Відео

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Thanks a ton, Explained so clearly. Your channel deserves more views!!

really helpful thanks

The answer is 1. Multiplication by juxtaposition takes precedence over division. Also, you can easily solve this problem by using multiply by inverse to both sides after doing the parenthesis. USA is the only country that does PEMDAS btw.

Hello Professor, great videos! I only see 22 videos; are there more/any change you will make more to cover the Full APCS P course? Thanks

SUPER Lecture! Just what I needed to shed light on this subject. THX!

Very helpful 🙏

hey bro, is that video covering the whole lesson 8?

Thank you so much for explaining this. You are correct, most people/math teachers just say that's the way it is and just accept it.

Very well explained. I've checked out numerous explanations on this topic for how accurate the analogue signal relates to the reconstructed signal and professionals including and electronics expert all day that that the analogue signal is exactly the same coming out as going in. Yet in your breakdown the reconstructed signal can only ever be an approximation and that the process of rounding also means that it's not exact. I know in audio that with the amount of sampling and bit depth that the reconstruction may be very close but it can't be exact. I was also looking for how this process of ad-da reconstructs the curve of the signal and this is the first time I've heard, in your words, that it is an estimation, which would mean another lacking exactitude! I've often wondered how thousands of harmonics in an audio signal is affected by this analogue to digital and back again process ( not thinking of Nyquist here) in its processing ability to reconstruct it all faithfully. Of course there's the filter roll off depending on sampling rate, 44.1, 48, 96, that can affect aliasing etc In the world of audio perhaps it doesn't matter these days with enough sampling rate and bit depth that you get very high quality music. Yet to me it's always had a slightly different sound from an original analogue source (forgetting analogue recording formats for a mo) noticing years ago when digital mixing desks took over from analogue. I suppose because ad-da is a process it's bound not to remain identical. But very useful these days. Anyway, I enjoyed your explanation of this process.

Thank you sir

3 and 4 digits by one digit with distributibe property??? Please please😢😢

Pin first comment plus I subscribed

Great explnation!

bro why ur face purple ?

thank you ! Khan academy's content in this particular topic is little complex for me but you explain in a very smooth way ! THANKS TO PROFFESOR CUNNINGHAM

Using "literally" in a figurative sense has been in use for hundreds of years. It's not new.

Excellent lecture Dr. Cunningham. Very clear & concise with a more modern, youthful, & invigorating tone plus using audio as an application motivator. ... I couldn't have done any better myself.

Great walk-through!

Thank you so much, this helped me a lot!

thank you! trying to learn everything before the exam😭

I have a problem with that as I learned from algebra, calculus, etc., that implied multiplication comes before division. Implied or juxtaposed multiplication occurs when there is a number next to an open parenthesis without a multiplication symbol. So for me and most engineers the answer is one. And most scientific calculators agree.

When encoding, we only change the values of y to binary. Additionally, there will be many x values. At the quantized y value (at this particular point), I didn't understand how the computer reads the values of x and y and reconstructs them. Could you explain?

Nearly 60% of people answered 1 because it's the correct answer.

Thank you so much! This video helped me a lot.

8÷2(2+2) is not the same as 8÷2*(2+2). Can't just drop the ( ) and makes it to be *.

So Mr author you are say 8÷2×4 =1. You can stand on your head and whistle through your backside the answers is 16. . But I love pema instead of pemdas. Rule states change ÷ to × And invert divisor. If I have 5 - 2 + 1. Whether I do the addition first or the subtraction first then answer is 4. So I am suggesting BOMA instead of Bodmas. BOMA stand for brackets , of, multiplication, addition. Eg. What is 1/2 of 2+2. Most will say 2. But 1/2 of 2 =1 +2 =3. Think about this. Maths is a precise language. there's no ambiguity and if you apply the rules correctly we would all get the same answer. Of you use you own parenthesis you may change the whole question. Thanks

2(2 + 2) is a group.

I make the answer to be 1 - not because I think multiplication comes before division, but because I was taught that implied multiplication (or multiplication by juxtaposition) has priority over signed multiplication.

This isn't an issue of PEMDAS. It's an issue about implied multiplication, which should be done before regular multiplication and division. For instance 1/2x≠x/2. 1/2x=1/(2x). This is the convention used in many maths, physics and engineering journals, both in America and around the world. Thus 8/2*(2+2)=16, but 8/2(2+2)=1.

PEJMDAS is rule .

So, after listening to you, the correct answer is 1. Thanks!

Totally incorrect. It is 8÷2×4 not 8÷(2×4). You don't know grade 5 maths

Can you come work at my university and teach my class please? 🥹

The thing is the obelus is indicative of a fraction

8÷(2(2+2)

Answer is 1 8÷8

The video and some comments have really gone on my nerves, I think I want to take the more radical position that even something like: 2+2 * 2 evaluates to 8, rather than 6. Actually thinking about the author's intent is way more important than any convention.

How tf do you think that's "objectively" right? Who communicates first dividing by two and then multiplying with eight like that? 8 ÷ 2(2+2) There's spaces on BOTH sides of the division symbol and multiplication is just written via juxtaposition. No, if anything the "objectively" right answer is 1.

PEMDAS is very incomplete. It covers only the five most basic binary arithmetic operations. It does not address unary arithmeic operations at all. It does not address comparison operators nor logical operators, nor any of numerous other categories of mathematical operations. Let's see where we can fit in unary arithmetic operators. Let's tackle the first step of decomposing sin 4u into an expression in terms of sin u and cos u by using double angle formulas: sin 4u = 2 sin 2u cos 2u. Should the unary operators sin and cos be carried out before all the multiplications (higher level of precedence than MD), after all the multiplcations (lower level of precedence than MD), or left to right simultaneously with the multiplications (have U join MD)? The unary sin and cos cannot be carried out befire the multiplications 2u are done. The unary sin and cos cannot be done after the multiplications are done because the multiplications of 2, sin, and cos cannot be done until sin and cos are evaluated. The unary sin and cos cannot be at the MD level because working left to right as required by PEMDAS requires the product of 2 and to be done first, but we do not know the value of sin to multiply by 2 until we have multiplied the 2u as its operand, but that multiplication is farther right and not to be done so early. This means we must split M into two separate levels and put the unary operations in between. So, how do we know which multiplications go in the higher precedence level and which go in the lower precedence level? After all, all of the multiplications are implicit. The factors in the multiplications that are done early are juxtaposed--no intervening space. The other multiplications have factors that have an intervening space, so they are not juxtaposed. Exponentiations remain at higher precedence, because we still need the juxtaposed product ab² to mean a(b²), not (ab)². Now professional technical publishers have numerous rules of typography, and some of them involve spacing. The juxtaposition versus separation of factors is caused by this need for distinction of tight coupling of factors of a product that constitutes an operand, especially but not exclusively an operand of a unary operator. The typography rules are intended to guide the eye to help emphasize, rather than conflict with, the precedence rules. The brain should not be getting dissonant signals from the eye looking at the format of text and the brain applying the precedence rules. The cause-effect rationale is that we do the juxtaposition versus spatial separation of factors in a multiplication because of the needed precedence hierarchy, not vice versa. Then knowing the typography rules are derived from the precedence rules, we can use typography to enable a cleaner simplified state of the precedence rules under the assumption that writers will know, understand, and obey the typography rules to convey a stronger message of intent instead of a self-contradictory message. That works well with professionally published technical documents, but social media users tend to neither know nor care about such rules. It could be a good UA-cam video topic, how to use variations of font (upright vs. italic, normal weight vs. bold, serif vs. sans serif), vertical placement (baseline vs. superscript vs. subscript, use of vinculum as grouping symbol in division with dividend above and divisor below, etc. Anyway. 8/2 × (2 + 2) = 16, 8/2 (2 + 2) = 16, 8/2(2 + 2) = 1. This has nothing to do with obelus (÷) vs. solidus (/), distributivity, parentheses as a grouping symbol, etc. What I have described has been traditional practice among professional research mathematicians and physicists, with style guides explicitly stating things like a/bc means a/(bc), whereas PEMDAS requires it to mean(a/b)c. However, with technical difficulties of writing mathematical text in a context forcing linear text rather than allowing text with vertical structuring, there has been a lot of slop posted online triggering a lot of miscommunication, so much that the style guides for many technical organizations and publishers now declaring something along the lines of a division textually followed by a multiplication or another division is invalid syntax and has no defined meaning. That means that 8/2(2 + 2) is undefined, which PEMDAS violates as well.

Juxtaposition is higher priority than other multiplication/division, therfore the correct answer is 1.

thank you so much youve helped me so much

Your assertion that the answer is 16, and your PEMA acronym, are in contravention to the style guides of both the American Mathematical Society and the American Physical Society. You would need to change it to PEJMA, where J is "multiplication by Juxtaposition". The correct answer (according to both societies) is 1 ... not 16. Also, you cannot do all the multiplications and divisions "at the same time" as stated. Neither the human brain, nor most computers, can perform parallel computations. You have to choose an order in which to do it (like Left to Right).

no #3 was wrong on your part you had the teacher and the whole class befuddled

The answer is 1. Because you forgot about Multiplication by Juxtaposition (look it up)

Mr funk there is no ambiguity. 8 × 1/2 (4) = 16. You have my email, you can challenge me any time. I am not a professor or an engineer or a computer programmer. I am just a south african indian who had excellent teachers in my primary school days

8 ÷ 2(2 + 2) = ? If your answer = 16 2x ÷ x = ? 2x ÷ 1x = ? If your answer = 1 2x ÷ x = ? 2x ÷ 1x = ?

The correct answer is (16+1)/2 = 8,5

One more comment. You should put a disclaimer at the top of you description stating that the answer give in the video is for 8 ÷ 2 x (2+2) and not for 8 ÷ 2 (2+2) as PEMDAS Does Not account for juxtaposed/implied/coefficient priority orders of operations as shown in the original expression " 8 ÷ 2 (2+2) "

1st, the correct answer is 1, not 16. 2nd, whether the division symbol "/" or "÷" is irrelevant to the problem being solved correctly as both symbols mean the same thing. 3rd. PEMDAS is meant and was developed for early grades education and is a "simplified and incomplete" order of operations that does not take in to account juxtaposed/implied/coefficient relationships when using parentheses. Since PEMDAS was/is meant for grade schoolers below 6th or 7th grades, including instruction regarding juxtaposed/implied/coefficient relationships would simply complicate matters for the young learners unnecessarily. 4th. In higher mathematic, sciences, engineering textbook the usage of juxtaposed/implied/coefficient relationships is universally used. The last thing mathematicians, scientists and engineers want to do is add more sets of parentheses that is needed if long multi-term equations where if juxtaposed relations can server the same purpose and eliminate possible error of have an extra set or missing set of parentheses would cause mis-intended results. 5th. You are correct, 8 ÷ 2(2+2) could be written as 8 ÷ (2(2+2)) to eliminate ambiguity, but to those educated in mathematic beyond the elementary level, it is not needed and more of an impracticality to likely cause errors in longer non-simple mathematics. 8 ÷ 2(2+2) = 8 ÷ (2(2+2)) = 1, additionally 8 ÷ 2(2+2) = 1 doesn't not equal 8 ÷ 2 x (2+2) = 16 which is the equations you solved. 6. Do a simple experiment using the calculator (scientific mode) that comes with Window/Microsoft that comes on you lap top. Type "2" followed "(". The calculator will insert an "x" between the "2" and the "(" and display "2 x (" and will give you an answer of 16. This is due to the calculator not taking into account that juxtaposition and recognizing that "2(" as being a higher priority multiplication versus using "2 x (" format. To get the desired calculation and a result of "1", the used is forced into adding an extra set of parentheses. However, the default of the Windows calculator to not recognize juxtaposed relationship is not universal in calculator or even by brand of calculators as some Casio/TI calculators do recognize juxtaposed relationship and other don't. The users need to understand their calculator's default setting and configure it (if allowed by the calculator) according to the user preferred method of use. 7. The misuse of PEMDAS is due partly that 90-95% of people don't deal with more complex mathematics than that intended by PEMDAS, including many elementary level educators. The issue is not that PEMDAS is wrong (it is not), but it is just incomplete and not intended to cover "all" orders of operations as PEMDAS be ts intended use in "elementary" education. In elementary education we don't teach our students about "i" which is used in complex mathematic. Because the use and meaning of "i" is not taught to elementary students (similar to juxtaposed relationships) doesn't mean it doesn't exist. Perhaps the best way to resolve the problem is to add limit statement to the PEMDAS convention.