@@peterthomas5792 it really isn't wrong. I used this method in a question in my coding course. You have to know about pemdas for coding. The result was correct because I followed this explanation.
@@Islam-and-boxing Coding knows nothing about juxtaposed multiplication or stacked exponentiation, so coding will never teach you why PEMDAS is wrong. Try doing a maths course taught by someone who actually USES maths professionally such as, well, a mathematician, physicist or engineer.
@@mathically You are INCORRECT with your "invisible times". __ONLY__ the USA teaches this nonsense in middle/high school. If you ever take math (e.g. physics or engineering) in college/university you'll fail. 16 / 4 ( 3 + 1 ) = 16 / 4 ( 4 ) = 16 / (4 * 4 ) .... aka distributive property... it's math. If a rule applies in one location, it applies everywhere. = 16 / ( 16 ) = 1. Your mistake and it's SAME with ALL U.S. HIGH school teachers ... is inserting a magical multiplication sign. 16 / 4 ( 3 + 1 ) DOES NOT EQUAL 16 / 4 * ( 3 + 1 ) Ask any human (who is suitably trained in math) what does 2x/2x result in? The answer is 1. However with your logic (and the same for Google) the answer is x^2. This is 100% wrong. Similarly try evaluating 3^2x ... that's not 9x ... that's 3^(2x) ... since we don't know what x is ... the expression is already in its simplest form. All of this is explained under JUXTAPOSITION. PLEASE STOP TEACHING PEMDAS. PEMDAS IS ***WRONG*** (unless you're just teaching elementary school math).
@macbain1395 PEMDAS doesn't break any rules of algebra, the interpretation people lay on expressions DO, however. In addition with the obelus, which is not a vinculum, is basically a fraction with a numerator on the left side and on the right side. Writing in text has a difference between writing in paper, which often uses a vinculum rather than an ambiguous obelus or solidus. The simple PEMDAS interpretation of the expression 16/4(3 + 1) is not breaking any rules of algebra whatsoever, since if we break 16/4 down to its multiplicative inverse, we find that we have that as the coefficient of the term (3 + 1), THEN distribute within the parentheses. That's where you went wrong on the distributive property, the coefficient of (3 + 1) is not 4, but it is 16(4^(-1)) juxtaposition is still in application regardless, you have to remember that without the parentheses to group the entire denominator, say: a/bc, as per the interpretation of a solidus, not a vinculum it goes: a/bc = (a/b)c = ac/b Algebra does not fall apart in the midst of PEMDAS, it's the overcomplication and the misunderstanding of simple mathematical perspective on the given.
Implicit multiplication ALWAYS takes priority over explicit multiplication/division. The perenthesis (implicit multiplication) do not become a multiplication sign (explicit multiplication). The answer is 1.
@@kelanth462 implicit multiplication comes before explicit multiplication in arithmatic AND algebra. Even texas instruments has stated officially, that while implicit multiplication has higher priority than explicit, they are selling primarily to North American school teachers (and their students) and that primary school teachers in North America are the only group explicitly stating that they want to ignore this mathematical rule. College professors, mathemeticians, engineers, physicists, and scientists all teach that implicit multiplication comes first. So do primary school teachers everywhere outside north america. Its a universal thing. Except, for some reason, when it comes to bachelor degree non-mathemeticians teaching children mathematics in north america. That said... the person writing this equation is lazy. This ambiguity is KNOWN, and the equation can be written in a way that removes it... by adding parenthesis to show exactly which order they expect to be used.
@@marcush4741 2x÷2x=1. If x=3 then (2*3)÷(2*3) still equals 1. In arithmetic 2(3)÷2(3)=9 People confuse and conflate two different types of Implicit multiplication .... One without a delimiter and one with a delimiter.. Type 1... Implicit Multiplication between a coefficient and variable... A special relationship given to coefficients and variables that are directly prefixed i.e. juxtaposed WITHOUT a delimiter and forms a composite quantity by Algebraic Convention... Example 2y or BC This type of Implicit Multiplication is given priority over Division and most other operations but not all other operations... This can be seen in most Algebra text books or Physics book. Physics uses this type of Implicit Multiplication quite heavily.. Type 2... Implicit Multiplication between a TERM and a Parenthetical value that have been juxtaposed without an explicit operator but WITH a delimiter...The parentheses serve to delimit the two sub-expressions..
@@marcush4741 Once you complete the parentheses (3+2)=5 all you have left is 100÷4x5 Do you really need extra grouping to solve that? Can't you just follow step 3 of Order of Operations and solve working left to right?
@@kelanth462 16÷4(4) is not the same as 16÷4x4. Using parenthesis makes this implicit multiplication. Using the × symbol makes it explicit multiplication. Left to right at all costs is only taught in North American primary schools. It is UNTAUGHT when you go into mathematics, engineering, physics, medicine, trades. Everywhere that uses mathematics in the real world, outside of teaching children. The rule is implicit, left to right... then explicit left to right. If the model being used is ONLY used in primary schools, but not being used anywhere it applies to real world jobs... and is heavily criticized anywhere it is used outside education... then the education model is incorrect. The answer is 1 because 4(4) takes priority over 16÷4 everywhere it matters in the real world. Especially when the field of advanced mathematics literally says so. And the companies doing otherwise state directly in their manuals that this change only exists because people educating children in one continent have overwhelmingly created demand for an incorrect product. TIs words are literally that this is incorrect, but they are meeting the desires of their largest market.
Parenthesis inners first, and parenthesis outers second is how we learned it early 2000s. The parenthesis do not disappear just because you worked out the inner bit.
Ron Larson, a famous author of Algebra and Calculus, considers 4(3+1) as implied multiplication in his Algebra book. According to him 16 / 4(3+1) means 16 / [4(3+1)] = 1 while 16 / 4 * (3+1) means ( 16 / 4 ) * (3+1) = 16
Not according to Americans doing Common Core math! But to be clear, I agree with you. 4(4) is not the same as 4 * 4. It's just like saying 4^4 is not the same as 4*4.
@@macbain1395 You've hit the nail on the head "Americans." A lot of other countries use a different method and would get the answer as 1. 16÷4(3+1) >> 16÷(12+4) >> 16÷16 =1.
Exactly. It's called juxtaposed multiplication. What's 2a/2a? PEMDAS says the answer is a² The correct answer is 1. Why does the USA teach this PEMDAS nonsense?
@@graysiadhi No it's not. It's 16÷4(4). The 4(4) has IMPLIED parentheses (look up juxtaposed multiplication). So 16÷(4(4)). Learn maths as it's practiced by mathematicians, physicists and engineers, not how it's taught in primary schools.
Speaking as an engineer with a PhD, implicit multiplication has a higher order of preference than explicit multiplication or division. For instance, 1/2a means 1/(2a), not a/2, and there’s no reason why arithmetic should be different from algebra.
This is on my exam today with fractional expressions so I just need a reminder lol... nervous because I could never grasp this 😅 wish me luck on my test yall !
Another example of why PEMDAS is only suitable for young children:- 2^^2^^3 PEMDAS evaluates it as 64 It's actually 256 PEMDAS is a primary school tool that breaks down with anything more advanced than very basic math.
Answer changes depends on what sybol you use. If you are using ÷ which is only used in primaly school the anwser can be 16 however if you use / for example 16/4(4) you its actually says 16/(4(4)) so the anwser is 1 and thats the way scientists and engineers are using in their papers
No. Literally no. 🤦 It doesn't take a rocket scientist to know that / is the same as ÷ What you've done in your example is added imaginary brackets that didn't exist to begin with. Let me break it down in simple terms. Say you have: 2 / 5 x 5 or 2 ÷ 5 x 5 Both are the same. To put 2 over the entirety of 5 x 5 would require brackets. The problem would need to look like this: 2 / (5 x 5) or 2 ÷ (5 x 5) Those are the same. Now if you wanted to write 2 ÷ 5 x 5 in fraction format it would look like this: 2/5 x 5 But either way you'd still solve from left to right. This is elementary people.
The trouble is that different countries use different methods of teaching. For me the answer is 1 because I was taught that the 4 belongs to the (3+1). For me to get the answer to be 16, the equation would need to be written like this (16÷4)(3+1)
Agree. The REAL point is that this statement is expressed ambiguously and that is bad maths. It needs one additional pair of () to become unambiguous. Either yours or 16÷ (4(3 +)). This statement crops up a lot on YT and I reckon its a form of clickbait.
Theres no ambiguity. Implied multiplication takes place on the MD step, but it always has higher priority than explicit multiplication. PEJMDAS (juxtaposition) is the way everybody does it EXCEPT American primary school. Engineers, mathemeticians, colleges, and every other nations primary schools teach that juxtaposition comes prior to explicit multiplication/division.
As a poorly recovering math head (have been an on and off math tutor to friends and family since 1963, when algebra was introduced to the class) I despise PEMDAS. Mathematics is universal; PEMDAS is strictly limited to the 17% of the world's population that speaks English. Even more restrictive, only the USA and France use PEMDAS; in the rest of the English speaking world it is BODMAS. In Germany it is "Punktrechnung vor Strichrechnung" and everywhere it is unreliable. We never know if the crafter of the expression recognized PEMDAS. Use parentheses, nested as necessary, to avoid misunderstanding.
BODMAS/PEMDAS isn't the issue here. It's how the 4(3+1) is treated. It's arguably ambiguous (though you could argue that once the brackets are worked out you lose the brackets so are left with 44 or 4×4. Treating it as 44 is daft so we are left with 4×4 and then 16÷4×4 is clearly 16.)
> ...,though you could argue that once the brackets are worked out you lose the brackets No you don't. Once the INSIDE of the brackets are worked out, you're left with 4(4). There are STILL brackets, so they get worked out next to leave 16. Only THEN do you do multiply & divide.
You can’t change a parentheses to a multiplication sign. That’s implicit multiplication vs explicit multiplication. Implicit multiplication takes precedence over explicit division and explicit multiplication. It’s been stated by the American Mathematical Society and the American Physical Society says multiplication takes precedence over division in general. PEMDAS was created by an educator guys. Not some mathematical society, and it’s not a mathematical law. Since the beginning of time, implicit multiplication (multiplication by juxtaposition) has always had to be completed before anything else. I hate the fact people try to teach math on RU-vid and don’t even research before they do something.
im originally South African so im used to just call it B O D M A S B = Brackets First [()] O = Order of Operations [x², √xyz, etc] D = Division [÷ / ½] M = Multiplication [× / *] A = Addition [+] S = Subtraction [-]
You can use, but it just adds unnecessary extra work. It is necessary to use it when the operation in the parentheses can't be done (for example the addition of two different variables)
Her tutorial is wrong, the correct answer is 1 Because there is no sign of multiplication in the given. in pemdas rule, The parenthesis is also a multiplication even without a sign of multiplication but you can't change or replace it in multiplication sign. if you want to know how the answer became 1, here's the correct solution below. 16÷4(3+1) 16÷4(4) 16÷16 =1 If you confused, you can try it to solve in scientific calculator.
She did it correctly 4(4)=4x4 a single number in parentheses signifies multiplication not priority. I used Wolframalpha Cymath mathpapa symbolab and Microsoft math solver all confirm 16 is correct
You have to distribute the 4 across (3+1) 🤦🏾♂️🤦🏾♂️🤦🏾♂️. The answer is 1. PEMDAS is convention. Distribution is a mathematical law. 16÷4(3+1) = 16÷(4(4+1) = 16÷(4×4) = 1
Why do I remember an alternate rule where you have to multiply the number in front of the parenthesis then? Seriously, Idk why I’m thinking that. Eg. In this example, 4x3 and 4x1, then add?
Wrong. PEMDAS is only fit for primary school level maths. The answer is 1. Learn about the priority of juxtaposed multiplications. PEMDAS says 2a/2a = a² But 2a/2a = 1. Ask anyone who actually USES math professionally instead of just learning ridiculous rules by rote. THIS is the video you should be watching ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-lLCDca6dYpA.html
This is the day I’ve learned about the left to right rule. I was a algebra student and could’ve sworn my teacher skipped over this while teaching us PEMDAS. That or I have really bad memory
But why did you use addition first? It's second to the last, before Subtraction, i didn't get the logic for this one, since you mentioned earlier that pemdas is the proper ORDER we need to follow but you didn't follow it really.
Perhaps you'd all be better off asking ChatGPT instead of some random RU-vidr:- a) What is 16 ÷ 4(3 + 1) ChatGPT To solve the expression 16 ÷ 4(3 + 1), you need to follow the order of operations, which is often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). So, first, you should solve what's inside the parentheses: 3 + 1 = 4 Then, you multiply: 4(4) = 16 Finally, you divide: 16 ÷ 16 = 1 So, 16 ÷ 4(3 + 1) equals 1. ------------------------------------------------------------------------------------- Conversely:- What is 16 ÷ 4 x (3 + 1) ChatGPT To correctly solve the expression 16 ÷ 4 x (3 + 1), we follow the order of operations: Parentheses: Evaluate what's inside the parentheses. Multiplication and Division (from left to right). Addition and Subtraction (from left to right). So: Inside the parentheses, we have 3 + 1 = 4. Now, we perform the multiplication and division from left to right. We first divide 16 by 4: 16 ÷ 4 = 4 Now, we multiply the result by 4: 4 x 4 = 16 So, the result of the expression 16 ÷ 4 x (3 + 1) is 16. ------------------------------------------------------------------------------------- NOTE THE DIFFERENCE IN PRECEDDENCE BETWEEN EXPLICIT AND IMLICIT/JUXTAPOSED MULTIPLICATION.
@@kelanth462 The AI does it that way because that's the way mathematicians and engineers do it. Some RU-vid content creators (not all, thankfully) think they know better and do it differently - and are just perpetuating errors.
If you rewrite this as fractions it will give you a different answer. PEMDAS does not match the way formulas are solved in engineering and mathematics books. In those books multiplication is done before division. This is a very interesting subject.
@@pillowfromtpotreal They are the modern day British. Self-righteous and ignorant of others. Yes I realize that's a generalization but if it's true for close to 50% ... it's relatively good one. More importantly, they and more relevant to this conversation: 1.) They don't study mathematics to a high enough level 2.) They insist, without even listening, to the other point of view. 3.) Because someone taught them PEMDAS (and then later changed it to Order Of Operations), they think that the world followed. 4.) They spread LIES about it being formalized in 1917 or 14 or whatever -- the truth is that there is NO AGREED CONVENTION ___BUT___ if you bother to ready ISO-80000-2 it clearly says that expressions must be written such that misunderstanding is not possible, i.e. CONVENTION MUST BE AGREED PRIOR. And so on. 5.) Americans are now of the opinion that Google is the answer. Google can be wrong and DEFINITELY IS wrong ... just ask it to calculate "5!!" ... then look up a math book. The answer is 15 but NOT according to Google. 6.) Yes you went to the moon. And yes you were first. Big whoop. Half your population believes it's a hoax and 40% (I think) continues to think the world is flat. Do I really need to go on? If I was arguing with a learned mathematician, sure. But this is tik-tok/youtube gen-pop with no grounding in anything except "I wanna be rich and I don't want to go anything".
And that's exactly NOT what mathematicians, physicists and engineers do... and also all math books or papers. Also it's not what HP calculators do. PEMDAS is not the only rule. PEMDAS is used to teach kids. For mathematicians, the answer is 1. And also for my HP 10s.
From what I remember TI and cheaper calcs from certain companies (that use TI chips) use pure PEMDAS but even they have a big old warning in their manuals to add extra brackets around implied multiplication to get the correct answer
you can't prove why I should calculate from right to left! you also can't prove if it's a simple divide or a fraction bar. But I can prove to you that in some countries it is calculated that way and in other countries it is calculated differently
She's clearly US educated, i.e. deficient in math. Note the way that she writes X. Lack of cursive lettering. This is literally why people need to be (i) home-schooled. (ii) foreign schooled (e.g. Europe) (iii) have to retake math for science/engineering courses.
See, this is why I hate Math teachers. They taught me the PEMDAS rule, but they forgot to mention the “hidden rule”. So I’ve been doing it wrong for the past 30 years!
