Fraction Reducer – Simplify to Lowest Terms

Reducing a fraction divides top and bottom by their greatest common divisor, leaving an equivalent fraction that is easier to read and compute with. For 84/126, Euclid’s algorithm finds the GCD quickly: 126 mod 84 = 42, then 84 mod 42 = 0, so g = 42. Dividing gives 84÷42 = 2 and 126÷42 = 3, hence 2/3. The reducer prints these Euclid steps so the method is transparent, handles improper fractions (99/45 → 11/5) and negatives (−18/24 → −3/4, sign carried on top), and shows the decimal value (2/3 = 0.666…) so you can confirm nothing changed but the form. When the GCD is 1 the fraction is already fully reduced, as with 8/15. Reducing first also prevents overflow when the fraction later feeds into multiplication or addition problems.

1. 1

   Enter numerator and denominator

   Any integers, including negative or improper fractions

2. 2

   Run Euclid’s algorithm

   The GCD steps are printed: GCD(84,126) → GCD(126,84)... shows 42

3. 3

   Divide both parts

   Top and bottom are divided by the GCD

4. 4

   Confirm equivalence

   The decimal value of both forms is displayed side by side

• 1

  Divide numerator AND denominator — changing one alters the value

• 2

  GCD = 1 means the fraction is already in lowest terms

• 3

  Reducing before multiplying keeps numbers small: (84/126)(10/14) → (2/3)(5/7)

• Dividing only the numerator, silently changing the value

• Stopping at a common divisor instead of the greatest one: 84/126 → 14/21 → 2/3 wastes a step

• Dropping the negative sign when reducing −18/24

• Reducing across an addition: in 1/2 + 1/4 you cannot cancel the 2 and 4