Simplifying A Fraction That Can't Be Simplified

[willgtl]

So let me start off by saying I am horrible at math and always have been. Despite considering myself highly intelligent, I suck at math. It's what led me into computer programming instead of physics like I wanted.

Simply, I want to ask, say I have a fraction or a ratio that can't be simplified, say like 131,234:1,715, how would I go about rounding it to a smaller-numbered ratio that's more readily conceivable? It doesn't have to be an exact number, just a number that is close enough and small enough. Thanks!

 

[robphy]

When plugged into a calculator, you get 76.5212827988.
So, you could use 765/100, then simplify further if you wish. (Edit... Oops... 765/10. Thanks SteamKing)

You could also try out possible denominators
and see which numerator suits your taste.

 

[willgtl]

Ah, thank you! I was thinking that but didn't trust that I was on the right path.

 

[Vanadium 50]

With a spreadsheet, or even a programmable calculator, you can look for others just with trial and error. The best one with a three digit denominator is 73690/963, the best one with a two digit denominator is 7193/94, and the best one with a single digit denominator is 153/2.

 

[SteamKing]

When plugged into a calculator, you get 76.5212827988.
So, you could use 765/100, then simplify further if you wish.

You could also try out possible denominators
and see which numerator suits your taste.

Uhhh... 765 / 100 = 7.65, not 76.5

 

[DrClaude]

You can also use WolframAlpha to get what are called Egyptian fractions:

$$
\begin{align}
\frac{131234}{1715} &= 76 + \frac{1}{2} + \frac{1}{47} + \frac{1}{161210} \\
&\approx \frac{7193}{94}
\end{align}
$$
(keeping only the first two fractions).