Exact fraction arithmetic keeps information a decimal can hide
For addition and subtraction, fractions are moved to a common denominator before the numerators are combined. Multiplication multiplies numerators and denominators directly, while division multiplies by the reciprocal of the second fraction.
After every operation, Toolmera reduces the result by the greatest common divisor so an answer such as 22/16 is shown as 11/8 rather than left unsimplified.
Additiona/b + c/d = (ad + bc) / bd
Multiplicationa/b × c/d = ac / bd
Divisiona/b ÷ c/d = ad / bc
Improper fractions, mixed numbers and decimals answer different needs
An improper fraction such as 11/8 is often the cleanest exact result for further calculation. The mixed-number form 1 3/8 can be easier to read in everyday measurements, while 1.375 is convenient when the next step expects a decimal.
Showing all three avoids forcing one representation onto every workflow and makes it easier to verify that the simplified fraction and decimal agree.
Zero denominators are errors, not special values
A denominator of zero does not define a real fraction, so the calculator stops and asks for a valid denominator instead of returning Infinity or a misleading result.
Division by a second fraction whose numerator is zero is also undefined because taking its reciprocal would create a zero denominator.