Why the fuck is everyone so afraid of fractions? I simply do not get it. I am a masters student in mathematics and when I TA about 90% of the students will first write a problem down and then change any fraction to a decimal. What in the fuck? Why would you waste your time doing that, especially when you're not allowed a calculator on tests? WHY? Most of them will only write 1-2 decimal points too, so they have an answer which is slightly off due to round off answers.
When I ask them why they do this they don't really have an answer. I just do not understand. WHAT THE FUCK IS SO HARD TO UNDERSTAND ABOUT FRACTIONS?
Please, /sci/, help me understand.
poor excuse. the rules are simple as fuck. you have to memorize letters, words and grammatical rules to write a sentence. why does math get shit on for being "rote" when any other subject is 10x worse?
>Why the fuck is everyone so afraid of fractions?
Did you ask toddlers?
If your peers find fractions hard, there are two possibilities:
1) They are toddlers
2) They are retarded
Either way, find better peers to hang around.
Maybe it isn't fear. Maybe the fractions just don't seem like as much of a real number as the decimal version. Maybe because it is two numbers with a math symbol between them, they don't think of it as complete until they "solve" that bit too, even though it is less accurate after they do.
After all, you're taught to simplify fractions, so it seems like the natural next step in the process after that at first.
Not OP, but your willful mis-reading / total absence of reading comprehension viz. his post goes like this:
1) OP sets up, right away, in the third sentence, that the people he's interacting with are what it is completely reasonable to assume are undergrads.
2) OP, by contrast (according to the exact same sentence) is a master's student, ergo a /graduate/, having obtained a higher academic degree than those he his teaching, or tutoring. Thus, according to him, these people that OP is interacting with are literally /not his peers/.
3) It is furthermore reasonable to assume that a requirement of OP's master's program entails teaching undergrad material. In other words, he signed up for it, and he doesn't get to get out of it.
So your advice to OP "derp find better peers" is double-stupid. Because he's not complaining about peers, but about the poor mathematical habits of his students / "the" students.
Your characterization of the (undergrad) students themselves is warranted, but the third and most relevant possibility, which you didn't mention, is: they received a shitty grammar school education. There is an important distinction between poor education and personal stupidity, although the two are siblings.s.
I neglected to mention in the above that your thing is hypocritical in the sense that you couldn't be bothered to take the ten seconds to read OP's post correctly. In other words, you're as bad as the retarded toddlers you've just described, which is known because of how you thought they were OP's "peers", as I've explained.
I think you just hit the nail on the head for a lot of misconceptions about numbers. Its all based on people thinking that the decimal representation is the only "real" representation of a number.
People who think of irrationals as "non-repeating decimals" instead of "numbers that aren't a ratio of integers"
People who don't believe .999...=1.
People who somehow think it's significant that the decimal expansion of pi contains other numbers, ie their birthday
I'm also sorta-sniffing bullshit.
American Math graduate here who did math homework in collaboration and close proximity with maybe a dozen others during undergrad. I never saw anything like what OP is describing in others' work. Maybe I just went to a good school with a smarter student body.
Fractions are decimals too. "Converting" a fraction to a decimal is basically multiplying it so that the donominantor is a power of ten. Why people go that extra step is beyond me as well - I don't.
Literally solve it instantly in my head. Dividing, then adding takes longer.
When I was an engineering student I used to change fractions to decimals to make stuff fit better in the equations. Same for the converse though, if the problem gave dimensions in rational decimals, I might sometimes convert to fractions (again, to fit the numbers into the equation more easily/elegantly).
I don't know about math classes though, that sounds bizzare.
I have a very strong preference for leaving everything in fraction form.
It make algebra way easier to do.
I can attest to this. I tutor 15 year olds, most of them really afraid of fractions.
Many of them are now past this fear and actually agree with me when I say that fractions are actually easier than decimals (especially when a calculator is not allowed) and they say that it actually saves them time in exams.
Some of them are however not able to push past their fear and lock up completely when confronted with fractions.
Some context: Germany, 9th / 10th grade. These kids have to have a big exam at the end of the school year (so in like 3 months) that basically equals a graduation for the first / second school level in Germany.
Those that have understood fractions are all going to pass easily as that level of understanding seems to have dislodged some fear of math in their brains and they begun to really dig in to some completely unrelated problems. Basically, my feeling is that those who pushed past their fear of fractions will have no problems in their finals.
Those that still fear them, will have trouble and worry me in that regard.
Can anyone replicate these observations?
I'd wager it's because of what this guy >>7781074 said along with the proliferation of calculators over the last 50 years. As calculators made their way into academia and everyday life, fractions became less and less useful for doing everyday rithmatic so people gradually moved more and more in the direction of the decimal system.
back in high school, it took ages for my peers to understand that pi + sqrt(2) is a completely valid answer and there's nothing left to "solve"
>that's when I realized I was a special snowflake
Because working with fractions requires the person to have learned their multiplication tables as they were supposed to do when they were in middle school, but guess what, only the nerds who end up going (and have any business going) in STEM bothered to learn them. The others just scored shittily at their middle school math classes and once they were through with it never bothered to learn them.
Seriously, i'm not fucking with you. The average person never learned or have long forgotten their multiplication tables, as crazy as it may sound.
This. If you're not using, bare minimum, the 1-10 multiplication table in your head on a near-daily basis for some thought process, task, job function, something is actually wrong with you and you're actually a dumb person. I have enough faith that most people actually do do this constantly whether they're analyzing their own thought processes, they may just not happen to use 7x8, say, or 7x9 all that often.
I find the idea that a simple "multiplication-table" exercise takes until middle school somewhere (pubescent years) disturbing. I'm a Murrican and we were doing ours around age 8-9, in third grade, that is, in elementary school (IB4 lol pleb I was coding perfect number finders at age 3). Pretty soon the brighter kids were going to town with long multiplications for extra credit. It did occur to me that you may have had a more complicated form of multiplication in mind, but your "table" thing suggests straight babby-school.
Pic related is my impression of what learning elementary multiplication for the first time feels like. Anecdotally, this is a pretty autobiographical sense of the big stuff that was shown to me/that I appreciated right away. So a task of memorizing, say 144~150 different things boils down to 30~40. Which, since we have more than 5 neurons and you're supposed to be using this information constantly in daily life, is a perfectly reasonable workload to put permanently in long-term memory.
Simplifying fractions itself entails GCD checks, but in small cases these are things we can literally do in our heads (and I suspect you can too hence your confusion), so we don't even think about it in simple cases.
The meaning of the phrase/practice "fraction simplification" itself, that is of fractions with natural-number components, is to convert that fraction to one where its two parts /are/ coprime (that is, when their GCD is one), because this is both a unique and "smallest" arrangement of the original expression's information, and therefore desirable.
Therefore, if you have some fraction and you don't know whether it's simplified and you're being tested on this basic concept in, say, the sixth grade, it would be helpful to have a method (Euclid's algorithm like that anon said) to determine the GCD. If it's greater than 1, you can just divide through by the GCD (it divides both, after all!) such that the end result is a fraction with coprime components, thus simplified.
With small fractions (which is all that's really needed to make sure someone has actually got the concept down, which is the important bit), people who aren't innumerate r-tards can just do this in their heads by drawing on previously learned information such as >>7784780 . Unless of course you're learning this stuff for the first time in which case the other anon advocates exposure to Euclid's algorithm as a base/motivational starting point, but even I have a hard time believing that the algorithm itself would stick in schoolkids' heads as long as they're comfy with basic relationships of small numbers like I sketched in the multiplication case.
e.g. "simplify the fraction 595 / 700 "; -> Euc.Alg -> GCD(595,700)=35 -> div. num & denom by 35 -> GCD(17,20)=1 -> 17/20
don't be a dope, guy.
Shit, is that serious? I have been required to write down answers in the exact form since the first we've learned of irrational numbers. If someone gave the answer as an approximation they didn't get any points for the answer, just the method mostly, so we never had to expand irrationals after we first learned them, and so the surface of a equilateral triangle will be written as Asqrt(3)/4 and that's a correct answer
Is this why poland ranks relatively high in PISA tests?
Somehow math is turned into this game of finding The One True Answer so when they see 1/4 = 0.25 they hone in on the 0.25 and think it's the important shit. And 1/3 + 1/4 is 0.33 + 0.25 instead of 4/12 + 3/12 because god forbid that kids should think about what things are and how you can express them.