Someone save me from my math!

[Mr. Moon]

Before I make my dog eat it. Seriously. No matter how hard I try, I cannot figure out how to find x when adding and subtracting rationals.

Here's the question I'm stuck on:

"State the value of the variable for which the equation is undefined, (easy. x =/= o) then solve it."

5/x - 2/x = 1/2

I just know it's going to be something terrificly easy that'll make me feel stupid for asking...

The slashes are supposed to represent fractions, not dividing. I have no clue how to do fractions in text without a ton of coding I don't have the patience for.

Now, if one of you math geeks here can sort of nudge me in the right direction, I would love you forever.

[Deathslayer7]

Before I make my dog eat it. Seriously. No matter how hard I try, I cannot figure out how to find x when adding and subtracting rationals.

Here's the question I'm stuck on:

"State the value of the variable for which the equation is undefined, (easy. x =/= o) then solve it."

5/x - 2/x = 1/2

I just know it's going to be something terrificly easy that'll make me feel stupid for asking...

The slashes are supposed to represent fractions, not dividing. I have no clue how to do fractions in text without a ton of coding I don't have the patience for.

Now, if one of you math geeks here can sort of nudge me in the right direction, I would love you forever.

multiple both sides by x. Distribute the x through the left side, so you get this

5x/x + 2x/x = x/2

Do it from there.

sorry made a typo. fixed it now.

[Pyrian]

Alternately, the first thing you could notice is that since the denominators are equal (x), you can just simplify the subtraction, so you get:

(5-2)/x = 1/2

3/x = 1/2

[Deathslayer7]

I also should point this out.

When you have the same denominators (the bottom part of the fraction, and in this case x), then you can add or subtract the fractions together.

ninja'ed

[Moff Chumley]

BTW, the answer is 6. Just saying.

[Mr. Moon]

You see? Terrificly easy answer I completely missed.

But, while I'm here, what do I do if I get a question like this:

3/2x = 4/3x -1/ 2

[Moff Chumley]

Multiply by 6x, so you get 9=8-3x, which becomes 3x=1, or x=1/3.

[Mr. Moon]

I tried multplying by six, but I got

9x/12x^2 = 24x/18x^2 - 6x/12x

And I have no idea how to reduce that mess. Did I do something wrong?

[Bookman]

It's a fraction so you only multiply the top number by the whole number (Think of whole numbers like 5x/1)

[Pyrian]

...what do I do if...

3/2x = 4/3x -1/ 2

Heh, I'm not sure if that's supposed to be (3/2)x - which is technically what you wrote - or 3/(2x), which is how Moff Chumley took it.

The cool thing about algebra is that there's all sorts of things you can do. One standard principle, though, is to "isolate the unknown", i.e., try to re-form the equation into something of the "x=..." variety. So, when you start with x on both sides, simply put all the x's on one side, then remove everything else, as follows:

3/(2x) = 4/(3x) - 1/2
3/(2x) - 4/(3x) = -1/2
3/2 - 4/3 = -x/2
x = -2(3/2 - 4/3)

From there, you just crunch the left side:

(-2)(3/2) - (-2)(4/3)
-3 + 8/3
8/3 - 3
8/3 - 9/3
-1/3

It certainly takes longer than Moff Chumley's solution, but it's more general and you're less likely to be embarrassingly wrong...

EDIT:

Hmm, perhaps it was (3/2)x. Let's do that one:

(3/2)x = (4/3)x - 1/2

First, get the x's all on one side by subtracting (4/3)x from both sides:

(3/2)x - (4/3)x = -1/2

Now, pull the x's out:

x(3/2 - 4/3) = -1/2

And move the numbers to the other side by dividing both sides:

x = -1/(2(3/2 - 4/3))

Now, it's just crunching numbers:

-1/(3 - 8/3)
-1/(9/3 - 8/3)
-1/(1/3)
-3

[Mr. Moon]

[It's a fraction so you only multiply the top number by the whole number (Think of whole numbers like 5x/1)

...
Wait, what?
You mean the numerator?

So it should turn out like this... *scribbles*

18x/2x = 24x/3x - 6x/2

Okay. Now what?

3/(2x) = 4/(3x) - 1/2
3/(2x) - 4/(3x) = -1/2
3/2 - 4/3 = -x/2
x = -2(3/2 - 4/3)

I could follow you just fine up until the third one. I can has words, please? I can't think in numbers. It doesn't work.

Edit: Nope. It's 3/(2x) My bad, I thought that was obvious. See? I suck at this number thing.

[Pyrian]

Okay, that third step is multiplying both sides of the equation by x. So, you go from:

3/(2x) - 4/(3x) = -1/2

Multiply both sides by x, and you now have:

x(3/(2x) - 4/(3x)) = x(-1/2)

Distribute the x's, and you get:

(3x)/(2x) - (4x)/(3x) = -x/2

At this point, you can cancel all four x's on the left side (which is why we multiplied by x):

(3/2)(x/x) - (4/3)(x/x) = -x/2

And that leads to:

3/2 - 4/3 = -x/2

From there, you multiply both sides by -2, and you've got an equation of the form "x=..."

[Douglas]

3/2x = 4/3x -1/2

First step, get that x out of the denominator by multiplying the equation by x.

3/2 = 4/3 - x/2.

Now, since this is a simple linear equation, get all terms that don't include x on one side and all terms that do on the other. Things get a little more complicated when you have things like x^2 in the equation, especially when a simple x is there at the same time.

3/2 - 4/3 = -x/2

Since the left side is all constants, go ahead and do the subtraction. This requires getting the denominators the same, so change 3/2 to 9/6 and 4/3 to 8/6.

1/6 = -x/2

Last step, get rid of the negative sign and fraction involved in the x term by multiplying both sides by -2.

-1/3 = x

Also, note that you can switch the left and right sides of the equation at any time. Anyway, x = -1/3.

[LiteYear]

I know this will be ninja'ed, but here goes anyway.

3/(2x) - 4/(3x) = -1/2

Now, you want to multiply all the values by the lowest common denominator, which, in this case, will be 6x, so:

(6x)*(3/(2x)) - (6x)*(4/(3x)) = (6x)*(-1/2)
((6x*3)/(2x)) - ((6x*4)/(3x)) = ((6x*-1) / 2))
(18x/2x) - (24x/3x) = (-6x/2)

Now, since x/x = 1, you can eliminate x from both values of the left hand side of the equation, so you get:

(18/2) - (24/3) = (-6x/2)

Which becomes:

9 - 8 = (-6x/2)

You can reduce (-6x/2) to -3x, so the equation now is:

1 = -3x

Which means x = -1/3

Edit: Corrected a simple division error :/

[Mr. Moon]

Oh, okay. That makes sense. Sort of. I think.

Thanks guys. I'll bug you again tommorow when I realize I didn't ask something I should have.

[Gray Jester]

Alright, what you probably should learn are basic fraction rules.

Adding/Subtracting:

Make the denominators the same (Multiply the first fraction by the denominator of the second fraction over itself, and the second fraction by the denominator of the first over itself, --that's the easiest way, but you might have to simply), add/subtract the numerator.

E.x. 3/2 + 2/3 => 3/2*3/3+2/3*2/2 => 9/6+4/6 => 13/6

Multiplying:

Multiply the numerator by the numerator of the other one, and the denominator by the denominator of the other one.

E.x. 2/3 * 3/2 = 6/6

Dividing:

Multiply by the reciprocal of the fraction that's dividing.

(2/3)/(2/3) => 2/3 * 3/2

Now, just do that and follow basic rules for isolating and solving for x. It's nothing new, just synthesis of different ideas. Key thing to remember is that 'x' doesn't actually make things all that harder, you just have to treat it like a separate type of number that you don't actually know the identity of.

[Knaight]

Right, the easiest method is to get x off of the bottom. Easiest method is to multiply both sides by x, so you get something like
2/x+3/2x=3 to 2+3/2=3x, to 3.5=3x
At which point just divide both sides by 3. x=1 1/6, which is about 1.166

[Deathslayer7]

yes. I concur with Gray Jester.

You shouldn't be afraid of fractions. They aren't all that bad. They are only misunderstood. Besides, plenty of more fractions come appear as the higher math level you go to, so you need to be able to add/subtract, and multiply/divide them.

[Destichado]

And if you live in the US, you'll need them all the time with our friendly Imperial Measurements system!

[Felixaar]

*flys in out of nowhere (where?) on a rope and pulls Moon Called from her desk, flying out again before letting go of the rope and leaning on a conveniently placed hilltop (it's a big rope)*

...Oh, you wanted us to actually DO the math... Yeah...

x is 6.

I mean... if 5/x - 2/x equals 1/2, then 3/x equals 1/2, making it 3/6.

(though there could be some deep, subtle rythm that I fail to grasp.)
(I passed math with flying colours, but I wasn't paying a lot of attention at the time.)

[Thufir]

OK, this has already been well answered by other people, but I feel I should point out:

The slashes are supposed to represent fractions, not dividing. I have no clue how to do fractions in text without a ton of coding I don't have the patience for.

Fractions and dividing are the same thing. A half is 1 divided by 2, 2 thirds is 2 divided by 3, etc.

[Felixaar]

Thufir's right again. (this seems to happen a lot).

Though, the first time I read that, I assumed the /'s to be multiplication signs for some reason...
(oh, must have been since 2x means 2 multiplied by x, and 2/x seems pretty close to that. I never really got used to / meaning division)

[Thufir]

Thufir's right again. (this seems to happen a lot).

Will be sig'd when I go back to my non-catmuffin sig.

[Player_Zero]

Now prove every sequence has a monotonic subsequence.

...And also that every natural number greater than or equal to four can be expressed as the sum of two primes. Do it.

[Exachix]

*latches onto the maths thread*
*doesn't let go*

Fractions (and rationals) are fun! Maths is fun!

Proofs are not. No Player_Zero. I shall not prove those.

[Thufir]

Fractions (and rationals) are fun! Maths is fun!

Hell yeah it is.

Proofs are not. No Player_Zero. I shall not prove those.

I could, since they're in my notes from either 1st or 2nd year, but finding them would be too much effort.

[Player_Zero]

I could, since they're in my notes from either 1st or 2nd year, but finding them would be too much effort.

You can prove the Goldbach conjecture?

[Pronounceable]

You shouldn't be afraid of fractions. They aren't all that bad. They are only misunderstood.

Yes, fractions are among the friendliest guys this side of calculus. Beware the functions however...

Fractions (and rationals) are fun! Maths is fun!

Proofs are not. No Player_Zero. I shall not prove those.

You're just looking at the wrong proofs. The right proofs are so much fun (right proofs being the wrong ones that contain obscure math mistakes that let stuff such as 2+2=5 being proven).

[Player_Zero]

You're just looking at the wrong proofs. The right proofs are so much fun (right proofs being the wrong ones that contain obscure math mistakes that let stuff such as 2+2=5 being proven).

Point of note: If you can prove even one thing that isn't true then you can prove that both everything is true and nothing is true at the same time.

[Thufir]

You can prove the Goldbach conjecture?

...Damn. I didn't actually check. No, I can't, it just sounded like some of the things I've seen proofs of. I can do the other one, though.