CalculateY
Quick Answer
24/36 simplifies to 2/3. The GCD of 24 and 36 is 12, so divide both by 12.
Common Examples
| Input | Result |
|---|---|
| 24/36 | 2/3 (GCD = 12) |
| 15/25 | 3/5 (GCD = 5) |
| 7/13 | 7/13 (already simplified) |
| 100/250 | 2/5 (GCD = 50) |
| 48/64 | 3/4 (GCD = 16) |
How It Works
The method
Simplifying a fraction means dividing both the numerator and denominator by their greatest common divisor (GCD), the largest number that divides evenly into both.
Step 1: Find the GCD of the numerator and denominator.
Step 2: Divide both by the GCD.
Worked example
Simplify 48/64:
Find GCD(48, 64) using the Euclidean algorithm:
- 64 = 1 x 48 + 16
- 48 = 3 x 16 + 0
GCD = 16.
Divide both: 48 / 16 = 3, and 64 / 16 = 4.
48/64 = 3/4
The Euclidean algorithm
The Euclidean algorithm finds the GCD efficiently. Repeatedly divide the larger number by the smaller and take the remainder, until the remainder is zero. The last non-zero remainder is the GCD.
For GCD(252, 105):
- 252 = 2 x 105 + 42
- 105 = 2 x 42 + 21
- 42 = 2 x 21 + 0
GCD = 21, so 252/105 simplifies to 12/5.
When is a fraction already simplified?
A fraction is in lowest terms when the GCD of its numerator and denominator is 1. This happens when the two numbers share no common prime factors. For example, 7/13 is already simplified because 7 and 13 are both prime and not equal.