Math & Statistics
Fraction & Mixed Number Calculator
Updated Sep 3, 2026 Reviewed Sep 3, 2026
Add, subtract, multiply, divide, simplify, and compare proper, improper, or mixed-number fractions with exact results plus decimal and percentage conversions.
Exact fraction arithmetic
Enter two fractions or mixed numbers
Result
Calculation summary
Enter values to see the result
Your result, breakdown, assumptions, and warnings will appear here.
Fraction model
Parts of a whole
Formula
a/b + c/d = (ad + bc)/bd
- Improper fraction
- —
- Mixed number
- —
- Decimal
- —
How to use this calculator
- 1Choose an arithmetic or comparison operation.
- 2Enter the whole, numerator, and denominator parts.
- 3Calculate to see exact and decimal forms.
Formula
a/b + c/d = (ad + bc) / bd
Integer cross-products are reduced by their greatest common divisor.
Calculation steps
- Convert mixed numbers to improper fractions.
- Apply the selected operation with integer arithmetic.
- Normalize the sign and reduce the result.
Worked example
1 1/2 + 3/4 = 9/4 = 2 1/4.
Assumptions
- Denominators are positive and non-zero.
- Integer arithmetic is exact before decimal conversion.
- A negative mixed number applies to the complete value.
Sources
Frequently asked questions
Why can the denominator not be zero?
Division by zero is undefined.
What is an improper fraction?
Its numerator magnitude is at least its denominator.
Are results reduced?
Yes, automatically to lowest terms.
Is comparison rounded?
No, it uses exact cross-products.
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