Fraction Calculator
Add, subtract, multiply, or divide fractions — simplified automatically.
How the calculator works
Addition and subtraction first rewrite both fractions over a common denominator — the product of the two denominators, reduced afterwards — then combine the numerators. Multiplication is the easy one: numerators times numerators, denominators times denominators. Division flips the second fraction and multiplies. In every case the result is then reduced by dividing both parts by their greatest common divisor, and the sign is normalized so the denominator stays positive. Mixed-number conversion divides the numerator by the denominator: the quotient becomes the whole part and the remainder becomes the new numerator, so 7/3 reads as 2 and 1/3. The decimal value is the numerator divided by the denominator, shown to up to six places.
Formula
a/b × c/d = (ac) ÷ (bd)
a/b ÷ c/d = (ad) ÷ (bc)
Where:
- a/b — the first fraction
- c/d — the second fraction
- The result is always simplified by the greatest common divisor
Example
Take 1/2 + 1/3. A common denominator is 6, giving 3/6 + 2/6 = 5/6 ≈ 0.833333 — already in lowest terms. Now try 4/8 ÷ 2/3: flipping the second fraction gives 4/8 × 3/2 = 12/16, which simplifies by the common divisor 4 to a clean 3/4, or 0.75 as a decimal. The same three-line logic covers every operation the calculator performs.