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@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?

@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.

@chevalier26 @actuallyautistic

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 @actuallyautistic Yeah, it depends on what they mean by "understand fractions", I guess. Potential subtext and all that.

@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. 😊

@dweebish

@chevalier26 @actuallyautistic so we've definitely seen textbooks that attempt to define "proper fraction" as one that is in lowest terms, has a value less than 1, and is made only of integers

but like we don't think that textbooks written for 12-year-olds should be considered the last word on technical jargon

@chevalier26 @actuallyautistic anyway, leaving aside whether "proper" is a term of art here, and how exactly it should be defined, you are absolutely correct that it's a fraction

@chevalier26 @actuallyautistic the matter is also complicated because, like, elementary-school curricula have a lot of variation in how much time they spend relating fractions to decimals

@chevalier26 @actuallyautistic the unpleasant truth that nobody really wants to admit to is that a lot of things that are taught as infallible truth to children are things some writer made up because they needed to simplify the topic, and a teacher repeated it without fully understanding the context it was invented in

@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.

@chevalier26 @actuallyautistic "proper fraction" is a mathematical term too: mathsisfun.com/proper-fraction (the rest are improper fractions. No, really).

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.

www.mathsisfun.comProper FractionsSee how the top number is smaller than the bottom number in each example? That makes it a Proper Fraction. ... More Examples (interactive)

@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

Proper is contextual.

.5 is as common form of expressing 1/2 as 1/2 is, so your fraction is nested.

@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.

@chevalier26 @actuallyautistic Math is more rules, I think, the only part of our language that does have rules, actually...

@chevalier26 All the definitions I can find for fractions in French state or imply that the numerator and denominator must be integers.

However, wikipedia's English definition gives an example with √2 as the numerator...

@chevalier26 @actuallyautistic

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 😅.

@chevalier26 @actuallyautistic A fun (to me) fact related to #fractions but really not to the rest of the topic: there exists an esoteric programming language in which every program is simply a list of fractions. It's called #FRACTRAN and was invented by John #Conway:
en.wikipedia.org/wiki/FRACTRAN

en.wikipedia.orgFRACTRAN - Wikipedia