>I have no problem solving problems but this like cant be real
It's probably not, but a frickton of people have trouble with fractions well past school.
Course a frickton of people have trouble with PEMDAS well past school too.
>You're making it more complicated
I'm not. >Just remember fraction on the denominator will get flipped
That's not how shit technically works though. As an example 1⁄1÷1⁄0 does not equal 1⁄1*0⁄1.
It's a good shortcut in most situations but dividing by a fraction and multiplying by the inverse of the fraction is not actually the same thing.
>dividing by a fraction and multiplying by the inverse of the fraction is not actually the same thing.
They are, by definition. Division by a number is the same as multiplying by the multiplicative inverse of that number. the reason you can't manipulate 1⁄1÷1⁄0 to 1⁄1*0⁄1. is because division by zero is undefined (equivalently: zero has no multiplicative inverse), so the first expression is meaningless. You can move some symbols around, but if you start with nonsense, you'll end with nonsense.
2 months ago
Anonymous
>They are, by definition
They are not, by definition, or else 1⁄1*0⁄1 would equal 1⁄1÷1⁄0.
Also you originally just said fricking flip the fraction in the denominator and I just said inverse, not multiplicative inverse, even if you did want to get into a philosophical debate about whether something which doesn't fricking exist could be different from something which does or whatever fricking nonsense you are trying to argue to save face. Flipping the fraction does not fricking work in all fricking cases and rather than learning shortcuts that can trip you up in higher level math, it's better to just learn to do shit as written.
2 months ago
Anonymous
>They are not, by definition, or else 1⁄1*0⁄1 would equal 1⁄1÷1⁄0.
that's not what "by definition" means
>Also you originally just said fricking flip the fraction in the denominator
NTA, but flipping the fraction always works if the fraction you're working with is well-defined. "if the thing you're working with is well defined" is not usually specified when talking about math, for the same reason a cookbook doesn't remind you to check whether your ingredients aren't rotten, or a guide for changing a tire doesn't remind you that you need to have a car.
>I just said inverse, not multiplicative inverse,
Yes, you said inverse, I was more specific because there are technically multiple kinds of inverse and I am a pedantic autistic asshat. We are talking about the same thing.
2 months ago
Anonymous
>that's not what "by definition" means
You're really pulling a Clinton what is is? I don't think I've ever seen that level of clownery in the wild before.
Lmao.
2 months ago
Anonymous
"by definition" needs to invoke the definition. Division is usually defined, in discussions rigorous enough where it needs to be defined, as multiplication by the multiplicative inverse. You can't say that they are "by definition" not the things they are defined to be. That's not hair-splitting, that's telling up from down.
2 months ago
Anonymous
>"by definition" needs to invoke the definition
It does not, by definition. But even if it did, I FRICKING DID with ÷((a)÷(b)). Which is obviously not *((b)÷(a)) in all cases.
2 months ago
Anonymous
1 / (a/b) = 1 * (b/a)
how is this not true?
the definition of division is the inverse of multiplication as long as the multiplier isn't 0
Why are you asking how something isn't true and then immediately replying with why it isn't true? The definition you're giving for division by fractions does not work for all values. The definition I gave does.
2 months ago
Anonymous
if you think math is something you can win a debate against, you don't understand math. You're wrong on this point, no matter how right you think you are, and it's interfering with your ability to learn.
2 months ago
Anonymous
I'm not debating math. I was right on the math from the start. Motherfrickers are debating semantics. Badly. There is not a one to one correspondence between multiplication and division and you can't tell people to act like there is without noting the difference.
Don't tutor people badly then b***h about getting called out.
2 months ago
Anonymous
Division by a number is always the same as multiplying by the reciprocal of a number. There is no exception, none. There are times when division is undefined, but in those cases the reciprocal is also undefined, so there are absolutely no exceptions.
2 months ago
Anonymous
The original dumbshit claim was that you can just flip a fraction to go from division to multiplication. >Just remember fraction on the denominator will get flipped lol.
Flipping 1⁄0 gives you 0⁄1, which last I checked is defined.
You are a dumb c**t.
2 months ago
Anonymous
You can flip any fraction. 1/0 isn't a fraction, because it's undefined.
2 months ago
Anonymous
>You can flip any fraction
You can flip 0⁄1?
So 1*0⁄1 is the same thing as 1/1⁄0?
2 months ago
Anonymous
OK, you got me, I was not pedantic enough, and I lost the random internet encounter, unironically
2 months ago
Anonymous
1/0 appears naturally in denominators of combinatorics such as in binomial coefficient
Do you have problems with other math or just fractions? If you struggle with math in general maybe your teachers as a kid were just shit, or you have dyscalculia or something. Not the end of the world but will make things harder
If it's literally just fractions there's probably some specific misunderstanding you have about them. If you can manipulate mathematical symbols to do algebra and calculus and whatever, *except for the symbols that represent fractions,* either you've learned something wrong about fractions specifically, or you have an extremely interesting neurological disorder.
Its hard to explain. Its like this with almost everything. I have zero problem solving any problems, as a kid I even did pretty well in math/logical competitions but I just cant wrap my head around anything. I ace all the practice tests I have but I still dont get it. Its like I dont understand whats going on "under the hood"
What's the actual problem you're running into, then? I think a lot of people realize they're like that by college, as long as they're not actually studying mathematics it might not be an issue.
dividing by a division makes no intuitive sense and you just have to accept it. if you have half an apple and you divide that half by half you get a full apple. why? you just do OK
>dividing by a division makes no intuitive sense and you just have to accept it.
The question "how often does a 1/4 slice of a whole pizza fit into a 3/4s of a whole pizza" really doesn't make any sense to you? >what if the slices don't have comparable sizes (e.g. one pizza is the size of an entire house)?
Then you scale one side beforehand >what if you can't even compare them because one side is a pie, the other a pizza? (i.e. they'd have different denominators)
Then you take both sides and convert them into some abstract measure, like (continuing with the analogy), calling them both just "foodstuff".
Saying dividing by divisions makes no intuitive sense has to be the ultimate mathlet filter.
I was like you, filtered hard by fractions in my teen years, and somewhat even past 20. I hated not understanding the deep roots of things and where they came from. I liked physics and natural science from childhood and was disappointed if I just gave it all up.
The remedy to this illness was Basic Mathematics by Serge Lang, cover to cover, all exercises, everyday until finished.
If you want to do something and can't immediately do a small part of it you should give up. If you give up then you won because you are in control of the situation which means you can't lose. You are then entitled to begin hating the thing you wanted to originally do and say that it is shit and you don't want to do it anyway and the people that do it are idiots
you're scaling the value to the denominator then taking numerator parts thereof. so a half divided by a half is scaling half up by 2 and taking 1 of them. dividing 1/2 by 1/4 is scaling the half up by 4 and taking 1 of them. if you're halving, you're scaling by 1 and taking 2 parts etc
>but why does multiplying by the reciprocal work? Like whats going in the "background" like what exactly is happening and why?
Read Allendoerfer and Oakley's Principles of Mathematics if you want a comprenhensive theoretical background, i.e., the logical answer to most of those "why" questions.
[math]frac{2}{5} div frac{3}{10}[/math] is how many times [math]frac{3}{10}[/math] goes into [math]frac{2}{5}[/math]. Because [math]frac{3}{10} times frac{10}{3} = frac{30}{30} = 1[/math], [math]frac{3}{10}[/math] goes into 1 exactly [math]frac{10}{3}[/math] times. To find how many times [math]frac{3}{10}[/math] goes into [math]frac{2}{5}[/math], we multiply how many times [math]frac{3}{10}[/math] goes into 1 by how many times 1 goes into [math]frac{2}{5}[/math].
if you divide it by ten, it becomes ten times smaller
if you divide it by one, it remains the same
if you divide it by one tenth, it becomes ten times larger
Probably it's not the best rationalization, but maybe it can help you more than the better one.
I wouldn't say there's anything "going on;" it's not like division is just some shortcut to represent some mystical invisible process that's what we're really interested in. Division is just an arithmetic operation. It has certain properties. It doesn't have those properties because of anything else, it has them because we wanted an operation with those properties.
You can ask WHY an operation with those properties works to represent a specific situation, like cutting up an apple or whatever, but that will boil down to showing how the situation matches the operation. The operation comes first, it isn't based on any specific situation.
what I mean its like you can say 5*5 is 5+5+5+5+5. How do you elaborate divison by fractions?
2 months ago
Anonymous
There might be something you're looking for that isn't this, but assuming b and c nonzero: [math]adivfrac{b}{c} =adiv(bc^{-1})=a(bc^{-1})^{-1}=a(b^{-1}(c^{-1})^{-1})=a(b^{-1}c)=atimesfrac{c}{b}[/math]
like I cant visualize it or imagine it. I can "imagine" dividing and multiplying but I cant wrap my hands around dividing fractions by fractions. I have no issue with dividing fractions by normal numbers. Its way beyond me but it shouldnt
Hard to diagnose without knowing exactly how you're visualizing dividing and multiplying. If you can imagine dividing by a quantity, what about that image is incompatible with dividing by non-whole-number quantities?
2 months ago
Anonymous
idk I guess I dont see fractions the same way as normal numbers. Like it cant exist on its own. Idk if Im explaining it right
2 months ago
Anonymous
so you're fine with division by, say, 1.5 but not 3/2?
like I cant visualize it or imagine it. I can "imagine" dividing and multiplying but I cant wrap my hands around dividing fractions by fractions. I have no issue with dividing fractions by normal numbers. Its way beyond me but it shouldnt
>filtered by 4th grade math
yeah, it's over for you. start filling out job applications at gas stations.
I have no problem solving problems but this like cant be real
>I have no problem solving problems but this like cant be real
It's probably not, but a frickton of people have trouble with fractions well past school.
Course a frickton of people have trouble with PEMDAS well past school too.
Just rewrite fractional a over b as ((a)÷(b)). So pic would become ((2)÷(5))÷((3)÷(10)). Then just use BODMAS. Fractions aren't that hard.
You're making it more complicated. Just remember fraction on the denominator will get flipped lol.
>You're making it more complicated
I'm not.
>Just remember fraction on the denominator will get flipped
That's not how shit technically works though. As an example 1⁄1÷1⁄0 does not equal 1⁄1*0⁄1.
It's a good shortcut in most situations but dividing by a fraction and multiplying by the inverse of the fraction is not actually the same thing.
>dividing by a fraction and multiplying by the inverse of the fraction is not actually the same thing.
They are, by definition. Division by a number is the same as multiplying by the multiplicative inverse of that number. the reason you can't manipulate 1⁄1÷1⁄0 to 1⁄1*0⁄1. is because division by zero is undefined (equivalently: zero has no multiplicative inverse), so the first expression is meaningless. You can move some symbols around, but if you start with nonsense, you'll end with nonsense.
>They are, by definition
They are not, by definition, or else 1⁄1*0⁄1 would equal 1⁄1÷1⁄0.
Also you originally just said fricking flip the fraction in the denominator and I just said inverse, not multiplicative inverse, even if you did want to get into a philosophical debate about whether something which doesn't fricking exist could be different from something which does or whatever fricking nonsense you are trying to argue to save face. Flipping the fraction does not fricking work in all fricking cases and rather than learning shortcuts that can trip you up in higher level math, it's better to just learn to do shit as written.
>They are not, by definition, or else 1⁄1*0⁄1 would equal 1⁄1÷1⁄0.
that's not what "by definition" means
>Also you originally just said fricking flip the fraction in the denominator
NTA, but flipping the fraction always works if the fraction you're working with is well-defined. "if the thing you're working with is well defined" is not usually specified when talking about math, for the same reason a cookbook doesn't remind you to check whether your ingredients aren't rotten, or a guide for changing a tire doesn't remind you that you need to have a car.
>I just said inverse, not multiplicative inverse,
Yes, you said inverse, I was more specific because there are technically multiple kinds of inverse and I am a pedantic autistic asshat. We are talking about the same thing.
>that's not what "by definition" means
You're really pulling a Clinton what is is? I don't think I've ever seen that level of clownery in the wild before.
Lmao.
"by definition" needs to invoke the definition. Division is usually defined, in discussions rigorous enough where it needs to be defined, as multiplication by the multiplicative inverse. You can't say that they are "by definition" not the things they are defined to be. That's not hair-splitting, that's telling up from down.
>"by definition" needs to invoke the definition
It does not, by definition. But even if it did, I FRICKING DID with ÷((a)÷(b)). Which is obviously not *((b)÷(a)) in all cases.
1 / (a/b) = 1 * (b/a)
how is this not true?
the definition of division is the inverse of multiplication as long as the multiplier isn't 0
1 /(3/7) = 1 * (7/3) = 7/3
1 / (3/7) = (3/7)^-1 = ((7/3)^-1^)-1 = 7/3
Why are you asking how something isn't true and then immediately replying with why it isn't true? The definition you're giving for division by fractions does not work for all values. The definition I gave does.
if you think math is something you can win a debate against, you don't understand math. You're wrong on this point, no matter how right you think you are, and it's interfering with your ability to learn.
I'm not debating math. I was right on the math from the start. Motherfrickers are debating semantics. Badly. There is not a one to one correspondence between multiplication and division and you can't tell people to act like there is without noting the difference.
Don't tutor people badly then b***h about getting called out.
Division by a number is always the same as multiplying by the reciprocal of a number. There is no exception, none. There are times when division is undefined, but in those cases the reciprocal is also undefined, so there are absolutely no exceptions.
The original dumbshit claim was that you can just flip a fraction to go from division to multiplication.
>Just remember fraction on the denominator will get flipped lol.
Flipping 1⁄0 gives you 0⁄1, which last I checked is defined.
You are a dumb c**t.
You can flip any fraction. 1/0 isn't a fraction, because it's undefined.
>You can flip any fraction
You can flip 0⁄1?
So 1*0⁄1 is the same thing as 1/1⁄0?
OK, you got me, I was not pedantic enough, and I lost the random internet encounter, unironically
1/0 appears naturally in denominators of combinatorics such as in binomial coefficient
a/b = a*b^-1
(a/b)^-1 = b/a
Do you have problems with other math or just fractions? If you struggle with math in general maybe your teachers as a kid were just shit, or you have dyscalculia or something. Not the end of the world but will make things harder
If it's literally just fractions there's probably some specific misunderstanding you have about them. If you can manipulate mathematical symbols to do algebra and calculus and whatever, *except for the symbols that represent fractions,* either you've learned something wrong about fractions specifically, or you have an extremely interesting neurological disorder.
Its hard to explain. Its like this with almost everything. I have zero problem solving any problems, as a kid I even did pretty well in math/logical competitions but I just cant wrap my head around anything. I ace all the practice tests I have but I still dont get it. Its like I dont understand whats going on "under the hood"
What's the actual problem you're running into, then? I think a lot of people realize they're like that by college, as long as they're not actually studying mathematics it might not be an issue.
dividing by a division makes no intuitive sense and you just have to accept it. if you have half an apple and you divide that half by half you get a full apple. why? you just do OK
how do you cope with that?
same way I cope with irrational numbers. math is just fundamentally flawed but it works in practise so I move on
>How many half-apples are there in half an apple?
One.
It's not even conceptually difficult.
>dividing by a division makes no intuitive sense and you just have to accept it.
The question "how often does a 1/4 slice of a whole pizza fit into a 3/4s of a whole pizza" really doesn't make any sense to you?
>what if the slices don't have comparable sizes (e.g. one pizza is the size of an entire house)?
Then you scale one side beforehand
>what if you can't even compare them because one side is a pie, the other a pizza? (i.e. they'd have different denominators)
Then you take both sides and convert them into some abstract measure, like (continuing with the analogy), calling them both just "foodstuff".
Saying dividing by divisions makes no intuitive sense has to be the ultimate mathlet filter.
I was like you, filtered hard by fractions in my teen years, and somewhat even past 20. I hated not understanding the deep roots of things and where they came from. I liked physics and natural science from childhood and was disappointed if I just gave it all up.
The remedy to this illness was Basic Mathematics by Serge Lang, cover to cover, all exercises, everyday until finished.
If you want to do something and can't immediately do a small part of it you should give up. If you give up then you won because you are in control of the situation which means you can't lose. You are then entitled to begin hating the thing you wanted to originally do and say that it is shit and you don't want to do it anyway and the people that do it are idiots
I think Im actually starting to understand
>using the ÷ symbol ever
lmfao
maybe if we taught division in terms of multiplying by the reciprocal instead of cutting up apples this wouldn't be so confusing
but why does multiplying by the reciprocal work? Like whats going in the "background" like what exactly is happening and why?
you're scaling the value to the denominator then taking numerator parts thereof. so a half divided by a half is scaling half up by 2 and taking 1 of them. dividing 1/2 by 1/4 is scaling the half up by 4 and taking 1 of them. if you're halving, you're scaling by 1 and taking 2 parts etc
>but why does multiplying by the reciprocal work? Like whats going in the "background" like what exactly is happening and why?
Read Allendoerfer and Oakley's Principles of Mathematics if you want a comprenhensive theoretical background, i.e., the logical answer to most of those "why" questions.
[math]frac{2}{5} div frac{3}{10}[/math] is how many times [math]frac{3}{10}[/math] goes into [math]frac{2}{5}[/math]. Because [math]frac{3}{10} times frac{10}{3} = frac{30}{30} = 1[/math], [math]frac{3}{10}[/math] goes into 1 exactly [math]frac{10}{3}[/math] times. To find how many times [math]frac{3}{10}[/math] goes into [math]frac{2}{5}[/math], we multiply how many times [math]frac{3}{10}[/math] goes into 1 by how many times 1 goes into [math]frac{2}{5}[/math].
>103
>10
>3
> times
lost me there
103 is 37.3*3
>90+21+0.9=103
wew lad
A thing [math]frac{10}{3}[/math] times is one third of that thing, ten times. Or equivalently, three of it, plus one third of it.
3% of 57 = 57% of 3
[math] displaystyle
frac{3}{100}57 = frac{57}{100}3 = frac{3 cdot 57}{100}
[/math]
Scabs
If you divide, you just invert and multiple. What’s there to be getting filtered about?
>fractions
You need to be 18 to post here
want a tutor?
want a bawbeh
if you divide it by ten, it becomes ten times smaller
if you divide it by one, it remains the same
if you divide it by one tenth, it becomes ten times larger
Probably it's not the best rationalization, but maybe it can help you more than the better one.
The thing is I already know and understand all this but like what the frick is going?
I wouldn't say there's anything "going on;" it's not like division is just some shortcut to represent some mystical invisible process that's what we're really interested in. Division is just an arithmetic operation. It has certain properties. It doesn't have those properties because of anything else, it has them because we wanted an operation with those properties.
You can ask WHY an operation with those properties works to represent a specific situation, like cutting up an apple or whatever, but that will boil down to showing how the situation matches the operation. The operation comes first, it isn't based on any specific situation.
what I mean its like you can say 5*5 is 5+5+5+5+5. How do you elaborate divison by fractions?
There might be something you're looking for that isn't this, but assuming b and c nonzero: [math]adivfrac{b}{c} =adiv(bc^{-1})=a(bc^{-1})^{-1}=a(b^{-1}(c^{-1})^{-1})=a(b^{-1}c)=atimesfrac{c}{b}[/math]
Hard to diagnose without knowing exactly how you're visualizing dividing and multiplying. If you can imagine dividing by a quantity, what about that image is incompatible with dividing by non-whole-number quantities?
idk I guess I dont see fractions the same way as normal numbers. Like it cant exist on its own. Idk if Im explaining it right
so you're fine with division by, say, 1.5 but not 3/2?
somehow yes
like I cant visualize it or imagine it. I can "imagine" dividing and multiplying but I cant wrap my hands around dividing fractions by fractions. I have no issue with dividing fractions by normal numbers. Its way beyond me but it shouldnt
Convert them to decimal numbers if you're having trouble affirming whether the answer is right intuitively
If you're talking about pic, then I think this is just well-formed math -- you can arrive to it with some algebraic manipulation.