Okay, so in preparation for STEM, I've decided to go and try to brush up on everything from the ground up, going from Fractions -> Algebra -> Calculus -> whatever
So I'm at Fractions right now, and I think I understand the gist of it. I understand mixed numbers and how they work, along with improper fractions, but I'm a bit confused about conversions.
Okay, so 11/10 = 1 1/10. That makes sense. 1 whole in this sense would 10/10, and 11/10's numerator has a single 10 that goes evenly into it, thus it has a single whole, and all that's left is 1 part of another. 1 1/10.
But to convert this into an improper, you multiply the whole number by the denominator, then add that to the numerator.
My question is why is it that this works? How come multiplying the whole number of a mixed number by the denominator and then adding that to the numerator gives you the correct mixed number? All the explanations I've tried to look up on this online are just >becus thats how u do it :^) I want to know WHY you do it though.
The trick is understanding what each part of the fraction means.
The denominator is the size of piece you cut each whole number into.
The numerator is the number of pieces you have.
When combining fractions, or converting from mixed fractions to improper fractions, the pieces need to be the same size. Think of 1 1/10 as 1/1 + 1/10. In order to combine them, you need to chop up the 1 into 10 pieces. If you chop something into 10 pieces, you get 10 of them (hence multiplying by the denominator).
So 1 1/10 = 1/1 + 1/10 = 10/10 + 1/10 = 11/10
Levi King
>How come multiplying the whole number of a mixed number by the denominator and then adding that to the numerator gives you the correct mixed number?
You have 1 which is 10 tenth. You add 1 tenth. that gives you 11 tenth, that is 11/10
Brody Carter
Ah that makes much more sense. Thanks.
Cameron Gutierrez
Oh wow in retrospect this is really neat. I almost completely forgot that whole numbers can be expressed as fractions.
So the number 1, it's actually a fraction, 1/1, and it's just a number that is actually cut into pieces that are 1 sized. Alright that's pretty neat. Fractions are cool.
Gabriel Howard
You're welcome.
Math is kinda beautiful when it all starts to click together. By extension, you'll also notice that any whole number can be expressed as a fraction: 3 = 3/1 and can be expressed further as fractions of smaller pieces: 3 = 3/1 = 6/2
It's all fractions, man.
On a side note, this whole comment shows the problem with math teaching nowadays: >becus thats how u do it :^)
Schools don't teach math to understand, just to memorize. All people come out of school with is the ability to know HOW to do get the right answer, but not WHY it's right. It's no wonder there are too many people who think math is hard.
Henry Sullivan
Yeah this is really neat. I have my scratch paper infront of me right now and I'm playing around with it and it's all making much more sense now that I know that numbers are also expressed as fractions.
So if I have 1 1/2, I actually have 1/1 and 1/2, and since the denominator is just how big the pieces of something are, and the numerator is how many I have, I can take that 1/1 and I can cut it into 2 equal sized pieces, giving me 2/2, since I still technically have the same amount of pieces, but just in different sizes now, and I can take that 2/2 and add it to that 1/2 to get 3/2, since I'm taking another equally sized 1/2 piece and putting it into the group of other 1/2 sized pieces I have, giving me 3 total 1/2 pieces.
That was the most retarded and convoluted shitty explanation I've written on Veeky Forums, and it is very hard to follow, but I understand it. Literally just shat that out.
Man, I wish Veeky Forums had like, proper formatting for fractions and shit somehow. Like how /g/ gets their [code] [/code].
And yeah, school fucking failed me.
I always thought I was just shitty at math and it was too hard, and when I went to 'special classes', I grew to HATE it because of the teacher who would literally YELL IN MY FACE if I didn't understand.
I dropped out of middle school and started studying at my own pace, and I managed to get my GED with honors with my shitty math understanding, but now I'm putting more effort into things and going out of my way to find out the why, and I'm having way more fun and enjoyment and satisfaction out of this stuff. Math is really cool.
I am legitimately sad that I never got to enjoy this in grade school.
Kevin Smith
Not the user you were talking too, but I'm glad you're enjoying it.
I myself used to hate math with a passion back in high school, and thought it was an intimidating subject that was only for the really smart and gifted people.
Now I'm finishing up calc 4 at my local community college, and am planning to transfer to a University next fall to major in computer Engineering.
As said, schools don't want you to understand the material taught. They just want you to memorize enough so that you can graduate and get out. When I started working with teachers that actually gave a shit about making me learn the material, and took the time to explain stuff to me I surprised myself with how much I started to enjoy the material.
You have the right attitude user, don't give up.
Jonathan Gomez
Holy shit I just went and did an algebra problem I pooped out and it made 100x more sense now that I know how this fraction shit works a lot better.
3x + 5 = 7, so x will be equal to 2/3, because 3 * 2/3 is basically 3/1 * 2/3, since the 3 is just me having 3 pieces that are size 1, and multiplied I get 3/1 * 2/3 = 6/3, simplified down to 2/1, and then 2/1 + 5 is 2/1 + 5/1, meaning I get 7/1, and 7/1 is 7, making it correct.
Damn, I knew how to solve equations, but I didn't know why the x value was correct, but now that I have this fraction shit down I understand it more. That's pretty neat. I can't wait to learn more.
Isaiah Cooper
>Man, I wish Veeky Forums had like, proper formatting for fractions and shit somehow. Like how /g/ gets their [code] [/code].
