How to use this fraction calculator
Enter the numerator above each fraction line and the denominator below it. Choose Add, Subtract, Multiply, or Divide from the operation menu. The result updates immediately. Negative numerators are supported; a denominator cannot be zero. For division, the second fraction must also be nonzero because dividing by zero is undefined.
How the calculation works
A fraction represents a numerator divided by a denominator. Equivalent fractions can use different numbers while describing the same value, such as 1/2 and 3/6. Simplifying divides both parts by their greatest common divisor without changing the value.
Addition and subtraction require a common denominator so the parts describe equal-sized pieces. Multiplication works across the numerators and denominators. Division uses the reciprocal of the second fraction, turning the operation into multiplication before the result is reduced.
Formulas
Add or subtract
Multiply
Divide
Worked examples
Add one-half and one-third
1/2 + 1/3 = (1 × 3 + 1 × 2) / 6 = 5/6. The result is already in lowest terms.
Divide three-quarters by two-fifths
3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8, which is 1 7/8 as a mixed number.
Common uses
Recipes and measurements
Combine or scale fractional cups, lengths, quantities, and portions while keeping an exact answer. Fractions are especially useful when the measuring tool is marked in halves, quarters, eighths, or sixteenths.
Schoolwork and skill checks
Verify fraction arithmetic, lowest terms, improper fractions, and mixed-number conversions after working a problem by hand. The displayed exact result makes it easier to compare each algebraic step.
Projects and shared quantities
Add material lengths, divide a quantity into equal shares, or compare fractional allocations without introducing decimal rounding. Confirm that every value refers to the same unit before calculating.
Accuracy and limitations
The calculator uses whole-number arithmetic for numerators and denominators, then reduces the exact result by the greatest common divisor. It does not approximate the fraction with a floating-point decimal.
A denominator of zero and division by a zero-valued fraction are undefined and produce an error. Real measurements may still carry uncertainty that exact fraction arithmetic cannot remove.
Frequently asked questions
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. For example, the greatest common divisor of 18 and 24 is 6, so 18/24 simplifies to 3/4.
Why do addition and subtraction need a common denominator?
The denominator defines the size of each part. Fractions can be combined directly only when those parts are the same size, so both fractions must first be expressed with a common denominator.
Can I enter improper fractions?
Yes. A numerator may be larger than its denominator. The calculator returns the exact improper fraction and also displays a mixed number where appropriate.
Can fractions be negative?
Yes. Enter a negative numerator. The result is normalized so a negative sign appears with the numerator rather than the denominator.
Why can the denominator not be zero?
A fraction means division, and division by zero is undefined. The calculator reports an error instead of producing a misleading value.
Is the fraction calculator free to use?
Yes. NumUtility is free, requires no account, and places no limit on ordinary calculations.
Are my entries stored?
No. The calculation runs in your browser. Values entered into the tool are not sent to NumUtility or saved by us.