Utility
Fraction Calculator
Fraction arithmetic without the scratch paper. Enter two fractions, pick an operation, and get the answer fully simplified — with the mixed-number and decimal versions alongside.
Simplified result
5/4
Mixed number
1 1/4
Decimal
1.25
Results are reduced to lowest terms using the greatest common divisor. Use whole numbers for numerators and denominators — for mixed numbers like 2 1/3, enter the improper fraction 7/3.
How it works
Adding and subtracting fractions requires a common denominator: a/b ± c/d = (ad ± cb) / bd. Multiplying is simpler — multiply straight across. Dividing means multiplying by the reciprocal: flip the second fraction and multiply.
The raw result is then reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD). 6/8 becomes 3/4 because both share a factor of 2.
When the numerator exceeds the denominator, the result is an improper fraction like 5/4. That's mathematically fine, but the calculator also shows the mixed-number form (1 1/4), which is usually what recipes, measurements, and teachers want.
a/b + c/d = (ad + cb) / bd a/b × c/d = ac / bd
a/b − c/d = (ad − cb) / bd a/b ÷ c/d = ad / bc
then divide top and bottom by gcd
Example: 1/2 + 3/4 = (4 + 6) / 8 = 10/8 = 5/4 = 1 1/4Frequently asked questions
How do I enter a mixed number like 2 1/3?
Convert it to an improper fraction first: multiply the whole number by the denominator and add the numerator. 2 1/3 = (2 × 3 + 1)/3 = 7/3. The result panel converts back to mixed form for you.
Why do fractions need a common denominator to add?
You can only add like units — halves with halves, twelfths with twelfths. 1/2 + 1/3 doesn't add directly because the pieces are different sizes; rewritten as 3/6 + 2/6, both count sixths, so they sum to 5/6.
Why does dividing by a fraction mean flipping it?
Dividing asks 'how many of these fit?' Dividing by 1/2 asks how many halves fit — which is 2 per whole, the same as multiplying by 2/1. In general, dividing by a/b is identical to multiplying by b/a.
How does simplifying work?
Find the greatest common divisor of the numerator and denominator and divide both by it. For 18/24, the GCD is 6, giving 3/4. A fraction is fully simplified when the GCD is 1.
Can I use negative fractions?
Yes — enter a negative numerator (or denominator; the calculator normalizes the sign to the top). All four operations handle negatives correctly.