- 25 May '05 01:09 / 1 editlet's say that we have 2y+10 over x + 3. We need to add that fraction to 2y+20 over 1/2x + 1.5 . the logical thing to do would be to multiply the second fraction by 2 to get common denominators, right? so we should multiply the top of the second fraction by 2 over the bottom half times 2. but if you multiply something by 2 over 2, isn't that kind of just like multiplying it by one? 2/2= 1...

2y+ 20 x 2

-------- --

1/2x+1.5 2... 2/2 is one, so why do we get a different fraction when multiplying by one?

what about simplifying? how can you simplify something like 20/4 by dividing it by 2 on each side? 2/2 is one - 25 May '05 03:29 / 1 edit

The whole POINT of multiplying by, say, 2/2 is that you're not changing the value of something, just the way of writing it. What's paradoxical about that?*Originally posted by Duck Duck Goose***let's say that we have 2y+10 over x + 3. We need to add that fraction to 2y+20 over 1/2x + 1.5 . the logical thing to do would be to multiply the second fraction by 2 to get common denominators, right? so we should multiply the ...[text shortened]... y something like 20/4 by dividing it by 2 on each side? 2/2 is one**

20/4 = 5, and 10/2 = 5, and 5/1 = 5. The whole aim is to write something in the simplest way possible.

There are no 'sides' to your 20/4 example, by the way, an EQUATION has sides. - 25 May '05 11:02 / 1 edit

EXACTLY! That's what I'm saying. What is your problem with that idea?*Originally posted by Duck Duck Goose***but isn't 2/2 one? that way, when you multiply the fraction by 1, it doesn't change anything**

You said in your first post, "you get a different fraction". It's a differently written fraction WITH THE SAME VALUE.

Try putting any value of x in both of your fractions, you will get exactly the same answer. - 01 Jun '05 08:37Yeah, we're friendly...

You'll agree that your second fraction is 'ugly'. To write is in a simpler form you have to do something to it, without changing the value of the fraction in all points x.

EG instead of writing 1/(1/2) you simply write 2. What we did here is multiply 1/(1/2) with 1=2/2. The same trick can be done to other fractions as well, like yours for example.

Multiplying with 1 doesn't do anything, you're right about that. But i CAN change the way we write something. There are many way to write one single fraction. We resort to tricks like this to write them in the most convenient form. - 01 Jun '05 09:25

it can be very useful, for instance 2/(2^0.5), i.e. two divided by root two, is actually root two! miltiply by (2^0.5)/(2^0.5),*Originally posted by TheMaster37***Yeah, we're friendly...**

You'll agree that your second fraction is 'ugly'. To write is in a simpler form you have to do something to it, without changing the value of the fraction in all points x.

EG instead of writing 1/(1/2) you simply write 2. What we did here is multiply 1/(1/2) with 1=2/2. The same trick can be done to other fractions as we ...[text shortened]... te one single fraction. We resort to tricks like this to write them in the most convenient form.

2 2^0.5

------- x -------

2^0.5 2^0.5

=2 x 2^0.5

--------------

. 2

the two's cancel, so your left with 2^0.5. i still find that beautiful... - 02 Jun '05 16:59

actualy this example isn't even as complex as that.*Originally posted by genius***it can be very useful, for instance 2/(2^0.5), i.e. two divided by root two, is actually root two! miltiply by (2^0.5)/(2^0.5),**

2 2^0.5

------- x -------

2^0.5 2^0.5

=2 x 2^0.5

--------------

. 2

the two's cancel, so your left with 2^0.5. i still find that beautiful...

x/(x^.5)=(x^.5)^2*(x^.5)^-1=(x^.5)^(2-1)=(x^.5)^1=x^.5