Simplifying Fractions

paulb203 · 2025-04-15 22:25:18

Key;
o=radius when in orbit
E=radius when on surface of Earth

**
Simplify the following fraction to the point where the ‘Gm1m2’ part is simplified to ‘1’.

Numerator; (Gm1m2)/(ro)^2
Denominator; (Gm1m2/(rE)^2

Sorry for the unorthodox way of stating this but I haven’t yet mastered BBcode (I haven’t even started with it yet).

**
The only way I can think of simplifying Gm1m2 to 1 is to divide it by Gm1m2. But then I would also have to divide the denominators by Gm1m2 and that doesn’t look possible.

ktesla39 · 2025-04-15 22:49:40

Hi,
If you want to reduce the Gm1m2 part, heres a way:

let, a be the answer

[Gm1m2/(ro)2]
------------------ = a #I also dont know BBCode
[Gm1m2/(re)2]

Now cross multiply

Gm1m2 Gm1m2*a
--------- = -----------
(ro)2 (re)2

Divide both sides by Gm1m2:

1 a
------ = -----
ro2 re2

Again cross multiply

re2
----- = a Is the reduced form.
ro2

Is this what you wanted?

Last edited by ktesla39 (2025-04-15 22:51:42)

ktesla39 · 2025-04-15 23:02:35

Or even a simpler way:

a
----
b
----------- Compare with ur eqn.
a
-----
c

a a
------ x (------)^-1
b c

a c
------- x ------
b a

Cancel out a and a-1

c
-------- Is simplified form.
b

Bob · 2025-04-16 00:27:16

To divide by a fraction, invert it and multiply.

Do you know why this works? **

**

Multiply top and bottom by d/c

bbcode: Get started here: https://www.mathisfunforum.com/viewtopic.php?id=4397

If you click on any part of the above you will see the underlying code.

It looks complicated because of the nested fractions. The command for a fraction is \frac{numerator}{denominator}

I often get in a muddle with the number of {{{ }}}.

What is not shown by that is that each line starts square bracket math and ends square bracket /math

Bob

ktesla39 · 2025-04-16 00:49:28

I tried LATEX but couldn't get any sucess. How to type latex command here or what's the syntax? I am also learning symPy to display such equations in python.

Bob · 2025-04-16 02:12:53

Latex commands are 'called' by inserting them between the opening and closing command math

It used to be possible to suppress the action be using another bbcode command, code, but it seems to no longer work, probably happened when the forum switched to a new server. So I'll leave off the first open bracket and the last close bracket to avoid the code interpreter trying to action the code. Then I'll repeat but with all the brackets, so you can see what the command does.

math] commands here [/math

So to make a simple fraction

math] \frac{3}{4} [/math

Here's an integral

math] \int_0^\infty x^{x+2} + \alpha x .dx [/math

Years ago the member Dross wrote a tutorial to get people started https://www.mathisfunforum.com/viewtopic.php?id=4397

and others added to the thread. I find the code commands are blacked out now and some other commands no longer work but there's still a lot of useful stuff here. I go there if I want something I haven't used before eg. the infinity in the line above.

You can also do an internet search for the right command but this can be frustrating as not all are implemented here.

^ for to the power of works simply if followed by a single character eg

math] x^7 [/math

but if you want a more complicated power the power must be enclosed in {}

math] x^{y + 7} [/math

Otherwise this happens

If you see some Latex and want to see the underlying commands just click on it.

Hope that gets you started.

Bob

ktesla39 · 2025-04-16 02:46:16

Now I can do it. Thanks Bob

Last edited by ktesla39 (2025-04-16 02:52:17)

paulb203 · 2025-04-16 22:49:26

Thanks, ktesla39, thanks, Bob, really helpful, as ever.

“To divide by a fraction, invert it and multiply.”

Ah, of course. Thanks, Bob. KFC (the mnemonic).

Keep. Flip. Change.

Keep the first fraction as it is.
Flip the second fraction.
Change the sign.

“Do you know why this works?”

I think I’m getting there.

Example.

(10/1)/(2/1) = (10/1)(1/2)
(10/1)(1/2) = 10/2
10/2=5

In words;

Ten divided by two...
...is the same as...
...a half of ten.

(To half something is to divide it by two)

Is that the basic idea?

Bob · 2025-04-17 04:34:04

Yes that's about it. Or you could think of it like this.
Divide is the inverse of multiply. Turning a fraction up the other way inverts it. By doing both you maintain the "purpose" of the calculation .

Bob

Phrzby Phil · 2025-04-17 08:18:55

As a tutor, I also point out to students that math rules typically do not depend on the form in which a number is represented - i.e., the numerals.

So we are correctly taught that to divide by a fraction, we multiply by the reciprocal.

I point out (just to point out the obvious) that this is also true for dividing by a whole number (although we don't do it this way).

So: 10 divided by 2 = 10 times 1/2.

paulb203 · 2025-04-17 22:27:12

Thanks, Bob

Thanks, Phil

(You are in bold and italics respectively because I'm practicing my BBcode)

paulb203 · 2025-04-17 22:39:30

This is what I as after.

(I'll abbreviate Gm1m2 to simply 'G'. And I’ll abbreviate the denominators to simply 'o' and 'e'.
I think this will work just as well)

(G/o)/(G/e)

= (G/o)*(e/G)

simplify by crossing out the G's;

(1/o)*(e/1)

= e/o

And, replacing the original terms, gives us;

numerator; (re)^2
denominator; (ro)^2

Is that correct?

ktesla39 · 2025-04-17 23:31:01

Ya for sure it's correct. I was taught it in 9 class. But wasn't explained.

paulb203 · 2025-04-18 22:30:37

Thanks, ktesla39.

Math Is Fun Forum

#1 2025-04-15 22:25:18

Simplifying Fractions

#2 2025-04-15 22:49:40

Re: Simplifying Fractions

#3 2025-04-15 23:02:35

Re: Simplifying Fractions

#4 2025-04-16 00:27:16

Re: Simplifying Fractions

#5 2025-04-16 00:49:28

Re: Simplifying Fractions

#6 2025-04-16 02:12:53

Re: Simplifying Fractions

#7 2025-04-16 02:46:16

Re: Simplifying Fractions

#8 2025-04-16 22:49:26

Re: Simplifying Fractions

#9 2025-04-17 04:34:04

Re: Simplifying Fractions

#10 2025-04-17 08:18:55

Re: Simplifying Fractions

#11 2025-04-17 22:27:12

Re: Simplifying Fractions

#12 2025-04-17 22:39:30

Re: Simplifying Fractions

#13 2025-04-17 23:31:01

Re: Simplifying Fractions

#14 2025-04-18 22:30:37

Re: Simplifying Fractions

Board footer