How to simplify a fraction
To simplify (or reduce) a fraction, find the greatest common divisor of the numerator and denominator, then divide both by it. For 8/12 the GCD is 4, so the fraction becomes 8÷4 / 12÷4 = 2/3. The value is unchanged — only the numbers get smaller.
Dividing top and bottom by the same number is the same as dividing the fraction by 1, so the value survives untouched. Using the greatest common divisor rather than any shared factor reaches lowest terms in one step; dividing 8/12 by 2 only gives 4/6. A simplified fraction is easier to convert, and the fraction to decimal calculator will give you its decimal value.
How to use this calculator
Enter the numerator (top) and denominator (bottom). The denominator cannot be zero. The result is the fraction in lowest terms, along with the GCD used. To find that divisor on its own, see the GCF calculator.
The reported GCD is worth reading, not just the answer. A GCD of 1 means nothing could be reduced. Inputs are treated as whole numbers, so convert any decimal to an integer pair first — 1.5/2 becomes 15/20, which reduces to 3/4.
When a fraction is already simplified
A fraction is in lowest terms when its numerator and denominator share no common factor other than 1 — that is, when their GCD is 1. For example, 5/9 cannot be reduced further. This tool reports the GCD so you can confirm whether any reduction happened.
A shortcut: if both numbers are prime, or one is prime and does not divide the other, the fraction is already in lowest terms. A numerator of 0 always reduces to 0/1. If the numerator is larger than the denominator, the mixed number and improper fraction calculator rewrites it as a whole number plus a remainder.
Frequently asked questions
- How do I simplify a fraction?
- Divide the numerator and denominator by their greatest common divisor. For 8/12, divide both by 4 to get 2/3.
- What is 8/12 simplified?
- 2/3. The GCD of 8 and 12 is 4, and 8÷4 = 2, 12÷4 = 3.
- Can the denominator be zero?
- No. A denominator of zero is undefined, so this calculator requires a non-zero denominator.
- How do I know a fraction is fully reduced?
- It is fully reduced when the GCD of numerator and denominator is 1, meaning they share no common factor.
- What happens with a negative fraction?
- The sign is kept but moved to the numerator, so −8/12 and 8/−12 both return −2/3. This is the standard convention: a reduced fraction carries its sign on top and always has a positive denominator, which makes comparing and adding fractions much easier.