1 over anything is its inverse. the opposite of multiplying is dividing. when you say a quarter of something, you mean x multiplied by a 1/4 (which is the same as dividing it by 4), so it figures that dividing it by 1/4 will have opposite effect ie. multiplying it by 4.
Rules of indices changed ma life, srsly <333
1/2 divided by 1/4 is the same as 1/2 times by 4/1?
Yeah, I could have probably edited that post a little better but fact is I know how it works. There's a difference between making a mathematical mistake and not understanding mathematics at a basic level.
Someone's asking for the logic of a mathematical operation to be explained. It's perfectly reasonable. I for one remember being quite perplexed by the fact you could make something bigger by dividing it by something else the first time I found out. Evidently it was never explained to her exactly what was going on. Hardly her fault, is it. And frankly, considering some of the responses, like "Just multiply by the reciprocal", which does indeed give you a method of calculating the answer but does absolutely nothing to explain the logic behind, and indeed "It's like asking why we call it a 'sunrise'", I'm sceptical as to how firm a grip the majority here have on the basic concepts of arithmetic.
You don't actually make anything bigger, you give it a new name.
cake  in total you still have half a cake, you have just decided to call it TWO 1/4s of cake.
Nothing has really changed.
You split it in 2. What does it mean to divide something by 3? You split it in 3. What does it mean to divide something by 1/2? You split it in 1/2. No, wait... That can't be right; that's just the same as splitting it in 2. OH GOD, WHAT'S GOING ON?!
I still think it's a sad reflection on our education system that this question even needed to be asked, let alone that people seem not to find it remotely strange.
but will come down hard on people who aren't doing well at English.
I would say the issue in the original post is one that involves English, though. Surely basic maths begins with knowing what
1

2
represents  one divided by two  but also that it is commonly known as a 'half'. Similarly
1

4
is known as a quarter. We know what a quarter is outside of maths, we can see it in our heads for any object. And we also know that two quarters make a half. This isn't maths, this is part of English, part of life. Just as learning the times tables isn't about maths at all, it's about you knowing immediately that 7 x 6 is 42 without having to calculate it so that other mathematical calculations will be much easier.
but in basic maths, you don't generally divide or multiply by fractions. It's not something that you generally need for everyday life, and something that's not early in the syllabus for that reason. Given the mathematics involved in the dividing that you do from a young age and the linguistic idea of dividing something always making it smaller, it's natural for many people to be confused by the idea that 0.25/0.5 = 2.
Even the cake examples given above are counter intuitive, because they don't work the way we're taught in the first place... a typical cake related example would be "If I have two cakes and divide them into 4 portions, how much cake does each person have." We all know that's a half.
2
 = x
4
The examples above are different though, both in language and in terms of algebra. Using the numbers I've given, here, they're asking "if I have two cakes and divide them into halves, how many pieces do I have?" i.e.
2 ... 1
 = 
x ... 2
The algebra is very different, your unknown is in a different place and it's not something that's taught from a young age  as much because decimals are often preferred to fractions as anything else. Worse still, stick more fractions in there and it just becomes a mess...
1

2
 = x
1

4
Is it really any surprise that people who don't have particularly logical minds struggle with it?
but also a fairly acceptable question, i suppose. I mean, fractions ARE kinda difficult to get your head around, and sometimes the rules (more complicated than simple division, natch) get me confused.
But i love them. i love maths, and it's rules. it makes sense to me. much more sense than that bullshit called english. who's with me.
do it as 50 divided by 25
in other words as a %
make sense?
not to me, no.
surely its 1/2 divided by 1/4, not 50, divided by 25.
i mean by that,
0.5 / 0.25
.
there are 2 1/4s in a 1/2
think of it like pie
4 is the inverse of 1/4
1 over anything is its inverse. the opposite of multiplying is dividing. when you say a quarter of something, you mean x multiplied by a 1/4 (which is the same as dividing it by 4), so it figures that dividing it by 1/4 will have opposite effect ie. multiplying it by 4.
Rules of indices changed ma life, srsly <333
1/2 divided by 1/4 is the same as 1/2 times by 4/1?
There are 2 quarters in a half
How many quarter cakes are there in half a cake? There are 2.
It all makes sense with cake
This programme is making me wish I was still at school so I could get maths homework
I really used to enjoy neatly writing out all the equations on that squared paper, with my good pen. Golden years.
it's making me really reconsider becoming a primary school teacher
making such young children take exams like that seems ridiculous
in primary school teaching you have to learn about stuff like
all the times tables by constant multiplication by 2, just incase some weirdo child does it that way.
i dont even understand what that is.
im going to be awful at this
we weren't allowed to use ink in maths
it sent out the totally wrong message to the children, like, kids ur inevitbly gonna do it wrong you are all such bampots.
We weren't allowed pens in primary school either.
It's hardly dumbing down. Pencils have been traditional school fodder since their invention, I'd guess.
who said primary school?
cheer up Theo
Ah,
Should have read^
Ah, yellow and blackstriped with a red cap
Zeebo has all the answers.
http://www.coolmath4kids.com/fractions/fractions08whichfractionisgreater01.html
please, allow me to interject;
LOL
What the fuck?
I take it you failed GCSE maths?
a half = 1 divided into 2 or 1/2
a quarter is 1 divided into 4 or 1/4
This is like asking why 1 and 1 is 2 or why we call it a 'sunrise' and not a 'remote helium fusion unit ascension', surely?
well I'll be using remote helium fusion unit ascension in future, that's for sure
Sorry but it's beyond elementary maths into why is a table called a table.
But not in a chinstrokey, goatee wearing, I'm cool but in reality I'm not sort of way.
i take it you failed gcse english
*sigh*
Yeah, I could have probably edited that post a little better but fact is I know how it works. There's a difference between making a mathematical mistake and not understanding mathematics at a basic level.
Not really
Someone's asking for the logic of a mathematical operation to be explained. It's perfectly reasonable. I for one remember being quite perplexed by the fact you could make something bigger by dividing it by something else the first time I found out. Evidently it was never explained to her exactly what was going on. Hardly her fault, is it. And frankly, considering some of the responses, like "Just multiply by the reciprocal", which does indeed give you a method of calculating the answer but does absolutely nothing to explain the logic behind, and indeed "It's like asking why we call it a 'sunrise'", I'm sceptical as to how firm a grip the majority here have on the basic concepts of arithmetic.
http://www.youtube.com/watch?v=2QamU48NUw
You can make something bigger by dividing it by something?
Oh yeah, anything less than one. Oh yeah.
You don't actually make anything bigger, you give it a new name
cake  in total you still have half a cake, you have just decided to call it TWO 1/4s of cake.
Nothing has really changed.
I think you should do that math again
I'm flattered, here goes
You don't actually make anything bigger, you give it a new name.
cake  in total you still have half a cake, you have just decided to call it TWO 1/4s of cake.
Nothing has really changed.
omg are you calling me bad at maths?
I'm having trouble understanding why it needs an explanation.
It's just there staring you in the face.
What does it mean to divide something by 2?
You split it in 2. What does it mean to divide something by 3? You split it in 3. What does it mean to divide something by 1/2? You split it in 1/2. No, wait... That can't be right; that's just the same as splitting it in 2. OH GOD, WHAT'S GOING ON?!
As I said below Colinzeal's post, I was very wrong in this thread.
And I'm sorry.
...
Bloody hell
It's commonly thought
(and indeed taught in GCSE science) that solar energey is generated by hydrogen fusion.
Good point.
Duh!
OH MY GOD WHAT A BUNCH OF IDIOTS...
everyone in this thread is ridiculously smug
bit meansounding, but essentially a very fair point
this is pretty basic maths, no?
Shit, I'm really REALLY sorry now if brusma reckons it was fair but a bit mean sounding...
guys guys guys,
theo has a BINARY watch. just ignore him.
I thought it was obvious
when dividing by less than one you end up multiplying.
When multiplying by less than one you end up dividing do you not? 4 x 0.5 is obviously 2 so why is it difficult to understand the opposite way around?
I'm rubbish at explaining, stick to the cake...
what about when you're dividing by negative integers
essentially you're calcuting how many times 1/4 will go into 1/2
this is the best explanation
zapsta and his cake also works.
calcuting? calculating*, even
how did i only get 13/14?
boy that maths degree was a waste of time
how did i only get 13/14?
boy that maths degree was a waste of time
maths is for gays
is it?
do they need it to have gay sex?
they probably refer to boners as minus eights.
I love things about numbers
I struggle to understand them as I'm a bit of a douche but I still love them
The Horizon's show about Infinity was pretty good
http://www.bbc.co.uk/iplayer/episode/b00qszch/b00qsz5w/Horizon_20092010_To_Infinity_and_Beyond/
Yeah it was alright but it went on forever
*polite applause*
nice.
That was great.
Parts of it made my head hurt a bit though.
Just wait till you hear about 0.9 recurring
your head will asplode
IT'S ACTUALLY ONE!!!!!!
I love that. SO MUCH!
i have this proof on a postit note
on the side of my work computer.
my boyfriend refuses to believe that 0.9 recurring is exactly the
same number as one.
IT IS THOUGH
check it
1 divided by 3 = 0.3 recurring
0.3 recurring x 3 = 0.9 recurring
so 0.9 recurring = 1
they are exactly the same! he's still like 'they can't be EXACTLY the same, but they are. MATHS
I would like to apologise for my behaviour in this thread.
I still think it's a sad reflection on our education system that this question even needed to be asked, let alone that people seem not to find it remotely strange.
it's a simple disconnect between linguistic logic and mathematical logic
the word 'divide' in its linguistic usage implies splitting into smaller groups, in its mathematical usage the groups aren't necessarily smaller
some people are wired more linguistically than mathematically, some vice versa, many learn to balance through technique and learning
there's nothing more to it than that
Unfortunately UK society is happy to let people get away with being rubbish at maths
but will come down hard on people who aren't doing well at English.
I would say the issue in the original post is one that involves English, though. Surely basic maths begins with knowing what
1

2
represents  one divided by two  but also that it is commonly known as a 'half'. Similarly
1

4
is known as a quarter. We know what a quarter is outside of maths, we can see it in our heads for any object. And we also know that two quarters make a half. This isn't maths, this is part of English, part of life. Just as learning the times tables isn't about maths at all, it's about you knowing immediately that 7 x 6 is 42 without having to calculate it so that other mathematical calculations will be much easier.
Yes
but in basic maths, you don't generally divide or multiply by fractions. It's not something that you generally need for everyday life, and something that's not early in the syllabus for that reason. Given the mathematics involved in the dividing that you do from a young age and the linguistic idea of dividing something always making it smaller, it's natural for many people to be confused by the idea that 0.25/0.5 = 2.
Even the cake examples given above are counter intuitive, because they don't work the way we're taught in the first place... a typical cake related example would be "If I have two cakes and divide them into 4 portions, how much cake does each person have." We all know that's a half.
2
 = x
4
The examples above are different though, both in language and in terms of algebra. Using the numbers I've given, here, they're asking "if I have two cakes and divide them into halves, how many pieces do I have?" i.e.
2 ... 1
 = 
x ... 2
The algebra is very different, your unknown is in a different place and it's not something that's taught from a young age  as much because decimals are often preferred to fractions as anything else. Worse still, stick more fractions in there and it just becomes a mess...
1

2
 = x
1

4
Is it really any surprise that people who don't have particularly logical minds struggle with it?
Fair dos.
I accept my very wrongness here.
Sorry.
APOLOGY REJECTED
I'll reject you!
Happy birthday x
kinky
x
this is quite funny, true
but also a fairly acceptable question, i suppose. I mean, fractions ARE kinda difficult to get your head around, and sometimes the rules (more complicated than simple division, natch) get me confused.
But i love them. i love maths, and it's rules. it makes sense to me. much more sense than that bullshit called english. who's with me.
You need both.
And physics.
Biology and chemistry can get tae fuck, though.
steady on about chemistry, son
Biology:
The ladies' science.
:safety wink:, obviously
In this thread:
"SHE'S A GIRL SO IT'S FINE, EVERYONE. THIS IS HARD FOR SOME PEOPLE, OK??"
RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE RABBLE
the reason for this strange behaviour?  'We must be working for the skin trade'
verbalise it, how many 1/4s go into 1/2?
i.e. 2
I hate maths.
It's like taking a shit after a vindaloo; necessary, but a pain in the arse regardless.