Free Fraction Simplifier
Reduce a fraction to its simplest form instantly. Enter an integer numerator and denominator to find the greatest common divisor, see the reduction steps and get the fraction in lowest terms.
Simplify a Fraction
Enter an integer numerator and denominator. The denominator cannot be zero.
How to Simplify Fractions
A fraction is in simplest form, also called lowest terms, when its numerator and denominator have no common factor greater than 1.
The ToolZippy Fraction Simplifier finds the greatest common divisor (GCD) of the numerator and denominator and divides both numbers by that same value. Because the numerator and denominator are divided by the same nonzero number, the value represented by the fraction does not change.
How to Use the Fraction Simplifier
Enter the numerator in the first field and the denominator in the second. Both values must be whole integers. Then select Simplify Fraction.
The calculator displays the reduced fraction, the GCD and the division performed on both parts of the original fraction.
Fraction Simplification Formula
The GCD is the largest positive integer that divides both the numerator and denominator without leaving a remainder.
Example: Simplify 18/24
The common factors of 18 and 24 include 1, 2, 3 and 6. The greatest common divisor is therefore 6.
The fraction 3/4 cannot be reduced further because 3 and 4 have no common factor greater than 1.
More Fraction Simplification Examples
Simplifying Negative Fractions
Negative fractions can also be simplified. This calculator normalizes the sign so the denominator is positive. For example, −8/12 simplifies to −2/3.
If both the numerator and denominator are negative, the fraction is positive. For example, −8/−12 simplifies to 2/3.
What Happens When the Numerator Is Zero?
A fraction with a zero numerator and a nonzero denominator equals zero. For example, 0/15 simplifies to 0.
A denominator of zero is not permitted. An expression such as 5/0 does not represent an ordinary defined fraction, so the calculator will ask you to change the denominator.
How Do I Know a Fraction Is Fully Simplified?
A fraction is fully simplified when the GCD of its numerator and denominator is 1. For example, 5/7 is already in lowest terms because the only positive common factor of 5 and 7 is 1.
| Original Fraction | GCD | Simplified Fraction | Status |
|---|---|---|---|
| 18/24 | 6 | 3/4 | Reduced |
| 12/30 | 6 | 2/5 | Reduced |
| 15/25 | 5 | 3/5 | Reduced |
| 5/7 | 1 | 5/7 | Already simplest |
Why Simplify a Fraction?
Simplifying a fraction makes it easier to read, compare and use in later calculations. Equivalent fractions represent the same value, but the simplest form normally communicates that value with the smallest whole-number numerator and denominator.
- Reduce answers in math exercises to lowest terms.
- Make equivalent fractions easier to recognize.
- Prepare fractions for comparison or further calculations.
- Check manual fraction reduction using the GCD.
- Simplify ratios that are expressed as fractions.
Integer Inputs and Calculator Limits
This Fraction Simplifier is designed for fractions whose numerator and denominator are integers. It does not silently convert decimal inputs into integers. If you enter a decimal, the calculator asks you to use whole numbers instead.
If you need to work with percentages or decimal values, try the Decimal to Percentage Calculator or Percentage to Decimal Calculator.
Tip: A simplified fraction is equivalent to the original fraction. Reduction changes the form of the fraction, not its mathematical value.
Fraction Simplifier FAQs
What is a fraction simplifier?
A fraction simplifier reduces a numerator and denominator to their lowest terms by dividing both by their greatest common divisor.
How do you simplify a fraction?
Find the greatest common divisor of the numerator and denominator, then divide both numbers by that GCD.
What is the simplest form of 18/24?
The GCD of 18 and 24 is 6. Dividing both numbers by 6 gives 3/4, so 18/24 simplifies to 3/4.
Can a negative fraction be simplified?
Yes. Negative fractions are simplified using the absolute values for the GCD while preserving the overall sign. For example, −8/12 simplifies to −2/3.
Can the denominator be zero?
No. Division by zero is undefined, so zero cannot be used as the denominator of an ordinary fraction.
What happens if the numerator is zero?
If the denominator is nonzero, a zero numerator represents zero. For example, 0/15 simplifies to 0.
Can I enter decimal numbers?
This calculator is designed for integer fractions. Enter whole numbers for the numerator and denominator rather than decimal values.
How do I know if a fraction is already simplified?
If the greatest common divisor of the numerator and denominator is 1, the fraction is already in simplest form.