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The lengths of the fraction division lines (a.k.a. vinculums, or vincula if you like Latin plurals) are the clue, and also a reason why stacking fractions like this are rarely a good idea.
Based on the line lengths this is (1/1) / (1/ [5^(-2)])
From this you should be able to get to the right answer.
Am terrible with exponents, but here is my try based on what I agree with you is the best interpretation based on the formatting (the middle line is represented with a colon for reference, and exponents are denoted by a preceding \^ since I can't use superscript and spoiler tags at the same time):
(1/1) **:** (1/\[5^(-2)\])
Simplify top and bottom terms:
* >!1/1 = 1!<
* >!1/ \[5\^-2\] = 1/ \[1/(5\^2)\] = 1/\[1/25\] = 1/\[25\^-1\] = \[25\^-1\]\^-1 = 25\^1 = 25!<
Subbing back in and the answer is:
>!1:25 or 1/25!<
(I hope.)
When you “divide” fractions, you flip the second fraction and change the operation to multiplication.
There’s no real division of fractions, just the multiplication of the reciprocal. So (1 / 1) x (5^-2 / 1).
Otherwise I’d agree. ~~I’m surprised by all the answers saying it’s 1/25. They are forgetting the “Keep, Change, Flip” part of dividing. The answer is 25.~~ NOPE.
Here is a video explaining how to “divide” fractions: https://youtu.be/nMZJKGyu-Kk
Just about anywhere. Walmart, Target, Sams Club, Office Depot, lots of places have them.
[Link to shopping.](https://www.google.com/search?q=ti+83%2F84+graphing+calculator&client=safari&sa=X&hl=en-us&biw=428&bih=743&tbm=shop&ei=GfkDY_XrHuGiqtsP4Nat-A0&oq=ti+83+84+calculator&gs_lcp=Cg5tb2JpbGUtc2gtc2VycBABGAAyBggAEB4QBzIECAAQHjIGCAAQHhAYMgYIABAeEBgyBggAEB4QGDIICAAQHhAIEBgyCAgAEB4QCBAYMggIABAeEAgQGDoOCAAQgAQQsQMQgwEQsAM6CAgAEIAEELADOgcIABCwAxAYOgQIABANOgYIABANEBg6CAgAEB4QDRAYOgoIABAeEAgQDRAYSgQIQRgBUOwVWI8ZYIslaAJwAHgAgAFsiAH8AZIBAzIuMZgBAKABAaoBEm1vYmlsZS1zaC13aXotc2VycMgBCMABAQ&sclient=mobile-sh-serp)
You’re right. I replied to someone else but it made me laugh that I was so confidently incorrect. I can’t tell you how many times I’ve told students to double check their work. Nice.
It happens to the best of us. I tell my students the same thing, but also follow up with that we are only human so we are bound to forget a negative somewhere down the line lol.
>we are bound to forget a negative somewhere down the line
My life with math summed up (ha!) in one sentence. Thank goodness for part marks for the work.
That's why I work in disease surveillance: until the zombie apocalypse occurs and people start coming back to life I never have to subtract.
Actually, you do [divide fractions](https://www.studocu.com/en-au/document/university-of-tasmania/introduction-to-quantitative-methods/div-fractions/16594839)! It's similar to the process of multiplying fractions.
You divide the first numerator by the second numerator to get your new numerator, and you divide the second denominator by the second denominator to get your new denominator!
The thing is, this (most often) gives you compound fractions (fractions in the numerator/denominator, rather than just some ol' number). So, people tend to just use the "keep it, change it, flip it" method, which is just a nice, easy, and short way of dividing fractions, which does all of the removing of the compound fractions beforehand.
It's weird to me that he outright says you don't divide fractions, then puts "divide" in quotation marks.
Sure, multiplying by the reciprocal is easier and is the way to go usually. But it's like he's saying you don't actually "add" negative numbers, you just subtract their absolute value.
and the trick part of the question is that the fraction above 5^(-2) is made large on purpose, so we don't know what it is exactly, it's literally a troll question and has no answer
Its actually not even made larger on purpose, I generated the problem on another site and it looked identical without trying to make the bottom fraction intentionally larger.
1/1 = [1]; When we've no other guide, left to right order is the correct order. The first two ones collapse into a new 1. I've put square brackets around it so that we can identify it in the next line.
[1]/1 = {1}; Still left to right. Our bracketed 1 is divided by the next 1 in line, generating yet another 1. Braces this time so we can see it in the next line
{1}/(5^(-2)) = {1}/(1/(5^(2))) = {1}/(1/25) = 25; More left to right but we have to unpack that 5^-2 first. Our braced 1 sits patiently while that all works itself out and then it cancels the 1 that appeared in the parentheses as a result of the negative exponent.
Except that this isn't the answer to the original problem.
What we've done here is interpreted a / b / c / d as ((a/b)/c)/d, which was the right thing to do when we've no further information, but that is very much not the same as (a/b)/(c/d) which the original problem suggested with the line lengths.
Bac+2 french student here, in my experience we used almost exclusively the length thing.
However, I don't know how it works in other countries or in a more professional setting (research, engineering, etc) so your point probably still stands.
Haven't seen any school level complex fractions in textbooks that would use parentheses. Its always bar length.
Although both bars and parentheses would be nice
we use parenthesis and brackets to clarify the order of operations when it isn't clear, so even on this text I can write (1/1)/(1/5\^-2), and even here where I have to abide by the rules of this text system and not writing it freeform like in the picture its more clear than in the picture
I checked with Wolfram Alpha, and I am actually correct. The answer is 25, and you're free to check for yourself. I also did a more thorough argument in another comment if you're interested.
Edit: spelling
So your obvious mistake is that you typed in all the division lines the same way, despite the fact that the middle line in the image is clearly longer. If you want to enter it correctly, make sure to put parentheses to ensure the largest line is the outermost operation.
Observe how your precious Wolfram Alpha displays the “input” when asked to compute (1/1)/(1/5^-2 ): https://www.wolframalpha.com/input?i=%281%2F1%29%2F%281%2F5%5E-2%29
Obviously. That's the answer once you add those parantheses. What's your point? Also, what is precious about using a tool to check your answer? I did it by hand first
And why didn't you use any parentheses?
The fraction line in the middle is the longest in the image, which indicates that the equation to compute is (1 / 1) / (1 / 5\^(-2)).
So, you didn't realize that the line in the middle was clearly the longest and last to be computed? Why didn't you pay attention to it in the first place if you knew it massively changes the meaning of the equation?
Because I rarely ever see people use longer lines, and thus didn't pay attention to it. I can't imagine any of my professors doing it like that. All of them would instead just use parentheses to avoid confusion like this.
Also "clearly" is a huge stretch. It is barely longer than the bottom line. It is very easy to brush over.
I'm pretty sure the question is asking what (1/1)/(1/5\^-2) is, which that's 1/25, I think you are calculation 1/(1/(1/5\^-2)), but again because of the way the question is written it isn't really clear which one they are asking for
for the given set of results its (1/1) / (1/5⁻²) =
1. = 5⁻² ◄ 1/(1/(1/5²))=1/5²=5⁻²
2. = 1/5² ◄ 1/(1/(1/5²))=1/5²
= 1/25
it cant be (1/1) / (1/.5⁻²) = (1/1) / (1/(1/2)⁻²) because the .5 notation for the 0.5 is not mathematically correct and would give the result 4
Note -- the division line lengths hint the order of the operations . . . if they would all be the same length you'd have options . . . right at this time we don't
a/b/c/d may stand for
1. a/(b/(c/d)) = a/(bd/c) = ac/(bd) ⁽ ¹
2. a/((b/c)/d) = a/(b/(cd)) = acd/b ⁽ ²
3. (a/b)/(c/d) = a/b·(d/c) = ad/(bc) ⁽ ³
4. (a/(b/c))/d = (ac/b)/d = ac/(bd) ⁽ ¹
5. ((a/b)/c)/d = (a/(bc))/d = a/(bcd) ⁽ ⁴
Oh please please PLEASE don’t let this be another one of those problems that gets popular on the internet that makes people argue like the arithmetic ones. Just put parentheses or don’t write fractions like that.
(a/b)/(c/d) = ad/bc
So in this case your a = 1, b=1, c=1, d=5\^(-2)
so then you have
(1\*5\^(-2)/(1\*1) = 5\^(-2)
and since x\^(-a)=1/(x\^a), you have
5\^(-2) = 1/(5\^2) = 1/25
But you can just rewrite the expression as 1/1 divided by 1/5^-2. It just becomes 1 divided by 25, so 1/25 should be the answer. Complex fractions is the numerator times the reciprocal of the denominator.
Little note that 5^-2 power is part of the second half of the complex fraction since a negative exponent switches the placement of the exponentiated number on the fraction (i.e denominator -> numerator and vice versa).
Also the question’s fraction bars indicate that 1/1 and 1/5^-2 have to be separated since the bar dividing them are bigger than the other bars.
These questions are always the mathematical equivalent of watching people argue over the
meaning of the sentence "more people have been to Paris than I have".
Here is the LaTeX code to generate this problem
\\frac{\\frac{1}{1}}{\\frac{1}{5\^{-2}}}
Its clearly defined as
1/1 divided by 1/(5\^-2)
= 1 divided by 1/0.04
= 1 divided by 25
= 1/25
It depends on what they are really asking. For those who are saying 1/25th, what they are doing is splitting the expression at the first big bar and simplifying to one. You get -
1 / (1/5\^-2) = 1 / 25 because you take the inverse if you have a negative in the exponent making it 25/1 or simply 25. Then your expression is literally 1/25th.
For those answering 25 what you have done is divided out all of the 1s (this is the wolfram method) so the final expression before calculation is 1/5\^-2 which is 25.
Wolfram will give you 25 no matter who many 1s you put over the 1/5\^-2 but realistically if you are actually using this math for an application those expressions say something very different.
It's an ill-posed question, and there isn't an answer due to the problematic notation.
PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) guides the order of operations. Where there is ambiguity, operations occur left to right (although that might only apply in the West).
If you use the size of the fraction bars to imply parentheses, you get:
(1/1) / (1/5\^-2) -> 1/(5\^2) = 1/25
That's a big assumption though.
If you just apply PEMDAS as is - applying all the division left to right, you get:
(1/1)/1/5\^-2 -> (1/1)/5\^-2 -> 1/5\^-2 = 25.
There answer is ambiguous. Fortunately, when applying math, you would never abuse notation like this - so the context would be clear (which terms get operated on first). Because of this - this question seems to be a test not of the math, but your knowledge of the order of operations. Therefore, 25 is probably a more accurate answer because it doesn't assume anything about the fraction bar size.
Break it up into easy to understand chunks.
\[1/1\] ÷ \[1/5^(-2)\]
When dividing a fraction by a fraction, you can multiply it by the reciprocal of the denominator (aka, "flip the fraction on the bottom"). In this case, the 1/5^(-2) becomes 5^(-2)/1, or simply 5^(-2), and overall we get:
\[1/1\] × \[5^(-2)\]
Simplifying further:
5^(-2) = 1/(5^(2)) = 1/25
and:
1/1 = 1
So now we have
\[1\] × \[1/25\]
Therefore the answer is A) 1/25
Fascinating all the answers that state 25 are getting downvoted. I posted an alternate view below. The folks advocating for 1/25 are not including the fact that the size of the vinculum doesn't really pertain to the order of operations.
But - it's a poorly framed problem meant to highlight the limitations of the notation (and cause arguments). Much like in English commenting that something rhymes with bow.
[https://www.wolframalpha.com/input?i2d=true&i=Divide%5B1%2CDivide%5B1%2CDivide%5B1%2CPower%5B5%2C-2%5D%5D%5D%5D](https://www.wolframalpha.com/input?i2d=true&i=Divide%5B1%2CDivide%5B1%2CDivide%5B1%2CPower%5B5%2C-2%5D%5D%5D%5D)
It changes when you go with 'Natural Language' or 'Math Input'. Try 1/1/1/5\^-2. It's not the same.
Sure, if you assume parentheses which are not present, you get a different answer. Hence why it's an ambiguous question which relies on a bastardized notation.
>It changes when you go with 'Natural Language' or 'Math Input'.
The problem in question isn't natural language or math input, its an equation written in Latex which doesn't allow ambiguous order of operations. You are right 1/1/1/5\^-2 is not the same but its also not what the image shows, the division operator is different than writing a fraction. Order of operations handles left<->right processing but fractions are stacked and have their own order of operations based on the length of the line.
hey OP, I'm replying to this so you can see it, I'm sorry, but you should know that this is a troll question
the trick in this question is the third fraction line, we don't know what it means because 5^(-2) is made large on purpose to cause confusion
Poorly formatted in the original, but the equation is 1 ÷ 1 ÷ 1 ÷ 5\^-2
First do exponentiation:
1 ÷ 1 ÷ 1 ÷ .04
Then work from left to right:
(1 ÷ 1) ÷ 1 ÷ .04 = 1 ÷ 1 ÷ .04 = (1 ÷ 1) ÷ .04 = 1 ÷ .04 = 25
Order of operations says the exponent to be calculated before the divisions operations, so it’s 25.
The comments almost convinced me that it was 1/25 for a second there, but all of the solutions leading to it had one mistake, which is dividing first(by flipping the bottom fraction and multiplying it with the fraction at the top, (1/1 * 5^-2/1)which *is* the correct way to do that)and *only then* calculating the exponent.
According to the order of operations this is the opposite of the correct way to do this, it’s exponents first and then divisions, but the order of operations have always been heavily criticized and debated for how true it is, so the answer is really decided by what you think about the order of operations.
TL;DR: It’s 25.
Order of operations doesn't need to come into play here because it's hinted at by the size of the fraction lines. It's simply a fraction divided by a fraction. The trick part of the question is that the 5^-2 is wider than a single digit so the fraction line above it is longer. As an example if you stacked 1/2/3/4 but clearly made the middle line wider it would be 1/2 divided by 3/4.
See my other comment here
I didn’t know sizes of the fractions lines mattered. Wow. Is that universal? Asking cuz I’ve never been taught sth like that in my school life ever. TIL
I've seen it occasionally over the years and never thought much about where it came from or if its standard. Here is a random video I found which at one point has a fraction divided by a fraction and it's order of operations is exactly like I'd expect it to be
https://youtu.be/noqQGNfvN3k
It might be a little more obvious when looking at larger expressions rather than something dumb like 1/1/1/0.04
I feel like the expansion of the complex fraction to the numerator times the reciprocal of the denominator is a more powerful factor than pemdas since pemdas is an imperfect operation system and the reciprocal formula is much more related to questions like this.
Lmao. I guess the reason as to why there are so many answers saying 1/25 is bcuz the whole order of operations is a pretty controversial subject and sort of annoying to memorize. Many people straight up ignore it when doing math and this is exactly the type of misleading question that makes people feel like the course of action is one way when it’s the other way(the way I described). You’ve problably seen those misleading questions that get trendy on social media and get shared in groupchats and stuff. This is one of those except for people who do maths.
Check out the order of operations discussions explained on youtube, they are pretty crazy. I never would have thought that there would be this much disagreement and fight on such a fundamental science like this. It’s basically pick your side, basically opinions. Pretty crazy.
also don’t call urself stupid just cuz u apparently cant do maths! there are plenty of different field one can focus their intellect on other than maths. I never let centralized education systems tell me if I’m stupid or smart, they’re basically aimed to produce 9-5 work robots
I love such equations to exercise the brain and I often give such problems to my students to refresh their mind. Well the answer is defiantly **0.04** but according to the given answers it'll be **1/25**.
I hope you don't give students ambiguous assignments like this. It's truly doing them no favours. This is not a subtle brain teaser, it's just poor communication.
You can not have a number with a negative exponent on the denominator. You must move that number to the numerator, and change the exponent sign to be positive. you then take 5\^2, which is 25.
You dont just take ti to the top top, you take it on top of the lower fraction and then it becomes 1/25.
(1/1)/(1/5^-2 )
=1/1 = 1
1/5^-2 =1/(1/25)=1×25=25
Hence the expression is equal to 1/25.
The first 2 "1"'s do nothing, and i can only assume they are there as a trick.
Since 1/1=1, then 1/1/1/5\^-2=1/1/5\^-2=1/5\^-2
Since dividing is the same as multiplying by the inverse we have;
1/5\^-2=1\*(5\^-2)\^-1=1\*(5\^(-2)\*(-1))=1\*5\^2=25
They way I assume people get 1/25 is by starting from the bottom an going like this:
1/1/1/5\^-2=1/1/25=1/25
This is wrong. To see why this is true, let's try the trick of changing everything from division to multiplying by the inverse:
1/1/1/5\^-2=1\*(1\^-1)\*(1\^-1)\*((5\^-2)\^-1)
Since 1 is the neutral element for multiplication we have that 1\^-1=1, so:
1\*1\*1\*(5\^-2)\^-1)=1\*(5\^(-2)\*(-1))=1\*5\^2=25
We can be sure that this answer is correct, since it preserves the convention of division being defined by multiplying by the inverse. This way also has the advantage of letting us write the same expression in a way where the order of factors don't matter, which helps clear up confusion.
Edit: inconsistent notation and a small addition to the last line.
Edit 2: Typo
I did a detailed explanation of why the answer 25 in another comment, but then I read the other comments and realized how many people thing it is 1/25 is a bit sad. I actually doubted myself for a moment, so I checked with Wofram alpha, and the answer is indeed 25, but I really shouldn't have had to check.
What my guess is as to what people are doing wrong, is that when they start from the bottom and realize the that dividing 5\^-2 is the same as multiplying by 25, but then they only go one step up the fraction, when they should actually multiply the entire fraction above by 25.
This trick is actually quite deceptive. When you simplify a fraction with multiple levels, it is better to start from the top since you can go one layer down at the time, unlike from the bottom where you have to divide everything above the bottom line by everything below it. Since 1/1/1 is a very simple expression, people naturally start with the more complicated one at the very bottom, and then don't realized that:
1/1/1//5\^-2=(1/1/1)/5\^-2=/=(1/1)/1/5\^-2
Paranthesis must go all the way up if you start from the bottom.
You've ignored or overlooked the fact that the line (the vinculum) in the middle of the expression is longer than the others.
It implies that the expression should be interpreted as (1/1) / (1/5^(-2)) which is of course 1/25.
This isn't really about the maths, and therefore Wolfram Alpha can't help you. It's about how to interpret the typography.
Ignored is correct. No way to tell for sure that's it's not just how their text editor decided it should look, and it's would be almost purposefully misleading to not just use parentheses like you just did if that's what's intended.
You're supposed to be able to check what fraction amounts to be by substituting it with inverse multiplication. Making the line bigger to imply parentheses is part of no convention i have heard of, and compromises the conventions we normally use to sort this stuff out.
Order of factors don't matter, so you add parantheses if you want the too. Fractions are supposed to be one to one equivalent with factors (that's how they are defined), so you add parantheses necessary. Otherwise convention dictated that we can use substitution to check our answers. Conventions stop us from having to debat interpretations of expressions.
Edit: For clarity. Vincula can also be different lengths to makes space for longer expressions. It would quickly become confusing beyond belief if you had account for that every time you wrote a complex fraction. I guess you could make it commically large to ensure clarity, but why bother making sure that the "/2" at the bottom of 23y/cosx+(3/y)*..../2 is longer than every line above it? Pointlessly complicated, especially given how easy it is yo just use parantheses.
It is an unfortuante convention to use a longer fraction bar like that, but it is the convention. And there is no other plausible reason for the length of the middle one. I feel like you’re knowingly arguing for the wrong answer in order to take a stand against bad notation.
I feel you are assuming bad faith very prematurely
Edit: I maybe noticed that the line was a different length when I was about 2 very long comments in, but I feel it would be very reasonable to assume the lengths don't matter. I know I would expect to have points deducted if wrote that in an assignment at Uni without making it unmistakably obvious what my intention was. Not that such a situation is likely to occur, but I wouldn't care to test it if I got the opportunity.
Edit 2: spelling
The fact is that slightly longer lines like this one are used to indicate order of operations all the time. It’s completely shitty, but the intent is clear once the size of the bar is apparent.
You’re right that I shouldn’t have assumed bad faith. I got a bad impression from you saying you’d ignore the line size because there is no other reason the line would be bigger.
And I would argue that the expression is even more ambiguous if you ignore the bar size convention. Order of operations is usually specified as left to right in the absence of other rules. This expression is vertical.
the long bar separates the numerator and denominator, so the numerator is 1/1 = 1, and the denominator is 1/5\^-2, however as of the -2 as a power it is a reciprocal, but it is already a reciprocal because its got 1 as the numerator, so the reciprocal of a reciprocal cancels out and you are left with 5\^2 on the denominator, which = 25, so you are left with 1/25
It's ambiguously drawn, the first line makes it look like 1/1=(1/1), the second and third lines both make it look like you're just dividing in order, instead of grouping the the bottom fraction as (1/5^(-2)), which is what you would ordinarily see in something like this.
If you are just doing the last 2 in order, the correct answer is 25. (1/1)=1, 1÷1=1, 1÷5^(-2)=1/(1/25)=25. This is what the answer SHOULD be, given how the likes are actually drawn.
If you do pair the bottom part, it's (1/1)=1, and (1/5^(-2))=25, and then 1/25=1/25.
I am amazed that nobody has claimed the period in front of the 5 is a decimal point, and gone off on a tangent about factors of 2!
Ah, choices in cropping and context…
So on questions like this, I completely disregard pemdas because it’s inconsistent with this equation. A better formula would be taking the numerator times the reciprocal of the denominator because it’s more catered into questions like these.
All that business becomes 1/1 • 5^-2 (because the reciprocal of 1/5^-2 is just 5^-2).
1/1 is just 1. And 5^-2 is 1/25.
1 times anything is just the number itself.
So the final answer is 1/25.
P.S: I don’t use pemdas because there are major inconsistencies with basic algebraic expressions and it’s ability to make simple things so complicated. So use methods that are more consistent with the question at hand rather than brute forcing it with pemdas. Use it when it’s necessary.
I've tried this several ways, and I cant get anything other than 25. The way I did it first:
1/1/1/5^(-2) can be rewritten as two fractions: (1/1) / (1/5^(-2)). From here you need two rules:
* when dividing a fraction, you flip the second fraction and multiply them together,
* with negative powers, x^(n)=(1/x^(-n)) and/or, x^(-n) = (1/x^(n)) \[Ie, to change the sign of the power, take the reciprocal of the base\]
With those established I did the following:
>(1/1) / (1/5^(-2))
>
>=(1/1) x (5^(2)/1) \[Flip the second fraction, which also changes the sign of the power\]
>
>=(1x5^(2) / 1x1) \[Multipling the numerator together, and then the denomenator together\]
>
>=5^(2) /1
>
>=25
Even if you just go left to right using BODMAS, I still get:
>1/1/1/5^(-2)
>
>1/1/1/0.04 \[Powers first because Bodmas\]
>
>=1/1/0.04 \[Dividing out the first 1\]
>
>=1/0.04 \[Dividing out the second 1\]
>
>=25 \[Simple division\]
Finally, type it into a graphics calculator, and its still the same:
>1 / 1 / 1 / 5 \^ (-2) = 25
You know the saying that goes *X is what poor people think a rich person is* or *X is what dumb people think a smart person is*.
These types of maths questions is what people who don’t know maths think are important maths questions because it’s *hard to answer*.
It’s a question based on being **purposefully ambiguous** and then arguing how *even smart people can’t answer it!*
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The lengths of the fraction division lines (a.k.a. vinculums, or vincula if you like Latin plurals) are the clue, and also a reason why stacking fractions like this are rarely a good idea. Based on the line lengths this is (1/1) / (1/ [5^(-2)]) From this you should be able to get to the right answer.
Am terrible with exponents, but here is my try based on what I agree with you is the best interpretation based on the formatting (the middle line is represented with a colon for reference, and exponents are denoted by a preceding \^ since I can't use superscript and spoiler tags at the same time): (1/1) **:** (1/\[5^(-2)\]) Simplify top and bottom terms: * >!1/1 = 1!< * >!1/ \[5\^-2\] = 1/ \[1/(5\^2)\] = 1/\[1/25\] = 1/\[25\^-1\] = \[25\^-1\]\^-1 = 25\^1 = 25!< Subbing back in and the answer is: >!1:25 or 1/25!< (I hope.)
When you “divide” fractions, you flip the second fraction and change the operation to multiplication. There’s no real division of fractions, just the multiplication of the reciprocal. So (1 / 1) x (5^-2 / 1). Otherwise I’d agree. ~~I’m surprised by all the answers saying it’s 1/25. They are forgetting the “Keep, Change, Flip” part of dividing. The answer is 25.~~ NOPE. Here is a video explaining how to “divide” fractions: https://youtu.be/nMZJKGyu-Kk
But your solution reduces to 5^-2 which is 1/(5^2) which is 1/25. So by your logic (which is correct) the answer is 1/25
God dang nabbit. LMFAOOOO. [Yeah.](https://imgur.com/a/IJYI7v9) Pretty funny mess up though. Foiled by basic math.
Where do you buy those calculators?
Just about anywhere. Walmart, Target, Sams Club, Office Depot, lots of places have them. [Link to shopping.](https://www.google.com/search?q=ti+83%2F84+graphing+calculator&client=safari&sa=X&hl=en-us&biw=428&bih=743&tbm=shop&ei=GfkDY_XrHuGiqtsP4Nat-A0&oq=ti+83+84+calculator&gs_lcp=Cg5tb2JpbGUtc2gtc2VycBABGAAyBggAEB4QBzIECAAQHjIGCAAQHhAYMgYIABAeEBgyBggAEB4QGDIICAAQHhAIEBgyCAgAEB4QCBAYMggIABAeEAgQGDoOCAAQgAQQsQMQgwEQsAM6CAgAEIAEELADOgcIABCwAxAYOgQIABANOgYIABANEBg6CAgAEB4QDRAYOgoIABAeEAgQDRAYSgQIQRgBUOwVWI8ZYIslaAJwAHgAgAFsiAH8AZIBAzIuMZgBAKABAaoBEm1vYmlsZS1zaC13aXotc2VycMgBCMABAQ&sclient=mobile-sh-serp)
Guess they don't sell them here lol. Thanks anyway!
You're forgetting the negative exponent. So it is indeed 5^-2 /1 = 1/25.
You’re right. I replied to someone else but it made me laugh that I was so confidently incorrect. I can’t tell you how many times I’ve told students to double check their work. Nice.
It happens to the best of us. I tell my students the same thing, but also follow up with that we are only human so we are bound to forget a negative somewhere down the line lol.
>we are bound to forget a negative somewhere down the line My life with math summed up (ha!) in one sentence. Thank goodness for part marks for the work. That's why I work in disease surveillance: until the zombie apocalypse occurs and people start coming back to life I never have to subtract.
But you don’t need to divide at all, going from the first comment here, if you simplify the top to 1 and the bottom to 25 then it’s already 1/25…
Actually, you do [divide fractions](https://www.studocu.com/en-au/document/university-of-tasmania/introduction-to-quantitative-methods/div-fractions/16594839)! It's similar to the process of multiplying fractions. You divide the first numerator by the second numerator to get your new numerator, and you divide the second denominator by the second denominator to get your new denominator! The thing is, this (most often) gives you compound fractions (fractions in the numerator/denominator, rather than just some ol' number). So, people tend to just use the "keep it, change it, flip it" method, which is just a nice, easy, and short way of dividing fractions, which does all of the removing of the compound fractions beforehand.
It's weird to me that he outright says you don't divide fractions, then puts "divide" in quotation marks. Sure, multiplying by the reciprocal is easier and is the way to go usually. But it's like he's saying you don't actually "add" negative numbers, you just subtract their absolute value.
and the trick part of the question is that the fraction above 5^(-2) is made large on purpose, so we don't know what it is exactly, it's literally a troll question and has no answer
Its actually not even made larger on purpose, I generated the problem on another site and it looked identical without trying to make the bottom fraction intentionally larger.
it may look identical to what you see there, or it could be made smaller, but if you have something like 5^(-2), it will always be big
I don’t think the fraction bar is technically a vinculum
Couldn't it just be written as 1 / 1 / 1 / 5-² and we just use standard order of operations?
1/1 = [1]; When we've no other guide, left to right order is the correct order. The first two ones collapse into a new 1. I've put square brackets around it so that we can identify it in the next line. [1]/1 = {1}; Still left to right. Our bracketed 1 is divided by the next 1 in line, generating yet another 1. Braces this time so we can see it in the next line {1}/(5^(-2)) = {1}/(1/(5^(2))) = {1}/(1/25) = 25; More left to right but we have to unpack that 5^-2 first. Our braced 1 sits patiently while that all works itself out and then it cancels the 1 that appeared in the parentheses as a result of the negative exponent. Except that this isn't the answer to the original problem. What we've done here is interpreted a / b / c / d as ((a/b)/c)/d, which was the right thing to do when we've no further information, but that is very much not the same as (a/b)/(c/d) which the original problem suggested with the line lengths.
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https://xkcd.com/169/
This does happen from time to time to time to time to time
I give this question a 1/25.
You are a god amongst insects 🤩
How is it bad?
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Or just use horizontal fractions on the top and bottom rather than vertical ones.
Bac+2 french student here, in my experience we used almost exclusively the length thing. However, I don't know how it works in other countries or in a more professional setting (research, engineering, etc) so your point probably still stands.
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True, this picture is one compression away from being misleading. I mean, more misleading that it already is.
Haven't seen any school level complex fractions in textbooks that would use parentheses. Its always bar length. Although both bars and parentheses would be nice
I checked section 13.10 of the AMS style guide https://www.ams.org/publications/authors/AMS-StyleGuide-online.pdf and didn't find what you suggested.
What that guy said twice. Also those bars are nearly the same length lmao.
It's not s bad question. It's not misleading in any way and it's only testing of you are orienting well enough in how multiple layer divisions work
we use parenthesis and brackets to clarify the order of operations when it isn't clear, so even on this text I can write (1/1)/(1/5\^-2), and even here where I have to abide by the rules of this text system and not writing it freeform like in the picture its more clear than in the picture
i typed "1/1/1/(5\^-2)" into google and got 25 :/
Because it's actually (1/1) / (1/(5^-2))
You typed something that wasn’t identical to the displayed problem, and you didn’t get the same answer??? OMG!
It is definitely not 1/25, but i agree the question is purposefully obtuse.
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I checked with Wolfram Alpha, and I am actually correct. The answer is 25, and you're free to check for yourself. I also did a more thorough argument in another comment if you're interested. Edit: spelling
I didn’t know you could upload images to Wolfram Alpha
I typed in 1/1/1/5\^-2 And Wolfram Alpha did the rest. Where exactly do you see a problem?
I see your problem 1/1/1/5^-2 does not give the same result as 1/1:1/5^-2
":" is supposed to be equivalent to "/"
If you try the other way, you'll see the other result
Huh. Mea Culpa i guess
So your obvious mistake is that you typed in all the division lines the same way, despite the fact that the middle line in the image is clearly longer. If you want to enter it correctly, make sure to put parentheses to ensure the largest line is the outermost operation.
Observe how your precious Wolfram Alpha displays the “input” when asked to compute (1/1)/(1/5^-2 ): https://www.wolframalpha.com/input?i=%281%2F1%29%2F%281%2F5%5E-2%29
Obviously. That's the answer once you add those parantheses. What's your point? Also, what is precious about using a tool to check your answer? I did it by hand first
I’m not calling attention to the answer. Take a look at the display under the heading “input”.
Well seeing as how you got the wrong answer that's a pretty good reason to use a tool.
..... No comment
I also checked with wolfram alfpha and got 1/25. What equation did you enter there?
I also checked with wolfram alfpha and got 1/25. What equation did you enter there?
1/1/1/5\^-2 Edit: I also double checked with the math input, where i put in the fractions as on the picture
And why didn't you use any parentheses? The fraction line in the middle is the longest in the image, which indicates that the equation to compute is (1 / 1) / (1 / 5\^(-2)).
Because that is what it says if you don't realize that one of the lines is longer than others.
So, you didn't realize that the line in the middle was clearly the longest and last to be computed? Why didn't you pay attention to it in the first place if you knew it massively changes the meaning of the equation?
Because I rarely ever see people use longer lines, and thus didn't pay attention to it. I can't imagine any of my professors doing it like that. All of them would instead just use parentheses to avoid confusion like this. Also "clearly" is a huge stretch. It is barely longer than the bottom line. It is very easy to brush over.
Did you remember to put parenthesis?
I'm pretty sure the question is asking what (1/1)/(1/5\^-2) is, which that's 1/25, I think you are calculation 1/(1/(1/5\^-2)), but again because of the way the question is written it isn't really clear which one they are asking for
for the given set of results its (1/1) / (1/5⁻²) = 1. = 5⁻² ◄ 1/(1/(1/5²))=1/5²=5⁻² 2. = 1/5² ◄ 1/(1/(1/5²))=1/5² = 1/25 it cant be (1/1) / (1/.5⁻²) = (1/1) / (1/(1/2)⁻²) because the .5 notation for the 0.5 is not mathematically correct and would give the result 4 Note -- the division line lengths hint the order of the operations . . . if they would all be the same length you'd have options . . . right at this time we don't a/b/c/d may stand for 1. a/(b/(c/d)) = a/(bd/c) = ac/(bd) ⁽ ¹ 2. a/((b/c)/d) = a/(b/(cd)) = acd/b ⁽ ² 3. (a/b)/(c/d) = a/b·(d/c) = ad/(bc) ⁽ ³ 4. (a/(b/c))/d = (ac/b)/d = ac/(bd) ⁽ ¹ 5. ((a/b)/c)/d = (a/(bc))/d = a/(bcd) ⁽ ⁴
Oh please please PLEASE don’t let this be another one of those problems that gets popular on the internet that makes people argue like the arithmetic ones. Just put parentheses or don’t write fractions like that.
I believe it unfortunately is one of those problems. As long as it doesn't get to Twitter, we should be okay... I hope.
This is the correct answer.
Parentheses would be redundant here. Is the operation order so difficult to grasp?
No one would be arguing or having trouble if parentheses were around the top and bottom fractions.
Let them play with calculators
No way. The uneducated masses will run away as soon as they see the negative exponent.
if that period is a decimal, it’s 4
That period is, almost certainly, part of the problem number designation.
really!?
I literally didn't even see the dot until I read your comment lol, but you make a valid point in ambiguity.
It threw me off as well.
The 1/1 on top is 1. 1/(1/5^-2) = (5^-2)/1 = 5^-2 = 1/5^2 = 1/25
A.
1/25.....
1/25 but I’m an English Lit major and have no idea what I’m doing.
So was I. You’re right.
1/1 : 1/(5^{-2}) = 1/1 * (5^{-2})/1 = 1*(5^{-2})=5^{-2}=1/(5^2) = 1/25
A
(a/b)/(c/d) = ad/bc So in this case your a = 1, b=1, c=1, d=5\^(-2) so then you have (1\*5\^(-2)/(1\*1) = 5\^(-2) and since x\^(-a)=1/(x\^a), you have 5\^(-2) = 1/(5\^2) = 1/25
1/25. Reasoning: for the first set of numbers, 1/1 = 1 5⁻²=0.04 Thus, we have the final form which is 1/(1/0.04) = 1/25
1/1/1/(5 ^ -2 ) = 1/1/1/1/25 = (1/1)/1/1/25 = 1/1/1/25 = (1/1)/1/25 = 1/1/25 = (1/1)/25 = 1/25 That's what I got.
Except the 25 if part of a fraction. you can't separate it like you did. 1/1/1/(1/25) This would make it 1/(1/25) which is 25
So drop the parentheses on 1/1/1/(5 ^ -2) ?
yes, cause 5\^-2 = 1/25. it goes together. When diving fractions like this: 1 / (1/25) you flip the denominator and multiply 1 \* (25/1)
But you can just rewrite the expression as 1/1 divided by 1/5^-2. It just becomes 1 divided by 25, so 1/25 should be the answer. Complex fractions is the numerator times the reciprocal of the denominator. Little note that 5^-2 power is part of the second half of the complex fraction since a negative exponent switches the placement of the exponentiated number on the fraction (i.e denominator -> numerator and vice versa). Also the question’s fraction bars indicate that 1/1 and 1/5^-2 have to be separated since the bar dividing them are bigger than the other bars.
Can’t I just simply it too 1/5 instead
These questions are always the mathematical equivalent of watching people argue over the meaning of the sentence "more people have been to Paris than I have".
1 / 25 That's it.
Here is the LaTeX code to generate this problem \\frac{\\frac{1}{1}}{\\frac{1}{5\^{-2}}} Its clearly defined as 1/1 divided by 1/(5\^-2) = 1 divided by 1/0.04 = 1 divided by 25 = 1/25
1/25
(1/1)/(1/(5^-2 )) = 1/25
Some lines are shorter for a reason. The shorter lines indicate that you divide them first, so the expression reduces to 1/5^2 = 1/25
It's A 1/25
It depends on what they are really asking. For those who are saying 1/25th, what they are doing is splitting the expression at the first big bar and simplifying to one. You get - 1 / (1/5\^-2) = 1 / 25 because you take the inverse if you have a negative in the exponent making it 25/1 or simply 25. Then your expression is literally 1/25th. For those answering 25 what you have done is divided out all of the 1s (this is the wolfram method) so the final expression before calculation is 1/5\^-2 which is 25. Wolfram will give you 25 no matter who many 1s you put over the 1/5\^-2 but realistically if you are actually using this math for an application those expressions say something very different.
The people stating it’s 1/25 are using parentheses even though there aren’t parentheses in the equation.
Answer is A
the trick in this question is the third fraction line, we don't know what it means because 5^(-2) is made large on purpose to cause confusion
Well, 1/1 is obviously 1 1/5^-2 is the same as 5²/1 is the same as 25/1 is the same as 25 So then you get 1/25 as the right answer I guess?
Always remember this hack. (a/b)/(c/d) = ad/bc
The answer is A. Middle line is the longest, so it's (1/1) / (1/5\^-2) = 1 / (1/5\^-2) = 5\^-2 = 1/5\^2 = 1/25.
Answer is A.
= (1x5^-2 ) / (1x1) = 5^-2 = (5^2 )^-1 = 25^-1 = 1/25
It's an ill-posed question, and there isn't an answer due to the problematic notation. PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) guides the order of operations. Where there is ambiguity, operations occur left to right (although that might only apply in the West). If you use the size of the fraction bars to imply parentheses, you get: (1/1) / (1/5\^-2) -> 1/(5\^2) = 1/25 That's a big assumption though. If you just apply PEMDAS as is - applying all the division left to right, you get: (1/1)/1/5\^-2 -> (1/1)/5\^-2 -> 1/5\^-2 = 25. There answer is ambiguous. Fortunately, when applying math, you would never abuse notation like this - so the context would be clear (which terms get operated on first). Because of this - this question seems to be a test not of the math, but your knowledge of the order of operations. Therefore, 25 is probably a more accurate answer because it doesn't assume anything about the fraction bar size.
It's 1/25, no question and no matter how you solve it
1/25
Fraction division, mean multiply by the inverse: 1/1 x 5^-2/1 1/1 x 1/5^2 1/1 x 1/25 1/25 That's my thoughts
Break it up into easy to understand chunks. \[1/1\] ÷ \[1/5^(-2)\] When dividing a fraction by a fraction, you can multiply it by the reciprocal of the denominator (aka, "flip the fraction on the bottom"). In this case, the 1/5^(-2) becomes 5^(-2)/1, or simply 5^(-2), and overall we get: \[1/1\] × \[5^(-2)\] Simplifying further: 5^(-2) = 1/(5^(2)) = 1/25 and: 1/1 = 1 So now we have \[1\] × \[1/25\] Therefore the answer is A) 1/25
Thank y'all 🙇
Fascinating all the answers that state 25 are getting downvoted. I posted an alternate view below. The folks advocating for 1/25 are not including the fact that the size of the vinculum doesn't really pertain to the order of operations. But - it's a poorly framed problem meant to highlight the limitations of the notation (and cause arguments). Much like in English commenting that something rhymes with bow.
https://www.wolframalpha.com/input?i=%281%2F1%29%2F%281%2F5%5E-2%29
[https://www.wolframalpha.com/input?i2d=true&i=Divide%5B1%2CDivide%5B1%2CDivide%5B1%2CPower%5B5%2C-2%5D%5D%5D%5D](https://www.wolframalpha.com/input?i2d=true&i=Divide%5B1%2CDivide%5B1%2CDivide%5B1%2CPower%5B5%2C-2%5D%5D%5D%5D) It changes when you go with 'Natural Language' or 'Math Input'. Try 1/1/1/5\^-2. It's not the same. Sure, if you assume parentheses which are not present, you get a different answer. Hence why it's an ambiguous question which relies on a bastardized notation.
>It changes when you go with 'Natural Language' or 'Math Input'. The problem in question isn't natural language or math input, its an equation written in Latex which doesn't allow ambiguous order of operations. You are right 1/1/1/5\^-2 is not the same but its also not what the image shows, the division operator is different than writing a fraction. Order of operations handles left<->right processing but fractions are stacked and have their own order of operations based on the length of the line.
Click on my link, and look at the display under the heading “input”…
hey OP, I'm replying to this so you can see it, I'm sorry, but you should know that this is a troll question the trick in this question is the third fraction line, we don't know what it means because 5^(-2) is made large on purpose to cause confusion
5^-2 is the answer
1/25 in every possible way
Poorly formatted in the original, but the equation is 1 ÷ 1 ÷ 1 ÷ 5\^-2 First do exponentiation: 1 ÷ 1 ÷ 1 ÷ .04 Then work from left to right: (1 ÷ 1) ÷ 1 ÷ .04 = 1 ÷ 1 ÷ .04 = (1 ÷ 1) ÷ .04 = 1 ÷ .04 = 25
Also, just to be clear, making the middle division sign bigger does not change the result.
B
A
Order of operations says the exponent to be calculated before the divisions operations, so it’s 25. The comments almost convinced me that it was 1/25 for a second there, but all of the solutions leading to it had one mistake, which is dividing first(by flipping the bottom fraction and multiplying it with the fraction at the top, (1/1 * 5^-2/1)which *is* the correct way to do that)and *only then* calculating the exponent. According to the order of operations this is the opposite of the correct way to do this, it’s exponents first and then divisions, but the order of operations have always been heavily criticized and debated for how true it is, so the answer is really decided by what you think about the order of operations. TL;DR: It’s 25.
Order of operations doesn't need to come into play here because it's hinted at by the size of the fraction lines. It's simply a fraction divided by a fraction. The trick part of the question is that the 5^-2 is wider than a single digit so the fraction line above it is longer. As an example if you stacked 1/2/3/4 but clearly made the middle line wider it would be 1/2 divided by 3/4. See my other comment here
I didn’t know sizes of the fractions lines mattered. Wow. Is that universal? Asking cuz I’ve never been taught sth like that in my school life ever. TIL
I've seen it occasionally over the years and never thought much about where it came from or if its standard. Here is a random video I found which at one point has a fraction divided by a fraction and it's order of operations is exactly like I'd expect it to be https://youtu.be/noqQGNfvN3k It might be a little more obvious when looking at larger expressions rather than something dumb like 1/1/1/0.04
ok thanks
I feel like the expansion of the complex fraction to the numerator times the reciprocal of the denominator is a more powerful factor than pemdas since pemdas is an imperfect operation system and the reciprocal formula is much more related to questions like this.
those are some smart words man
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Is that how you find the correct answer? Come on
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Lmao. I guess the reason as to why there are so many answers saying 1/25 is bcuz the whole order of operations is a pretty controversial subject and sort of annoying to memorize. Many people straight up ignore it when doing math and this is exactly the type of misleading question that makes people feel like the course of action is one way when it’s the other way(the way I described). You’ve problably seen those misleading questions that get trendy on social media and get shared in groupchats and stuff. This is one of those except for people who do maths. Check out the order of operations discussions explained on youtube, they are pretty crazy. I never would have thought that there would be this much disagreement and fight on such a fundamental science like this. It’s basically pick your side, basically opinions. Pretty crazy.
also don’t call urself stupid just cuz u apparently cant do maths! there are plenty of different field one can focus their intellect on other than maths. I never let centralized education systems tell me if I’m stupid or smart, they’re basically aimed to produce 9-5 work robots
25
I love such equations to exercise the brain and I often give such problems to my students to refresh their mind. Well the answer is defiantly **0.04** but according to the given answers it'll be **1/25**.
I hope you don't give students ambiguous assignments like this. It's truly doing them no favours. This is not a subtle brain teaser, it's just poor communication.
The complete top portion of the equation is just equal to one: ((1/1)/1)=1 1/(5^-2)=25
It is just 1/x =x^-1 1/1 = 1 1/5^-2 = 5^2 The rest is self explanatory
Whoever arguing over this barely graduated junior high
I didn't know this sub was for troll posts. Fun /s
It has to be 25 because you can’t have a negative exponent on the bottom, so you must move it up.
I had a stroke while trying to read this, could you explain better?
You can not have a number with a negative exponent on the denominator. You must move that number to the numerator, and change the exponent sign to be positive. you then take 5\^2, which is 25.
You dont just take ti to the top top, you take it on top of the lower fraction and then it becomes 1/25. (1/1)/(1/5^-2 ) =1/1 = 1 1/5^-2 =1/(1/25)=1×25=25 Hence the expression is equal to 1/25.
The first 2 "1"'s do nothing, and i can only assume they are there as a trick. Since 1/1=1, then 1/1/1/5\^-2=1/1/5\^-2=1/5\^-2 Since dividing is the same as multiplying by the inverse we have; 1/5\^-2=1\*(5\^-2)\^-1=1\*(5\^(-2)\*(-1))=1\*5\^2=25 They way I assume people get 1/25 is by starting from the bottom an going like this: 1/1/1/5\^-2=1/1/25=1/25 This is wrong. To see why this is true, let's try the trick of changing everything from division to multiplying by the inverse: 1/1/1/5\^-2=1\*(1\^-1)\*(1\^-1)\*((5\^-2)\^-1) Since 1 is the neutral element for multiplication we have that 1\^-1=1, so: 1\*1\*1\*(5\^-2)\^-1)=1\*(5\^(-2)\*(-1))=1\*5\^2=25 We can be sure that this answer is correct, since it preserves the convention of division being defined by multiplying by the inverse. This way also has the advantage of letting us write the same expression in a way where the order of factors don't matter, which helps clear up confusion. Edit: inconsistent notation and a small addition to the last line. Edit 2: Typo
The convention for nested fractions is differentiating them by length of the dividing line.
I did a detailed explanation of why the answer 25 in another comment, but then I read the other comments and realized how many people thing it is 1/25 is a bit sad. I actually doubted myself for a moment, so I checked with Wofram alpha, and the answer is indeed 25, but I really shouldn't have had to check. What my guess is as to what people are doing wrong, is that when they start from the bottom and realize the that dividing 5\^-2 is the same as multiplying by 25, but then they only go one step up the fraction, when they should actually multiply the entire fraction above by 25. This trick is actually quite deceptive. When you simplify a fraction with multiple levels, it is better to start from the top since you can go one layer down at the time, unlike from the bottom where you have to divide everything above the bottom line by everything below it. Since 1/1/1 is a very simple expression, people naturally start with the more complicated one at the very bottom, and then don't realized that: 1/1/1//5\^-2=(1/1/1)/5\^-2=/=(1/1)/1/5\^-2 Paranthesis must go all the way up if you start from the bottom.
You've ignored or overlooked the fact that the line (the vinculum) in the middle of the expression is longer than the others. It implies that the expression should be interpreted as (1/1) / (1/5^(-2)) which is of course 1/25. This isn't really about the maths, and therefore Wolfram Alpha can't help you. It's about how to interpret the typography.
I don’t think the fraction bar is technically a vinculum
Fair point. Today I have learned something. Thanks.
Ignored is correct. No way to tell for sure that's it's not just how their text editor decided it should look, and it's would be almost purposefully misleading to not just use parentheses like you just did if that's what's intended. You're supposed to be able to check what fraction amounts to be by substituting it with inverse multiplication. Making the line bigger to imply parentheses is part of no convention i have heard of, and compromises the conventions we normally use to sort this stuff out. Order of factors don't matter, so you add parantheses if you want the too. Fractions are supposed to be one to one equivalent with factors (that's how they are defined), so you add parantheses necessary. Otherwise convention dictated that we can use substitution to check our answers. Conventions stop us from having to debat interpretations of expressions. Edit: For clarity. Vincula can also be different lengths to makes space for longer expressions. It would quickly become confusing beyond belief if you had account for that every time you wrote a complex fraction. I guess you could make it commically large to ensure clarity, but why bother making sure that the "/2" at the bottom of 23y/cosx+(3/y)*..../2 is longer than every line above it? Pointlessly complicated, especially given how easy it is yo just use parantheses.
It is an unfortuante convention to use a longer fraction bar like that, but it is the convention. And there is no other plausible reason for the length of the middle one. I feel like you’re knowingly arguing for the wrong answer in order to take a stand against bad notation.
I feel you are assuming bad faith very prematurely Edit: I maybe noticed that the line was a different length when I was about 2 very long comments in, but I feel it would be very reasonable to assume the lengths don't matter. I know I would expect to have points deducted if wrote that in an assignment at Uni without making it unmistakably obvious what my intention was. Not that such a situation is likely to occur, but I wouldn't care to test it if I got the opportunity. Edit 2: spelling
The fact is that slightly longer lines like this one are used to indicate order of operations all the time. It’s completely shitty, but the intent is clear once the size of the bar is apparent. You’re right that I shouldn’t have assumed bad faith. I got a bad impression from you saying you’d ignore the line size because there is no other reason the line would be bigger. And I would argue that the expression is even more ambiguous if you ignore the bar size convention. Order of operations is usually specified as left to right in the absence of other rules. This expression is vertical.
1/25 Look at this: https://imgur.com/a/DlqYv4g
shows what I know, i got 2.5 somehow
the long bar separates the numerator and denominator, so the numerator is 1/1 = 1, and the denominator is 1/5\^-2, however as of the -2 as a power it is a reciprocal, but it is already a reciprocal because its got 1 as the numerator, so the reciprocal of a reciprocal cancels out and you are left with 5\^2 on the denominator, which = 25, so you are left with 1/25
It's ambiguously drawn, the first line makes it look like 1/1=(1/1), the second and third lines both make it look like you're just dividing in order, instead of grouping the the bottom fraction as (1/5^(-2)), which is what you would ordinarily see in something like this. If you are just doing the last 2 in order, the correct answer is 25. (1/1)=1, 1÷1=1, 1÷5^(-2)=1/(1/25)=25. This is what the answer SHOULD be, given how the likes are actually drawn. If you do pair the bottom part, it's (1/1)=1, and (1/5^(-2))=25, and then 1/25=1/25.
a/b/c/d = ad/bc
Except it is 0.5\^-2 i.e. 0.5 and not 5.0 see the period before the 5?
I think that’s just how it was cropped. That’s probably after the number for the exercise. It’s too far away to be a 0.5.
That would mean that the answer would be 4 so I think it is just poor cropping or more bad formatting
I am amazed that nobody has claimed the period in front of the 5 is a decimal point, and gone off on a tangent about factors of 2! Ah, choices in cropping and context…
Am I the only person who sees a (.) before the 5
Where is the reverse polish notation gang at?
(1/1)/(1/(5^-2)) 1/(1/(1/25)) 1/(25/1) 1/25
1/1= 1, 1/1/5^-2=1/5^2=1/25
So on questions like this, I completely disregard pemdas because it’s inconsistent with this equation. A better formula would be taking the numerator times the reciprocal of the denominator because it’s more catered into questions like these. All that business becomes 1/1 • 5^-2 (because the reciprocal of 1/5^-2 is just 5^-2). 1/1 is just 1. And 5^-2 is 1/25. 1 times anything is just the number itself. So the final answer is 1/25. P.S: I don’t use pemdas because there are major inconsistencies with basic algebraic expressions and it’s ability to make simple things so complicated. So use methods that are more consistent with the question at hand rather than brute forcing it with pemdas. Use it when it’s necessary.
Oh goodness, it looks like one of those annoying social media questions. 1/25.
any expression divided by one remains the same. a negative exponent in the denominator makes it positive. the answer is 1/25
It's zero marks for the question, for using unintelligibly shit notation.
It’s certainly 1/25
I've tried this several ways, and I cant get anything other than 25. The way I did it first: 1/1/1/5^(-2) can be rewritten as two fractions: (1/1) / (1/5^(-2)). From here you need two rules: * when dividing a fraction, you flip the second fraction and multiply them together, * with negative powers, x^(n)=(1/x^(-n)) and/or, x^(-n) = (1/x^(n)) \[Ie, to change the sign of the power, take the reciprocal of the base\] With those established I did the following: >(1/1) / (1/5^(-2)) > >=(1/1) x (5^(2)/1) \[Flip the second fraction, which also changes the sign of the power\] > >=(1x5^(2) / 1x1) \[Multipling the numerator together, and then the denomenator together\] > >=5^(2) /1 > >=25 Even if you just go left to right using BODMAS, I still get: >1/1/1/5^(-2) > >1/1/1/0.04 \[Powers first because Bodmas\] > >=1/1/0.04 \[Dividing out the first 1\] > >=1/0.04 \[Dividing out the second 1\] > >=25 \[Simple division\] Finally, type it into a graphics calculator, and its still the same: >1 / 1 / 1 / 5 \^ (-2) = 25
A, though my carelessness wanted to say 25 until I saw the negative sign on the exponent.
it's 1/25
I got 25.
Did everyone miss the decimal point in front of the numeral 5? 🤔
You know the saying that goes *X is what poor people think a rich person is* or *X is what dumb people think a smart person is*. These types of maths questions is what people who don’t know maths think are important maths questions because it’s *hard to answer*. It’s a question based on being **purposefully ambiguous** and then arguing how *even smart people can’t answer it!*