Fraction Calculator
Add, subtract, multiply and divide fractions, with the result simplified and shown as a decimal and percentage.
Your details
This calculator runs entirely on your device. Nothing you enter is uploaded, stored, or sold. How this works
Result
19/12
3/4 + 5/6
Includes your inputs, the full breakdown, and every row of the table.
Simplified
19/12
Mixed number
1 7/12
As a decimal
1.583333
As a percentage
158.33%
- First fraction
- 3/4 = 0.7500
- Second fraction
- 5/6 = 0.8333
- Unsimplified result
- 38/24
- Divided by GCD of 2
- 19/12
What this means
- Adding and subtracting requires a common denominator, which is why both fractions get scaled before the numerators are combined.
- The raw answer 38/24 shares a common factor of 2, so it simplifies.
How the fraction calculation works
Fraction arithmetic follows different rules for each operation, which is why it trips people up long after they have mastered decimals. Multiplication is the simplest case: numerators multiply, denominators multiply, and no preparation is needed. Division is multiplication in disguise — flip the second fraction and multiply. Addition and subtraction are the awkward ones, because you cannot combine parts of different sizes without first rewriting both over a common denominator.
Simplifying at the end matters for readability rather than correctness. Dividing both parts by their greatest common divisor gives the lowest terms, so 8/12 becomes 2/3. Fractions remain the exact representation where decimals cannot be: one third is 0.333… forever as a decimal but is precise and finite as a fraction, which is why recipes, engineering drawings and music notation still use them.
Frequently asked questions
Why do I need a common denominator to add fractions?
Because the denominator defines the size of each piece, and you cannot add pieces of different sizes directly. A quarter and a sixth are not the same quantity, so both are rewritten over twelfths — three twelfths and two twelfths — after which the numerators can simply be added.
How do I convert an improper fraction into a mixed number?
Divide the numerator by the denominator. The whole-number part of that division becomes the whole number, and the remainder stays over the original denominator. So 11/4 gives 2 with a remainder of 3, which is 2 and 3/4.
Why does dividing by a fraction make the answer bigger?
Because you are asking how many of the smaller quantity fit into the larger one. Dividing 3 by one half asks how many halves are in three, and the answer is six. Dividing by any number below one always increases the result, which is exactly what multiplying by the reciprocal does.
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Disclaimer. This calculator is provided for general information and educational purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Results are estimates based on the inputs you provide and the assumptions described above. Confirm any figure with a qualified professional before acting on it.