All calculatorsSimplify Fractions Calculator
Reduce any fraction to its simplest form using the GCD — and optionally see step-by-step work, mixed number form, and decimal form.
Background
A fraction is simplified when the numerator and denominator share no common factor greater than 1. We find the greatest common divisor (GCD) and divide both by it.
How to use this calculator
- Enter a fraction using Numerator/Denominator or Text mode.
- Click Simplify to reduce it to lowest terms.
- Turn on Steps to see the GCD and cancellation.
- Optionally show mixed number, decimal, and equivalent fractions.
How this calculator works
- Parses your input into an exact fraction n/d with d > 0.
- Computes GCD(n, d) using the Euclidean algorithm.
- Divides numerator and denominator by the GCD to get the simplest form.
Formula & Equation Used
Simplify: n/d = (n ÷ gcd(n,d)) / (d ÷ gcd(n,d))
Euclidean Algorithm: gcd(a,b) = gcd(b, a mod b) until the remainder is 0.
Example Problems & Step-by-Step Solutions
Example 1 — Simplify 42/56
gcd(42,56)=14, so 42/56 = 3/4.
Example 2 — Mixed number: -2 1/4
-2 1/4 = -(9/4). It’s already simplified.
Example 3 — Decimal: 0.125
0.125 = 125/1000, simplify by dividing by 125 → 1/8.
Frequently Asked Questions
Q: What does “simplest form” mean?
It means the numerator and denominator have no common factor greater than 1.
Q: What if the denominator is negative?
The calculator moves the negative sign to the numerator so the denominator stays positive.
Q: Can I paste decimals like 0.125?
Yes — in Text mode. The calculator converts the decimal into an exact fraction, then simplifies it.