Last updated: March 2026
How to Simplify Fractions Step by Step
Simplifying a fraction means finding the smallest equivalent fraction by dividing both the numerator and denominator by their Greatest Common Divisor (GCD). For example, to simplify 24/36: find GCD(24, 36) = 12, then divide both by 12 to get 2/3.
This calculator shows every step of the process so you can learn the method, not just get the answer. Enter any fraction above and see the complete step-by-step reduction with visual fraction bar illustrations.
Finding the Greatest Common Divisor
The GCD (also called Greatest Common Factor or HCF) is the largest number that divides both the numerator and denominator evenly. The most efficient way to find it is the Euclidean algorithm, which repeatedly divides and takes remainders until reaching zero.
For small numbers, you can also list the factors of each number and find the largest one in common. For example: factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24; factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest common factor is 12.
Frequently Asked Questions
What does it mean to simplify a fraction?
Simplifying a fraction means reducing it to its lowest terms — the smallest numerator and denominator that represent the same value. For example, 6/8 simplifies to 3/4. Both represent the same amount, but 3/4 is in simplest form because no number other than 1 divides both evenly.
How do you find the GCD of two numbers?
The most efficient method is the Euclidean algorithm: divide the larger number by the smaller, then divide the smaller by the remainder, and repeat until the remainder is 0. The last non-zero remainder is the GCD. For example: GCD(24, 36) → 36÷24 = 1 remainder 12, 24÷12 = 2 remainder 0 → GCD = 12.
How do you know when a fraction is fully simplified?
A fraction is fully simplified when the only number that divides both the numerator and denominator evenly is 1 — in other words, when the GCD is 1. For example, 7/12 is fully simplified because GCD(7, 12) = 1.
Can you simplify improper fractions?
Yes! Simplify an improper fraction the same way — find the GCD and divide both parts. For example, 18/12 → GCD = 6 → 3/2. You can then also convert it to a mixed number: 3/2 = 1½.
What is a prime fraction?
A fraction where the numerator and denominator are coprime (their GCD is 1) is said to be in simplest form or lowest terms. If the numerator is a prime number and doesn't divide the denominator, the fraction is already simplified. For example, 7/9 cannot be simplified further.
Why do we simplify fractions?
Simplified fractions are easier to understand, compare, and use in further calculations. It's easier to see that 1/2 is larger than 1/3 than to compare 6/12 with 4/12. In math class, teachers typically require answers in simplest form.