Back to maths

[Oprale]

After two years of inactivity I'm back to school. I'm doing maths because it's the only requirement I doesn't have yet for my diploma. Basic things like algebra, graphics, percentages etc

I was certain I was going to absolutely hate it as I never licked it before. But then, surprise ! First class of the year today, and 2 hours and a half of the 3 seem to have passed in 20 minutes.

First exercises were pretty easy and made me wonder why I ever found them difficult. Others looked like they were supposed to be a piece of cake but I just didn't got it.

Spoiler

Like, can someone tell me how I'm supposed to multiply the numerators in an equation when I changed all denominators to be the same ? ( like when 2a + 5 /3 = 18a - 21 /6 becomes 2a/12 + 5 /12 = 18a/12 -21/12 for example ). I feel like a f*cking idiot I tried to ask my teacher but he answered so fast I just faked I understood. Bad, bad mistake.

Basically I found out as long as I'm solving problems instead of being stuck, time flies. I also love how the class is different from what I knew. The teacher doesn't stand in front of the student and talks, I can just sit in a corner with my book, do my things and ask whenever I don't understand. Yeeees.

I hope everything will keep on this way. If it does, I might actually start licking maths. Weird.

 

[Cheeseumpuffs]

God, I fucking love math.

Like, can someone tell me how I'm supposed to multiply the numerators in an equation when I changed all denominators to be the same ? ( like when 2a + 5 /3 = 18a - 21 /6 becomes 2a/12 + 5 /12 = 18a/12 -21/12 for example ). I feel like a f*cking idiot I tried to ask my teacher but he answered so fast I just faked I understood. Bad, bad mistake.

2a + 5 /3 = 18a - 21 /6 should not become 2a/12 + 5 /12 = 18a/12 -21/12, it looks like you're ignoring the denominators already there.

For the problem 2a + 5/3 = 18a - 21/6 I'd start by moving like terms to the same side, so subtract 2a from both sides and add 21/6 to both.

You'll get 5/3 + 21/6 = 16a. Now you need to add those fractions but you can't do that unless the denominators are the same. You can see that the 3 in 5/3 will equal 6 if multiplied by 2, so multiply 5/3 by 2/2 since this is effectively multiplying by 1. This will give you 10/6+21/6=16a or 31/6=16a.

Now all that's left to do is get that a by itself by dividing both sides by 16. This gives (31/6)/16=a
or
a = 31/(6x16) = 31/96.

(I assume the object of this problem is to solve for a)

Spoiler

EDIT:
Oh I think I see what your question is. What you multiply the numerators by depends on the denominator in the original term.

For the terms 2a and 18a, to get them to look like <something>/12, you just multiply them by 12 (since that's basically multiplying 2a/1 and 18a/1 by 12/12), so they'll end up being 24a/12 and 216a/12, respectively.

To get the other two terms to be <something>/12, it's a little different, since they already have denominators. For instance, taking 5/3 and making the denominator equal to 12 is only like multiplying by 1/4, since there's already that 3 down there. So, in order to maintain the equality, you need to multiply 5/3 by 4/4 and you end up with 20/12. I'll let you sort out how to do 21/6 as an exercise

Spoiler

It's 42/12

I might actually start licking maths.

lol. I wish I could lick math. I'd lick that baby all night long

 

[Tannhauser]

Pretending to understand the quick answer -- we've all done that one

 

[Oprale]

Hey thanks for all the help ! Yes the answer to my question was more like answer 2 but both were helpful.

lol. I wish I could lick math. I'd lick that baby all night long

Omg. Thanks for pointing it out. I think will leave that mistake as it is. Makes the pun priceless.

we've all done that one

The fate of all lunatic students I guess

 

[HDINTP]

Lots of time left if you are just 19 I guess... I also had changable relationship with mathematics in the past and now I major in it... What would you like to study after you get your diploma you wrote about...?

 

[Oprale]

I hope my situation will turn out somewhat like yours. Maybe not majoring in maths but at least liking the subject. I feel like this could open doors to lots of knew knowledge.

The more I think about it the more it seems like I hated maths just because I wasn't good at it. I wanted to do everything on my own but I couldn't, and as stubborn as I was, I chose giving up on asking for help and actually working hard, wich led me to failure.

I don't know for sure what I want to study after that. I like arts like drawing, painting and writing, but sadly those kind of studies rarely pay off in the end. Maybe languages to become a translator, if I don't have other appealing choices. Or something about history. As you can see I really have no clear idea yet.

 

[Tannhauser]

I think math is taught in the worst way possible, which I believe is why most INTPs hate math. It is not really taught as math, but rather as a collection of arbitrary, seemingly meaningless rules.

Everything in math was invented for a reason, and was usually a result of the preferences of those who invented them. This is never told to students, for some reason. Instead it is taught as rules carved in stone, which makes it extremely boring to learn.

 

[Ex-User (9086)]

I think math is taught in the worst way possible, which I believe is why most INTPs hate math. It is not really taught as math, but rather as a collection of arbitrary, seemingly meaningless rules.

Everything in math was invented for a reason, and was usually a result of the preferences of those who invented them. This is never told to students, for some reason. Instead it is taught as rules carved in stone, which makes it extremely boring to learn.

Yes, very true.

 

[Sir Eus Lee]

What if education grabbed the smarter kids and had them deduce math alone?

For example, get them to develop their own independent notation for math principles, and get them to basically conjecture about math. I don't know how it would be possible to get them to go on a certain path of reasoning without showing how it was previously done, when they get into later math they could make conjectures others never thought of because they created the beginnings on their own.

My explanation was subpar but I hope you understood it.

 

[Oprale]

I think math is taught in the worst way possible, which I believe is why most INTPs hate math. It is not really taught as math, but rather as a collection of arbitrary, seemingly meaningless rules.

Everything in math was invented for a reason, and was usually a result of the preferences of those who invented them. This is never told to students, for some reason. Instead it is taught as rules carved in stone, which makes it extremely boring to learn.

It would be nice to see the bigger picture before learning the details, if this is what you meant I approve 100%.

 

[_cdub]

What if education grabbed the smarter kids and had them deduce math alone?

For example, get them to develop their own independent notation for math principles, and get them to basically conjecture about math. I don't know how it would be possible to get them to go on a certain path of reasoning without showing how it was previously done, when they get into later math they could make conjectures others never thought of because they created the beginnings on their own.

My explanation was subpar but I hope you understood it.

Trying to independently recreate the principles of some math topics would take forever unless you had a need to come up with it in the first place.

Some of the early stuff also depends on stuff that comes much later. For example: -B/(2a) to find the vertex of a parabola comes from the derivative of the quadratic equation (y = ax^2 + bx + c) solved for zero. Starting off algebra one, you won't be able to do that let alone generalize it.

Also, later math has many notations and conventions. Having your own set would be so confusing.

Stuff within their grasp though, I think they should be able to do some proofs so they can extend it later on.

Also...Hi first post, I saw this and had to chime in.

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[Sir Eus Lee]

Trying to independently recreate the principles of some math topics would take forever unless you had a need to come up with it in the first place.

Some of the early stuff also depends on stuff that comes much later. For example: -B/(2a) to find the vertex of a parabola comes from the derivative of the quadratic equation (y = ax^2 + bx + c) solved for zero. Starting off algebra one, you won't be able to do that let alone generalize it.

Also, later math has many notations and conventions. Having your own set would be so confusing.

Stuff within their grasp though, I think they should be able to do some proofs so they can extend it later on.

Also...Hi first post, I saw this and had to chime in.

That's awesome, its a good place to be. Mostly.

That's too bad. Maybe the school could create a need or something, I don't know.

What type are you? Just curious. I didn't see one on your profile.

(edited because this is not perC)

 

[_cdub]

INTP

And I really do think that they should have students do proofs at any math level. Everything is exposed in the process.

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[Sir Eus Lee]

That would be good, but public school is just not ideal for those things. independent study methods would be good to include that.

Some proofs aren't very explanatory though... but I wouldn't know. I took trig and I just remember that I really wasn't able to grab... I guess the essence of trig? I understood the graphs and their make up, but things like the double and half angle formulas just weren't clicking for me.

In geometry though, and algebra, im sure proofs would be much easier to grasp.

 

[Cheeseumpuffs]

I had to do proofs in my high school geometry class and they were the worst. When I got to college and had to start doing proofs again, I found them much more entertaining/intuitive.

I think kids should start earlier on that "higher" math (in my experience, several elements of higher math are simpler and more fundamental than anything you learn in high school).

I have more to say and better ways to say it but I literally just woke up and my brain still hasn't really turned on