The fraction calculator performs arithmetic on two fractions and simplifies the result using integer numerator and denominator arithmetic. It can also present a mixed number when the absolute improper fraction is greater than one.
How to use this calculator
Enter integer numerators and nonzero denominators, choose an operation, and calculate. Negative values may be entered in either numerator. Division requires the second fraction to be nonzero.
Formula & calculation method
a/b + c/d = (ad + cb)/bd; a/b ÷ c/d = ad/bcAddition and subtraction use a common denominator, multiplication combines numerators and denominators, and division multiplies by the reciprocal. The result is reduced by the greatest common divisor and normalized with a positive denominator.
Worked example
One-half plus one-third produces five-sixths. One-half divided by one-third produces three-halves, which is also displayed as the mixed number one and one-half.
Why this is useful
Exact integer reduction avoids the rounding errors that can occur when fractions are converted to decimals too early. Mixed-number output complements the simplified fraction for everyday measurements and schoolwork.
Limitations to keep in mind
Inputs must be integers within the safe numeric range. Very large intermediate products can lose integer precision in JavaScript, so the calculator rejects values outside a conservative limit rather than presenting an unreliable exact fraction.
Frequently asked questions
Can a denominator be negative?
Yes, but the simplified result is normalized so the denominator is positive and the sign appears in the numerator.
Why can't I divide by a zero fraction?
Dividing by zero is undefined. If the second numerator is zero, its reciprocal has a zero denominator.
What is a mixed number?
It combines a whole number and a proper fraction, such as 1 1/2 instead of the equivalent improper fraction 3/2.