Fraction Calculator

Adding fractions requires a common denominator because a fraction is a count of equal parts, and you cannot count parts of different sizes. 1/2 + 1/3 is not 2/5 — halves and thirds are different units. Convert both to sixths and it becomes 3/6 + 2/6 = 5/6. The lowest common denominator is just the LCM of the two denominators.

Multiplication needs no such step: multiply the numerators and the denominators, so2/3 × 3/4 = 6/12 = 1/2. Division is multiplication by the reciprocal — flip the second fraction and multiply. The rule "invert and multiply" is not arbitrary: dividing by 3/4 asks how many three-quarters fit into the number, and that is the same as multiplying by 4/3.

Simplifying means dividing both parts by their greatest common factor, so 18/24becomes 3/4. An improper fraction has a numerator larger than its denominator and converts to a mixed number by division — 17/5 is 3 remainder 2, or 3 2/5. Mixed numbers read more naturally but are awkward to compute with, so convert back to improper form before doing arithmetic and simplify at the end.