How to Simplify Fractions (Step by Step)
To simplify a fraction, divide both the numerator and the denominator by their Greatest Common Divisor (GCD). The GCD is the largest number that divides both values evenly.
- Find the GCD of the numerator and denominator.
- Divide the numerator by the GCD.
- Divide the denominator by the GCD.
- The result is the fraction in its simplest form.
Example: Simplify 12/16
Frequently Asked Questions
What does simplifying a fraction mean?
Simplifying (or reducing) a fraction means dividing both numerator and denominator by their Greatest Common Divisor (GCD) until no common factor remains other than 1. For example, 8/12 simplifies to 2/3 because GCD(8,12) = 4.
How do I simplify 8/12?
Find the GCD of 8 and 12, which is 4. Divide both: 8÷4 = 2, 12÷4 = 3. So 8/12 = 2/3.
What is the GCD?
GCD stands for Greatest Common Divisor — the largest number that divides both numerator and denominator evenly. It can be found with the Euclidean algorithm: GCD(a,b) = GCD(b, a mod b), repeated until the remainder is 0.
Can I simplify an improper fraction?
Yes. Improper fractions (where the numerator is larger than the denominator) simplify exactly the same way. For example, 18/12 → GCD(18,12) = 6 → 18/12 = 3/2.
What if GCD is 1?
If GCD = 1, the fraction is already in its simplest form. For example, 3/7 — GCD(3,7) = 1, so it cannot be reduced further.
How do I simplify negative fractions?
The same rule applies. The sign stays with the numerator. For example, −6/8: GCD(6,8) = 2, so −6/8 = −3/4.
What is the Euclidean algorithm?
The Euclidean algorithm is an efficient method to find the GCD. It works by repeated division: GCD(48, 18) → GCD(18, 12) → GCD(12, 6) → GCD(6, 0) = 6. This calculator uses it internally for instant results.