Fraction Calculator
Add, subtract, multiply, and divide fractions — simplified result, mixed number, decimal, and every step of the work shown.
- 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6
How to use this tool
- Enter two fractions (whole numbers work too — just use 1 as the denominator or type the number over 1).
- Pick the operation: + − × ÷.
- Read the simplified result, its mixed-number form, the decimal — and the worked steps below.
How it works
The calculator shows its work the way a teacher would: to add fractions it finds the least common denominator, converts both, adds numerators, then reduces by the greatest common divisor (found with Euclid's algorithm — repeatedly replace the larger number with the remainder of dividing it by the smaller). Reducing 84/126: gcd is 42, so it simplifies to 2/3.
Addition and subtraction use the common denominator: a/b ± c/d = (ad ± cb)/bd. Multiplication multiplies straight across; division multiplies by the reciprocal (flip the second fraction). The result is then reduced by the greatest common divisor — and the tool shows each of those steps, because seeing the method is how the homework actually gets learned.
Frequently asked questions
Why do fractions need a common denominator to add but not to multiply?
Addition combines parts of the same-sized whole, so the pieces must be the same size first. Multiplication is 'a fraction of a fraction' — half of a third is a sixth — which works directly on numerators and denominators.
How do I add fractions with different denominators?
Rewrite both over a common denominator, then add the numerators: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. The tool shows this step for your numbers.
How do I divide fractions?
Multiply by the reciprocal: (2/3) ÷ (4/5) = (2/3) × (5/4) = 10/12 = 5/6.
What does 'simplified' mean?
Numerator and denominator divided by their greatest common divisor, so 10/12 becomes 5/6. If the result is top-heavy, the mixed-number form (like 1 1/2) is shown too.