Square root of 64 divided by 1/2 times 2 = ? Many don’t get this BASIC Math!

How to solve a math problem with square roots, fractions and multiplication and division - order of operations (PEMDAS). Learn more math at TCMathAcademy.....
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[@MusicNewb]

Communication is important in math. Any expression should be conveyed without ambiguity.

[@coachklc]

Order of operation and left to right does that.

[@gavindeane3670]

​@@coachklcThe author has mixed two different division symbols in the same expression here. There's absolutely no excuse for that.

[@coachklc]

@@gavindeane3670 you got it wrong, huh? Ever worked in scientific or mathematics fields?

[@gavindeane3670]

​​@@coachklcI have indeed worked in that field. That's why I understand mathematical notation and I therefore know that the expression in this video is complete gibberish. I didn't get this wrong. I spotted the error in the question immediately. Not least because he had fairly recently posted a similar video where he made the same mistake.

[@ronrice1931]

I think we all agree that this is a poorly written expression that could be interpreted more than one way: 8 ÷ 1 / 2 x 2 = 8 / 2 x 2 = 4 x 2 = 8 8 ÷ (1/2) x 2 = 16 x 2 = 32

[@fluxrider7027]

So, 8 divided by 1/2 is 16, not 4, Dividing by 1/2 is not the same as dividing by 2. The only way your first example could be what was expressed is iff there were parentheses starting the expression with the closing bracket just after the 1. Then it would be a different expression, and would evaluate to 8. But that's not what's written.

[@gavindeane3670]

​@@fluxrider7027You've got that backwards. The only way the question can be interpreted the second way they wrote it, to give the answer 32, is if the 1/2 is enclosed in parentheses. Well, there is another way: you can get 32 if you change the meaning of (at least) one of the division symbols. As written in the video, without changing the meaning of any of the symbols the expression evaluates to 8.

[@robertdeland3390]

You said that 1/2 should be treated as if it is parenthesized. Why? How would I know that? Pemdos doesn't say that.

[@marscience7819]

That's absolutely right. If it to be treated as if it has parentheses, then he should put parentheses around it!! It is inexcusable to leave it ambiguous.

[@flummer7]

@@marscience7819 One could argue it is not ambigious but plain wrong notation if you intend 1/2 to be the fraction one half. When written inline 1/2 is not a fraction but simple division thus making the result 8.

[@marscience7819]

@@flummer7 Yes. Exactly. Now try to get the guy making the video understand this

[@williamhouse432]

PEMDAS: First: Sqrt 64=8 FROM Right. 2x2=4, 1/(2×2)=1/4 Then 8/(1/4)=8×4=32

[@stevenjohnson1143]

@@robertdeland3390 no need to put brackets around the fraction dividing by a fraction the rule states invert and multiply

[@notme444]

The '/' character is not included anywhere in PEMDAS. This explanation only works if some additional rule makes a fraction written like '1/2' a number which in this case is equal to one half. There seems to be an unwritten assumption that separating the fraction from the rest of the expression with spaces front and back means it should be read that way. Maybe such a conventions exist in the minds of some people, but I've never heard of it, and the result is very confusing. This should be taught as something to be aware of, but is actually a mistake. If your aim is to explain to someone how to do this calculation using a typical calculator, don't tell them to divide by one half. Presumably, you know what the meaning of the expression is, so just tell them to multiply by 2. If it's some more fancy calculation, just tell them what keys they need to press. When writing on paper, fractions can be more clearly written with a horizontal line drawn under all of the numerator and over all of the denominator. The universally recognized convention that this implies parenthesis around the fraction allows PEMDAS to be applied, eliminating any ambiguity. When entering an expression into some document, explicitly use parenthesis - in this case '(1/2)' - if no other method is available. Teachers of written style, always prefer clarity, and not making the reader strain to understand the meaning of a sentence. Clarity is all the more important when writing on a mathematical subject. Another comment here notes that that the unicode ½ could be used in text. The writer would have to get the ½ from the list of symbols in whatever document editor they are using, but the result would be compact, and could be visually more appealing. Like the '/' character, these special characters are also not included in the PEDMAS rule, but the meaning would be perfectly clear in my opinion. When writing on paper, the fraction could be written in a similar way, and that would be just fine too. When writing an arithmetic expression in a computer program, usually the PEMDAS rule applies. Generally however, '÷' cannot be used, and instead, '/' is used to indicate division. This means that the '/' in the fraction will be handled left to right, the same as the other divisions and multiplications in the expression. To stop this happening, the fraction must be in parenthesis. If you let your students think it is ok to write expressions like the example in the video, they could be mightily confused when they later have a go at programming.

[@gavindeane3670]

The notation in the question is certainly very poor, but why do you keep going on about the / symbol being non-standard and not part of PEMDAS? In mathematical notation the inline operator for division is the / character. It is completely standard (there is literally an international standard for this - it is ISO 80000-2 and it defines / as division) and therefore it is part of the MD step in PEMDAS. The non-standard character here is the ÷. Using inline notation, the correct way to write this expression to give the answer 32 is √64 / (1/2) × 2

[@lawrencejwinkler]

PEMDAS is teacher speak and is nonsense in the real world. In the computer world we use operator precedence and left to right scanning and some rules for left or right associativity. The idea is we will make only one pass of the string to evaluate it, not multiple passes which PEMDAS requires. / is an operator and 1/2 is not a numeric object. If you use a product like Mathematica, it’s possible to enter 1/2 as a numeric object, but that is not done here.

[@MrZcar350]

@@gavindeane3670 In the American Physical Society journals style guide multiplication unequivocally takes precedence over division and slashing is one of the accepted forms of fractions: In mathematical formulas this is the accepted order of operations: 1. raising to a power, 2. multiplication, 3. division, 4. addition and subtraction Note addition and subtraction are combined but multiplication and division are not. So the formula above would pretty clearly be interpreted as: sqrt(64)/((1/2)2 ) - they also prescribe against using multiplication symbols for simple products. The point is, this is all a problem of notation and convention and different ones being used in different contexts and taught a different times. PEMDAS is not a codified standard, it's more an organically grown set of rules of thumb.

[@gavindeane3670]

@@MrZcar350 Yes, I'm familiar with that. That's not a contradiction of PEMDAS. It's just an extension of PEMDAS to PEJMDAS. Well done for quoting the second bit about not using × for simple product. Most people who reference that source miss that bit.

[@MrZcar350]

@@gavindeane3670 yep. I wasn't trying to say it contradicted PEMDAS but show that PEMDAS isn't a universal COMPLETE standard but, as I said, a collection of rules of thumb that have been generally agreed. It's still in flux.

[@perssoh11]

NEVER ever use different symbols for division. If you used / only the anwer is 8.

[@jeremyhorne8383]

Okay… first, the obelus used after the sqrt64 doesn’t mean “divided by” but means “grand divided by” So, we rewrite the problem with parentheses as (Sqrt64) / (1/2x2) Next, the slash between the 1 and 2 means “divided by” and does NOT denote a fraction. So, we simplify on both sides of the obelus. Sqrt64 = 8 1/2x2 = 0.5•2 = 1 Finally, we perform grand division last by rule. 8 / 1 = 8 Of you had used the simple slash for division (the original symbol, btw) you would have Sqrt64 / 1 / 2 x 2 That would be 8/1/2x2 Left to right that’s 8/1/2•2 8/2•2 4•2 8 To get the steps and result you showed, you would need to not only use simple division (slash) after sqrt64 but you would also need to write one half as a fraction instead of using simple division (slash) or put it in parentheses to begin with of that’s what you meant and you don’t have the ability to write it as a fraction.

[@Bloozguy]

Na.... wrong. You rewrote the problem all wrong. You multiply & divide _in the order they appear_ Or vice versa ...which means (and since when did 1/2 ever NOT mean a fraction???? it's the exact same number as .5... so you could say it's √64 ÷ .05 x 2, no brackets required) So..the square root of 64 is 8 8 divided by 1/2 = 16 _NOT 8 divided by 1 then divided by 2, THEN multiply by 2!_ 16x2 = 32. I didn't even watch the video, but I already know I'm right. I'm wondering why you thought 1/2 is any different than 1/5.... 1/9...... 1/3 etc? I mean there IS the ÷ sign, and the / sign, which not quite the exact same thing. 1/2 EQUALS 1 ÷ 2, sure, but 1/2 is a _rational number,_ written in fraction form, so then √64 ÷ 1/2( OR.5) x 2. You do NOT take 8 and then divide it by 1. There is no other answer than 32. It's straight simple BEDMAS or PEDMAS rules (they are identical anyways, just different word for brackets= parenthesis...same thing) Alt key shortcuts are great for math equations. Class over.😎

[@jeremyhorne8383]

@@Bloozguy except you’re wrong. I don’t have to watch the video either. I just skip to the end to see the wrong answer and then put my degree to work. Everything you say about the fraction is correct (which I explain as an option for interpretation) but you fail to accept that in a problem with an obelus, you MUST perform THAT division LAST. It’s the whole reason the ancient Greeks invented the symbol, to represent DIVIDING LAST. So, NO. It’s NOT simple pemdas/bodmas. Now sit down in your desk and stop pretending to be the teacher. You’re confusing the other students. Class is over when I say it is.

[@heatherbartusch5239]

Yes. PEDMS. In my head and by calculator. Thank you for all your videos. They are indeed helpful. Bless you.

[@terryjohinke8065]

Did it in my head BUT I was a math teacher , like you, for 38 years.

[@patricklowe1926]

You must apply BODMAS (Brackets, Overheads, Divide, Multiply, Add, Subtract in that order). The square root of 64 is 8. Then 8÷2 =4. Then 4x2 = 8.

[@Kualinar]

It's C, 32 Square root of 64 is 8. Dividing by one half is the same as multiplying by 2, so, 16. Then, multiply be 2 = 32. A few second in my head. I sometimes use PERDMAS instead of PEMDAS. Parentheses, (exponent and radical), (division and multiplication), (addition and subtraction)

[@Ayelmar]

Solved in my head at the thumbnail, and using the problem as stated in the title, my answer is c) 32. That's assuming we treat 1/2 as the fraction, evaluating to 0.5. If we treat it as to separate operands, 1 and 2, and using order of operations, the answer would be a) 8. In the first case, SQRT(64) / (1/2) * 2 = 8 / (1/2) * 2 = 16 * 2 = 32. In the second case, SQRT)64) / 1 / 2 * 2 = 8 / 2 * 2 = 4 * 2 = 8.

[@francisdelpuech6415]

Dividing by a fraction is multiplying by the inverted fraction in this case is multiplying by 2 after getting the square root. A fraction is 2 separate numbers but still has to be treated as a whole

[@Ayelmar]

@@francisdelpuech6415 exactly. Just as I demonstrated when I showed how I worked out my main answer of 32. However, I also showed how it could be a bit ambiguous as written, especially for those with a computer programming background.

[@chrisdissanayake6979]

Yes, in order to do well in Math, we shouldn’t be in a rush to get the answer, especially when we are not in a competition or doing a timed exam. Also, it is always nice to be in good spirits for our mental as well as physical health. After all, it is not the end of the world! It is just a simple Math problem.

[@ludwigr.reindl4146]

I converted the "1/2" into a decimal and it worked out too.

[@marthatamez8698]

1/2 conversion to a number is 0.5

[@slm3945]

@@marthatamez8698 Why do you think this should be done first?

[@marscience7819]

According to PEMDAS, that should NOT be done first. It has no parenthesis, and it is not an exponent. You know, the PE in PEMDAS.

[@ludwigr.reindl4146]

@@marscience7819 My error was all too apparent.

[@slm3945]

There is no S for Space in PEMDAS. Just ask ChatGPT!

[@kcl9116]

What would be the result if instead of 1/2 you had 0.5? Similarly, what would be the result if you had 64^1/2 divided by 0.5^1 multiplied by 2^1? How would PEMDAS deal with those integers.

[@gavindeane3670]

Exponents are calculated in the E step of PEMDAS.

[@kristendelaney5196]

Yeah, leave it to the internet, but these are some of the dumbest questions in math. Indeed, you need to be careful with syntax when coding, for instance, but being intentionally ambiguous (for instance using both a division sign and a slash for a fraction) is begging mis-interpretation and a 'gotcha' answer. Leave mere semantics and conventions to those who need the precision to code, to Algebra I students, and all the rest who who can't do math.

[@faireplaymedia7622]

PEMDAS Left to right Left to right multiplication and division which ever comes first… In this case going left to right division comes first. The square root of 64 =8 8/ .5 = 16x2=32

[@bigdog3628]

rewrite to √64 * 4 [ flip the 1/2 you get 2 and since the other number is also multiply by 2 we can combine and say times 4] √64 = 8. 8 * 4 = 32 super simple no need for calculator or scrap paper.

[@MrEvanston]

Mr. KZbin Math Man: Congrats, you are the first teacher who taught me about the "Order Of Operations." How could I have missed this concept?

[@MsChemicalEngineer]

I don't know how you missed it I learned it in 6th grade.

[@kirksully]

Like, apparently, so many other aggrieved watchers I so badly wanted 8/.5 to = 4. Finally, I just asked Alexa, ‘Alexa (or if from New England) Alexar, what is 8/.5?’ That Australian Alexa A.I. chick is smart; w/o hesitation: “8 divided by 0.5 is 16.” How many times on lots of years of construction math have I made the mistake of txing ‘divided by’ as multiplied by!? Maybe not many but ordering concrete? Once is one time way too often. Thank you mathman.

[@dougpattison5499]

Using the calculator I got the right answer if I did the following: Square Root of 64 ÷ (1÷2)×2 Which brings it to Square Root of 64 × 2 × 2 Doesn't really seem to me that that's really what the question was asking

[@olfatmonsef7867]

32

[@josephlaura7387]

c) 32

[@manuelquitevis6794]

8:2 = 4 x 2 = 8 ( A )

[@dianelewis7469]

😀😃 i got it right 32

[@RS-Amsterdam]

Do you want a balloon

[@MrMousley]

Square root of 64 divided by 1/2 times 2 8 divided by 1/2 times 2 16 times 2 32

[@IvarHyngstrom]

Please change careers. The answer is A and D. You wrote the equation in a sloppy manner. If you wanted the answer to be 32 then it was your responsibility to put parentheses around the (1/2). Please correct this video as you are misleading your “students”

[@jimmcdiarmid7308]

Whats the point?

[@rgrinnell]

C

[@FrankD71864]

I plugged into my calculator and got 16. I typed in the square root of 64 divided .5 times 2 equals 16

[@gavindeane3670]

Are you sure? Exactly what did you enter into your calculator?

[@topkatz58]

8 × 2 × 2 = 32

[@Ca_milo_G]

c

[@BartHoward-cn4ui]

C) 32

[@user-og1de7dd3d]

Of course logic has no place from some spaced out calculation that nobody would be able to calculate. 8 is the obviously logical calculation the other is from a spaced out theory that nobody could calculate. What is the point here?

[@lesross4442]

A and B are the same answer, but really A

[@Subcritical96]

We will agree to disagree. The answer is 8! For the answer to be 32, the 1/2 must be in parenthesis.

[@gavindeane3670]

Absolutely right. But the guy doesn't care. He's done exactly this before and I expect he'll do it again. He's inventing his own personal dialect and aiming it at an audience that will include many people who don't know any better. People who will watch this video and think this is an acceptable way to write.

[@marscience7819]

Yes, or write the 1/2 with a horizontal line instead of a forward slash. The forward slash is ALWAYS to be interpreted as "divide by".

[@vaticancartel136]

You are completely wrong. 1/2 = 0.5

[@gavindeane3670]

@@vaticancartel136 In isolation 1/2 is obviously the same as 0.5. And in isolation it is normal to write a fraction like "one half" as 1/2 if you're using inline notation. But that does not mean that everywhere you see the text "1/2" within a larger expression you can blindly replace it with "0.5" regardless of the context. That is completely misconceived. If that was how it worked then 3/4² would be the same as 0.75². Context matters. 1/2 when seen as part of a larger expression cannot be anything other than two separate numbers with a division operator between them. That is the definition of the / symbol. So the only way this expression evaluates to anything other than 8 is if you treat the ÷ symbol as something other than a simple division operator. The correct way to write the expression he's trying to write, using inline notation, is √64/(1/2)×2

[@marpool8029]

The problem really is sqrt(64)×2×2. or sqrt(64)/0.5x2. can you follow the rules? that's really what this convention is about. I think parenthesis should always be used to convey desired order of operation.

[@mahamunibalakrishnan8263]

C. 32

[@lamper2]

32? before watching YAY!

[@leoclayboss7215]

A - 8

[@patricianneryan9299]

A=8

[@hendrikvan3411]

1/2 = ½ = 0.5= half

[@gavindeane3670]

That is obviously true for 1/2 in isolation. But that doesn't mean that everywhere you see the text "1/2" in isolation you can blindly replace it with "0.5". For example, 1+3/4 is the same as 1+0.75. But 3/4² is NOT the same as 0.75². Context matters.

[@lovettwimberlysr.8355]

4

[@dave-in-nj9393]

new math changed the rules when they don't understand that you follow PEMDAS in sequence. it is not PE (M or D) AS

[@gavindeane3670]

You don't follow PEMDAS in sequence like that. That's a common and understandable misconception. It's probably the biggest problem with these silly six letter acronyms, but even a simple example like 3-2+1 will show you that PEMDAS is not 6 separate steps.

[@bradabbott4892]

I guess my 73 years hasn't dulled too many brain cell's 32 came out quickly 😊😊😊😊😊

[@johnnydawson7675]

8

[@jithe3rd]

32?

[@stephenmetcalfe848]

The obvious answer is 8. The correct answer is 32.

[@kingdavid255]

C.

[@nixxonnor]

When you add ambiguity and different kinds of division/fraction you have designed a mess on purpose.

[@gavindeane3670]

I think it is on purpose. Last time he did exactly the same error in one of his videos, it generated far, far more comments than he normally gets. I suspect he's doing this deliberately to generate engagement on his KZbin channel, and he knows full well, and doesn't care, that it's at the expense of his students.

[@todd8155]

It's a mess, but consider if it was square root of 8, divided by 1, divided by 2... This makes no sense as a division by 1 doesn't do anything, and since the '/' is used between the 1 and the 2, with a different division sign before, and spaces before and after the 1/2, therefore it's logical to conclude that the 1/2 is a fraction. Then it's simple, and one get 32.

[@gavindeane3670]

@@todd8155 Division by 1 makes complete sense. I know exactly what division by 1 is.

[@todd8155]

@@gavindeane3670 - It doesn't make sense in that it doesn't change the calculation. It doesn't do anything, it doesn't have any relevance, and it doesn't go anywhere. Other than a gotcha, it would have no purpose. In conjunction with the other clues 1/2 as a fraction makes more sense. It's not definitive, but it is what makes the most sense.

[@gavindeane3670]

@@todd8155 I know what the effect of dividing by 1 is. It is a well defined calculation - so it makes sense. Indeed, unless you redefine the meaning of at least one of the division symbols in this expression, then dividing by 1 is exactly what it tells you to do (notwithstanding the fact that we might suspect the author intended to instruct us to do something else).

[@martinmulvany1157]

32

[@dougpattison5499]

8

[@rajeshvyas934]

c

[@kjellg6532]

Forget about PEMDAS, it is not always crystal clear. Use parentesis so expressions are not ambiguous. The purpose is not to make traps, but to wright your expression in such a way that they are not misinterpreted by the reader.

[@gavindeane3670]

PEMDAS is not the issue here. The issue here is that there is absolutely no excuse for mixing ÷ and / in the same expression.

[@michaelterry1000]

I agree USE PARENTHESES. The comment section clearly shows that there has been needless debate over the order of operations. The video is flat out telling you that your calculator is wrong. USE PARENTHESES. Then everyone will agree and communication is greatly improved.

[@douglastovey2685]

@@kjellg6532 no parenthesis needed for this simple fraction.

[@kjellg6532]

@@douglastovey2685 OK. What about this one: 12/2x =? given x=3

[@douglastovey2685]

@@kjellg6532 I would read it out loud. Twelve divided by 2X 2x = 6 Twelve divided by 6 = 2 If it were written with operators 12 divided by 2 times 3 that would be different.

[@alex-qe8qn]

The method taught to me in Scotland over 65 years ago gives the answer 32; but I think that different countries etc. may have different methods of applying operators - clearly, we need to have universal agreement on operators - and a more liberal use of brackets/parentheses would be sensible.

[@gavindeane3670]

There is universal agreement, at least amongst people who actually understand mathematical notation. It's even defined in an intentional standard. / is the division operator and ÷ should not be used. Using ÷ at all is dubious enough, but using ÷ and / in the same expression is absolutely inexcusable. The correct way to write this, using inline notation, is √64 / (1/2) × 2

[@alex-qe8qn]

@@gavindeane3670 Thank you!

[@nathanw4018]

Only a teacher or exam writer would structure a fraction and ÷ symbol in an equation. First you run the risk that you have written it wrong and two you risk the reader interprets your intention incorrectly. Order of operations should be kept simple. People should not be guessing what is in the denominator and what is in the numerator. In my line of work, I would fire someone if I saw a calculation setup like this one. It could be so much clearer when written algebraically - no need for order of operations except for the square root.

[@gavindeane3670]

Don't tar all teachers and examiners with the same brush. Only an idiot would use ÷ and / in the same expression like this. No halfway competent teacher or examiner would ever write anything like this. It's complete gibberish. It's not proper mathematical notation at all.

[@fluxrider7027]

It's just a question that identifies whether you can parse sub-optimally phrased math.

[@gavindeane3670]

@@fluxrider7027 Nearly. It's a question that identifies whether you happen to parse incorrectly phrased math in the same way as the plonker who wrote it, assuming you choose to try and parse it at all.

[@fluxrider7027]

@@gavindeane3670 I'll agree with that, but math is about putting a situation into an equation, and a basic math skill is putting it into a better form. To do that, you need to be able to understand the syntax of the current equation.

[@fluxrider7027]

Are we sure that "Plonk" is not an advanced field of mathematics?

[@SodalisUK]

As written the formula is confusing as to whether 1/2 represents the number 0.5 or the partial formula 1 divided by 2. If you assume that / is the same as ÷ then the answer is 8 - if you assume that the 1/2 represents a number then the answer is 32.

[@gavindeane3670]

If you think that ÷ is a division operator then / absolutely is the same as ÷. Because / certainly is a division operator. That's part of the basic definition of the language of mathematical notation.

[@SodalisUK]

@@gavindeane3670 "1/2" (three separate characters) is different to using either "½" (single character) or the number 1 directly over a bar over the number 2 (which I can't type but you know what I mean. In this specific case, the video says "sqrt(64) ÷ 1 / 2 x 2" which SHOULD be read as "divided by one, then divided by 2 then multiplied by 2". If they wanted to indicate ½ then they should have used the single unicode character or shown it as 1 vertically over a bar vertically over a 2 - but they didn't.

[@gavindeane3670]

​@@SodalisUK I completely agree. I was really just suggesting that this bit should be the other way around: "if you assume that / is the same as ÷" / is a defined symbol in mathematical notation so there's no scope for considering it to have any different meaning. It means division. The only symbol here that you can potentially play around with the meaning of to get an answer other than 8 is the ÷ symbol, which is not a formally defined symbol.

[@marscience7819]

Yep, you are absolutely correct.

[@whoff59]

Tricky question. It is explained only in the text form of the question "divided by 1/2" which is clearly equivalent to "*2". But in the formular you find "÷1/2" where "/" is just a sign for division (without brackets). So according to PEMDAS it is first "divide by 1" then "divide by 2". And this is sth. totally different from the first case.

[@blainealmeida]

I GOT CC 32 BY USING MY 71 YR EXPERIENCED BRAIN CELLS! THANKS😅

[@dave-in-nj9393]

to rewrite the problem : 8 / 1/ 2 * 2 now, do the math again. just because you use two different division symbols does not alter the sequence.

[@Bloozguy]

If it was originally written that way, then for sure I would have got 8. But, since the ÷ was used first before the 1/2, I auto assumed that 1/2 was a fraction, which gives 32. All this talk could have been saved had he done (1/2), so I think he was trying to catch people and instigate everything we see written here, lol.

[@fayolivier2416]

I understand how you got the answer but there are no parentheses so it can be confusing

[@johnoehrle5973]

Cmon, what is 1/1/2, I say 1/2 you say 2!

[@deborahstahl5982]

How many" halfs" are there in a whole? 2.

[@gavindeane3670]

​@@deborahstahl5982Of course there are two "halfs" in a whole. That's not the issue. The issue is that 1/1/2 is not asking how many halfs there are in a whole, even if the author of the video thinks it is.

[@maxinemcafee4893]

C) 32

[@abilioandrade9727]

8x2x2=32

[@howardludwig6837]

Both ÷ and / are division operators, equivalent in PEMDAS. If you wish 1/2 to be treated as an inseparable entity, you must use the vinculum (horizontal bar) form instead, with the 1 above and 2 below, as the vinculum plays the dual role of being both a division indicator and a grouping indicator. The slash / is only a division indicator. There is no sound justification of using both ÷ and / in the same expression. Professional mathematicians abandoned the ÷ symbol long ago. That would cut down a lot of these nonsense questions.

[@shakirhamoodi5009]

The right answer is 8. If you really intended what you say here, you should have put the fraction 1/2 in a parentheses. This is the second KZbin where you make the same mistake. Please review and revise your solutions.

[@HugoRH444]

Very easy. I don't understand people's confusion. Square root of 64 is 8 8 divided by 1/2 is like multiply it by 2, so 8x2 is 16 Then 16 times 2 equals 32.

[@panlomito]

Exactly what I did, but I prefer to de-escalate this situation in the Ukraine in stead of the very sick war mongering that is promoted by Western nations.

[@marscience7819]

It depends on how you decide to treat the symbol "/", a forward slash. A forward slash is UNIVERSALLY treated as "divide by" and not "treat as fraction". If we interpret that forward slash properly, the answer is 100% 8.

[@Kualinar]

@@marscience7819 When you have ÷1/2, that «/» is absolutely to be treated as a fraction. The actual proper interpretation gives 100% C

[@gavindeane3670]

​@@KualinarYou have that exactly backwards. The / symbol is the one you cannot change the meaning of. / is part of the basic definition of mathematical notation. It is the division operator. The ÷ symbol is not formally defined, so that's the only flexibility in interpretating this question. The only way to get an answer other than 8 here is to treat ÷ as something other than a simple division operator. Ultimately, the notation is just silly. Mixing two different division symbols in the same expression is inexcusable. The correct way to write what he's trying to write, using inline notation, is √64 / (1/2) × 2

[@marscience7819]

@@Kualinar Show me the rule in PEMDAS that says that. You aren't going to find it.....

[@roundtwo3321]

No one ever got the right answer rushing through a math question. Dividing by one half = Multiplying by 2

[@marscience7819]

Not if the division is preceded by other division or multiplication. That's the whole point of PEMDAS, setting a rule so that people don't just decide for themselves what to do first in an expression.

[@roundtwo3321]

@@marscience7819 No relation.

[@PREGO1966]

@@roundtwo3321 you are correct. People read dividing BY 1/2 the same way they read dividing IN half. Not the same folks, they are opposite

[@gavindeane3670]

​@@PREGO1966Some people might be making that error but that is not what @marscience7819 is saying. You have missed their point completely. The point they are making - quite correctly - is that this notation does not tell us to divide anything by one half. This notation tells us to divide √64 by 1, then divide the result of that by 2, then finally to multiply the result of all that by 2. As written, the expression evaluates to 8, not 32. In the video he is treating the 1/2 as if it was enclosed in parentheses. He is evaluating the expression he meant to write, not the expression he actually wrote.

[@devonwilson5776]

Greetings. 32, absolutely.

[@danafarrar3583]

32

[@kitcarsoncarson615]

I think the way you pose the question matters. Just throwing numbers up there without grouping symbols and then change it when you begin to solve is the definition of trickery. There's always going to be someone who sees it the way you do without grouping symbols. But the whole point in using grouping symbols is to have everyone on the same page. I too would have said 8 but with grouping symbols I would have said 32 if the grouping symbols said that. All of math is important not just numbers that's why we have rules such as unless there's a (-) sign, it's (+).

[@richardpooley2785]

It is 8! He is wrong- too ambiguous explanation.

[@stevenjohnson1143]

Simple c 32 getting there is easy ✓64 primary root 8 dividing and fraction invert and multiply creating 16*2=32

[@petersearls4443]

In your other examples when specifying fractions you don’t use “/“ you use “-“ as in 1 over 2. Here you are using the commonly accepted division symbol so by your own standards the answer would be 8 not 32.

[@gavindeane3670]

Oh, here we go. It's this rubbish again. Those of us who already understand mathematical notation can see what you're trying to do. You're trying to write an expression that evaluates to 32. But we also know that in mathematics the / symbol is the division operator. So we can see that unless you're treating the ÷ symbol as something OTHER then a simple division operator, you've actually written an expression that evaluates to 8. And we know that the correct way to write what you're trying to write, using inline notation, is √64 / (1/2) × 2 But that's for those of us who already understand mathematical notation. The problem is, your target audience almost certainly includes people who wouldn't know any better. People who don't know enough yet to realise that this notation is completely incorrect. People who will see your video and will come away thinking this is an acceptable way to write mathematics, when it absolutely is not. For a teacher, that is utterly shameful behaviour. You should not be using the ÷ symbol in mathematics notation and you CERTAINLY should not be mixing ÷ and / in the same expression. That is inexcusable. The comments section has barely quieted down since the last time you did this in a previous video. It is hard to shake the suspicion that you are doing this deliberately to generate KZbin engagement for your channel at the expense of your students. Do better.

[@marscience7819]

In english, we have a similar problem. "Let's eat, grandma" and "Let's eat grandma" are totally different statements, and it is just a lousy "," that completely changes the meaning. Here, the teacher is saying one thing, but what he actually writes taken as it is written has to give 8.

[@gavindeane3670]

​@@marscience7819That's a bit of a different problem. It is clear what both those sentences mean. They are both correct English. The point about that example is that a tiny, careless change (forgetting the comma) can alter the sentence from one unambiguous meaning to another, completely different unambiguous meaning. What we're dealing with here is a sentence more like "Lets ate Gamma." Not correct English at all and it just ends up as nonsense.

[@acrobatslimer8878]

My answer is a) 8

[@kennethhubbard2027]

32

[@russelllomando8460]

Got it 32. Easy pemdas thanks for the fun

[@KW-gb9cd]

Before watching the video: √64 ÷ 1/2 × 2 = 8 × 2 × 2 = 8 × 4 = 32. No need to muck it up with Pemdas.

[@kjellg6532]

Congrat! You used order of operation to reach this answer!

[@jhenshaw102]

You're still using PEMDAS, order of operations. Gotta muck it up a little because if you started with (1/2) x 2 = 1, you would have (√64) ÷1 = 8.

[@bw9538]

He should make the problem more direct because the way he wrote it makes the method he used to solve really convoluted and not actually solvable the way he is saying is the correct way

[@larryrichards3668]

32

[@user-hy9gy9we3e]

Thank you for your programs. I always need refresher classes. Will you ever go up to Caculus or higher? Thank you. Keep doing what you do. Your manor of teaching is quite clear. Teaching some basic information and examples first will make learning easier for students. I think your "classes" are a great foundation leading to into their first class of algebra.

[@tomtke7351]

Last lesson WAS calculus

[@photographedemode]

8 divided by .5 X 2 = 32, thank you

[@LionkingCMSL]

Whenever I run across a fraction in math I always convert it to its decimal equivalent and go from there. For this problem, I automatically converted 1/2 to .5 and worked from there, knowing when dividing by a positive amount less than one you have to multiply its reciprocal.

[@mauriziograndi1750]

You are 💯 right because the 1/2 should instead have been (1/2) this changing the division result from 4 to 16.

[@mlaiuppa]

That is an excellent way to check answers. The problem being people that can’t do this likely have problems with decimals too.

[@gavindeane3670]

When you divide by ANYTHING you are multiplying by its reciprocal. That's the definition of division. Dividing by 2? That's multiplying by 0.5. Dividing by -100? That's multiplying by -0.01. Dividing by ⅓? That's multiplying by 3. It doesn't just work for positive numbers less than one. It works for ALL numbers, by definition. (Except dividing by zero, which isn't possible precisely because 0 has no reciprocal)

[@mauriziograndi1750]

@@gavindeane3670 Hi Gavin thanks for the comment.

[@stevelaferney3579]

I guarantee you in the real world of commerce there is no way you get 32. You would always get 8. Pretend you start with 64 widgets and you split them into groups of 8. Continue with one group split in half 4, change your mind add them or you double them 2x, back in you still have 8. IF, reversing the 1/2 to 2/1 is correct, and I know I passed algebra, then I must have said F**K it and let roll over me cause my Dad, a retail mgr would have had a fit if I showed him this. I find no logic to flipping 1/2 to 2/1 and multiplying when dividing was the deal.😊

[@tusk242]

I get confused how you get the answer when you take different problems and explain how to do that problem 64devided by 1/2times 2 PEMDAS ? Don't I have to find out what number I am dividing 64 by? how do I get that, but then you give another problem 64 take to 1/2 power, so as if see 1/2 of 64=32 which is what (c) said 32, but then I get confused when you show order operation 10 divided by2X5 line under 5x5=25. I do not have a calculator. I did not see (brackets around1/2 ) but when I divided 64 got 32 which is (c) answer 32, we now have 8 divided by 1/2 x2 is where I start getting confused. OH have to turn 2over 1 still confused Did not stick in my head the turning of 1/2 and 2/1 and multiply

[@PrebenMunter]

So if I have a car and my distance pr sec is 28 m (~ 100 km/h). I know it can accelerate to this speed in 5 sec. Calculate acceleration! 28÷1 gives speed 28÷1/4 must then give acceleration. According to you acceleration is 112 m/s² - ridiculous! Much larger than acc due to gravity. Correct answer is of course 7 m/s².

[@SarahThor-ht4qy]

Dear TabletMath Table: God would like you to know that I would like to correct my answer I did yesterday on the slope problem video of yours, because I made a mistake and wrote my answer was a four. The correct answer is two, because that is the ratio of the vertical point over the horizontal point! The x axis is a given two; I solved for the y axis by plugging in the two and raised it to the power of two, and I got a four for y! In addition, God would like you to know that I got eight for my answer to this problem on your video, because the square root of sixty four is eight. I divided eight by one half and I got a four. Then, I multiplied the dividend by two and I got eight for the product! In the name of Jesus Christ, Amen! Sincerely, God and Sarah Thor-ht4qy

[@panlomito]

V64 = 8 8 / ½ = 8 x 2 = 16 16 x 2 = 32 so answer A 🤪

[@user-gv4cx7vz8t]

@@panlomito ...so answer C! Don't drop the ball so late in the game lol.

[@panlomito]

@@user-gv4cx7vz8t I hate these multiple choice answers so I like to sabotage them.

[@user-gv4cx7vz8t]

@@panlomito You win a silly prize, then.

[@gavindeane3670]

​​@@user-gv4cx7vz8tExcept answer a (and d) is actually correct.

[@tcmxiyw]

This is a useless exercise. Those who use mathematics write for clarity. They do not write expression with the goal of making difficult to parse puzzles. Yes, I had to learn the order of operations rules, but in my career both reading and writing mathematics, I’ve never really had to think about these rules. A well crafted expression leaves no doubt as to what it means.

[@dave-in-nj9393]

The simple fact that this has to be explained means we are not doing it right. How can you check my math if you don't follow the same rules that I was taught.

[@larrystuder6378]

I got fooled by "divided by 1/2" ONCE. This is a bad way of expressing the problem, a trick use of language.

[@seesee61]

Learn a lot from you... but please pick up the pace, and try not to digress so much... This video is twice as long as it needed to be...

[@mlaiuppa]

32. It’s order of operations and how to multiply and Divide with fractions. This is sixth grade math.

[@Gideon_Judges6]

The fractional notation here leaves a bit to be desired. Why not use the unicode ½, or at least use parentheses (1/2)? Using the full size font just makes the / look like a division symbol on a computer system where it it might not be convenient to render ÷. Instead you have an implied parentheses and ambiguity since this "fraction operator" is not in PEMDAS/BODMAS (and frankly this isn't even a pure fraction operator which would be a horizontal line with a numerator above it and denominator below it).

[@splat_rick3369]

As a teacher, I would never fool my students like this. As a mathematician, I will always consider fractions to be divisions (because they are). I would accept both answers (assuming that the reasoning is correct).

[@gavindeane3670]

​@@splat_rick3369As a teacher and mathematician, I would hope you are never mixing two different division symbols in the first place. That is the fundamental and inexcusable error in the notation here.

[@gavindeane3670]

It doesn't just leave a bit to be desired. It's straight up incorrect. The correct way to write this, using inline notation, is √64 / (1/2) × 2

[@lant7123]

Big reason I always write fractions with the horizontal bar, not the slash. However, I think the spacing made this problem very clear, on top of using the division sign.

[@gavindeane3670]

​@@lant7123The problem with that is, spacing is not a symbol in mathematical notation and the standard inline operator for division is / not ÷. Those of us who already understand mathematical notation know all this. We can see how he's trying to write something that evaluates to 32. We can see that he's actually written something that evaluates to 8 (unless you treat ÷ here as something other than simply a division operator). But what if there are people who view his videos and don't realise he's using his own personal dialect? What if people come away thinking that this is how mathematics is written? They are just going to have to unlearn a load of crap in future. There's no excuse for someone who purports to be a teacher to do such a disservice to his students.

[@Toshie69]

Any expression that contains the least bit of ambiguity is improperly written and has no meaning.

[@sharonberkner9714]

I figured the 64 one and came up with 64. I figured the 10 correct so you are wrong.

[@chrisdissanayake6979]

Thank you, Sir! I see that I got confused with the square root sign. I should have just solved left to right.

[@francisdelpuech6415]

I hesitate too! But a square root as he very well explained it is a fractional exponential and though comes before division and multiplication. Great job!

[@chrisdissanayake6979]

⁠Thank you soo much. That makes sense neatly! Yes. Square root of 64 is 64^1/2. So, it is an “exponent”, which represents “E” in PEMDAS. After that comes multiplication and division or division and multiplication left to right. 👏🏽👏🏽👏🏽

[@Christopherdpenha]

John the JACKASS, who has an immense ability to make mountains of molehills

[@DennisHolmberg-sl1hz]

Division by a fraction is the same as multiplication...

[@lornamurdocheaton624]

I'm more confused than ever. I H@E bloody maths.

[@tombailey2210]

When I went to school PEMDAS wasn’t taught at all!