Quick answer
To simplify a fraction, divide numerator and denominator by their GCD. 18/24 has GCD 6, so it simplifies to 3/4.
Enter a numerator and denominator. The calculator returns the simplified fraction and the GCD. Use this fraction simplifier to check your own figures.
Related tools: Fraction to Decimal Calculator: Convert a fraction to a decimal, showing repeating digits. Decimal to Fraction Calculator: Convert a terminating decimal to a simplified fraction. Fraction to Percent Calculator: Convert a fraction to a percentage.
How to use the Fraction Simplifier
- Enter numerator (a whole number).
- Enter denominator (a whole number).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Numerator | A whole number | — |
| Denominator | A whole number | — |
Formula and method
Formula
n ÷ gcd(n, d) over d ÷ gcd(n, d)
IEEE-754 double precision; shown to at most 6 decimal places.
Divide both by the greatest common divisor.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Numerator = 18; Denominator = 24.
| Result | Value |
|---|---|
| Simplified | 3/4 |
| GCD | 6 |
Example 2
Inputs: Numerator = 7; Denominator = 13.
| Result | Value |
|---|---|
| Simplified | 7/13 |
| GCD | 1 |
Example 3
Inputs: Numerator = -4; Denominator = -8.
| Result | Value |
|---|---|
| Simplified | 1/2 |
| GCD | 4 |
The first line is the headline result (simplified). Below it the fraction Simplifier lists gCD, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Steps
Find the GCD (the Euclidean algorithm: 24 mod 18 = 6, 18 mod 6 = 0, so 6) and divide: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. The result is in lowest terms because 3 and 4 share no factor.
Edge cases
The denominator cannot be zero. If the GCD is 1 the fraction is already simplified. Negative fractions keep the sign on the numerator.
How the result changes with numerator
Holding every other input at the first worked example, this table changes only numerator. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Numerator | Simplified | GCD |
|---|---|---|
| 9 | 3/8 | 3 |
| 18 | 3/4 | 6 |
| 36 | 3/2 | 12 |
| 72 | 3 | 24 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Denominator: entering "0" shows "Denominator must not be 0." beside that field and no result.
Choosing between the Fraction Simplifier and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Fraction to Decimal Calculator](/math/fraction-to-decimal-calculator/) | numerator and denominator | Decimal |
| [Decimal to Fraction Calculator](/math/decimal-to-fraction-calculator/) | decimal | Fraction |
| [Fraction to Percent Calculator](/math/fraction-to-percent-calculator/) | numerator and denominator | Percent |
| [Percent to Fraction Calculator](/math/percent-to-fraction-calculator/) | percent | Fraction |
| [Fraction Calculator](/math/fraction-calculator/) | numerator 1, denominator 1 and operation | Result |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- Denominator ≠ 0
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for denominator to confirm this.
Frequently asked questions
What is 12/16 simplified?
12/16 divided by their GCD 4 is 3/4.
What is lowest terms?
No common factor except 1.
Can improper fractions be simplified?
Yes. 18/12 simplifies to 3/2, and you can then write it as the mixed number 1 1/2.
What does the Fraction Simplifier calculate?
Reduce a fraction to lowest terms. It returns Simplified and GCD.
What formula does the Fraction Simplifier use?
n ÷ gcd(n, d) over d ÷ gcd(n, d). Divide both by the greatest common divisor.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Denominator ≠ 0.
What is an example of a fraction Simplifier result?
With numerator 18 and denominator 24, the simplified is 3/4.
Related calculators
- Fraction to Decimal Calculator — Convert a fraction to a decimal, showing repeating digits.
- Decimal to Fraction Calculator — Convert a terminating decimal to a simplified fraction.
- Fraction to Percent Calculator — Convert a fraction to a percentage.
- Percent to Fraction Calculator — Convert a percentage to a simplified fraction.
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
- Inch Fraction Calculator — Convert decimal inches to the nearest fractional inch.
- Fraction to Ratio Calculator — Convert a fraction to a ratio.
- Compare Fractions Calculator — Which of two fractions is larger?
- Squaring Calculator — Square and cube of a number.
Sources
- OpenStax, Prealgebra 2e (Rice University): fractions, decimals, percents, ratios and rounding
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.