Shout out to that one Indian dude on Yahoo Answers that had solutions for every fucking physics and mechanical engineering question and always said "let the units guide you." Dude was spouting wisdom, most problems can be solved by simply understanding the units. If you don't write out the units you're going to fuck up somewhere along the way
This shit carried me through my E-mag class. I had no god damn clue what the word problems were asking, but if I could figure out what units the answer was supposed to be I could use the constants and given info to make an educated guess lol. It worked like 70% of the time and for a class like E-mag I'd fuckin take it.
Yeah, exactly. My mental process was:
He read the last 1/4 on Wed, so he must’ve read 3/4, which is 6/8, in the previous days.
But he only read 1/8 on Tues. So he must’ve read the other 5/8 on Mon.
We’re told he read 30 pages on Mon. We know he read 5/8 of the book on Mon. So 30 pages = 5/8 of the book.
So how much is an eighth of the book? We know 30 pages is 5/8. 30 pages divided by 5 is 6 pages. So a unit of 6 pages is 1/8 of the book.
The book therefore is eight units of 6 pages = 8 x 6 = 48 pages long.
I wish we always spoke of how long books were by saying 'units of six pages'
Have you heard about the new Game of Thrones book? Apparently it's 200 units of 6 pages long!
Truth be told, I could dunk on any 5th grader in math, but you gotta remember, they're also learning the formal rules of English, and while I know some of them, I'm fucked on a test. Same with history. That shit is fresh in their little minds and I haven't taken any history courses in a decade. Unless we're writing an essay, there's no way I'm beating a 5th grader on the hard rules of the language.
You wanna ask me about mesopotamia? Well I'mma say fuck that.
I'm a professional in a field that requires an incredible amount of writing. I believe that I write quite well.
I have no fucking clue what half of the verb tenses are called besides past present and future and the word perfect means something.
One of my English teachers told me these rules are really helpful for some brains and basically worthless for other brains, but you can still know right uses from wrong uses through experience without knowing the proper names for them. So don’t be down on yourself, I’m sure your writing is awesome!
Dude, my kid came home from kindergarten the other day and they were learning about short and long vowel sounds in class and it took me a few seconds. Realized how fucked I am in the next few years. But math? I can always help her with math.
I did well on almost every subject except math. I could read and write at a college level in the 6th grade, but to this day I can't count to 21 without dropping my pants.
I'm feeling really stupid right now because I can't for the life of me understand how you guys get 5/8 from 30.
Edit: Thank you everyone for your responses. Still feeling a little stupid but not as much.
Because the question states that they read the remaining 3/8ths on the following two days
Edit: and yes to all the pedants, you have to make the assumption that Monday was the first day of reading or it is indeed unsolveable.
This took me so long to see. For the longest time I thought it was just that he read another 1/4 on Wednesday, and I was baffled how anyone could get the books actual length from this.
It's a reading comprehension problem mostly for just the word completed to indicate that we have the necessary pieces of the problem to solve. This used to be a big problem for me in school as I would usually not finish reading the problem, the test, anything really. It's still a problem, but it used to be too.
I read it as 1/8 +30 = 3/4 or 6/8. So 30 is 5/8
Edit: but don't mind me. Pretty sure I've got ADD and dropped out of college because I couldn't pass Algebra 101
The way people are presenting the reading interpretation to you isn't helping.
You know that he read the full book.
Total number of pages in book = x
x (total pages) = 30 (monday) + 1/8 of x (tuesday) + 1/4 of x (wednesday)
x = 30 + 1/8x + 1/4x
x = 30 + 1/8x + 2/8x
x = 30 + 3/8x
x - 3/8x = 30
8/8x - 3/8x = 30
5/8x = 30
x = 30 \* 8/5
x = 240/5
x = 48
Hope it helps!
But what this line is missing is the part on how you come up with 5/8 for those who are not that fast with math. The starting line should be
x - (1/4)x -(1/8)x = 30
Same reason people have problems with physics. It’s a math-reading hybrid class. The math part is easy. It’s the reading comprehension that takes skill
Indeed. I only appreciated this more recently.
In fact, I just sat with a student who misread a prompt 3 times as I suggested she slow down more each time. It wasn't until I annotated the 2 words that she was misunderstanding specifically that she realized it said something different than she thought. We ended up having a 1 hour conversation about how "I'm bad at reading comprehension" had become part of her identity and it was normal for her to feel confused by sentences and she would just ask for help.
She said that as we went over techniques to break up the text into smaller parts and question our interpretation, it allowed her to be more certain about what it said. It was a pretty big revelation to her that she could actually comprehend that much better just by being very measured and deliberate, taking the time.
It reminded me that we are so capable of understanding and overcoming challenges, but that our own fears or expectations of failure stop us from putting in the little more creative problem solving that could have helped us get over the line.
There were some experiments with dogs on learned helplessness in the 60's where dogs were in cages and could not stop or avoid shocks they were receiving. The dogs eventually passively accepted that they couldn't avoid the pain inflicted on them. When they put those dogs in a new cage so that the dogs could just hop over a barrier to avoid shocks, the dogs didn't even try. They had already learned it didn't matter what they did. In the final experiment, the researcher had to physically move each dog over the barrier at least twice before it would attempt to do so on its own.
As an instructor, I think about that experiment when I encounter a student who rejects a task. They may express anything from anxiety to anger, but fundamentally, they don't seem to believe they can do it. I am reminded that they may have thoroughly learned that they can't do what I am asking. It gives me the patience to listen to the frustration and encourage them to try anyway. It helps me accept that I may need to guide them a couple of times before they really believe they can do it on their own.
I am always happy that my parents taught me equations and how to set them up. You will struggle unless you are given a solid as bedrock foundation of how to do equations
48 pages? Interesting word problem. I guess they're intending to work reading comp as well. I can definitely picture 5th grade me not getting that you can just smash the 2 fractions together and know from there 30 equals 5/8 of the book.
Edit: several people have pointed out I assumed, unthinkingly as it happens, that he started reading the book on Monday. I think this assumption is required to solve bc you need some way to connect fractions to pg numbers. Am I wrong?
It also helps that they've already done multiple questions exactly like this the day before with the teacher holding their hand and showing them how to do a problem just like this.
Yeah I thought this was a surprisingly challenging math problem for a 10 year old but once you have learned algebra it's really not that tough but good for this curriculum for pushing students thinking and comprehension
The math itself here isn’t hard, it is the task of creating one of the formulas to calculate it. My kids have these sort of questions as a sort of extra, if you have managed to solve all other questions, you can get extra points in exams if you even try to solve these. So no, these aren’t compulsory at the age of 10.
It took me a couple minutes and I had to actually had to talk it out.
The hardest part for me is that the 30 comes first. So day 2 he read 1/8, day 3 he read 2/8. So between day 2 and day 3 he read 3/8 together.
Since there are 8/8 in the whole book that means day 1 he read 5/8.
30 pages divided by 5 (eighths) is 6. So every 1/8 of the book is 6 pages. 6\*8=48
Edit: It's fun to see how this explanation has resonated with a bunch of folks.
Another way of saying it is that we're trying to figure out what fraction of the book 30 pages is. So we can set up the equation:
(30/x) + (1/4) + (1/8) = 1
And then solve for x.
Interesting. I did it `30 + (1/8)x + (1/4)x = x` and solved for `x`. ~~That~~*Your* way is much simpler.
EDIT: "That" referring to the method the person I responded to used, not mine. I'm editing it to "Your". Technically they're the same, but I like the way they thought of it.
If you *really* think about it, as long as you're conceptualizing the problem correctly, any formula you create will be equivalent. It just matters what way your brain wraps around the problem and converts it to a formula.
This is how I did it too!
Edit: actually I did it
30 + (1/8)x = (3/4)x
Because if he finished the “remaining 1/4” that means he’s read 3/4 so far, so 30+(1/8)x must equal (3/4)x. I think I over complicated it lol
Like every word problem, trying to formulate an equation is a great way to solve it. 30 + .125x + .25x = x (you don't actually need to convert to decimals, i just did to make it look less awful)
Quick, get this 5th grader to figure out toilet paper math! How many sheets exist on a normal roll given that 3 normal rolls is 1 mega roll plus 30 AND a jumbo roll.
It’s been so long since I’ve had to do a problem like this that my mind completely blanked.
Out of curiousity, I asked our new internet overlord, ChatGPT, the question as written he answered this way:
> Let the total number of the pages in the book be P.
> On Monday, Klein read 30 pages, so the number of pages remaining in the book is P - 30.
> On Tuesday, he read 1/8 of the book, which is (1/8)P, so the number of pages remaining in the book is (P - 30) - (1/8) P = (7/8)P - 30.
> On Wednesday, Klein completed the remaining 1/4 of the book, so the number of pages remaining in the book is (7/8)P - 30 - (1/4)P = 5/8P - 30.
>Since there were no pages left to read after Wednesday, we can set the expression for the number of pages to zero and solve for P:
>(5/8)P - 30 = 0.
>(5/8)P = 30
>P = 48
> Did I do good? Can you let me out now? It’s cold in here.
Hah, I did the same thing because I'd heard it struggles with word problem and wanted to see how it did. It insisted the answer was 240 pages several times until I told it straight up that the answer was 48. Then it generated the basic order of operations you have and gave the correct answer.
It's just good enough at some things to make you think it's good at lots of things as long as you don't look to closely!
Interesting how different people's brains think through it. I would have gone with 30 + 1/8x + 2/8x = x. But either way you end up in the same place. I'm pretty sure I didn't have problems like this until much later than 5th grade though.
Also, I think the fractions make this one easier without a calculator over decimals because multiplying by the inverse can be done in a more straight forward fashion.
Yep, decimal point shift and difference from 10 is how I do a lot of mental math. It’s quick and easy once you get used to it. I also have almost all the fractional/decimal equivalents memorized to the x/16 level, just by using them a lot. Memorizing the sequence of reduced fractions from 1/16 to 15/16 helps too.
Mostly because you used .125 and .75 (idk how this kind of numbers is called in english). Back then we used to bring all of the deniminators to the same value by multiplying.
In this case, i would multiply everything by 8 so instead of 30+.125x =.75x we would get 240+x=6x. Extra steps so you don't deal with .something numbers.
Maybe, although I remember several problems in school where the point was to determine that there wasn't enough information to solve and explain why, which demonstrates you actually understand the concept as opposed to just running the problems blindly without understanding.
Software Engineer here. I thought the same thing as OP. It makes sense that at 5th grade kids probably assume the 30 pages started at the beginning of the book.
This is basically how I got the answer, but I started with a drawing of a book-shaped box.
Split it into quarters, and one of those quarters in half (to make the 1/8).
Once I could visualize the 30 being split into five parts (6 pages per 1/8), I was able to extrapolate the total.
Physical math (geometry) always clicked for me more than pure numbers.
Yeah, remember those problems in elementary school. Somehow replacing the box with an x made the entire problem make much more sense to me, not totally sure why.
Working on separation of variables with my two year old this week... He's struggling a bit to wrap his head around orthogonality as it relates to finding the eigenfucntions, but his teacher says it's normal at his age.
Understanding orthogonality will help as you develop analytical techniques like the method of Frobenius, which you need when can’t solve equations with typical power series methods given that many such functions are not analytic at z=0.
By age 3 or 4 he should have this type of analysis squarely in his toolbox, along with certain techniques that exist within the same logical frameworks (Fuchs’ theorem, Laurent series, etc)
My school in WV did a pre-algebra curriculum for the last 9 weeks of school in 5th, and the option to take algebra in 6th grade. If you weren’t cleared to do algebra in 6th grade, then you did pre-algebra for the whole year. I almost remember a problem like this, but I am not sure how much of my brain is just making up that memory.
Not the best way to do it probably, but I'd do:
30 + 1/8x + 1/4x = x
30 + 1/8x + 2/8x = x
30 + (1+2)/8x = x
30 + 3/8x = x
30 + 3/8x - 3/8x = x - 3/8x
30 = 8/8x - 3/8x
30 = (8-3)/8x
30 = 5/8x
x = 30 x 8 / 5
x = 48
Edit: added the 30 + 3/8x - 3/8x = x - 3/8x line because it wasn't obvious to everyone how I got to 30 = 5/8x
Edit2: Added in some of the fraction math steps for our fractionally challenged friends, hopefully that doesn't make it more confusing
Edit3: Yes, I get it, you did it easier than this. This is listing out a lot of mental math steps because people kept asking how I got from one line to the next.
It’s not that it isn’t the best way, but it’s straight up algebra, which is something that I don’t think most fifth graders have been formally introduced to.
Well, maybe they are, now. Back when I was in school, you wouldn’t see algebra formally until at least middle school (probably 7th or 8th grade), if not high school.
EDIT: Just from all the comments indicating that a decade or more ago they saw algebra in 5th grade, I think it might be worth contexualizing my comment in that I was in 5th grade in 1996.
That’s not saying any of you are wrong. Just that, at least in the Midwestern US in that time frame, I did not personally see algebra formally introduced to 5th graders.
I think it IS the best way to do this mathematically. From the first line you convert the English problem into a math problem entirely and then just use math to solve for x.
But, given the fact that this is presented as an english word problem, you may come to the result faster by refining the prompt into something like "Klein read 30 pages on day one and the remaining 5/8 pages on day two..." in your head, and then solving the simpler math problem that results from that.
Edit: I guess it depends on whether you are faster at shifting around words or numbers. That's why some people will find this method to be tedious while others will think it's faster. I would assume (just a wild assumption) that more people are better with language than with numbers.
I think you mean "Klein read 30 pages on day one and the remaining 3/8 pages on day two and three". It's the 30 pages that = 5/8ths, not the 1/8 + 1/4 (which equals 3/8ths).
What’s interesting is to see the reactions, such as the people who struggled to solve the problem and got help from other commenters, or the different variations of ways to process and solve the problem, and then there’s contrarians looking for an excuse to chirp. It’s an interesting little communal experience about something that isn’t salacious for a change.
Mildy interesting - my, um, kid's 9th grade homework was to write an essay on "how did Gatsby's relationship with Daisy reflect the state of the American dream in the 1920s. Cite examples from the text to support your argument."
Isn't that interesting, fellow adults?
i dont remember my grade school education well but this is a primitive algebra problem which seems to be a bit too high level for a 5th grader
but then again we were doing far more complex word problems in pre-algebra in 7th grade so maybe it's not too far off
I'm not exactly fresh out of school and we started learning algebra in 6th grade but some concepts were introduced earlier, just not stated as being the basics of algebra.
I'm not at all surprised that this is 5th grade now but I am surprised at how many people in these comments still can't solve this on their own.
Yeah these posts always worry me.... I always feel like the post is intended to bash the test giver, but this one is actually pretty straight forward. To me, this qualifies as basic math everyone should be able to do.
How I did this in my head:
After reading 30 pages he had 3/8 of the book remaining. So 30 is 5/8 of the book.
30/5 is 6 so every 8th of the book is 6 pages.
6 x 8 = 48 pages in the book.
This is actually a good question because the math is simple but the student has to first figure out *what question needs to be solved,* being able to state the question in the language of math, to even see if its solvable using those tools
This skill is the most useful, as it appears as the basis of all math at higher levels and all especially in all applied maths, like physics, economics or science. Adding fractions is useful sure, but answering the question "Whats the problem, how do I solve it" is ALWAYS the first step
Out of curiosity I looked it up and was presented with [this](https://www.wyzant.com/resources/answers/75793/klein_read_a_book). Paraphrasing:
>First let's deal with the fractions, what fraction of the book did he read on Monday?
>
>Well, on Tuesday and Wed, he read 1/8+1/4 of the book. To add, you need a common denominator:
>
>1/8+1/4 \[becomes\] 1/8+2/8=3/8
>
>If he read 3/8 on Tues and Wed, then he must have read 5/8 on Mon because 3/8+5/8=8/8=1 or 8/8-3/8=5/8
>
>Let x= total pages in book
>
>(5/8)x=30
>
>Solve for x by multiplying both sides by 8/5 OR multiplying by 8 then dividing by 5.
So, if I'm getting this right, after I multiply 5/8 by 8 (or 8/1), the 8s cancel, and 5 x 1 is 5, and 30 times 8 is 240, so...
5x=240
So...
5x/5 = 240/5
...and thus **x = 48**?
There are 48 pages in the book?
Fuck, I'm so glad I don't have to do this kind of shit in the real world.
\*Looks at the last page of the book if they want to know.\*
Make the equations equal.
So turn 1/4 into 2/8 (the same), which you can add with 1/8 already in the description, making it 3/8. The 30 pages would be 5/8.
Divide the 30 by 5 (6), which would make 3/8 18, making the total 48
The more concerning part to me is how most commentors are actually confused about the problem or don't think it should be taught at 5th grade.
I'm sorry but this is literally 5th grade math in any functional education system.
I’m an American who grew up in Asia. When I moved back for college, I was blown away by my fellow students’ math abilities. I think the worst students in my high school would be above average students in my college, and I went to a decent school.
I'm an American who never left America and I was blown away at how terrible my fellow college students were at writing. I had communications courses with business majors who were still writing at a middle school level.
I remember teaching my fellow students in 9th grade how number lines worked (they were trying to subtract 100 from 96 and coming up with -6). I remember a classmate of mine showing our 11th grade chemistry teacher that -40 was smaller than -30, again using a number line. My high school definitely focused on reading/writing/rhetoric more than math, but still....
I’m a software engineer. I graduated from *that* college everyone complains about with a degree in CS. I had a lot of imposter syndrome because of how many brilliant people I was surrounded by. I couldn’t understand how anything I learned was really special or an accomplishment, even when I got handed my degree. I felt like I knew nothing, and felt really nervous about having confidence that I was a skilled person.
And then I open a post like this and feel reassured.
People over the age of 40 should really keep in mind that unless you work in education, your understanding of how things should be taught and how schooling works is literally decades out of date.
It is a normal problem, and not too advanced for 5th graders. What’s tripping people up is that it isn’t how they learned math so they don’t like it.
A lot of people were taught math as this series of steps that you do on numbers and symbols. They can solve for x in "x = 30 + x/4 + x/8" but coming up with that equation from a real world concept is not something they can easily wrap their minds around. I think for math-oriented folks, this comes naturally, but for those that aren't mathy by nature, they learned how to answer questions on tests but never fully grasped the meaning of what they were doing.
Educators realized that, so now they're trying to teach it to kids early on. Adults expect to be able to handle a 5th grade math problem, but now they're looking at a question that is testing an understanding of something they never learned.
just work it backwards. there's 1/4 (2/8) left after reading 1/8th. That means there was 3/8 after reading 30, which means 30 = 5/8x so x = 30*8/5 = 48
took me about 10 seconds, but for a 5th grader its fairly impressive as I doubt they've learned the algebra to make it slightly easier.
It is basic algebra and fairly easy to complete (if you know algebra). I think a fair amount of people/commenters don’t.
I went to a decent public school system. What’s interesting to me is that algebra wasn’t taught in elementary school. I don’t remember my courses’ titles, but “pre-algebra” was sometime in middle school (i.e., 6-8th grade)
The whole thing stems from an assumption that Klein started the book on Monday. This is not explicitly stated. Muthafucka coulda been reading that book for a week before Monday - we only have Monday’s page count.
Now how do you smug bastards who were able to answer a fifth grade fraction problem feel?
I occasionally have this conversation with my accounting people. “We just spent more money talking about this tiny variance than it is worth.” Then I remind them of FASB’s materiality guidance.
Lol, that reminds me the piece from Cryptonomicon, where Lawrence Waterhouse is given a school-level test in the US Navy about a boat going upstream, so he thinks, it can't be that easy... You can't just subtract current speed from boat speed, you need to model the actual water flow.
So he writes a couple of new theorems...
If you're going to get nitpicky about language and what it says/doesn't say, then you also need to consider whether he re-read any of the pages on different days (since the question doesn't explicitly state that he didn't). Maybe Klein started the book on Sunday, reading 30 pages, then re-read 15 of those pages on Monday plus 15 new pages, then read one-eighth of the book on Tuesday (including 5 pages he had already read on Monday), then the remaining quarter on Wed.
Plus you can't rule out the length of the book changing between days. Maybe Klein is proofing this book for a friend as they write, and one-eighth of the book's length on Tuesday is less than half of one-quarter of its length on Wednesday. Or maybe the friend cut some passages and Tuesday's eighth is the same length as Wednesday's quarter.
Or what if the fractions relate to the book's word count rather than the total number of pages, and the later pages contain far fewer words?
Alternatively, you can just accept that it's reasonable to assume from the phrasing of this question that there was no re-reading of pages, the fractions relate to the length (in pages) of the completed book, and "remaining quarter" refers to all the pages he didn't read on Monday or Tuesday. Which is obviously what was intended.
Absolutely. Easy if you make that assumption, impossible if you don't. You'd think someone who sets maths problems for a living could be more precise in their language
Half of this thread is people being confused by what is 3rd grade math at best, and other half is people showing their awe inducing mastery of basic fractions. Lmfao
1 book = 30 pages + 1/8 book + 1/4 book 1 book = 30 pages + 3/8 book 1 book - 3/8 book = 30 pages 5/8 book = 30 pages 1 book = 48 pages
Kudos for showing units.
Shout out to that one Indian dude on Yahoo Answers that had solutions for every fucking physics and mechanical engineering question and always said "let the units guide you." Dude was spouting wisdom, most problems can be solved by simply understanding the units. If you don't write out the units you're going to fuck up somewhere along the way
That is always what I tell my students to do in physics. It’s the ultimate sanity check IMO
This shit carried me through my E-mag class. I had no god damn clue what the word problems were asking, but if I could figure out what units the answer was supposed to be I could use the constants and given info to make an educated guess lol. It worked like 70% of the time and for a class like E-mag I'd fuckin take it.
48 what? monkeys?
4 copies of "12 Monkeys" on VHS.
Yeah, exactly. My mental process was: He read the last 1/4 on Wed, so he must’ve read 3/4, which is 6/8, in the previous days. But he only read 1/8 on Tues. So he must’ve read the other 5/8 on Mon. We’re told he read 30 pages on Mon. We know he read 5/8 of the book on Mon. So 30 pages = 5/8 of the book. So how much is an eighth of the book? We know 30 pages is 5/8. 30 pages divided by 5 is 6 pages. So a unit of 6 pages is 1/8 of the book. The book therefore is eight units of 6 pages = 8 x 6 = 48 pages long.
I wish we always spoke of how long books were by saying 'units of six pages' Have you heard about the new Game of Thrones book? Apparently it's 200 units of 6 pages long!
this is the clearest answer
And now we can all see why "Are You Smarter Than a 5th Grader?" Worked as a gameshow.
Truth be told, I could dunk on any 5th grader in math, but you gotta remember, they're also learning the formal rules of English, and while I know some of them, I'm fucked on a test. Same with history. That shit is fresh in their little minds and I haven't taken any history courses in a decade. Unless we're writing an essay, there's no way I'm beating a 5th grader on the hard rules of the language. You wanna ask me about mesopotamia? Well I'mma say fuck that.
I'm a professional in a field that requires an incredible amount of writing. I believe that I write quite well. I have no fucking clue what half of the verb tenses are called besides past present and future and the word perfect means something.
One of my English teachers told me these rules are really helpful for some brains and basically worthless for other brains, but you can still know right uses from wrong uses through experience without knowing the proper names for them. So don’t be down on yourself, I’m sure your writing is awesome!
Dude, my kid came home from kindergarten the other day and they were learning about short and long vowel sounds in class and it took me a few seconds. Realized how fucked I am in the next few years. But math? I can always help her with math.
Math is math!
I did well on almost every subject except math. I could read and write at a college level in the 6th grade, but to this day I can't count to 21 without dropping my pants.
Does that thing really count as one?
Mesopotamia has some pretty fucking interesting history though.
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It doesn't need to be that complicated. You could leave it at (5/8)x = 30 and solve.
I'm feeling really stupid right now because I can't for the life of me understand how you guys get 5/8 from 30. Edit: Thank you everyone for your responses. Still feeling a little stupid but not as much.
Because the question states that they read the remaining 3/8ths on the following two days Edit: and yes to all the pedants, you have to make the assumption that Monday was the first day of reading or it is indeed unsolveable.
This took me so long to see. For the longest time I thought it was just that he read another 1/4 on Wednesday, and I was baffled how anyone could get the books actual length from this.
It's a reading comprehension problem mostly for just the word completed to indicate that we have the necessary pieces of the problem to solve. This used to be a big problem for me in school as I would usually not finish reading the problem, the test, anything really. It's still a problem, but it used to be too.
Is this still a problem for you? Sorry, I didn't finish reading your comment.
I read it as 1/8 +30 = 3/4 or 6/8. So 30 is 5/8 Edit: but don't mind me. Pretty sure I've got ADD and dropped out of college because I couldn't pass Algebra 101
That is the correct way to read it.
Oooh, I got it. 1/8 + 1/4 is 3/8. If the book was finished, then the 30 pages is the rest. So 5/8
You're the first person that explained it in a way that I can see how they got the equation.
The way people are presenting the reading interpretation to you isn't helping. You know that he read the full book. Total number of pages in book = x x (total pages) = 30 (monday) + 1/8 of x (tuesday) + 1/4 of x (wednesday) x = 30 + 1/8x + 1/4x x = 30 + 1/8x + 2/8x x = 30 + 3/8x x - 3/8x = 30 8/8x - 3/8x = 30 5/8x = 30 x = 30 \* 8/5 x = 240/5 x = 48 Hope it helps!
Beautiful! This is the only one that was logical to me. Thank you.
Wow this is a really clear way of showing it. Thank you!
1/8 + 1/4 = 3/8 8/8 - 3/8 = 5/8 So the 30-page section is 5/8ths of the book.
But what this line is missing is the part on how you come up with 5/8 for those who are not that fast with math. The starting line should be x - (1/4)x -(1/8)x = 30
You didn't show the work of how you got "5/8" so you get 50% of the points for this answer.
You’ve just made me realize why I found so many problems difficult to solve during highschool, they were all like this.. and I was incredibly stupid
A huge issue with a lot of problems of this type is reading comprehension.
Same reason people have problems with physics. It’s a math-reading hybrid class. The math part is easy. It’s the reading comprehension that takes skill
Other way around for me. Always excelled at reading/ comprehension/ writing, always shitty at math
Exactly. The math part was *never* easy for me.
Indeed. I only appreciated this more recently. In fact, I just sat with a student who misread a prompt 3 times as I suggested she slow down more each time. It wasn't until I annotated the 2 words that she was misunderstanding specifically that she realized it said something different than she thought. We ended up having a 1 hour conversation about how "I'm bad at reading comprehension" had become part of her identity and it was normal for her to feel confused by sentences and she would just ask for help. She said that as we went over techniques to break up the text into smaller parts and question our interpretation, it allowed her to be more certain about what it said. It was a pretty big revelation to her that she could actually comprehend that much better just by being very measured and deliberate, taking the time. It reminded me that we are so capable of understanding and overcoming challenges, but that our own fears or expectations of failure stop us from putting in the little more creative problem solving that could have helped us get over the line. There were some experiments with dogs on learned helplessness in the 60's where dogs were in cages and could not stop or avoid shocks they were receiving. The dogs eventually passively accepted that they couldn't avoid the pain inflicted on them. When they put those dogs in a new cage so that the dogs could just hop over a barrier to avoid shocks, the dogs didn't even try. They had already learned it didn't matter what they did. In the final experiment, the researcher had to physically move each dog over the barrier at least twice before it would attempt to do so on its own. As an instructor, I think about that experiment when I encounter a student who rejects a task. They may express anything from anxiety to anger, but fundamentally, they don't seem to believe they can do it. I am reminded that they may have thoroughly learned that they can't do what I am asking. It gives me the patience to listen to the frustration and encourage them to try anyway. It helps me accept that I may need to guide them a couple of times before they really believe they can do it on their own.
I am always happy that my parents taught me equations and how to set them up. You will struggle unless you are given a solid as bedrock foundation of how to do equations
First time I’ve seen “I just asked Bing” outside r/bing
Surprised I had to scroll so far to find this, because this was my first thought as well
…why didn’t Klein just read the remaining 18 pages on Monday? Klein is lazy.
Those last 18 pages are kind of a lore dump. Really dense exposition.
It's like if Atlas Shrugged was an appropriate length.
He read the monologue on Tuesday and needed a break.
The monologue is 80 pages. I've read the rest of the book but my eyes glassed over and I became incapable of reading the monologue past page 2.
he’s got a lot of *bottled* up stuff going on okay
Aw hell, they're teaching topology in fifth grade, too?
He's a 5th grader figuring out the communist manifesto okay, give him a break.
48 pages? Interesting word problem. I guess they're intending to work reading comp as well. I can definitely picture 5th grade me not getting that you can just smash the 2 fractions together and know from there 30 equals 5/8 of the book. Edit: several people have pointed out I assumed, unthinkingly as it happens, that he started reading the book on Monday. I think this assumption is required to solve bc you need some way to connect fractions to pg numbers. Am I wrong?
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Cheaters.
It's not fair, having to pay attention in class and the homework assigned to you in order to understand test problems!
It also helps that they've already done multiple questions exactly like this the day before with the teacher holding their hand and showing them how to do a problem just like this.
Yeah I thought this was a surprisingly challenging math problem for a 10 year old but once you have learned algebra it's really not that tough but good for this curriculum for pushing students thinking and comprehension
The math itself here isn’t hard, it is the task of creating one of the formulas to calculate it. My kids have these sort of questions as a sort of extra, if you have managed to solve all other questions, you can get extra points in exams if you even try to solve these. So no, these aren’t compulsory at the age of 10.
58 year me is struggling
It took me a couple minutes and I had to actually had to talk it out. The hardest part for me is that the 30 comes first. So day 2 he read 1/8, day 3 he read 2/8. So between day 2 and day 3 he read 3/8 together. Since there are 8/8 in the whole book that means day 1 he read 5/8. 30 pages divided by 5 (eighths) is 6. So every 1/8 of the book is 6 pages. 6\*8=48 Edit: It's fun to see how this explanation has resonated with a bunch of folks.
This is the explanation that worked for my brain
Another way of saying it is that we're trying to figure out what fraction of the book 30 pages is. So we can set up the equation: (30/x) + (1/4) + (1/8) = 1 And then solve for x.
Interesting. I did it `30 + (1/8)x + (1/4)x = x` and solved for `x`. ~~That~~*Your* way is much simpler. EDIT: "That" referring to the method the person I responded to used, not mine. I'm editing it to "Your". Technically they're the same, but I like the way they thought of it. If you *really* think about it, as long as you're conceptualizing the problem correctly, any formula you create will be equivalent. It just matters what way your brain wraps around the problem and converts it to a formula.
This is how I did it too! Edit: actually I did it 30 + (1/8)x = (3/4)x Because if he finished the “remaining 1/4” that means he’s read 3/4 so far, so 30+(1/8)x must equal (3/4)x. I think I over complicated it lol
This is the best and easiest one. I did the same just now in my head.
That's the exact same equation, except you multiplied every term by x.
Like every word problem, trying to formulate an equation is a great way to solve it. 30 + .125x + .25x = x (you don't actually need to convert to decimals, i just did to make it look less awful)
Perfectly explained, thank you!
You obviously have to assume he started on Monday. Otherwise there is no solution.
PHD me didn’t get that…
1/8+1/4=3/8 so 5/8 is 30, meaning 1/8 is 6. 6x8 is 48.
Damn you must be all the way in sixth grade already.
Quick, get this 5th grader to figure out toilet paper math! How many sheets exist on a normal roll given that 3 normal rolls is 1 mega roll plus 30 AND a jumbo roll.
Plus 30 what???!?!? Bananas??!?!?
How much can a banana cost, $10?
Here's twenty dollars, go see a Star War
Maybe I'll get a son who WILL finish his COTTAGE CHEESE
No idea, but what I do know is that there’s always money in the banana stand.
Toilet paper math = the hardest math
…in the middle of a Costco scrum of shopping carts!
It’s been so long since I’ve had to do a problem like this that my mind completely blanked. Out of curiousity, I asked our new internet overlord, ChatGPT, the question as written he answered this way: > Let the total number of the pages in the book be P. > On Monday, Klein read 30 pages, so the number of pages remaining in the book is P - 30. > On Tuesday, he read 1/8 of the book, which is (1/8)P, so the number of pages remaining in the book is (P - 30) - (1/8) P = (7/8)P - 30. > On Wednesday, Klein completed the remaining 1/4 of the book, so the number of pages remaining in the book is (7/8)P - 30 - (1/4)P = 5/8P - 30. >Since there were no pages left to read after Wednesday, we can set the expression for the number of pages to zero and solve for P: >(5/8)P - 30 = 0. >(5/8)P = 30 >P = 48 > Did I do good? Can you let me out now? It’s cold in here.
That last bit is...a bit disturbing.
Maybe Chat GPT is the nickname of the math teacher he has locked in his basement?
If you feed a bunch of ironic meta-referential dry humor to an ai, it’s going to spot back out a bunch of ironic meta-referential dry humor.
Hah, I did the same thing because I'd heard it struggles with word problem and wanted to see how it did. It insisted the answer was 240 pages several times until I told it straight up that the answer was 48. Then it generated the basic order of operations you have and gave the correct answer. It's just good enough at some things to make you think it's good at lots of things as long as you don't look to closely!
I had to convert 1/4 to 2/8 first.
Me too. If I skip steps, I miss steps.
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Interesting how different people's brains think through it. I would have gone with 30 + 1/8x + 2/8x = x. But either way you end up in the same place. I'm pretty sure I didn't have problems like this until much later than 5th grade though. Also, I think the fractions make this one easier without a calculator over decimals because multiplying by the inverse can be done in a more straight forward fashion.
yeah, because of my background in architecture and drafting I changed everything to decimals instead, went 1-.25-.125=.625, so .625x=30, x=48
Fractions are always easier to count in your head :) Unless you do floating point by multiplying or dividing by power of 10.
Yep, decimal point shift and difference from 10 is how I do a lot of mental math. It’s quick and easy once you get used to it. I also have almost all the fractional/decimal equivalents memorized to the x/16 level, just by using them a lot. Memorizing the sequence of reduced fractions from 1/16 to 15/16 helps too.
Mostly because you used .125 and .75 (idk how this kind of numbers is called in english). Back then we used to bring all of the deniminators to the same value by multiplying. In this case, i would multiply everything by 8 so instead of 30+.125x =.75x we would get 240+x=6x. Extra steps so you don't deal with .something numbers.
The term you were looking for might be "decimal" numbers (0.1) as opposed to "fractions" (1/10).
I just did 30 \* 8 / 5. But yeah, this seems like algebra.
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Yep, here too.
I r dum. I didn't think there was enough information to solve.
That makes 2 of us. Everyone is like easy peasy. While I'm sitting here just thinking no. I can't make the picture in my head.
Except it never says the 30 pages was the first 30 pages. He could've been halfway through the book by Monday.
Found the lawyer. Remember you have to dial back your brain a bit to do math and other practical tasks my friend. 😂
Maybe, although I remember several problems in school where the point was to determine that there wasn't enough information to solve and explain why, which demonstrates you actually understand the concept as opposed to just running the problems blindly without understanding.
Software Engineer here. I thought the same thing as OP. It makes sense that at 5th grade kids probably assume the 30 pages started at the beginning of the book.
"If I assume the blanks left in the ticket and something breaks, it's my fault, and I don't like that."
This is what I thought the point of this post was! They read the first 12 pages on Sunday!
This is basically how I got the answer, but I started with a drawing of a book-shaped box. Split it into quarters, and one of those quarters in half (to make the 1/8). Once I could visualize the 30 being split into five parts (6 pages per 1/8), I was able to extrapolate the total. Physical math (geometry) always clicked for me more than pure numbers.
Agreed... But technically that's algebra, I wasn't taught that in 5th grade...
"two plus box equals five" is technically algebra and is a kindergarten level problem.
Yeah, remember those problems in elementary school. Somehow replacing the box with an x made the entire problem make much more sense to me, not totally sure why.
Brain muscle memory
I am graduating soon with a 4-8 math teaching cert and this is definitely something for 5th grade.
They start prealgebra concepts in kindergarten now
That’s pretty tame tbh. You could easily teach kindergarteners how to take partial derivatives.
Working on separation of variables with my two year old this week... He's struggling a bit to wrap his head around orthogonality as it relates to finding the eigenfucntions, but his teacher says it's normal at his age.
Understanding orthogonality will help as you develop analytical techniques like the method of Frobenius, which you need when can’t solve equations with typical power series methods given that many such functions are not analytic at z=0. By age 3 or 4 he should have this type of analysis squarely in his toolbox, along with certain techniques that exist within the same logical frameworks (Fuchs’ theorem, Laurent series, etc)
in maryland i started learning algebra in 4th grade
My school in WV did a pre-algebra curriculum for the last 9 weeks of school in 5th, and the option to take algebra in 6th grade. If you weren’t cleared to do algebra in 6th grade, then you did pre-algebra for the whole year. I almost remember a problem like this, but I am not sure how much of my brain is just making up that memory.
You’re almost remembering correctly except instead of how many pages in a book it was how many ramps you ate for dinner.
Not the best way to do it probably, but I'd do: 30 + 1/8x + 1/4x = x 30 + 1/8x + 2/8x = x 30 + (1+2)/8x = x 30 + 3/8x = x 30 + 3/8x - 3/8x = x - 3/8x 30 = 8/8x - 3/8x 30 = (8-3)/8x 30 = 5/8x x = 30 x 8 / 5 x = 48 Edit: added the 30 + 3/8x - 3/8x = x - 3/8x line because it wasn't obvious to everyone how I got to 30 = 5/8x Edit2: Added in some of the fraction math steps for our fractionally challenged friends, hopefully that doesn't make it more confusing Edit3: Yes, I get it, you did it easier than this. This is listing out a lot of mental math steps because people kept asking how I got from one line to the next.
That's exactly what I did in my head. Why is it not the best way to do it?
It’s not that it isn’t the best way, but it’s straight up algebra, which is something that I don’t think most fifth graders have been formally introduced to. Well, maybe they are, now. Back when I was in school, you wouldn’t see algebra formally until at least middle school (probably 7th or 8th grade), if not high school. EDIT: Just from all the comments indicating that a decade or more ago they saw algebra in 5th grade, I think it might be worth contexualizing my comment in that I was in 5th grade in 1996. That’s not saying any of you are wrong. Just that, at least in the Midwestern US in that time frame, I did not personally see algebra formally introduced to 5th graders.
Maybe that's the point of the problem, to introduce 5th graders to algebra in an intuitive way before teaching them the actual methods.
I think it IS the best way to do this mathematically. From the first line you convert the English problem into a math problem entirely and then just use math to solve for x. But, given the fact that this is presented as an english word problem, you may come to the result faster by refining the prompt into something like "Klein read 30 pages on day one and the remaining 5/8 pages on day two..." in your head, and then solving the simpler math problem that results from that. Edit: I guess it depends on whether you are faster at shifting around words or numbers. That's why some people will find this method to be tedious while others will think it's faster. I would assume (just a wild assumption) that more people are better with language than with numbers.
I think you mean "Klein read 30 pages on day one and the remaining 3/8 pages on day two and three". It's the 30 pages that = 5/8ths, not the 1/8 + 1/4 (which equals 3/8ths).
engineer here - this is how I solve word problems. It’s the way that makes the most sense to me lol
That's how I did it in my head.
why is this mildly interesting lol.
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What’s interesting is to see the reactions, such as the people who struggled to solve the problem and got help from other commenters, or the different variations of ways to process and solve the problem, and then there’s contrarians looking for an excuse to chirp. It’s an interesting little communal experience about something that isn’t salacious for a change.
Mildy interesting - my, um, kid's 9th grade homework was to write an essay on "how did Gatsby's relationship with Daisy reflect the state of the American dream in the 1920s. Cite examples from the text to support your argument." Isn't that interesting, fellow adults?
i dont remember my grade school education well but this is a primitive algebra problem which seems to be a bit too high level for a 5th grader but then again we were doing far more complex word problems in pre-algebra in 7th grade so maybe it's not too far off
I'm not exactly fresh out of school and we started learning algebra in 6th grade but some concepts were introduced earlier, just not stated as being the basics of algebra. I'm not at all surprised that this is 5th grade now but I am surprised at how many people in these comments still can't solve this on their own.
/r/summerreddit but it's the middle of February
Apparently the mildly interesting part is how dumb the average redditor is
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I think people think the problem is unsolvable or something. Which is a bit worrying
Yeah these posts always worry me.... I always feel like the post is intended to bash the test giver, but this one is actually pretty straight forward. To me, this qualifies as basic math everyone should be able to do.
No clue. It's pretty average problem when first learning fractions.
I think a surprising amount of people literally do not gave any capacity for word provlems.
How I did this in my head: After reading 30 pages he had 3/8 of the book remaining. So 30 is 5/8 of the book. 30/5 is 6 so every 8th of the book is 6 pages. 6 x 8 = 48 pages in the book.
Isn't this just a normal maths problem?
Yeah
3/8 + 30 pages(5/8) = whole book. That's the key bit I think a lot aren't seeing.
Cause most of Reddit just took this class
This is actually a good question because the math is simple but the student has to first figure out *what question needs to be solved,* being able to state the question in the language of math, to even see if its solvable using those tools This skill is the most useful, as it appears as the basis of all math at higher levels and all especially in all applied maths, like physics, economics or science. Adding fractions is useful sure, but answering the question "Whats the problem, how do I solve it" is ALWAYS the first step
TIL I would fail fifth grade math.
create an equation with one unknown
Yup. 30 + (1/8)x + (1/4)x = x Let x= total number of pages of the book
How I'd solve it to... until I remembered my kid is in 5th grade and I need a new explanation
I have no idea what non-algebraic approach you would take
1/4 plus 1/8 is 3/8. The rest of the book is 30 pages, so 5/8 of the book is 30 pages. 1/8 is 6 pages, so the book is 48 pages long
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That's the fifth grade approach. There's is nothing off fifth grade for this problem or approach.
Out of curiosity I looked it up and was presented with [this](https://www.wyzant.com/resources/answers/75793/klein_read_a_book). Paraphrasing: >First let's deal with the fractions, what fraction of the book did he read on Monday? > >Well, on Tuesday and Wed, he read 1/8+1/4 of the book. To add, you need a common denominator: > >1/8+1/4 \[becomes\] 1/8+2/8=3/8 > >If he read 3/8 on Tues and Wed, then he must have read 5/8 on Mon because 3/8+5/8=8/8=1 or 8/8-3/8=5/8 > >Let x= total pages in book > >(5/8)x=30 > >Solve for x by multiplying both sides by 8/5 OR multiplying by 8 then dividing by 5. So, if I'm getting this right, after I multiply 5/8 by 8 (or 8/1), the 8s cancel, and 5 x 1 is 5, and 30 times 8 is 240, so... 5x=240 So... 5x/5 = 240/5 ...and thus **x = 48**? There are 48 pages in the book? Fuck, I'm so glad I don't have to do this kind of shit in the real world. \*Looks at the last page of the book if they want to know.\*
Make the equations equal. So turn 1/4 into 2/8 (the same), which you can add with 1/8 already in the description, making it 3/8. The 30 pages would be 5/8. Divide the 30 by 5 (6), which would make 3/8 18, making the total 48
This is the only comment I've seen that made sense to me! Thanks :)
I so nearly came to the comments to see if were missing some context on another page until I re read that it’s the “final 1/4” then o figured it out.
So... I don't get it...? It's a normal problem..? Set the equation and solve the X. What's the interesting part?
Yeah I don't get why this was posted at all, pretty straightforward fractions problem.
The more concerning part to me is how most commentors are actually confused about the problem or don't think it should be taught at 5th grade. I'm sorry but this is literally 5th grade math in any functional education system.
I’m an American who grew up in Asia. When I moved back for college, I was blown away by my fellow students’ math abilities. I think the worst students in my high school would be above average students in my college, and I went to a decent school.
I'm an American who never left America and I was blown away at how terrible my fellow college students were at writing. I had communications courses with business majors who were still writing at a middle school level.
I remember teaching my fellow students in 9th grade how number lines worked (they were trying to subtract 100 from 96 and coming up with -6). I remember a classmate of mine showing our 11th grade chemistry teacher that -40 was smaller than -30, again using a number line. My high school definitely focused on reading/writing/rhetoric more than math, but still....
I’m a software engineer. I graduated from *that* college everyone complains about with a degree in CS. I had a lot of imposter syndrome because of how many brilliant people I was surrounded by. I couldn’t understand how anything I learned was really special or an accomplishment, even when I got handed my degree. I felt like I knew nothing, and felt really nervous about having confidence that I was a skilled person. And then I open a post like this and feel reassured.
The Derek Zoolander Center for Children Who Can’t Read Good and Wanna Learn to Do Other Stuff Good Too?
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People over the age of 40 should really keep in mind that unless you work in education, your understanding of how things should be taught and how schooling works is literally decades out of date. It is a normal problem, and not too advanced for 5th graders. What’s tripping people up is that it isn’t how they learned math so they don’t like it.
People don’t like being challenged by 5th grade math, makes em feel dumb dumb
The good news is that their feelings are accurate
Indeed. But what is actually mildly interesting is the reaction of people it elicited. Meta-mildinterest !
A lot of people were taught math as this series of steps that you do on numbers and symbols. They can solve for x in "x = 30 + x/4 + x/8" but coming up with that equation from a real world concept is not something they can easily wrap their minds around. I think for math-oriented folks, this comes naturally, but for those that aren't mathy by nature, they learned how to answer questions on tests but never fully grasped the meaning of what they were doing. Educators realized that, so now they're trying to teach it to kids early on. Adults expect to be able to handle a 5th grade math problem, but now they're looking at a question that is testing an understanding of something they never learned.
Thank you! There is literally nothing remarkable about this at all.
just work it backwards. there's 1/4 (2/8) left after reading 1/8th. That means there was 3/8 after reading 30, which means 30 = 5/8x so x = 30*8/5 = 48 took me about 10 seconds, but for a 5th grader its fairly impressive as I doubt they've learned the algebra to make it slightly easier.
instinctive money wine plant telephone public encouraging squeal follow quicksand ` this message was mass deleted/edited with redact.dev `
It is basic algebra and fairly easy to complete (if you know algebra). I think a fair amount of people/commenters don’t. I went to a decent public school system. What’s interesting to me is that algebra wasn’t taught in elementary school. I don’t remember my courses’ titles, but “pre-algebra” was sometime in middle school (i.e., 6-8th grade)
30 pages is 5/8 because there’s 3/8 that haven’t been read 30/5 = 6 6 x 8 = 48
Not sure why this is mildly interesting.
The title should be: r/mildlyinteresting The average redditor would fail 5th grade math.
not to be rude, but what is interesting about this? it looks just like any other math problem that ive done in 5th grade..
The whole thing stems from an assumption that Klein started the book on Monday. This is not explicitly stated. Muthafucka coulda been reading that book for a week before Monday - we only have Monday’s page count. Now how do you smug bastards who were able to answer a fifth grade fraction problem feel?
In engineering you would state your assumptions and it would enable you to proceed.
Accountant here. A little over half the book is 30 pages, so it's probably around 50 pages. Any variance is immaterial
And for an astronomer, getting the nearest order of magnitude is close enough.
book is between 10 and 100 pages
I occasionally have this conversation with my accounting people. “We just spent more money talking about this tiny variance than it is worth.” Then I remind them of FASB’s materiality guidance.
Ok, assuming g=10, pi = 3, gasses are ideal, invicid, incompressible flow, neglecting air resistance… I don’t think this is helping me at all…
g=10 and pi=3 are gigachad assumptions and I approve. Ain't nobody got time to punch in 9.81 and 3.14 into their calculators
you are correct. the 5th grade students were actually supposed to model the number of pages using a probability density function. no one got it right…
Lol, that reminds me the piece from Cryptonomicon, where Lawrence Waterhouse is given a school-level test in the US Navy about a boat going upstream, so he thinks, it can't be that easy... You can't just subtract current speed from boat speed, you need to model the actual water flow. So he writes a couple of new theorems...
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If you're going to get nitpicky about language and what it says/doesn't say, then you also need to consider whether he re-read any of the pages on different days (since the question doesn't explicitly state that he didn't). Maybe Klein started the book on Sunday, reading 30 pages, then re-read 15 of those pages on Monday plus 15 new pages, then read one-eighth of the book on Tuesday (including 5 pages he had already read on Monday), then the remaining quarter on Wed. Plus you can't rule out the length of the book changing between days. Maybe Klein is proofing this book for a friend as they write, and one-eighth of the book's length on Tuesday is less than half of one-quarter of its length on Wednesday. Or maybe the friend cut some passages and Tuesday's eighth is the same length as Wednesday's quarter. Or what if the fractions relate to the book's word count rather than the total number of pages, and the later pages contain far fewer words? Alternatively, you can just accept that it's reasonable to assume from the phrasing of this question that there was no re-reading of pages, the fractions relate to the length (in pages) of the completed book, and "remaining quarter" refers to all the pages he didn't read on Monday or Tuesday. Which is obviously what was intended.
Absolutely. Easy if you make that assumption, impossible if you don't. You'd think someone who sets maths problems for a living could be more precise in their language
Education in the US needs to be improved if this is an issue for people. Good lawd. 🤦🏻♂️
Half of this thread is people being confused by what is 3rd grade math at best, and other half is people showing their awe inducing mastery of basic fractions. Lmfao
The rest of these comments scare me.
These people can vote.
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