ToolwebHow to use this tool
- Enter the first value as a fraction, a mixed number or a decimal, such as 1/2, 2 1/3 or 0.25.
- Choose an operation and a second value. Swap inputs to reverse their order.
- Check the reduced numerator, denominator and mixed form, then save the representation you need.
Add a mixed number and a fraction
- Input and settings
- 2 1/3 + 3/4
- Result
- 37/12; mixed number 3 1/12
The decimal repeats, so its display is rounded while the exact fraction is retained.
Use unambiguous fraction notation
A mixed number places a space between its integer and fraction. The input -2 1/3 means -(2 + 1/3). A mixed number with an improper fractional part, such as 2 4/3, is rejected; enter an improper fraction directly instead.
A negative denominator is normalized by moving its sign to the numerator. Division multiplies by the reciprocal of the second operand. A zero denominator, or division by a second operand equal to zero, cannot produce a valid fraction.
Choose the appropriate result form
The result is divided by its greatest common divisor to produce a reduced fraction. Integer arithmetic is used for numerator and denominator, rather than trying to simplify a previously rounded decimal approximation.
The decimal is convenient for comparing magnitudes, while the fraction is appropriate for carrying an exact value into another computation. Inputs that would produce excessive integer sizes are bounded to keep the browser responsive.
Common questions
Is 0.1 converted exactly?
The decimal string is interpreted as 1/10. It is not first converted into a binary floating-point approximation.
Why does the decimal look different from the fraction?
They represent the same value, but a repeating decimal cannot fit in a finite display. The ≈ mark indicates rounding of that display only.