'?

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.,

Thank you for the ways to do 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.

@wlonsdale1

Ай бұрын

18*.5*4

@jessejordache1869

Ай бұрын

I'm sure 1/2 in the numerator is atomic, so the parens around 1/2 are assumed.

@jimbuxton2187

Ай бұрын

​@@jessejordache1869...there are no assumptions in math

@jessejordache1869

Ай бұрын

@@jimbuxton2187 That's actually, literally false. They're called axioms. Come join us in the 19th century.

@survivrs

Ай бұрын

*PEMDAS

18 ÷ 1/2 * 4 ÷ 3 18 * 2/1 * 4 ÷ 3 36 * 4 ÷ 3 144 ÷ 3 = 48 Therefore, the answer is d.

@robby1816

3 күн бұрын

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

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√ ∞ * ≈ ≠ ≤ ≥ ÷ •

@martinglenn27

2 ай бұрын

The answer is 48, and only 48.

@gavindeane3670

Ай бұрын

​@@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.

@joeblog2672

Ай бұрын

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)

@gavindeane3670

Ай бұрын

@@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.

@martinglenn27

Ай бұрын

@@gavindeane3670 as written, the only answer is 48.

YES YES YES!!! Took about 45 seconds and did it in my head! 🎉🎉

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.

@gavindeane3670

Ай бұрын

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.

@Chris-hf2sl

Ай бұрын

@@gavindeane3670 Sadly, it's not quite that simple. I've watched a few videos on KZread 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

Ай бұрын

You have to use an algebraic calculator.

@Chris-hf2sl

Ай бұрын

@@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.

@gavindeane3670

Ай бұрын

@@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.

Solved at the thumbnail, I'm getting c) 12. Using PEMDAS and interpreting "1/2" as "1 divided by 2" rather than "o.5" we just evaluate the top from left to right.

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.

@gavindeane3670

16 күн бұрын

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.

@thinkcivil1627

16 күн бұрын

@@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 KZread 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.

@user-do5vu3ue5v

4 күн бұрын

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.

@thinkcivil1627

3 күн бұрын

@@user-do5vu3ue5v 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.

@gavindeane3670

3 күн бұрын

​@@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.

D 48 Division and multiplication have the same value. Simply go left to right.

@gavindeane3670

8 күн бұрын

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.

@christianherzig1575

5 күн бұрын

@@gavindeane3670exactly. beats me why anyone gets to a different result as if 1/2 were a standalone symbol representing (1/2)

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.

@gcarap

5 күн бұрын

Frractions are always done first so there are implied brackets around the 1/2

@gavindeane3670

3 күн бұрын

​@@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).

@gcarap

3 күн бұрын

@@gavindeane3670 the expression 1/2 is a fraction and thus auto-defaults to ( ).

@gavindeane3670

3 күн бұрын

​@@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.

@gcarap

3 күн бұрын

@@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.

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.

@severn77

Ай бұрын

As in "eats shoots and leaves" or "nut screws washers and bolts" without commas

@lindakrzyz5512

Ай бұрын

Read and figured it three different ways/times. Getting 12, 3 and finally 48.

@gavindeane3670

Ай бұрын

​@@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.

Why, thanks for the award. But I would have had trouble with equations like this before I began watching your videos.

I am from Germany and we never used the / for division in school or university. We only had : for division or fractions with fraction bar. People misuse the / to write fractions in one text line. So I see 1/2 as a fraction. There are no parenthesis, so 18 ÷ and x 4 are not part of this fraction. => 18 ÷ 1/2 x 4 = 18 × 2/1 x 4 = 36 x 4 But I agree with the people who have learnt / is a division. Then of course from left to right. Btw. we also never used x for multiplikation in maths. x was always the unknown variable.

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.

@TheBlueScarecrow

Ай бұрын

The problem was crafted by a slothful individual. Run away.

@davidbrown8763

Ай бұрын

I agree, except that it is not an equation - it is an expression.

This is rubbish. The answer is 12. No. Nobody will sign up for your website.

@9999deoxys

2 күн бұрын

Correct...12 is the answer

thank you very much for sharing. we do it without thinking at school. well explain

Reminds me of math class where i would pay more attention to the music in my head than to the material.

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

@johnshaw6702

Ай бұрын

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.

@ericr2646

Ай бұрын

@@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.

@dazartingstall6680

Ай бұрын

@@ericr2646 In VBA this works: MsgBox (18 / (1 / 2) * 4) / 3

@johnshaw6702

Ай бұрын

@@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.

@joeblog2672

Ай бұрын

Looks good, worked inside out, same number of left and right brackets.

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.

@usrname_error

29 күн бұрын

Agreed

@zicowilco60

29 күн бұрын

Old school I got that too 12 😅😅😅

@joefergerson5243

29 күн бұрын

I agree, half of anything is HALF👍🏼

@bryanwiley5550

17 күн бұрын

@@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

@joepkortekaas8813

16 күн бұрын

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!

So simple. I'm 67 and did it in my head in 5 seconds.

@christianherzig1575

5 күн бұрын

Same timing for me. I’m 55 and the correct result is our age difference. Ain’t that funny!?

Something that really interested me about this problem was the fact that 1/2 does not always mean 1 divided by 2. Consider if the numerator here were re-written slightly. I'll use "DV" in place of the 'dot, line, dot' symbol: "18 DV 1 DV 2 x 4". The only change here is that I have replaced the 1/2 fraction with the "1 DV 2" expression. But now when order of operations (OOO) are applied, the numerator works out differently. 18 DV 1 becomes the first step which of course is 18. This is then divided by 2 as the next priority operation, yielding 9. This multiplied by 4 then gives a numerator of 36 (instead of 144) which then gives a final answer of 12 (not 48). I've known for the last 40 years that to divide by a fraction (as in the expression: a DV b/c) one simply inverts the dividing fraction and multiplies (ie: a x c/b). What I never realized in all that time is that fractions come with assumptive mathematical brackets when it comes to OOO related manipulations. If this were not true then dividing a quantity (a) by a fraction (b/c) would demand splitting the fraction apart. Instead of: a DV (b/c) one would have: a DV b (step 1) with this result then divided by c (just like the 18 DV 1 DV 2 earlier). The assumptive brackets of course ensure that a divisor fraction cannot be split apart by OOO priorities since brackets are top priority.

@gavindeane3670

Ай бұрын

When order of operations is applied to 18÷1/2×4 you get 36. The precedence of division in the order of operations does not change depending on which symbol you happen to have chosen to represent the operation. It's not "÷ means division and / means some sort of magic, higher precedence kind of division that gets implicit parentheses around itself" It's "/ means division and ÷ means division too, but ÷ is deprecated so should not be used".

@jessejordache1869

Ай бұрын

I don't think you can do that: 1/2 has to remain in that form, just as the numerator has to all be divided by three. You're actually better off if you put "over 1" over all the other terms, and solving that way.

18 :.5 x 4 = 144/3 = 48 (d)

@michi9816

Ай бұрын

I tried WolframAlpha: 18/1/2*4/3 = 12

@lynnee.pagels8896

Ай бұрын

48

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

@gavindeane3670

5 күн бұрын

BODMAS is just another name for PEMDAS. They're the same thing. There are lots of variations of the acronym.

Where would I ever use this ?

This may sound extreme, but why is it 18 divided by 1/2 (18 / 1/2) and not (18 / 1) / 2?

@bulldog6925

2 ай бұрын

1/2 is a position on the number line. You can not split that position with a symbol. Using decimal, 1/2 is .5

@Kevlar187

2 ай бұрын

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.

@edsherrod5216

2 ай бұрын

@@bulldog6925 makes sense especially when considering the decimal equivalent. Thank you.

@gavindeane3670

Ай бұрын

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.

@gavindeane3670

Ай бұрын

​@@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.

Another PEMDAS cream puff. Thanks Boss.

Old school math teacher here. Putposely 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.

@gavindeane3670

9 күн бұрын

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

@TheBackStory22

Күн бұрын

@@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)

This right here is why I hated math when in school and why I never even took algebra or geometry etc. Just two years of high school basic math and no college and had a nice 43 year career in IT.

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?

@gavindeane3670

Ай бұрын

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.

@happycamper6352

Ай бұрын

@@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.

@marscience7819

Ай бұрын

Yep you are correct.

@michi9816

Ай бұрын

stupid questions get stupid answers.

@user-vr8gr2dy8t

Ай бұрын

Winner-Winner-Chicken-Dinner

In the UK (1960's) we were taught "B-O-D-M-A-S" (Brackets, Of, Division, Multiplication, Addition, Subtraction). When did it change ???

@Volcano-Man

2 ай бұрын

@davecooper5951 The sequence is still BODMAS - Pedmas is the yanks who don't do mathematics only 'math' meaning more than 1 process confuses them.

@davecooper5951

2 ай бұрын

@@Volcano-Man But surely "PEMDAS" as per your example, transposes the 'M' (multiplication) and the 'D' (division) by order..... this will affect some problems I think ?

@dazartingstall6680

Ай бұрын

@@davecooper5951 It won't. M and D are a group. We work all multiplications and divisions in the order they appear in the problem, reading from left to right.

@davecooper5951

Ай бұрын

@@dazartingstall6680 Ah OK, I'm actually coaching someone at the moment - so I can continue with 'BODMAS' then....(I don't want to confuse them with too many acronyms !).

@dazartingstall6680

Ай бұрын

@@davecooper5951 BODMAS is fine. Just make sure to stress that the "DM" part doesn't force an order on multiplication and division. That seems to be the commonest stumbling block for people who learned an acronym.

I love math but I never really understood how to correctly work the operations in my homework.

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.

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.

This expression is purposedly designed to make people argue and bait reactions. The use of different operators for division ("½" and "÷") is not according to best mathematical practice. To get the "correct" answer, parenthesis should have been used. The "left to right" rule applied on all of the numerator withing the "MD" of "PEMDAS" should give the result 36/3=12. Sorry Mr. Mathman, this video is resulting in my first ever thumb down for you 😕

@gavindeane3670

Ай бұрын

I'm not sure it's purposely designed for that. I think it's just carelessly written.

@franhouston4620

Ай бұрын

You don't understand order of operations. MD does NOT mean that multiplication is always performed first. Multiplication or division in order from left to right. Therefore in this problem you perform 18 / (1/2) which is 18 x 2 which is 36.

@gavindeane3670

Ай бұрын

@@franhouston4620 You're correct that multiplication does not have higher precedence than division, but there are no parentheses around the 1/2 in this question so the first operation here is 18/1=18, then 18/2=9, then 9×4=36. The numerator evaluates to 36 so the final answer to the question he actually wrote is 12. What he should have written in the numerator is 18/(1/2)×4. No silly use of two different division symbols, and actually writing the parentheses where they're needed.

@user-mu6lp9sk7b

Ай бұрын

12

@freddonoso2299

Ай бұрын

It seemed pretty obvious to me that division was using ÷ and the slash was indicating a fraction.

You're wrong. 12. The lack of parentheses means the numerator is 18 divided by 1 (18) divided by 2 (that's 9) times 4 (36) divided by 3 (12). The 1/2 in the horizontal format WITHOUT PARENTHESES is not one half. It's 1 divided by 2. If you want to divide 18 by 1/2, you need to put the 1/2 in parentheses.

@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.

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.

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.

@jnesmld

Ай бұрын

Yep. No parentheses, so left to right: 18/1=18 18/2=9 9x4=36 36/3=12

@lindakrzyz5512

Ай бұрын

That's what I thought at first. Changed it to 3. We're both wrong apparently.

@rebeccavandam2834

Ай бұрын

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

@survivrs

Ай бұрын

@@jnesmld That was how I did it, and I'm 65!

@davidbrown8763

Ай бұрын

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.

Did anyone think about using ( ) around the dang part of the problem to be done first?

He is correct. Those who say it is 12 don’t know how to divide fractions.

@gavindeane3670

Ай бұрын

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.

@janetstotler399

Ай бұрын

And DON’T Care!

The answer is 3. Because many will confuse this " / " simple to mean "devide" but it's actually a fraction equal to "0.5".

@gavindeane3670

Ай бұрын

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

Ай бұрын

because it is .5, the correct answer is 48

@gavindeane3670

Ай бұрын

@@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.

@jerryz2541

29 күн бұрын

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.

@gavindeane3670

29 күн бұрын

@@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.

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.

@gavindeane3670

Ай бұрын

That's correct. That's what any calculator will tell you. The answer to the question he's written is 12.

You do have a parenthesis or grouping. The fraction is a grouping problem so that must be done first 1/2=.5.

@gavindeane3670

Ай бұрын

A division operator is not a grouping symbol. The only way to group the 1/2 using inline notation is with parentheses, as 18/(1/2)×4 Or you can actually write it as a fraction, as 1 18 / ----- × 4 2

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.

@gavindeane3670

Ай бұрын

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.

@richardcarlin1332

Ай бұрын

@@gavindeane3670 And this is why one should use parenthesis to avoid any confusion. My point precisely. 😀

@gavindeane3670

Ай бұрын

​@@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.

@bugtracker152

Ай бұрын

You don’t need parentheses. All y’all need is to learn the priorities of math operators.

@gavindeane3670

Ай бұрын

@@bugtracker152 That's the entire point. The video is treating the expression as if it had parentheses when it doesn't.

according to WolframAlpha the solution is the following: 18/1/2*4/3 = 12

@gavindeane3670

Ай бұрын

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

Ай бұрын

@@gavindeane3670 If you go left to right and solve the numerator before the denominator, it's 48.

@gavindeane3670

Ай бұрын

​@@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.

@omnipotent11

Ай бұрын

@@gavindeane3670 or, instead of 1/2, he could have used 0.5

@jessejordache1869

Ай бұрын

@@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.

18/.05=36x4=144/3=48

Thanks for the memories!

The 1/2 is not in parentheses so the problem should be considered in order of operations as 18 divided by 1 divided by 2 times 4 divided by 3 which gives us 12. If you want the problem to be using 1/2 “one half” as in your audio then that needs to be in parentheses

@Chris_Mack

2 ай бұрын

You cannot split the fraction, it is a number equal to .5

@laurendoe168

2 ай бұрын

@@Chris_Mack I'm a PEMDAS freak... but John is technically correct. Rather than using the symbols "1/2", the title and video should have used the symbol "½" to make it clear this was a fraction.

@MrSeezero

2 ай бұрын

Part of the giveaway is that there is either a space before and after any "external" operation symbol or that "external" symbol is vertical and relatively large compared to the rest of the expression while any "internal" operation symbols have no space before or after that symbol. The "internal" ones are understood to be done first while the "external" ones do have to follow the PEMDAS.

@DrR0BERT

2 ай бұрын

I agree with you on this. But really the problem is ambiguous. The author is the one at fault. 12 is a valid answer because of what you said. But then TCM is also correct. I hate these order of operations clickbait problems. They all are ambiguous.

@Kaj_Selin

2 ай бұрын

@@Chris_Mack Exactly, it is a number equal to 18.

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.

@redhatbear1135

29 күн бұрын

AMEN, the only clue is the heading says one half. There is no rule to do / before the first operator.

@billywilliams3204

26 күн бұрын

Divided by 1/2 , 1÷2=.5 Saying that divided by 1/2 not divided by 2

@gavindeane3670

26 күн бұрын

​@@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.

@Trifler500

25 күн бұрын

@@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.

@jameswinter6125

24 күн бұрын

Exactly. He purposely obfuscated the equation in order to confuse.

The answer depends on top of division line phrasing. You can actually get 2 answers. B or C depending on how you phrase.

@gavindeane3670

6 күн бұрын

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.

It should be written 18÷(1/2)x4 over 3. The fraction is a division and should not be in priority over the previous division, because you get wrong answer. 1/2 and 1÷2 is exactly the same.

@gavindeane3670

24 күн бұрын

Really it should be written 18/(1/2)×4 There's no justification for mixing two different division symbols in the same expression. The proper symbol for division is / so he should have used that.

Multiplier first 0.5X4 = 2 then first divider 18/2 = 9 then 2nd divider 9/3 = 3

@Tom-xf7wk

Ай бұрын

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

@truthseeker644

Ай бұрын

I also got 3.

18 divided by 1/2 times 4 all over 3 36 times 4 over 3 144 over 3 48

@silabhattacharya1071

Ай бұрын

Yup

@johnmondock6539

29 күн бұрын

Reduce 18 over 3, leaves 6 over 1, now complete the math in the numerator, 6 divided by 1/2 equals 3, and 3 times 4 equals 12. 12 over denominator of 1 equals your answer, 12

48! My mistakes was on the division of 18 divided by 1/2 instead of 2; thanks!

God bless my math teacher who told us that divided by half is basically x 2 I never forgot it.

(18÷1/2 x 4)/3 should be written as (18÷1÷2 x 4)/3 to prevent confusion. Also you have two different sets of multiple choice. 0:00-6:20 A18, B3, C12, D48 and 8:26-9:25 a18, b3, c9, d12. Assuming both multiple choice sets have the correct answer as an option 48 wasn't even a reasonable guess since it isn't even in both multiple choice options. You made errors in your math and overlooked using different answer choices.

@dgerdner

Ай бұрын

I believe his intention was 18 / .5 x 4 / 3. Dumb video because the formula is unclear. The first rule is, make the formula clear. Use parentheses if needed.

@marscience7819

Ай бұрын

@@dgerdner Yes, this is an AWFUL video. No wonder young minds get twisted around.

This equation as written was made to be intentionally confusing with the "1/2" instead of "0.5." The way it's written, the "/" can be translated as being the same as the division symbol, which make the order of operations above the large line to be 18 divided by 1 divided by 2 times 4. These internet math problems are always designed to create translation issues.

@gavindeane3670

Ай бұрын

I'm not sure this was designed to create the issue. I think it's just carelessness.

@jessejordache1869

Ай бұрын

That's not what I did. I had 18 div 1/2, for 36, then the result times 4, all divided by three. You know, the way x divided by y is the same thing as x multiplied by the reciprocal of y. But if you get 48 from that too, then ????

@yuuwhoo

Ай бұрын

Agree. If the problem is not understandable then ask the instructor what the hell he/she meant. In this case what he meant.

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!

@barleyeducated8714

6 күн бұрын

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. :)

It's 12 using bodmas, also division/multiplication and addition/subtraction are equal on their tiers. It's 12.

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!

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?

@gavindeane3670

Ай бұрын

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.

Any math problem that forces you to assume anything is poorly written.

Steps: get rid of the 3 by dividing it into 18. That gives 6 which you then double for the divide by 1/2, then multiply the resultant 12 by 4 to get 48. Easy peasy.

While I love this channel, this video was not well communicated. I would not recommend this video to my students.

@brucedonaldson3627

Ай бұрын

I think he purposely drags things out. You know...for the algorithms

@greghoward1561

Ай бұрын

Why, because you got it wrong? This guy explains very well and even the exceptions are explained.

@gavindeane3670

Ай бұрын

​@@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.

@davidmckibben1931

Ай бұрын

12

@marinecorpswarrior915

Ай бұрын

​@@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.

The correct answer is 12, NOT 48! "one half" is the same as "1 ÷ 2" and therefore indistinguishable from "1/2". Using P.E.M.D.A.S. the steps are as follows: (1) 18 ÷ 1 = 18, (2) 18 ÷ 2 = 9, (3) 9 × 4 = 36, and lastly (5) 36 ÷ 4 = 12. Note: If the numerator of the problem had been written as "18 ÷ 0.5 × 4" the answer is clearly 48. However, introducing the ambiguity of division by using both the "/" and the "÷" symbols causes the problem to potentially have more than one solution. Another way to have written the problem that would have indicated that the correct answer is 48 would have been to depict "one half" as a vulgar fraction with the symbol, ½, rather than 1/2: If "18 ÷ ½ × 4" is the numerator, then the answer is clearly 48.

@marscience7819

Ай бұрын

YES!!

@poetwriter83

Ай бұрын

When you divide by a fraction, you must flip the fraction and change the ÷ sign to x sign. Ex. 18÷2/1x4= 18×8=144/3=48

@gavindeane3670

Ай бұрын

​@@poetwriter83There is no division by a fraction in this question. He's solving it in the video as if he'd written parentheses around the 1/2. But he didn't write those parentheses. He's evaluating the expression he meant to write, not the expression he actually wrote.

@chrisatkins7959

Ай бұрын

What’s it like being wrong?

@gavindeane3670

Ай бұрын

​@@chrisatkins7959 They're not wrong. Put 18 1 / 2 / 4 * 3 / into your RPN calculator and see what you get.

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.

There are 3 different division symbols used in this video. When typing in text there is only one. Does 24 / 4 / 6 mean 24 divided by 4 the divided by 6 which equals 1 or does it mean 24 divided by two thirds which equals 36?

@anwaraisling

2 ай бұрын

With your example, you would have an improper fraction of 24 over 4 in the numerator of a fraction over 6. In PEMDAS form, it would be (24÷4)÷6 which is equal to 1. Edit: Truth is that written as 24/4/6 is indeterminate, which is why it is resolved from left to right. For clarity, it would be better in this form: (24/4)/6 or 24/(4/6) to denote actual fractional structure.

@sr6424

2 ай бұрын

@@anwaraisling I was giving this example to make a point. It impossible to tell whether 1/2 means 1 divided by 2 or a half. This will give two separate results when using PEDMAS. Like you say it always best use brackets. My view is PEDMAS isn’t fit for purpose in the digital age. It needs to be updated to include brackets for fractions!

@joeblog2672

Ай бұрын

That's why he used the antiquated division symbol (dot, line, dot)! I just realized this now. So the presenter here did pick up on this issue. In order to maintain their integrity, I believe fractions come with their own inherent brackets to ensure that their numerical value (avoiding algebra variables for simplicity) are first defined before being subject to order of operations (OOO) manipulations. Otherwise a fraction could be torn apart into two separate divisors, losing all integrity of the fraction in the process. This would also destroy the fundamental rule of flipping a fractional divisor and multiplying as a means of dividing by fractions. This would go against fundamental mathematical logic.

@gavindeane3670

Ай бұрын

​@@sr6424It's not impossible to tell at all. 1/2 means one divided by two. That's literally what the symbols mean. / is the division operator. It's clear from the video that what the author meant was 18÷(1/2)×4, but that's not what he wrote.

@marscience7819

Ай бұрын

It means 1 using PEMDAS. People are thinking too hard, projecting their own assumptions onto it. That's not what we are supposed to be doing....

18 : 1 / 2 x 4 / 3 = 18/2 x 4 / 3 = 9x4 / 3 = 36 / 3 =12 For me : and / are the same: divided by...

@GFlCh

2 ай бұрын

Here's a "÷" symbol for you to use. =)

@wingmannj

2 ай бұрын

@@GFlCh lol

@anwaraisling

2 ай бұрын

Well, you are wrong. ÷ and / are not equivalent. You can look to Algebra for a better understanding.

@gavindeane3670

Ай бұрын

​@@anwaraislingYou are wrong. ÷ and / are inline division operators. They mean exactly the same thing. The only difference between them is that ÷ is deprecated and should not be used. Using the proper symbol for division the numerator in the question would be written 18/1/2×4. Which I think makes it clear why more parentheses would not go amiss. Or better, still, don't use inline division operators at all.

@marscience7819

Ай бұрын

@@anwaraisling Where in PEDMAS does it say those two symbols are not equivalent? If you want, go read the wiki article on division. There, it says the two symbols are identical

Another example why PEMDAS should be entirely replaced by parentheses. Mathematics is not about a secret decoder ring.

@Pax.Alotin

2 ай бұрын

Yes it is - Ancients used maths in that way -- What do you think the Masons is all about ?

@martinglenn27

2 ай бұрын

The 'P' in PEMDAS means parentheses.

@flagmichael

29 күн бұрын

@@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.

@flagmichael

29 күн бұрын

@@Pax.Alotin Ancients did not use PEMDAS or similar. (Masons is a whole different thing.) Tongue in cheek, I presume.

@gavindeane3670

29 күн бұрын

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

I forgot to swap the second fraction. Simple math mistake. This is the first time I did it in PEMDAS. Very easy to forget to swap fractions for the division part.

Hello, I am going to take a test known as CASAS. Are you familiar with it? It's a competency test for adult education. I just need to focus on the math section. I took the test a second time but didn't pass by 6 points. They say I am at a 10 grade level and need to get to 11th grade to pass the test. I am currently studying the Level C/D which is a bit challenging. I am doing the section on Statistics. I know you mentioned your courses...where should I start? What section do I need to do? I was working in Statistics Two-Way tables last night. Would that be considered Algebra 1 or 2? Sorry it has been many years since I have been in Highschool and I can't remember the type of math that we learned? Thank you. ☺️

N: 18➗1/2x4x4> 18x2x4> 36x4=144. When dividing by a fraction, flip it and multiply. N/D: 144/3=48.

got it 48 simple pemdas thanks for the fun

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

@dazartingstall6680

Ай бұрын

Yeah, calculators don't recognise fractions. Try typing it in as 18÷(1÷2 )×4

@gavindeane3670

Ай бұрын

​@@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.

@dazartingstall6680

Ай бұрын

@@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.

@gavindeane3670

Ай бұрын

@@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.

@dazartingstall6680

Ай бұрын

@@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.

In the numerator, be careful with 1/2, divide don’t multiply.

D 48

12 is the correct answer if you apply the rule correctly 18 divided by 1/2 =9 9x4=36 36/3= 12

@vikkijohnson5117

Ай бұрын

you can't divide by a fraction, the fraction gets turned upside down so its 2/1. so the sum becomes 18 x 2 x 4/3

@squatch253

Ай бұрын

@@vikkijohnson5117 And this is one of the reasons why I always failed Algebra - too many instances where you arbitrarily change something around that goes against basic intuition - I didn't get very far in math but one thing I do remember a teacher saying is that you can't have a bigger number above a smaller number because it becomes an improper fraction - so with that rule burned into my brain, flipping that would never even enter my mind. The way my brain would go about this problem is first dividing 18 by 1 because I know how to do that, then multiplying 2 x 4 because I know how to do that, which turns it into 18 divided by 8 which is 2.25, then divided by 3 and the answer is 0.75. I know that's not even close to correct, and there's a theoretical set of "rules" somewhere to do it correctly that I'll never be able to remember because none of them make any sense; but what I laid out here is intuitive to my brain and makes perfect sense to me - which is why I always failed Algebra by going off of intuition. And nobody ever explains how you can create 2/1 and it's somehow still a fraction???

@KarlHeinzSpock

Ай бұрын

18 divided by 1/2 =36

@timkvernen4852

Ай бұрын

@@vikkijohnson5117 If he had written the 1/2 as a fraction, it has an implied set of parentheses. The way it is written, it is (18 / 1 / 2 x 4) / 3. The problem is written in a misleading way at best, but if you do PEMDAS on what is shown, you will get 12. The solution given is being interpreted as (18 / (1 / 2) * 4 ) / 3, but we can only guess what he means by the fact that he uses two different ways of denoting division. Either answer is defendable, which is a good sign that the question is poorly written.

@marscience7819

Ай бұрын

@@squatch253 This isn't really math. It's about interpreting a bunch of symbols. That's why there has to be set rules that we must follow, so that there is no ambiguity. It's very similar in any language, say English. "Let's eat Grandma" and "Let's eat, Grandma" mean extremely different things. It's no different in math. I'm seeing people all over the place not using commas in their sentences, and it completely changes the meaning, so we all have to try to interpret what the person is saying. It's the same with math.

Answer 12

9:15

1 half .50 to 50 into then devide into1800 =36 .is that wrong ?

48

The correct answer is 12. 1/2 is a division, so 18 divided by one =18 divided by 2 =9 multiplied by 4 = 36. 36/3 =12

@RobertETH

Ай бұрын

Lay 18 crackers out. Break them in half. Count how many pieces you have. 18 divided by one half is…18 divided into a new grouping of half pieces. You’ll have 36 pieces.

D 48. Order of precedence in this case is left to right .

@gavindeane3670

26 күн бұрын

If you read the numerator from left to right you get 36. Then divide all that by the 3 and the answer is 12.

Well, Your first incorrect solution you said. someone would say '18 divided by 1/2 is 9". They made a Math mistake, not an order of operations. Their order was perfectly correct. The answer, 12, was wrong because of their mathematics error. But generally, your explanations were very good.

@gavindeane3670

2 күн бұрын

Dividing 18 by the entire 1/2 when the 1/2 is not enclosed in parentheses is an order of operations error. Thinking that 18/(1/2) equals 9 is a mathematics error.

@thomasharding1838

Күн бұрын

@@gavindeane3670 I think that is what I said, they made a Math error, not an order of operation. The 1/2 is a number, "one half", not a math function and therefore would not be enclosed by parentheses and would be applied as an entity.

48 (18×2×4) ÷3