What this calculator does
Simplifying fractions means rewriting a fraction with the smallest possible whole numbers on the top and bottom, without changing its value. This simplifying fractions calculator takes any numerator and denominator and reduces the fraction to its lowest terms in one step, along with the greatest common divisor used to get there.
A fraction like 18/24 and its simplified form 3/4 represent exactly the same quantity, but 3/4 is easier to work with, compare and picture. Simplifying is the same step used before adding fractions with different denominators, and it is often the last step expected in a maths answer even when the arithmetic itself is already correct.
The formula
The greatest common divisor (GCD) of the numerator and denominator is the largest whole number that divides both exactly. Dividing both the numerator and the denominator by that GCD gives the simplified fraction, since dividing the top and bottom by the same number never changes the value of the fraction. If the GCD is 1, the fraction was already in lowest terms.
| Term | Meaning |
|---|---|
| Numerator | The top number of a fraction: how many parts are being counted. |
| Denominator | The bottom number of a fraction: how many equal parts make up a whole. |
| Greatest common divisor (GCD) | The largest whole number that divides both the numerator and denominator exactly, with no remainder. |
| Lowest terms | A fraction is in lowest terms once its numerator and denominator share no common divisor other than 1. |
The inputs explained
| Field | What to enter |
|---|---|
| Numerator | The numerator, the top number of the fraction. Can be zero or negative. |
| Denominator | The denominator, the bottom number of the fraction. Cannot be zero. |
When to use it
Reducing a fraction from a recipe or a measurement
Measurements often come out as an awkward fraction, such as 18/24 of a cup or 18/24 of an inch. Simplifying to 3/4 makes it far easier to read off a measuring cup or a ruler.
Finishing a maths problem correctly
Many maths exercises mark an answer wrong if the fraction is not fully simplified, even when the value is correct. This calculator confirms whether a fraction is already in lowest terms or shows the reduced form if not.
Comparing two fractions at a glance
Simplified fractions are easier to compare by eye, and this calculator also gives the decimal equivalent, useful for checking which of two fractions is larger.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Simplifying 18 over a range of denominators
The numerator held fixed at 18 while the denominator varies, showing how the greatest common divisor changes the simplified result.
| Denominator | Simplified fraction | Greatest common divisor used | Decimal value |
|---|---|---|---|
| 6 | 3/1 | 6 | 3.000 |
| 12 | 3/2 | 6 | 1.500 |
| 24 | 3/4 | 6 | 0.7500 |
| 36 | 1/2 | 18 | 0.5000 |
| 50 | 9/25 | 2 | 0.3600 |
Questions
What does it mean to simplify a fraction?
It means dividing both the numerator and denominator by their greatest common divisor, so the fraction is expressed with the smallest possible whole numbers while keeping exactly the same value.
How do I know if a fraction is already fully simplified?
A fraction is fully simplified, or in lowest terms, when its numerator and denominator share no common divisor other than 1. This calculator checks that directly and reports whether the fraction entered was already in lowest terms.
What happens if the simplified numerator is larger than the simplified denominator?
The fraction is improper, meaning its value is 1 or greater. Alongside the simplified fraction, the calculator also gives the equivalent mixed number, with a whole-number part and a smaller remaining fraction.
Is this the same as the fraction calculator for adding and multiplying fractions?
No. That calculator combines two fractions using an operation such as addition or multiplication and simplifies the result. This calculator simplifies a single fraction you already have, without any second fraction or operation involved.
To add, subtract, multiply or divide two fractions, see the fraction calculator. To convert a fraction to a percentage or back again, use the fraction to percentage calculator.