Transparent method
The formula
Worked example
Example inputs
How to interpret the result
A fraction reduced to lowest terms and its original, unreduced form are exactly equal in value. Simplifying changes nothing about the quantity, only how compactly it's written. That matters most when comparing two fractions or combining several: 6/8 and 3/4 won't visually match in a table even though they represent the identical amount, and an unreduced fraction can make a correct answer look wrong at a glance.
Before you rely on it
What to check
Confirm both fractions in a comparison are reduced to the same terms before judging whether they match or differ.
The common error
Where people go wrong with fraction simplifier calculator
Assuming an unreduced fraction is a calculation error. 6/8 isn't wrong; it's just not simplified, and the greatest-common-factor reduction is a presentation step, not a correction to the arithmetic.
Sensitivity evidence
How numerator changes the simplified numerator
| Numerator | Simplified numerator | Simplified denominator |
|---|---|---|
| 19 | 19 | 36 |
| 22 | 11 | 18 |
| 24worked example | 2 | 3 |
| 26 | 13 | 18 |
| 29 | 29 | 36 |
Every input, tested
Which input moves the simplified numerator most
| Input | Tested from | To | Simplified numerator at each end | Swing |
|---|---|---|---|---|
| Numerator | 22 | 26 | 11 to 13 | 2 (100%) |
| Denominator | 32 | 40 | 3 to 3 | none |
Two variables at once
Simplified numerator by numerator and denominator
| Numerator \ Denominator | 29 | 36 | 43 |
|---|---|---|---|
| 19 | 19 | 19 | 19 |
| 22 | 22 | 11 | 22 |
| 24 | 24 | 2 | 24 |
| 26 | 26 | 13 | 26 |
| 29 | 1 | 29 | 29 |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Numerator | 24 |
| Denominator | 36 |
| Simplified numerator | 2 |
| Simplified denominator | 3 |
Where the inputs come from
Enter the numerator and the denominator as whole numbers, with the denominator not zero. The calculator finds the greatest common factor of the two numbers and divides both by it, which reduces the fraction to lowest terms. If you have a mixed number, convert it to an improper fraction first. Negative fractions are simplified the same way, keeping the sign on the numerator by convention.
When the result stops applying
Simplifying does not change the value of the fraction, only its form, so 24/36 and 2/3 are the same amount. Numbers that are already coprime, such as 7 and 12, stay unchanged. Very large numbers take longer by hand but not for the calculator. For decimals, convert to a fraction first on the decimal to fraction calculator.
What to compare it with
Find the greatest common factor on the GCF and LCM calculator, and add or multiply fractions on the fraction calculator. The mixed number page converts to improper fractions, and the ratio simplifier applies the same method to ratios. The prime factorization tool shows why the factors match.
People also ask
Frequently asked questions
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common factor. For 24 over 36 the factor is 12, giving 2 over 3.
What does lowest terms mean?
The numerator and denominator have no common factor other than 1, so the fraction cannot be reduced further.
Does simplifying change the value?
No. The simplified fraction is equal to the original and represents exactly the same amount, only written with smaller numbers that are easier to compare.