Understanding your result
The calculator applies the selected operation, normalizes a negative denominator, and divides numerator and denominator by their greatest common divisor.
To express one whole-number amount as a percentage of another, use the Percentage Calculator in its ratio mode.
The formula
Addition and subtraction use a common denominator. Multiplication combines like parts, while division multiplies by the reciprocal of the second fraction.
Adding one half and one third
The common denominator is 6: 1/2 becomes 3/6 and 1/3 becomes 2/6. Their sum is 5/6, approximately 0.833333 or 83.3333%.
How to use this calculator
- Enter both numerators and nonzero denominators.
- Choose addition, subtraction, multiplication, or division.
- Calculate to reduce the result and view equivalent forms.
Reduction keeps the value unchanged
Dividing the numerator and denominator by the same nonzero number produces an equivalent fraction.
The greatest common divisor produces lowest terms in one step, such as reducing 12/18 to 2/3.
Improper fractions and signs
A result whose numerator is larger than its denominator is also shown as a mixed number.
The sign is carried by the numerator so the displayed denominator remains positive.
Assumptions & limitations
What this calculation assumes
- Inputs are whole-number numerators and denominators.
- Results are reduced to lowest terms.
- Decimal and percentage displays are rounded for presentation.
What to keep in mind
- Numerators and denominators are limited to whole numbers from −1 billion to 1 billion. Fraction and mixed-number results remain exact within those input bounds.
- Repeating decimals are displayed to a limited precision.
- A zero denominator and division by a zero fraction are undefined.
Common questions
Why do fractions need a common denominator?
Addition and subtraction combine equal-sized parts, so the parts must first use the same denominator.
Can I enter negative fractions?
Yes. Either numerator or denominator may be negative, but the final sign is shown on the numerator.
What is a mixed number?
It combines a whole number with a proper fraction, such as 1 1/2.