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

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

Ай бұрын

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.

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

@gavindeane3670

Ай бұрын

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 KZread channel, and he knows full well, and doesn't care, that it's at the expense of his students.

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

Ай бұрын

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

@michaelterry1000

6 күн бұрын

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

5 күн бұрын

@@kjellg6532 no parenthesis needed for this simple fraction.

@kjellg6532

5 күн бұрын

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

@douglastovey2685

5 күн бұрын

@@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.

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

@MsChemicalEngineer

Ай бұрын

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

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

Ай бұрын

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

Ай бұрын

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

Ай бұрын

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

@gavindeane3670

Ай бұрын

​@@KualinarYou have that exactly backwards. The / symbol is the one you cannot change the meaning of. / is part of the basic definition of mattress 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

Ай бұрын

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

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

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

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

Ай бұрын

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

Ай бұрын

@@gavindeane3670 Thank you!

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.

@Mr._Fit_Atheist

14 күн бұрын

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

14 күн бұрын

@@Mr._Fit_Atheist 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.

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

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

Ай бұрын

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

4 күн бұрын

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

3 күн бұрын

@@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

3 күн бұрын

@@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

3 күн бұрын

@@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.

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.

@Mr._Fit_Atheist

14 күн бұрын

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.

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.

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

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.

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.

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

Ай бұрын

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

Ай бұрын

@@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

Ай бұрын

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

@williamhouse432

12 күн бұрын

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

@stevenjohnson1143

10 күн бұрын

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

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

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 (+).

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

Ай бұрын

Last lesson WAS calculus

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

Ай бұрын

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

Ай бұрын

@@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

Ай бұрын

​@@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

Ай бұрын

Yep, you are absolutely correct.

8x2x2=32

Greetings. 32, absolutely.

Actually, I learn more than mathematics, when I visit here. One thing for sure. Mr John is an exceptional teacher, not only with great knowledge and experience in math, but also with a whole lot of patience 🙏🏽

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

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

@marscience7819

Ай бұрын

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

Ай бұрын

@@marscience7819 No relation.

@PREGO1966

Ай бұрын

@@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

Ай бұрын

​@@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.

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

Ай бұрын

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

Ай бұрын

​@@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

Ай бұрын

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

Ай бұрын

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

Ай бұрын

​@@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.

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.

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.

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

@marthatamez8698

Ай бұрын

1/2 conversion to a number is 0.5

@slm3945

Ай бұрын

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

@marscience7819

Ай бұрын

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

Ай бұрын

@@marscience7819 My error was all too apparent.

@slm3945

Ай бұрын

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

C) 32

Order of operations with no brackets. Good review. I remember the FOIL rule with y=mx + b.

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

Ай бұрын

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

@mlaiuppa

Ай бұрын

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

@gavindeane3670

Ай бұрын

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

Ай бұрын

@@gavindeane3670 Hi Gavin thanks for the comment.

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

@gavindeane3670

Ай бұрын

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

Ай бұрын

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

12 күн бұрын

You are completely wrong. 1/2 = 0.5

@gavindeane3670

12 күн бұрын

@@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

7 күн бұрын

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.

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

Ай бұрын

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

Ай бұрын

@@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.

Thanks!

I just noted this, you are correct with one major flaw; all square roots have both a positive and negative answer as sqrt64 will be 8 and-8 (I know that WITHOUT a calculator) which leads the final answer to be 32 and -32

@gavindeane3670

Ай бұрын

No, the √ symbol is more precisely defined than that. Yes, 64 has two square roots, but the expression √64 refers to exactly one of those square roots (the positive one). To refer to both square roots you would have to write ±√64. More importantly, the expression doesn't evaluate to 32 at all. It evaluates to 8 (unless you think the ÷ symbol is something other than a simple division operator).

I'd argue that there are six possible solutions: ±2, ±8, ±32 (depending on how the ambiguously written problem is interpreted). This problem is written extremely ambiguously. Let me walk you through my logic and reasoning: 1. We all agree that √64 is 8 2. The √64 is also -8, so another solution for each interpretation is possible. 3. The use of both ÷ and / symbols is simply careless. These symbols mean the same thing, so you should stick to one division symbol. 4. Lack of parentheses/brackets surrounding 1/2 causes issues because you dont know whether its supoosed to be ((8÷1)/2)*2 or 8÷(1/2)*2 5. More issues arise since you dont know whether the problem is (8÷1)/(2*2), same with 8÷((1/2)*2) and 8÷(1÷(2*2)).

@gavindeane3670

29 күн бұрын

It's definitely not 2 and not any of your negative answers. You can disregard your second point. √64 is not -8. √64 is 8. Yes, 64 has two square roots, but the expression √64 refers to exactly one of those square roots: the positive one. That is the definition of the radical symbol. If you want to refer to both of the square roots you must write ±√64. And to get the answer 2 you would have to give the multiplication higher precedence than the division, which is not how the grammar of mathematical notation works. Treating the ÷ operator as simply a division operator means the expression evaluates to 8. In the video he's treating it as if he'd written the 1/2 in parentheses.

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

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

@francisdelpuech6415

Ай бұрын

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

Ай бұрын

⁠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. 👏🏽👏🏽👏🏽

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.

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)

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

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

Ай бұрын

Exponents are calculated in the E step of PEMDAS.

I initially came up with 32. Square root of 64 is 8, divided by 1/2 is 16, times 2 is 32. But then I thought that there may be a trick and instead of 1/2 (.5), it's 8 divided by 1 then divided by 2, which is 4. So it depends on if you read "1/2" as being one-half, or if you read it as "one divided by 2", in which case you have to perform everything left to right.... divide by 1 then divide by 2. But I'm sticking with 32. Using a division symbol and then switching to a different division symbol would make it a bad way of expressing the formula. ... YAY!

@slm3945

Ай бұрын

What difference does it make which division symbol is used? They both require you to divide working left to right. PS: To resolve a fraction, you divide the numerator by the denominator.

Got it 32. Easy pemdas thanks for the fun

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

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

What is the word you used for the E in PEMDAS? I heard you say it several times but still didn't hear what the word was.

@gavindeane3670

29 күн бұрын

Exponents

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

@kjellg6532

Ай бұрын

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

@jhenshaw102

Ай бұрын

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.

Interesting.

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.

The basic version of the order of operations as in the video is simple enough for a primary school child to use to check they are calculating in the correct order when they are learning the order of operations. From the video it appears that it is too complicated for a maths teacher in the USA to use correctly. The basic version of the order of operations has limitations. If you are dealing with an expression that contains more than three numbers it might not give you the correct answer. The basic version is not used but it does explain the version that is used. The correct answer to 10÷2×5 is 1 The correct answer to ___ √64 ÷1/2×2 is 32 The person in the video appears to have got the correct answer more by luck than an understanding of basic maths. ___ √64 ÷1/2×2 8÷1/2×2 8÷1/4 8÷0.25 32

@gavindeane3670

29 күн бұрын

The correct answer to 10÷2×5 is not 1, it is 25. The only way it is 1 is if you treat the ÷ symbol as something other than a division operator. The correct response to the question in the video is to take it back to the person who wrote it and tell them to write it properly. Mixing two different division symbols in the same expression is inexcusable. But again, unless you treat the ÷ symbol as something other than a division operator then √64÷1/2×2 is 8.

@neildickinson6493

28 күн бұрын

@@gavindeane3670 10÷2×5=1 This can be viewed as two potential calculations +10÷2 and ÷2×5 or you can view it as consisting of three components +10, ÷2, and ×5 The basic order of operations works with the components. There are four levels of priority in the order of operations and rule one is you work from highest priority to lowest priority and rule two you work from left to right. 10÷2×5 Highest priority are brackets. There are none so you go down a level to orders. There are are no roots or powers so you go down to the next level. You are now down to the multiplication and division level. The 10 is +10 so is not on this level. This leaves the ÷2 and the ×5. They are next to each other and so form the expression ÷2×5 ÷ and × have the same priority. Rule two now applies and you calculate from left to right to give you a result of ÷10 You are now left with a ÷10 and a +10. ÷ has priority over + so you have +10÷10=1 Therefore 10÷2×5=1 Try it on something you already know the answer to 1×2=2 Because of calculating using the reciprocal you can rearrange the equation as 1÷1÷2=2 Apply your incorrect method 1÷1=1 then 1÷2=0.5 0.5 does not equal 2 Apply the correct method 1÷1÷2=2 is +1÷1÷2=2 As you work down through the priorities the first thing you come to is ÷1÷2. Rule two applies and you calculate from left to right ÷1÷2=÷0.5 This leaves you with ÷0.5 and +1. Division has priority above addition so +1÷0.5=2 which is the correct answer The basic order of operations has a problem in that it does not always give the correct answer to expressions that contain more than three numbers. 1) A×B×C 2) A×B÷C 3) A÷B÷C 4) A÷B×C In each of these four cases the A is actually +A and so has a lower priority than the B and the C . Technically you therefore should always calculate these four cases B and C first, but 1) A×B×C 2) A×B÷C Return the same result whether you calculate B and C first or A and B first So it is just 3) A÷B÷C 4) A÷B×C That have to be calculated B and C first. Rule two now becomes calculate from left to right unless indicated within the expression or equation From 3) and 4) the indicators you looking for are ÷ followed by ÷ or ÷ followed by × Using different symbols to represent division may be look messy but does not stop the calculation √64÷1/2×2 Highest priority is brackets but there are none here so you move down to orders. Here you have the √64 which you calculate to get 8 8÷1/2×2 You can replace the / with ÷ if you find it makes things more clear 8÷1÷2×2 You have a ÷ followed by a ÷ so you must calculate the 1÷2 instead of the 8÷1, but you also have a ÷ followed by a × You therefore must calculate the 2×2 instead of the 1÷2 8÷1÷2×2 8÷1÷4 8÷0.25 32 The correct answer to √64÷1/2×2 is 32

@gavindeane3670

5 күн бұрын

​​@@neildickinson6493The correct answer to 10÷2×5 is 25. There are three numbers: 10, 2, and 5. And two operations: one division and one multiplication. Because the two operations have equal precedence, the expression is simply read from left to right. The first operation is the division. Its two operands are 10 (the dividend) and 2 (the divisor), so the result of the division is 5. The next operation is the multiplication. Its first operand is the result of the division (which is 5) and its second operand is the 5 that's written in the expression. So the result of the multiplication is 25. And we're done. As for the rest of your post, I have never seen such a garbled and misconceived understanding of mathematical notation. I don't know where you got that from. Whoever it was that told you all that, you need to stop listening to them because they don't know what they're talking about. It's difficult to know where to start with unpicking your understanding. But a couple of thoughts: Consider how, despite you stating (correctly) that division and multiplication have equal precedence, and despite you stating (correctly) that operations of equal precedence are evaluated left to right, you have somehow managed to evaluate A÷B÷C and A÷B×C from right to left. Left to right means you start both of those with A÷B. You seem to have managed to evaluate 8÷1÷2×2 from right to left as well. And look up what a binary operation is. All these basic operations + and - and × and ÷ are called binary operations. That simply means they take TWO operands. So taking an expression like 10÷2×5 and breaking it up as you did into "components", with just A SINGLE NUMBER associated with each operation is nonsensical.

We always used BODMAS. Nice and simple 😊

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

I say 8 Oops! I did square tooth of 64 is 8 Then divided by 1/2 = 4 × 2 = 8 Though the 1/2 step got me confused ... I forgot the rule of switching Inverting the 1/2 to 2/1= All thanks to my mum n dud selling me out as baby to use me as biblical experiment making my life complicated much like math being complicated due to human error and mistakes of not knowing the order of procreation where mum n dud are suppose to be equipped established ready prepared to sustain maintain themselves n child or children with all that ls needed n required first n foremost before conception. Many dont know money n work is required In the beginning of situation to care provide for child/ children to avoid prevent many things from going wrong. Not to mention, the need for having brains and how to use and apply to life living but that's a whole nother story and video .. Much love n blessings to all and remember to have it together before pro creating another human being is what mathematics comes down to

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

@deborahstahl5982

Күн бұрын

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

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

The answer should be +/-32 if that convention is used. I think parenthesis should always be used to indicate operation intent. These are some of the things that make some individuals question Mathematics.

@gavindeane3670

6 күн бұрын

It's not ± anything. The √ symbol specifically means "principal square root", so √64 equals 8 and only 8.

@marpool8029

6 күн бұрын

@@gavindeane3670 This is another rule to keep answers attainable for beginners. in more advanced theoretical math that rule quickly fall on its face. you can force an imaginary number under the radical to approximate a desired outcome. And if you look into it, that rule can quickly be defeated when dealing with variables. why couldn't this be written as √((-8)^2).

@gavindeane3670

6 күн бұрын

​@@marpool8029Not quite sure what point you're making, but √((-8)²) equals 8 and only 8.

SqR64 = 8 /.50 = 4 x 2 = 8. Answer is (a) 8 !!

(1/2x5). Required.

32

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.

I'm crap at math, always was so here goes: In my mind I see the divide sign followed by a fraction which is another divide sign so I change it to 0.5 to make sense so 8 / 0.5 is 16 x2 =32. I did not see parenthesis around the 1/2 and I don't understand the why and all that and you did not properly explain about it. (5/10) lol

Using PEDMAS this is correct 💯.

@gavindeane3670

Ай бұрын

Unless you think that the ÷ symbol is something other than a division operator, then PEMDAS gives you the answer 8 here.

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

Whats the point?

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

@gavindeane3670

Ай бұрын

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

c) 32

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

When dividing by 1/2we multiply by 2.

Is this calculation ever needed in real life?

Sir, The square root of 64 is plus or minus 8. The answer is the set of 2 numbers -32 and +32. Remember the square root asks what number times itself makes the number you are taking the root of. -8*-8=64 and 8*8=64. Physicist here...

@gavindeane3670

25 күн бұрын

It is true that 64 has two square roots. But the notation √64 refers to exactly one of those square roots: the positive one. That is the definition of the √ symbol.

@howardludwig6837

17 күн бұрын

No, √ denotes the "principal square root" operator, which means only the nonnegative square root, not both square roots.

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

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

My answer is a) 8

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

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

6 күн бұрын

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.

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

8 × 2 × 2 = 32

Yup, got it

Strictly speaking, the correct answer is +/- 32 since the square root of 64 is +/- 8.

@gavindeane3670

6 күн бұрын

No it isn't. It's true that 64 has two square roots, but by definition the expression √64 refers to exactly one of those square roots. √64 equals 8 and only 8.

C

I mean the nice maths man👍☺️

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 KZread where you make the same mistake. Please review and revise your solutions.

A and B are the same answer, but really A

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.

c

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.

32.....sqrt64÷1/2×2= 8/1×2/1×2=32

😀😃 i got it right 32

@RS-Amsterdam

Ай бұрын

Do you want a balloon

32, i hope was answer

Heck I can make a case for 2

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

1/2 = ½ = 0.5= half

@gavindeane3670

25 күн бұрын

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.

8 for me

This is someone fixated on semantics. Like the proper way to say something. In short a formula means something! What it means is not clear. Use the python REPL and you would get the answer but even if you get it "right" the question remains: what does it represent. Formulas represent something. Furthermore, whoever arrived at the formula may yet have written it out incorrectly. You don't need PEMDAS unless you are trying to learn by rote. And I seriously advise against that approach if you wish to understand.

32 Square root of 64 is 8 8/.5 is 16 16x2 is 32

We'll let me see? 1+1 =2!!