18 divided by 1/2 times 4 all over 3 =? A BASIC Math problem MANY will get WRONG!
Vložit
- čas přidán 23. 04. 2024
- How to solve an order of operations problem following PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction). Learn more math at TCMathAcademy.com/.
TabletClass Math Academy - TCMathAcademy.com/
Help with Middle and High School Math
Test Prep for High School Math, College Math, Teacher Certification Math and More!
Popular Math Courses:
Math Foundations
tabletclass-academy.teachable...
Math Skills Rebuilder Course:
tabletclass-academy.teachable...
Pre-Algebra
tabletclass-academy.teachable...
Algebra
tabletclass-academy.teachable...
Geometry
tabletclass-academy.teachable...
Algebra 2
tabletclass-academy.teachable...
Pre-Calculus
tabletclass-academy.teachable...
Math Notes: tcmathshop.com/
If you’re looking for a math course for any of the following, check out my full Course Catalog at: TCMathAcademy.com/courses/
• MIDDLE & HIGH SCHOOL MATH
• HOMESCHOOL MATH
• COLLEGE MATH
• TEST PREP MATH
• TEACHER CERTIFICATION TEST MATH
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?
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)❤❤❤❤❤❤❤
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?
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.
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 CZcams 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.
@@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.
@@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.
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.
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.
Can you understand why some people dislike math so much? Math teachers are not always good communicators, especially to young people.
12
My Dear Aunt Sally; multiply, divide, add then subtract.
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.
This problem is mixing +, /, and ____ to represent division, fraction (half) and fraction (third) respectively. This is ambiguously specified.
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.,
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 CZcams 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.
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
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.
@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.
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.
YES YES YES!!! Took about 45 seconds and did it in my head! 🎉🎉
Why, thanks for the award. But I would have had trouble with equations like this before I began watching your videos.
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.
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
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.
Reminds me of math class where i would pay more attention to the music in my head than to the material.
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.
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.
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
Thank you for the ways to do 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!
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. :)
This is less maths and more 'did you catch the trick'?
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.
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".
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.
I love math but I never really understood how to correctly work the operations in my homework.
Did anyone think about using ( ) around the dang part of the problem to be done first?
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.
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 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
@@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
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.
thank you very much for sharing. we do it without thinking at school. well explain
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!
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
Where would I ever use this ?
You do have a parenthesis or grouping. The fraction is a grouping problem so that must be done first 1/2=.5.
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
Another PEMDAS cream puff. Thanks Boss.
In the UK (1960's) we were taught "B-O-D-M-A-S" (Brackets, Of, Division, Multiplication, Addition, Subtraction). When did it change ???
@davecooper5951 The sequence is still BODMAS - Pedmas is the yanks who don't do mathematics only 'math' meaning more than 1 process confuses them.
@@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 ?
@@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.
@@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 !).
@@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.
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?
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.
@@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!
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.
@@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.
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 * 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
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!
1 half .50 to 50 into then devide into1800 =36 .is that wrong ?
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. ☺️
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.
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.
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.
God bless my math teacher who told us that divided by half is basically x 2 I never forgot it.
D 48
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.
It's 12 using bodmas, also division/multiplication and addition/subtraction are equal on their tiers. It's 12.
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.
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.
I'm not sure this was designed to create the issue. I think it's just carelessness.
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 ????
Agree. If the problem is not understandable then ask the instructor what the hell he/she meant. In this case what he meant.
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.
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
48! My mistakes was on the division of 18 divided by 1/2 instead of 2; thanks!
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 😅😅😅
I agree, half of anything is HALF👍🏼
@@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!
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
You cannot split the fraction, it is a number equal to .5
@@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.
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.
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.
@@Chris_Mack Exactly, it is a number equal to 18.
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.
I am 63, and calculated two ways in my head under half minute, and got same 48. Such easy
Thanks for reminding me how much I forgot.
18 :.5 x 4 = 144/3 = 48 (d)
I tried WolframAlpha: 18/1/2*4/3 = 12
48
got it 48 simple pemdas thanks for the fun
Thanks for the memories!
what about bodmas
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 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.
I thought the numerator was 18 divided by 1 divided by 2 times 4. I don’t think the 1/2 is very clear
I knew I forgot something. "x or / in the order that it appears in the Numerator.
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 is rubbish. The answer is 12. No. Nobody will sign up for your website.
Correct...12 is the answer
Why if using PEMDAS you jumped to division over multiplication?
Because the division appears first in the expression.
P-E-MD-AS is a 4 step process. In the third step you calculate all the multiplications and divisions, working from left to right.
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.
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)
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.
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.
So simple. I'm 67 and did it in my head in 5 seconds.
Same timing for me.
I’m 55 and the correct result is our age difference. Ain’t that funny!?
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.
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)
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.
I forgot to flip the fraction
If you really think about it. A fraction bar is considered to be a grouping symbol. Thus, 1/2 would be done first resulting in the answer of 48.
When a horizontal line is used to separate numerator and denominator in a fraction, that is a grouping symbol.
But the / symbol is just a division operator and it absolutely is not a grouping symbol at all.
These ( ) are the grouping symbol the author needs. If he wants to indicate that the 18 is divided by the entire 1/2, then he must enclose the entire 1/2 in parentheses.
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.
(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.
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.
@@dgerdner Yes, this is an AWFUL video. No wonder young minds get twisted around.
Maybe the real issue is ambiguously written equations that almost create uncertainty and the potential for wrong answers. When math requires rules such as PEMDAS you are simply putting Band-Aids on a broken system. Yes it works but can't it be more concise?
The issue is the poorly written expression. But it's nothing to do with PEMDAS. PEMDAS *clarifies* things that would otherwise be ambiguous - that's the entire point of PEMDAS.
The issue here is that he's trying to use / and ÷ to mean different things, when what he should do is use one division symbol, not two different ones, along with parentheses where required.
He should have written the numerator as 18/(1/2)×4.
I've been terrible at math my whole life, old, but I always get these right? Why?
18 divided by 1/2 times 4 all over 3
36 times 4 over 3
144 over 3
48
Yup
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
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.
When realy used PEMDAS you must do 1/2 X 4 that gives 2. Then you part 18 by 2 ... that gives 9. And 9/3 = 3. So ( 18 ./. 1/2 x 4 ) ./. 3 = 3
PEMDAS gives division and multiplication equal priority and solves then left to right. So the numerator here is
18 divided by 1 = 18
Then take that 18 and divide it by 2 = 9
And finally 9 multiplied by 4 = 36
Divide the entire numerator by 3 and you have the final answer 12.
In the video he's solving it as if he'd written parentheses around the (1/2).
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
18 : 1 / 2 x 4 / 3 = 18/2 x 4 / 3 = 9x4 / 3 = 36 / 3 =12
For me : and / are the same: divided by...
Here's a "÷" symbol for you to use. =)
@@GFlCh lol
Well, you are wrong. ÷ and / are not equivalent. You can look to Algebra for a better understanding.
@@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.
@@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
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.
I got 48, initially, doing this in my heqd, but had to do the problem two more times written down just to make sure I had done the problem the time written, basically second and third guessing my answer. I knew this was an “order of operations” math problem, but still ended up working this out twice in my head, then twice written down on paper!
I am NO math whiz and waaaaay back in HS and College , once I got through trigonometry and algebra 1, it was all a steep doenhill slide for me, from there!
This is why I became an artist and basic industrial designer instead of trying to become a fully qualified engineer!
The advance mathamatics destroyed any early adult hopes of being any type of serious mechanical or structural engineer.
Most people go into the liberal arts side because there is no drug testing to be an Artist.
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.
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.
Math is sometimes over complicated depending on the instructor . This publication was great but where in the world would a problem like this be used in the real world though it is simplistic for your demonstration which I can see as a review product. I guess if I were to be required to use this on an on going usual basis it would become second nature . I get the PEMDAS objective .
Or order was M then D then A then S in the 60s when I was in middle and high school and 99%tile in math, becoming a Physics major and Attorney. So, we would have done multiplication before division before addition before subtraction. So numerator would be 18÷1 ÷ 2x4 or 18÷8 = 9÷4, so equation is then (9÷4)/3 then multiply by 1:
(9÷4)(1÷3)/(3)(1÷3)
(9÷12)/1 = 3/4 = 0.75
That's shockingly bad teaching! Treating those operations as separate steps, each higher priority than the next, has never been correct. Even a simple example like 3-2+1 will show you that.
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 😕
I'm not sure it's purposely designed for that. I think it's just carelessly written.
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.
@@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.
12
It seemed pretty obvious to me that division was using ÷ and the slash was indicating a fraction.
If that's how he writes equations, I pity his students.