@actuallyautistic#actuallyautistic Somehow got into an argument earlier about fractions with my parents, especially the fraction 15/16. I said that 7.5/8 is the same thing as 15/16, because they can be converted to each other by multiplying or dividing the numerator and denominator by 2.
My mom basically said, no, that's not right because it's not a "proper fraction" which doesn't make sense to me. The math checks out, and numerators can have decimal integers. Is there something I'm missing?
I see both sides in this, and if I had to choose a side, I'd pick yours. Been a long time since my undergrad math minor, so could be stoking the fire here. Ask them if they'd be ok with (15/2)/8?
I've had to carry around fractions like that in solving problems, especially if it was something like (1/3)/7 as an intermediate.
As such, (15/2)/8 is an acceptable form, and as far as I'm concerned, I'm good with reducing that numerator to 7.5, so 7.5/8 it is. 😬
@uss_oatmeal@actuallyautistic Unfortunately I think they'd say 15/2 is also not a proper fraction, and to be fair, it isn't one because the numerator is larger than the denominator. But "15/2" was absolutely the math I was doing in my head.
The issue arose because my mom uses a certain data entry system at her job that uses standard form fractions and decimal equivalents in sixteenths (e.g., 5/16 would be 0.5 in their system). Which is WAY more confusing to me than my own mental math 😅.
@katrinakatrinka@uss_oatmeal@actuallyautistic Yep! And that's why the system is confusing. It's set up so that 1/16 = 0.1, 2/16 = 0.2, etc. all the way up to 15/16 = 0.15 and 16/16 = 1.0. I have no idea who thought of this but it makes absolutely no sense.
The company is called Hood Container and they make packaging, corrugated, and graphic displays. My mom said that the sixteenths system is for determining the thickness of different types of corrugated, but that still doesn't explain WHY the system is set up that way. I really don't know.
@moz@katrinakatrinka@uss_oatmeal@actuallyautistic I think Hood Container might be using the decimal inch system for these measurements. At least, that's the closest thing I've found so far. But it still doesn't explain the decimal values for fractions over 9/16. My best guess is that it's a system unique to Hood Container, or at least to packaging companies.
@katrinakatrinka@uss_oatmeal@actuallyautistic So I heard my mom talking about this system again today, and I think she accidentally said the wrong things yesterday without realizing it. It should be 0.01 for 1/16, 0.02 for 2/16, etc.
She definitely got mixed up yesterday because I 100% heard her tell me that 0.1 was 1/16 in the system. I apologize for the confusion! I think it is actually the decimal inch system after all.
@chevalier26@actuallyautistic It's the same, but it's not a 'proper' fraction in that we express fractions as most people know them in common parlance as whole number/whole number. If you talk about the ratio of one integer to another, it's also the same, but when I type in '7.5/8', what comes up via the google is 15/16. Your 7.5/8 is an expression of the ratio, 15/16 is the fractional equivalent.
@servelan@actuallyautistic 100% agree. I think the underlying problem is that I approach math in terms of patterns (though admittedly, I make careless mistakes with a lot of the simple things), so all of those decimals, ratios, and fractions are floating around in my mind as equivalent even though they basically look nothing alike. Idk how to explain it.
It's why I struggled with some areas of math throughout high school because said areas took me longer to find patterns in.
Perhaps a computer language. But not human language.
While the "rules" of grammar are generally logical, they often aren't and are often inconsistent.
More importantly, they "rules of grammar" are not the summation of human language. We frequently ignore, break, or change the rules to facilitate communication. You can't really do that with math.
I think that math is a language, not the other way around
And there is so much implicit meaning and context in a lot of sentences that it feels more like the shorthand notes of a longer, more explicit conversation.
It almost feels to me as if grammar and structure mostly contribute to make text sound better, while adding little meaning.
I say that only autistic people actually communicate in language. Normal people hear something akin to the bleating of livestock, and modulate their words whether they want to antagonize or soothe. I find this absurdly frustrating, especially since they never even tell me that's what they're doing. I call it, "throwing my words in the garbage".
Kurt Vonnegut said the content of almost all human conversation is, "I'm alive and so are you."
@ndvirons@Uair@chevalier26@actuallyautistic Decades ago, it was discovered that six month old babies, who can't do math and don't have language to speak of, recognize that three tones equals three dots.
Noam Chomsky's 'black box' theory, that we have the capacity to learn language, includes math - 'how many' is part of language.
Try to describe this picture without using 'math words' and all you can do is say 'cookie' six times:
@servelan@ndvirons@Uair@chevalier26@actuallyautistic
whups - except that was apparently a different conversation.
I said, I do my math better in English, that “order of magnitude,” means something to me while “exponents,” not so much.
.
I go so far as to think I grasp deep time and big numbers as well or better than some, despite being math challenged. 🙄
Chomsky's theories are irrelevant to that finding.
Specifically, we know that infants are hardwired to look for co-occurring cues of all kinds.
They're working around the clock to sift through all their simultaneous sensory streams for patterns, and this also includes trying to induce how to move their body based on random movements.
That's General Intelligence, which is what Chomsky tried to claim we didn't use for language.
He was wrong. The so-called Language Acquisition Device is pseudoscience, unmotivated, and not in evidence now or then.
Consider that a body doesn't know how many limbs it will have, or what they will be like.
"How to move your limbs" isn't something that can be hardcoded, but "How to learn how to move your limbs" is.
It is the same with the senses (you might be myopic from birth, or hard-of-hearing or something else, or you might be that lucky first mutant with a functioning third eye at the nape of your neck) - so the brain can't have how-to-use hardcoded, but can have how-to-learn-how.
When I went to school (and google supports me now), a proper fraction was defined as one in which (numerator < denominator). Thus 9/8 is an improper fraction, and 7.5/8 is a proper fraction.
Typically people either use decimals or fractions, not both. The combo is kind of weird because if you're going to use decimals just use decimals. 3.5/5 or 0.7... you might as well just use the latter.
The real fun is prime denominators because that tweaks people who use imperial units. It's not 15/32nds of a furlong, it's 8/17ths.
@moz@actuallyautistic Yeah I get that; actually I think that's what threw my parents off. I was used to seeing those kinds of fractions on school assignments, and even school grades (e.g., 89.5 out of 100 points), and it never really crossed my mind that 7.5/8 was "weird," since I was just converting it to a decimal, 0.9375.
@moz@actuallyautistic I guess, really, the way to do this would not be 7.5/8, but instead (7 1/2)/8. That makes just as much sense in my head but keeps everything uniform.
@chevalier26@actuallyautistic Is she calling a non-proper fraction because of the decimal point in the numerator? Maybe? Because the math looks right to me. 🤷♀️
@JulieB@actuallyautistic Yep. That’s exactly why. She also said it’s “not normal” to see those types of fractions in academia and I was just speechless like…have you never taken any math classes ever 😭?
Just because one of her entry systems at her job only takes whole integer fractions doesn’t invalidate the mathematical reality of decimal numerators lol.
@actuallyautistic Not only that, but I was accused of "not knowing how fractions work" even though the math works perfectly and each time I was told I was "wrong," I explained what I actually said and it became clear that my parents misunderstood me.
They still don't agree that it is a valid fraction, even though there's no reason it shouldn't be. It may not be in "standard form" but it is a proper fraction.
Firstly, it depends on what she means by a "proper fraction." As others have said, there is a definition.
Secondly, it depends on how much math your parents have studied. I can make an argument that if they've had only a bit or have studied advanced mathematics at uni, in either case they might object to it as a fraction (though in the latter case, they'd probably not use the term "proper fraction").
After that, although arithmetically correct, it's usually not done. It can make equation manipulation a real headache (ok, more of a headache in some situations). It's more of a best practices thing. Were a student/offspring come to me with (7.5)/8, depending on their background I'd use different ways to dissuade them from using that notation.
So, yes, the arithmetic checks out. It's generally not represented in that way for reasons.
Edit to say: It may depend, too, on why you're reducing the fraction. If this is for a uni assignment, depending on the instructions/assignment professors may not accept it as a valid fraction.
@dweebish@actuallyautistic I completely agree on all fronts. I remember having to do complex math problems with fractions like that and they were indeed a pain in the neck lol.
My point in bringing it up in discussion was just a "this is equal to that" type thing. 15/16 is already in standard form, so there's not really a reason to simplify it further anyway.
Though I don't understand how equating 7.5/8 (a hypothetical) to 15/16 means I "don't understand fractions" as my parents claimed.
@chevalier26 If by "understand fractions" they mean "know and appreciate that by the definition we learned, it's a division with two integers", then they're technically correct. 😊