Simplify Fractions Calculator
Reduce any fraction to its lowest terms in one click. Enter a simple fraction (like 18/24) or switch to mixed-number mode (like 2 3/4) to get the simplified fraction, decimal value, percentage, equivalent fractions, and a full step-by-step worked solution.
Formula
Worked example
Take 18/24. The greatest common divisor of 18 and 24 is 6, since 18 = 6 x 3 and 24 = 6 x 4. Divide both by 6: 18 / 6 = 3 and 24 / 6 = 4, giving 3/4. As a decimal that is 0.75, as a percentage it is 75%, and because the numerator is smaller than the denominator there is no whole-number part. Equivalent fractions include 6/8, 9/12, and 12/16.
How simplifying a fraction works
Simplifying, or reducing, a fraction means rewriting it with the smallest possible whole numbers on top and bottom while keeping the same value. You do this by finding the greatest common divisor (GCD) of the numerator and denominator, the largest whole number that divides both exactly, and then dividing each part by that GCD. Because you divide the top and bottom by the same number, the value of the fraction never changes; only the way it is written becomes simpler. For example, 18/24 and 3/4 represent the same quantity: both describe three-quarters of a whole. The fraction 3/4 is the preferred form because the numbers are as small as they can be.
Finding the greatest common divisor
The most reliable way to find the GCD is the Euclidean algorithm, which this calculator uses. You repeatedly replace the larger number with the remainder of dividing the larger by the smaller, and continue until the remainder reaches zero; the last non-zero value is the GCD. For example, for 18 and 24: 24 mod 18 = 6, then 18 mod 6 = 0, so the GCD is 6. This method is far faster than listing every factor, especially for large numbers. An alternative approach is to factor both numbers into primes and multiply the shared prime factors together.
Decimals, percentages, and mixed numbers
A fraction can also be written as a decimal by dividing the numerator by the denominator, or as a percentage by multiplying that decimal by 100. So 3/4 = 0.75 = 75%. When the numerator is larger than the denominator the fraction is called improper; it can also be written as a mixed number that combines a whole-number part with a proper fraction. For instance, 7/4 becomes 1 3/4 because 4 goes into 7 once with 3 left over. This calculator gives you all four representations, making it easy to pick the format that fits your context.
Mixed number input and equivalent fractions
If your starting value is already written as a mixed number such as 2 3/4, switch to mixed-number mode. The calculator converts it to the improper fraction 11/4 first, then checks whether any simplification is possible. You also get a list of equivalent fractions, which are fractions that equal the same value but use different numbers. To build them you multiply the simplified numerator and denominator by the same integer (2, 3, 4 and so on). Equivalent fractions are useful when you need a common denominator to add or subtract two fractions.
Common fractions in lowest terms
| Original | GCD | Simplified | Decimal | Percentage |
|---|---|---|---|---|
| 2/4 | 2 | 1/2 | 0.5 | 50% |
| 4/6 | 2 | 2/3 | 0.6667 | 66.67% |
| 6/8 | 2 | 3/4 | 0.75 | 75% |
| 9/12 | 3 | 3/4 | 0.75 | 75% |
| 10/15 | 5 | 2/3 | 0.6667 | 66.67% |
| 12/16 | 4 | 3/4 | 0.75 | 75% |
| 18/24 | 6 | 3/4 | 0.75 | 75% |
| 20/30 | 10 | 2/3 | 0.6667 | 66.67% |
| 25/100 | 25 | 1/4 | 0.25 | 25% |
| 36/48 | 12 | 3/4 | 0.75 | 75% |
| 100/250 | 50 | 2/5 | 0.4 | 40% |
| 75/100 | 25 | 3/4 | 0.75 | 75% |
Each fraction on the left reduces to the simplest form on the right by dividing out the shared factor.
Frequently asked questions
What does it mean to simplify a fraction?
It means writing the fraction with the smallest whole numbers possible while keeping the same value. You divide both the numerator and denominator by their greatest common divisor, so 6/8 becomes 3/4. The two fractions are equal; 3/4 is just the cleaner way to write it.
How do I know a fraction is already in lowest terms?
A fraction is in lowest terms when the greatest common divisor of its numerator and denominator is 1, meaning they share no common factor other than 1. For example, 3/4 is fully reduced because nothing but 1 divides both 3 and 4 exactly.
Can I simplify a fraction with a negative number?
Yes. The calculator keeps the sign on the numerator and reduces the magnitudes normally, so -18/24 simplifies to -3/4. By convention the denominator is written as a positive number.
How do I simplify a mixed number like 2 3/6?
Switch to mixed-number mode, then enter the whole part (2) and the fractional part (3 and 6). The calculator converts the mixed number to an improper fraction first: 2 x 6 + 3 = 15, so it becomes 15/6. It then finds the GCD (3) and divides through: 15/3 = 5 and 6/3 = 2, giving the simplified improper fraction 5/2, which as a mixed number is 2 1/2.
How do I convert a simplified fraction to a percentage?
Divide the numerator by the denominator to get the decimal, then multiply by 100. So 3/4 = 0.75 = 75%. This calculator shows the percentage automatically alongside the simplified fraction.
What are equivalent fractions and how do I find them?
Equivalent fractions represent the same value but use different numbers. To find them, multiply both the numerator and denominator of the simplified fraction by the same integer. For 3/4: multiply by 2 to get 6/8, by 3 to get 9/12, by 4 to get 12/16, and so on. This calculator lists several equivalent fractions automatically.
Why does the calculator only accept whole numbers?
The GCD is defined for integers, so simplification in the classic sense only applies when both the numerator and denominator are whole numbers. If you have a decimal numerator or denominator (like 1.5/3), multiply both by a power of ten to make them integers first (3/6), then simplify.