Fraction Calculator

Enter two fractions

How it works

Adding and subtracting need a common denominator: each fraction is rewritten over the product of the two denominators, so a/b ± c/d = (a×d ± c×b) ÷ (b×d). Multiplying goes straight across: (a×c) ÷ (b×d). Dividing by a fraction is multiplying by its reciprocal — flip the second fraction and multiply: (a×d) ÷ (b×c).

Simplifying divides the top and bottom by their greatest common divisor (GCD) — the largest number that divides both. 18/12 simplifies by 6 to 3/2. A result bigger than 1 can also be written as a mixed number: 17/12 is 1 whole with 5/12 left over, written 1 5/12. An answer over 1 with a whole part is sometimes called an improper fraction before it is converted — both forms mean exactly the same amount.

Worked example: 3/4 + 2/3 = (3×3 + 2×4) ÷ (4×3) = 17/12, which is already simplified, equals the mixed number 1 5/12, and is about 1.416667 as a decimal.

Zero denominators: a fraction with 0 on the bottom is undefined — there is no answer — so the calculator refuses it instead of guessing. Dividing by a fraction that equals zero (like 0/5) is refused for the same reason.

Frequently asked questions

How do you add fractions with different denominators? Rewrite both over a common denominator (the product of the two denominators always works), add the numerators, then simplify. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

What is the difference between an improper fraction and a mixed number? Nothing in value — only in form. An improper fraction has a numerator at least as big as its denominator (7/4); the mixed number writes the same amount as a whole part plus a proper fraction (1 3/4).

Why flip the second fraction when dividing? Dividing by a number is the same as multiplying by 1 over that number. Dividing by 2/3 asks "how many 2/3 fit in here?", and multiplying by 3/2 answers it directly.