How to use
Enter two values and choose addition, subtraction, multiplication or division. Supported entries include ordinary fractions such as 3/4, mixed numbers such as 2 1/3, integers and finite decimals such as 1.5. Use a space between the whole and fractional parts of a mixed number.
A minus sign before a mixed number applies to its entire value: -2 1/3 means −7/3. The fractional part of a mixed number must be smaller than one. Enter an improper fraction directly when appropriate; 3/2 is accepted, while 2 3/2 is not a valid mixed-number entry.
Calculation method
Inputs become simplified rational numbers with integer numerators and denominators. Addition and subtraction use a common denominator. Multiplication multiplies numerators and denominators; division multiplies by the reciprocal of the second number. The final answer is reduced, with a positive denominator.
The exact fraction determines the result. Choosing 3, 6 or 12 decimal places changes only its approximate decimal display, not the arithmetic. Steps explain the conversion, operation and simplification.
Worked example
For 1/2 + 1/3, a common denominator is 6: 3/6 + 2/6 = 5/6. Dividing 1/2 by 1/3 instead gives 3/2, also shown as 1 1/2. Multiplying 2/3 by 9/10 gives 18/30, which reduces to 3/5. Decimal inputs 0.1 + 0.2 give exactly 3/10 in this model.
Input rules and limits
Zero denominators and division by a zero-valued second number are rejected. Use 1/2 rather than the single character ½. Arithmetic expressions, percentages, exponents and repeating-decimal notation are not parsed. Numerators and denominators in slash notation must be integers. Grouping and decimal separators must match the selected number format.
The tool has input-length and digit limits to keep calculations manageable. A result may contain more digits than a new input permits. For percentage interpretations of ratios use the percentage calculator; for price per equal quantity use the unit price calculator.
For the measurement and planning details, read fractions and mixed numbers: reading an exact result.