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Calculators / Math / Fraction arithmetic
Fraction arithmetic calculator
Add two fractions and simplify the result.
On this page
Simplified fraction5 / 6
Decimal0.83
Calculator controls
How to calculate
Add two fractions and simplify the result.
a/b + c/d = (ad + bc) / bd
Worked example
Example inputs
First numerator: 1 · First denominator: 2 · Second numerator: 1 · Second denominator: 3
Example resultSimplified fraction: 5 / 6 · Decimal: 0.83333333
Assumptions and limits
Whole-number numerators and positive denominators only.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
The simplified fraction is an exact representation of the sum. The decimal is a rounded display and can differ from the exact fraction for recurring decimals.
When this tool is useful
Add measured quantities or check fraction arithmetic without converting to decimal first.
Understanding your inputs
| Input | What to enter |
|---|---|
| First numerator | Enter a number of at least -1000000 and no more than 1000000. |
| First denominator | Enter a number of at least 1 and no more than 1000000. |
| Second numerator | Enter a number of at least -1000000 and no more than 1000000. |
| Second denominator | Enter a number of at least 1 and no more than 1000000. |
Frequently asked questions
Why do the denominators change?
Fractions need a common denominator before their numerators can be added. Multiplying across gives (a×d + c×b)/(b×d), which is then simplified.
Can a denominator be zero?
No. Division by zero does not define a finite fraction. Use nonzero integer denominators.