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Is there a mathematical formula to calculate the smallest division of a fraction with both numbers not being a division? I'm not a mathematician (and not English), so I hope I use the correct terms.

Example: $\frac{300}{400}=\frac{3}{4}$.

But what about $\frac{27}{9}$ or $\frac{2655}{425}$?

What is the smallest division without a fraction?

Kees C. Bakker
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    You need to find the "greater common divisor" of the numbers. – Daniel R May 23 '14 at 09:56
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    Divide from both numbers the greatest common divisor of them. For example, $gcd(300, 400) = 100$, $gcd(27, 9) = 9$, $gcd(2655, 425) = 5$. So $\frac{300}{400} = \frac{300/100}{400/100} = \frac 34$, $\frac{27}{9} = \frac{27/9}{9/9} = \frac{3}{1} = 3$, and $\frac{2655}{425} = \frac{2655/5}{425/5} = \frac{531}{85}$. For small numbers, computing gcd can be done by factorization by hand. For large numbers, it's faster to use the Euclidean algorithm. – Tunococ May 23 '14 at 10:03
  • The terminology you're looking for is reducing the fraction to lowest terms. A fraction in lowest terms is called irreducible. – user2357112 May 23 '14 at 11:11

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This is called: 'Reducing the fraction to lowest terms'. A fraction in lowest terms is called 'irreducible'.

Kees C. Bakker
  • 181