Fraction operations and reduced answers
Fraction and mixed-number answers use exact integer arithmetic and are reduced to lowest terms. Decimal and percentage values are rounded approximations. Open Calculation steps to see mixed-number conversion, the operation and reduction.
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
- Choose Fractions or Mixed numbers and select an operation.
- Enter the numerator and nonzero denominator for each value. In Mixed numbers mode, also enter each whole-number part.
- For a negative mixed number, put the minus sign on its whole-number part and keep the fractional numerator positive. With a whole-number part of zero, use a negative numerator for a negative proper fraction.
- The answer updates as you type. Open Calculation steps to see the working; Calculate updates immediately and Reset restores the example.
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.
Mixed numbers can be entered directly. A whole part of 1 with numerator 1 and denominator 2 represents 1 1/2, or 3/2. A whole part of −1 with the same fractional part represents −1 1/2, or −3/2.
Assumptions & limitations
What this calculation assumes
- Numerators, denominators and mixed-number whole parts are integers. A mixed-number denominator is positive; a negative whole part makes the entire mixed number negative.
- Results are reduced to lowest terms.
- Decimal and percentage displays are rounded for presentation.
What to keep in mind
- Each entered numerator, denominator and whole-number part is limited to integers from −1 billion to 1 billion. Fraction and mixed-number answers remain exact within those 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.
Can I calculate with mixed numbers?
Yes. Choose Mixed numbers and enter the whole part, numerator and denominator for each value. For example, 1 1/2 + 2 1/3 gives 23/6, or 3 5/6.
How can I simplify one fraction?
Leave the operation as Add and enter 0 over 1 as the second value. The result reduces the first fraction without changing its value.
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