1. ## Fraction Help

I have a ratio:

A/B the value of which is known e.g. 0.34 but I don't know A or B.

Apparently, if you divide A/B by (1 + A/B), you get A/(A+B).

I can do that maths to prove that this is the case, I don't understand the logic behind doing thing however.

In other words, how do I know to even attempt to convert A/B into A/(A+B)?

2. ## Re: Fraction Help

I'm not clear on what that gets you. Why do you think this is something that you should do?

What ultimately are you trying to solve?

3. ## Re: Fraction Help

Will this be useful?
$\frac{A}{B}=k$
$\implies \frac{A/B}{1}=\frac{k}{1}$
$\implies \frac{A/B}{1+A/B}=\frac{k}{1+k}$ ; adding numerator to denominator both sides
$\implies \frac{A}{A+B}=\frac{k}{1+k}$

4. ## Re: Fraction Help

$\displaystyle 1+ \frac{A}{B}= \frac{B}{B}+ \frac{A}{B}= \frac{A+ B}{B}$. Dividing by that is the same as multiplying by the invese:
$\displaystyle \frac{A}{B}\left(\frac{B}{A+ B}\right)= \frac{A}{A+ B}$ since the "B"s in numerator and denominator cancel.

I don't see what "A/B= 0.34" has to do with this.

5. ## Re: Fraction Help

Originally Posted by romsek
I'm not clear on what that gets you. Why do you think this is something that you should do?

What ultimately are you trying to solve?
Originally Posted by HallsofIvy
[tex]I don't see what "A/B= 0.34" has to do with this.
Well that's exactly my point, how do you know to do this.

It's related to accounting.

If you have a ratio of two numbers from financial statements (as the 0.34 example that I provided) specifically the debt to equity ratio, then you want to also calculate the proportion of debt and equity that results in this ratio. Generally you can look up the values for the amount of debt and the amount of equity in the company from financial statements, but I guess the point is that this info might not always be available in all cases, and as a result, you still want to be able to calculate the proportions of debt and equity but just from one number. But I'm just bemused by the fact that given this ratio, you're actually able to derive such an elegant result and was just trying to figure out the logic. I guess, a starting point is the fact that you have an initial ratio and you know you want to be able to calculate ratio and you go from there.

Originally Posted by zemozamster
Will this be useful?
$\frac{A}{B}=k$
$\implies \frac{A/B}{1}=\frac{k}{1}$
$\implies \frac{A/B}{1+A/B}=\frac{k}{1+k}$ ; adding numerator to denominator both sides
$\implies \frac{A}{A+B}=\frac{k}{1+k}$

6. ## Re: Fraction Help

Hi there, in the third line they multiplied the left hand side by $\displaystyle \frac{1}{1 + \frac{A}{B}}$ and the right hand side by $\displaystyle \frac{1}{1 + k}$ which maintains the equality because A/B = k

7. ## Re: Fraction Help

Originally Posted by Atomic_Sheep
I have a ratio:
A/B the value of which is known e.g. 0.34 but I don't know A or B.

Apparently, if you divide A/B by (1 + A/B), you get A/(A+B).

I can do that maths to prove that this is the case, I don't understand the logic behind doing thing however.

In other words, how do I know to even attempt to convert A/B into A/(A+B)?
Who says "you have to"?

A/B = R

Given B and R:
A = B*R

Given A and R:
B = A/R

Since you're given A or B, then above is all you need.

BUT if you're given the DIFFERENCE between A and B,
you can calculate BOTH A and B (D = difference = B-A):
A/(A+D) = R (given D and R)
A = D*R/(1-R)
and: B = A+D

EXAMPLE: A=600, B=800, so R=.75
GIVEN: D = 200, R = .75
A = D*R/(1-R) = 200*.75/(1-.75) = 150/.25 = 600
B = A + D = 600 + 200 = 800

HOKAY??

8. ## Re: Fraction Help

Originally Posted by Atomic_Sheep
I have a ratio:

A/B the value of which is known e.g. 0.34 but I don't know A or B.

Apparently, if you divide A/B by (1 + A/B), you get A/(A+B).

I can do that maths to prove that this is the case, I don't understand the logic behind doing thing however.

In other words, how do I know to even attempt to convert A/B into A/(A+B)?

Your equation is A/B = .34

If you are trying to find A and B then you don't have enough information. To find the value of two variables, you need two equations.

If you are trying to find something else, you haven't told us.

Steve