Help a retard with fractions

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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

>>8684857
>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

>>8684891
Ah that makes much more sense.
Thanks.

>>8684891
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.

>>8684919
You're welcome.

>>8684962
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.

>>8684984
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 4chan, and it is very hard to follow, but I understand it. Literally just shat that out.

Man, I wish /sci/ 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.

>>8684995

Not the anon 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 >>8684984
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 anon, don't give up.

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.

>>8684995
>Man, I wish /sci/ had like, proper formatting for fractions and shit somehow. Like how /g/ gets their [code] [/code].

We do, this board has [math] and [eqn] tags.

For example:
[math]
\frac{9}{10}
[/math]

>>8685013
Oh.
Pardon my new faggotry then.

>>8685013
I fucked that up, meant to say "math" and "eqn" tags.

You can read a little about TeX formatting for math

Jesus Christ.

>>8685017
[math]
1{\frac{1}{10}} = \frac{11}{10} = \frac{10}{10} + \frac{1}{10}
[/math]

>>8685006

First anon here.

>only for the really smart and gifted people

That's what it becomes. When you're not taught math properly, it's only the few individuals (like myself) for whom math comes naturally that actually end up understanding it. I can't say I was taught all that well either, I could just naturally understand it. But many of my classmates would fall hopelessly behind and they too figured that math was for the "smart kids."

In my experience, it's a unique problem for math. Most other subjects can be taught by memorization. Others, like science, require understanding, but it's easier to understand and make sense of the physical world because it's concrete. Math is more abstract and takes a much better teaching method for people to have a hope of getting it.

>>8685040
It's like they say, it's just that math requires a foundation, and if the kid lacks the foundation they just try to brute force it by 'teaching' them how to do the problems but not why what they do works. They just brute force it.

I'd like to say the American education system is at fault but isn't this a problem for almost every education system in the world when it comes to math? I can't think of a single example, sans some Asian school, where the people don't have these problems.

>>8685057

Agreed. That's what complicates it even further. Every bit of math is built on the previous. You can't learn calculus without algebra. You can't learn algebra properly without fractions. You can't learn fractions without division or multiplication. And on it goes. The further you fall behind, the harder it is to catch up.

And yeah, it's definitely not solely an American problem. Canadanon here, so other countries definitely have the same issues. Though I believe Canada's schools are generally better than the US, they're certainly not perfect.

>>8685068
I'm kind of thinking now I should probably start doing some more division and multiplication, and maybe even basic arithmetic because I actually have trouble with long division and multiplication.

I can't remember my multiplication tables at all, other than 2s, 5s, and 10s and 11s, and long division is kind of a mess for me.

So far for long division, I know the pattern is like, divide, then multiply, then bring subtract, then bring down, repeat until there's a remainder/nothing left, but if it's a big number like 1254/15, I just get fucked and lost.

Alright so about decimals...
I'm looking up now how to do shit with decimals, and from what I understand it's really easy shit, but multiplying and dividing is kind of doing that same
>lol u just do it this way cus it works :^)
So how come multiplying decimals together and shifting the decimal place produces the correct answer? A decimal and a fraction are both just representing the same thing only differently(?), but that's as far as I know about the similarities.

>>8685637
say you're multiplying 5.3 and 6.72
multiplying 53 by 672 and shifting the decimal works because 5.3=53*10^-1 and 6.72=672*10^-2 and so 5.3*6.72=(53*672)*(10^-1*10^-2)

>>8685637
because multiplication is commutative

>>8685649
>>8685657
Thanks.
So I'm starting to piece this shit together now. I know how to read decimals, and I know how they relate to percents and stuff. I've read how to find the percentage of a number over and over again for tests, but now that I know how that works, I have a good feeling I won't forget it now.

6% of 9 is just 6/100 * 9/1, which is 54/100, so 6% of 9 is 0.54

Neat.

>>8685637

Me again.

You're bang on about this.
>A decimal and a fraction are both just representing the same thing only differently(?)
Fractions and decimals are just two ways of representing the same number.

What's important to note, and what might help, is that decimals are essentially special fractions. In the case of decimals, the denominator is always a power of 10 (i.e. 10, 100, 1000, etc.)

For instance, [math]\frac{1}{4}[/math] represented as a decimal is [math]0.25[/math]. Why is this? All we're doing is converting to a denominator of 100:
[eqn]\frac{1}{4} = \frac{25}{100}[/eqn]

Furthermore, each digit can be expressed as its own fraction:
[eqn]\frac{1}{4} = \frac{25}{100} = \frac{2}{10} + \frac{5}{100}[/eqn]

Thus, when multiplying decimals, you're just multiplying fractions:
[eqn]0.2 \times 0.2 = \frac{2}{10} \times \frac{2}{10} = \frac{4}{100} = 0.04[/eqn]

So you see, that's why you just need to shift the decimal place, you're multiplying the denominators of the fractions together which, since they're powers of 10, give you another power of 10.

>>8685677
Ay.
And that's why with certain decimals, in order to convert them to a fraction, if you can't get it to be a perfect power of 10 you have to get it as close to 10 as you can?
Such as a fraction with a denominator of 999 or whatevs?

>>8685680

It's tougher when it comes to fractions that are repeating. Basically, you'd create an infinite series:
[eqn]\frac{1}{3} = \frac{3}{10} + \frac{3}{100} + \frac{3}{1000} + ... = 0.333...[/eqn]
Getting it as close to 10 as you can is more of a way to approximate it.

>>8685680
>>8685694

Note, this isn't exactly meant as a way to perform the calculation, since it has obvious limits, but it's more to understand what exactly is happening.

>>8685694
>>8685697
Well now I want to go be an even bigger autist and grab data from Planetside and calculate the percentage increase/decrease my kills per death is this month over last months. Shit this is fun.

Alright so if it goes
Multiplication -> Division -> Fractions -> Algebra -> Calculus,
Where does Geometry fit into this?

>>8685967

Offshoot of algebra, I figure. Geometry then leads to trig and trig gets married back up with calculus eventually.

>>8685978
Alright.
I guess I'll study Geometry after Algebra? It still doesn't sound right though. Some things in Geometry are a lot like fractions to me.

I still have about 5 months to get up to speed on it all so I guess I have plenty of time to figure it out before I take my entry exams, but I'm the type of faggot who likes to plan every little detail out, otherwise I'll just spend all night fretting and thinking in bed.

>>8685997

Nothing wrong with planning. But yeah, it's hard to figure out a linear progression with math. A lot of it is very intertwined. For pretty basic geometry, fractions can get you far. But once you get any of those geometric proofs or "find the value of x" problems, you'll need algebra.

I seem to still be missing something, as I'm fucking with finding percentage increases/decreases and having trouble. So if I go from 3 -> 5, that's +2 to the original number. which is a 66.67% increase.

The formula for this apparently
>Increase = New Number - Original Number
>% increase = Increase / Original Number * 100
The fuck does that all work out? I tried finding the percentage increase of 5 to 12 without following the formula and just going off what I knew, and I got 120%, but it was actually 140%. Where'd the extra 20% come from?

>>8687046
Nevermind I get it.
http://mathforum.org/library/drmath/view/58166.html
Fucking percentages, man. That per 100 shit tripped me. Stuff like 140% just wasn't making sense at all to me.

>>8687046
[math] \frac{5-3}{3} = \frac{x}{100} \\
x = 66.666...% \\
\\
\frac{12-5}{5} = \frac{y}{100} \\
y = 140% \\
[/math]

Why exactly is it so hard to find things like >>8687073 that actually go into a step by step that has explanations as to why the formulas work the way they do? It's ridiculous how hard I have to dig to find explanations for finding say, percentages of a whole, that aren't just
>u do da division and den u do this :^DDD
And more along the lines of
>Well, first, you do this, and the reason why you do this is blah blah, and then once you do this you are free to finally do this, because if you recall, rada rada

How fucking hard could going into detail be, especially on a site centered around explaining shit!?

>>8687090
percentage is nothing more than representing a fraction with "100" as the denominator.
same way as you can represent 2 as [math] \frac{4}{2} [/math] and [math] \frac{10}{5} [/math], you can also write it as [math] \frac{200}{100} [/math] or "200%".

>>8687117
Kinda like how decimals are special fractions with the denominator as a power of 10? Only percentages have strictly 100 as the denominator, with the exception of stuff like 999, 333?

>>8687132

What you need to understand about fractions is that if you multiply the denominator and numerator by the same number, such as [math] \frac{3}{2} \cdot \frac{7}{7} [/math] the value is unaltered, [math] \frac{3}{2} = \frac{21}{14} [/math]. As such, when you want to write a fraction as percentage, you need to figure out what number (let's call it "x") multiplied by the denominator equals 100, and then multiply the numerator by the same x.

Example: [math] \frac{1}{5} [/math] What number multiplied by 5 equals 100? 5x = 100; x = 100/5; x = 20.
[math] \frac{1}{5} \cdot \frac{20}{20} = \frac{20}{100} = 20% [/math] You can achieve this result quickly if you just write [math] \frac{1}{5} = \frac{x}{100} [/math] and solve for x.

>Kinda like how decimals are special fractions with the denominator as a power of 10?
No, decimal form has denominator "1". [math] 4.97 = \frac{4.97}{1} [/math]. But you could multiply the numerator and denominator by 100 and get [math] \frac{497}{100} [/math], no longer decimal form.

> with the exception of stuff like 999, 333?
No.

>>8687166
percentage sign isn't displaying for some reason.
20/100 = 20%, obviously.

>>8687166
Ah that makes much more sense. Thank ya.
And yeah, doing the same to the top and bottom is something I kind of keep forgetting to do sometimes, but conceptually it reminds me a lot of Algebraic equations I did on the GED. The whole "do the same for both sides to keep the balance of the equation/the same value". Maybe I can just think of it as keeping the fraction balanced.

>>8687308
Property of multiplicative identity:
[math] a \cdot 1 = a \\
\frac{7}{7} = 1 \\
a \cdot \frac{7}{7} = a [/math]

>>8687166
Wait, so 4.97 is 4.97/1, and 0.97 is 97/100... Alright I Guess. Think I'm getting it.

497/100, that would be... 497%! Well this shit is getting much easier. Damn, I remember having the worst time ever with this stuff in grade school...

Fucking like...

How did I even pass through to the 7th grade? I don't understand.

You know what, I have a story I wanna share, in my hypoglycemic haze.

I remember being in the special ed math class with a giant cunt of a teacher. I remember being granted privileges in normal math class to use a plastic bag full of math shit.

This plastic bag contained:
>A calculator(fucking WHY!?)
>A multiplication table
>A bunch of fraction blocks
>Useless miscellaneous shit

The time came for the TAKS test, which is the big end of grade test for Texans. I was allowed to use my bag of shit on it.

So I had all this stupid shit in it, but really the only useful thing was the calculator and the multiplication table, and I really didn't even use the calculator much. I just used the table.

I managed to get a 90 on the test.

Okay, so after the test week(we didnt have the scores in yet), my special ed teacher and math teacher took me out into the hall, and they were ANGRY that I didn't use much from the bag.

They were fucking ANGRY at me for not relying on a crutch to get me through an important math test.

They spent 10 minutes berating me while I stood there not knowing what to say, since I was a bashful little faggot.

Then, scores came in, I passed, and then their fucking tune changed to

>omg anon im so proud of u :^)

Like... I don't even

>>8687326
So about properties, I'm really interested in learning more about these formulas. Stuff like the one in your post,
and here:
>>8687080
>>8685694
>>8685026
Is there a good site that has all of these and more? Stuff like the commutative property is also really fascinating to me. I want to go and play around with these.

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>>8687462

You can likely find a khan academy video for each of these.

>>8685006
>Calc 4
This is interesting. Is that Differential Equations, does the school go by quarters rather than semesters, or is the sequence geared towards people who might need serious algebra refreshers?

>>8687483
Nice.
Is Serge's Basic Mathematics really as good as /sci/ says it is? That shit is like $50. I'm starting to get a good grip on fractions now so I wanna see if I'm ready to move onto some basic Geometry or whatever else is next.

Maybe I should learn about rationals and irrationals next though. I had a lot of trouble on the GED with keeping track of negative and positives as well.

Where do those all fit in? Do they fit into fractions too?