How this calculation works
Integer arithmetic keeps the fraction exact within the input limits. After the selected operation, the numerator and denominator are reduced by their greatest common divisor and the denominator is made positive.
a/b + c/d = (ad + bc)/(bd); simplify by the numerator-denominator GCDA worked example
1/2 + 1/3 = (3 + 2)/6 = 5/6, approximately 0.833333.
Good to know
An estimate under the stated inputs and model. Displayed decimals are rounded; verify assumptions before relying on the result.
A common denominator creates comparable pieces
One half and one third refer to differently sized pieces of the same whole. Rewriting them as three sixths and two sixths makes the pieces comparable, so adding gives five sixths.
The cross-multiplication formula performs that conversion automatically. Reducing the final numerator and denominator removes a common factor without changing the fraction’s value.
A decimal display can lose an exact repeating pattern
The fraction 1/3 is exact, while a finite decimal display such as 0.333333 is rounded. The tool keeps its integer fraction arithmetic exact within the input limits and labels the decimal as an approximation.
A zero denominator is not a valid fraction, and division by a fraction with zero numerator is division by zero. Negative denominators are accepted but normalized into a positive denominator in the result.
A few questions, answered
Can I enter mixed numbers?
Convert a mixed number to an improper fraction first, such as 1½ = 3/2.
Why does a whole-number result have no denominator?
A denominator of one is omitted for readability; 4/1 is the same as 4.