144
Simplify any fraction
On the default, 12/18: 2/3 — top and bottom both divisible by 6. Enter your own fraction below.
FREE TOOL · PERCENTAGE
Fraction Simplifier
Reduce any fraction to lowest terms in one step — 12/18 becomes 2/3 — with the greatest common divisor shown, plus the mixed number, decimal, and percent. Same value, smallest possible numbers.
What “lowest terms” means
A fraction is in lowest terms when the top and bottom share no common divisor except 1. 12/18 is not: both are divisible by 2, 3, and 6. Divide by the largest of those — the greatest common divisor (GCD), 6 — and you get 2/3, which cannot be reduced further. The value never changes; only the packaging gets smaller. That is the whole job: find the GCD, divide both parts by it, done.
Output · formula · meaning
| Output | Formula | What it means |
|---|---|---|
| Simplified fraction | numerator ÷ GCD / denominator ÷ GCD | 12/18 ÷ 6/6 = 2/3 — the smallest equivalent form. |
| Greatest common divisor | Euclid’s algorithm | 6 for 12 and 18 — the largest number dividing both. |
| Mixed number | whole + remainder/denominator | 27/6 = 4 1/2 — the form recipes and tape measures use. |
| Decimal & percent | top ÷ bottom, then × 100 | 2/3 = 0.666… = 66.67% — for comparing and calculating. |
Worked examples: 12/18 and 27/6
12/18: list the divisors of 12 (1, 2, 3, 4, 6, 12) and 18 (1, 2, 3, 6, 9, 18) — the biggest shared one is 6. 12 ÷ 6 = 2, 18 ÷ 6 = 3 → 2/3. 27/6: the GCD is 3 → 9/2, and since the top is bigger, 9/2 = 4 1/2 as a mixed number (4 × 2 = 8, remainder 1). The fast way to find the GCD is Euclid’s algorithm: 18 ÷ 12 leaves remainder 6; 12 ÷ 6 leaves 0 — the last nonzero remainder, 6, is the GCD.
Who uses this
- Students: “Write in lowest terms” is on every fractions worksheet — and on the tests.
- Cooks: scaling 4/8 cup down to the 1/2 the measuring cup actually has.
- Carpenters: reading 16/32 off a plan and cutting to 1/2.
- Teachers & tutors: checking homework with the GCD shown at every step.
Accuracy & limitations
Simplification uses exact integer math — no floating-point, no rounding, ever. Inputs must be whole numbers (no decimals); negatives are handled with the sign kept on the numerator (−12/18 → −2/3). A zero numerator simplifies to 0 (0/18 = 0); a zero denominator is rejected, since division by zero is undefined. Decimals and percents are shown to six and four places respectively.
Built a fraction from a decimal? The decimal to fraction converter simplifies automatically. Going the other way, the fraction to decimal chart turns 2/3 into 0.666… with repeating-digit notation.
Cite this calculatorBright Side Kit. “Fraction Simplifier.” brightoolbox.com, 2026.
Bright Side Kit. "Fraction Simplifier." https://brightoolbox.com/fraction-simplifier/ Accessed October 22, 2026.Frequently asked questions
What does “simplify a fraction” mean?
Write the same value with the smallest possible top and bottom. 12/18 simplifies to 2/3: both are divisible by 6, and 2 and 3 share no common divisor, so 2/3 is in lowest terms.
How do you simplify 12/18?
Find the GCD of 12 and 18 — it is 6 — then divide both parts: 12 ÷ 6 = 2, 18 ÷ 6 = 3. Answer: 2/3.
How do you simplify an improper fraction like 27/6?
Simplify first, then convert. The GCD of 27 and 6 is 3 → 9/2. Then 9 ÷ 2 = 4 remainder 1 → 4 1/2 as a mixed number.
What is Euclid’s algorithm for the GCD?
Divide the larger number by the smaller and keep the remainder; repeat with the smaller number and the remainder until a remainder of 0 appears. The last nonzero remainder is the GCD. For 12 and 18: 18 ÷ 12 = remainder 6; 12 ÷ 6 = remainder 0 → GCD is 6.
Can you simplify a negative fraction?
Yes — simplify the absolute values, then keep the sign on top. −12/18 becomes −2/3, and 12/−18 is the same value.
What is 0/18 simplified?
0. A zero numerator means zero of anything — the fraction equals 0 regardless of the denominator (as long as it is not zero itself).
Why simplify instead of just using 12/18?
Because 2/3 is the number’s real identity — it is easier to compare (2/3 vs 3/4 is obvious; 12/18 vs 27/36 is not), easier to remember, and every math class expects lowest terms in the answer.
What is the difference between simplifying and converting?
Simplifying keeps the fraction form but shrinks it (12/18 → 2/3). Converting changes the form entirely — to a decimal (2/3 → 0.666… on the fraction to decimal chart) or from a decimal (decimal to fraction converter).