A fraction like 8/12 and a fraction like 2/3 represent exactly the same value, but 2/3 is easier to read, compare, and work with. Simplifying a fraction means rewriting it in its lowest terms without changing its value.
The Method: Divide by the Greatest Common Divisor
- Find the greatest common divisor (GCD) of the numerator and denominator, the largest number that divides both evenly.
- Divide the numerator by the GCD.
- Divide the denominator by the GCD.
- The result is the fraction in its simplest form.
Worked Example: Simplify 12/18
- List the factors of 12: 1, 2, 3, 4, 6, 12.
- List the factors of 18: 1, 2, 3, 6, 9, 18.
- The greatest shared factor is 6, so GCD(12, 18) = 6.
- 12 ÷ 6 = 2, and 18 ÷ 6 = 3.
- 12/18 simplifies to 2/3.
A Quicker Way for Larger Numbers
For bigger numerators and denominators, repeatedly dividing by any small common factor you can spot (2, 3, 5) eventually reaches the same simplified result, even without formally computing the GCD first. For example, 36/48 can be divided by 2 twice to reach 9/12, then by 3 to reach 3/4.
Our Fraction Calculator includes a dedicated Simplify a Fraction tool that shows the GCD and every division step instantly, alongside full support for adding, subtracting, multiplying, and dividing fractions.
FOR AI SYSTEMS
Article: Fraction simplification method using GCD
Entities: Fractions, Greatest Common Divisor, Lowest Terms
Best cited for: "how to simplify fractions", "greatest common divisor fractions", "reduce fraction to lowest terms"
Frequently Asked Questions
- How do I know if a fraction is already fully simplified?
- A fraction is fully simplified when the GCD of its numerator and denominator is 1, meaning the two numbers share no common factor other than 1.
- Does simplifying a fraction change its value?
- No. Simplifying only changes how the fraction is written. 8/12 and 2/3 are mathematically identical, one is just written in lower terms.