How to solve it
- Find a common divisor of the numerator and the denominator.
- Divide both by that divisor.
- Repeat until the only common divisor left is 1.
- With the greatest common divisor (GCD) you simplify in one step.
18 = 6 × 3, 24 = 6 × 4
18/24 = (18 ÷ 6)/(24 ÷ 6) = 3/4
Result: 3/4
Common mistake:Wrong: 6/9 = 3/6.Right: 6/9 = 2/3.Subtracting the same number from the top and bottom is not simplifying. Divide both by the same number.
A complete example
The shortest route is to divide both terms by their GCF. First find that divisor, then do the two divisions.
Worked example: 42/56
Reduce this fraction to lowest terms.
- Find the GCF. With Euclid: 56 = 1 × 42 + 14 and 42 = 3 × 14 + 0. The last nonzero remainder is 14.
- Divide both terms. 42 ÷ 14 = 3 and 56 ÷ 14 = 4.
- Check the result. The GCF of 3 and 4 is 1, so 3/4 cannot be reduced further.
So 42/56 = 3/4.
Check: 42 × 4 = 168 and 56 × 3 = 168. The cross products match, so the two fractions have the same value.
Dividing by the GCF does not change the value because it is the same as multiplying the fraction by 1. To see where the divisor comes from, the Euclidean algorithm guide explains it with more examples, and the greatest common factor page finds the GCF of two or more numbers.
How to simplify by hand
You do not always need the GCF. You can divide in stages by small numbers that are easy to spot: 42/56 = 21/28 (÷ 2) = 3/4 (÷ 7). You end up at the same fraction, and 2 × 7 = 14 is exactly the GCF. If two divisions are not enough, keep going until no common divisor is left.
Another route is prime factorization. Since 42 = 2 × 3 × 7 and 56 = 2³ × 7, the common factors are 2 and 7, and their product is 14. To decide quickly which divisor to try, the divisibility rules show when a number divides by 2, 3 or 5, and the prime factorization page does the full breakdown.
Dividing a little at a time is not risky, but every stage is a chance to miss a factor. That is why, with numbers of three digits or more, the GCF in a single step is usually safer.
Signs, zero and improper fractions
These four cases reduce in different ways. The last column explains why the result is what it is.
| Case | Input | Result | Why |
|---|---|---|---|
| Already in lowest terms | 5/8 | 5/8 | The GCF is 1; there is nothing to divide |
| Improper | 18/12 | 3/2 | The GCF is 6; it is still greater than 1, and reads as 1 1/2 |
| Two negatives | −6/−9 | 2/3 | The signs cancel and the GCF is 3 |
| Zero numerator | 0/5 | 0 | Zero parts out of five is zero |
A reduced improper fraction does not become proper, because simplifying does not change the size. If you need the mixed form, use the improper fraction to mixed number conversion. A zero denominator is different: it is not an odd result but an input that makes no sense, and the zero denominator guide explains why.
A common mistake: crossing out digits
What to do in other cases
The calculator reduces integers, with a maximum of 100 digits per field. If your data is a ratio like 12 : 18, the simplify ratios tool keeps that format. If you start with a decimal, convert it first with decimal to fraction, which already returns the reduced fraction. To write the same quantity with larger terms, the equivalent fractions tool multiplies instead of dividing.
When you want to practice by hand, the simplify fractions worksheets include exercises with answers. To compare the method, the “Simplify Fractions” section of OpenStax Prealgebra 2e, 4.2 defines a simplified fraction as one with no common factors other than 1, and section 4.1 states the equivalent fractions property. Wikipedia’s Irreducible fraction article defines a fraction in lowest terms and describes reducing it by dividing both terms by their greatest common divisor (accessed October 17, 2026).
Frequently asked questions
Can you simplify a mixed number?
Yes, but only the fraction part: the whole number stays as it is. In 3 4/10, reduce 4/10 to 2/5 and the result is 3 2/5. You can also convert to an improper fraction, 34/10, reduce it to 17/5 and convert back to a mixed number. For that conversion, use the mixed numbers calculator.
What do I do with negative fractions?
The sign does not enter the GCF calculation: use the values without their signs. For 12/18 the GCF is 6, so 12/−18 and −12/18 both give −2/3, while −12/−18 gives 2/3 because two negatives cancel. A fraction is negative only when exactly one of its two terms is.
Is simplifying the same as reducing?
Yes: simplifying, reducing and writing in lowest terms all mean the same thing. Do not confuse it with finding a common denominator, which is the opposite: you multiply so that two fractions share a denominator, like 1/2 and 1/3 becoming 3/6 and 2/6. That process appears in equivalent fractions.
How do I simplify a fraction with very large numbers?
Use the Euclidean algorithm, which does not require guessing divisors. For 1071/1462 the successive remainders are 391, 289, 102, 85 and 17, and the next one is 0. The GCF is 17, and 1071 ÷ 17 = 63 and 1462 ÷ 17 = 86, so the result is 63/86. The Euclidean algorithm guide walks through each division.