Fraction calculator - add, subtract, multiply and divide fractions

• Addition and subtraction: convert to a common denominator, then add or subtract the numerators: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
• Multiplication: multiply numerators and denominators: 2/3 × 9/4 = 18/12 = 3/2.
• Division: multiply by the reciprocal: 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3. Dividing by zero is undefined.
• Mixed numbers: convert to an improper fraction first: 1 1/2 = (1·2 + 1)/2 = 3/2.
• Simplifying: divide numerator and denominator by their greatest common divisor: 18/24 = 3/4.

A fraction in lowest terms has a terminating decimal expansion if its denominator has only the prime factors 2 and 5 (1/8 = 0.125); otherwise it is recurring (1/3 = 0.(3), 1/6 = 0.1(6), 1/7 = 0.(142857)). The calculator also converts decimals, including recurring ones, back to fractions: 0.(3) = 1/3.

All arithmetic uses arbitrary-size integers, so results are exact with no floating-point rounding errors. In floating-point arithmetic 0.1 + 0.2 gives 0.30000000000000004; here 1/10 + 2/10 is exactly 3/10.

1. Convert to improper fractions: 1 1/2 = 3/2 and 2 3/4 = 11/4.
2. Find a common denominator of 4: 3/2 = 6/4.
3. Add the numerators: 6/4 + 11/4 = 17/4.
4. Write as a mixed number: 17/4 = 4 1/4, or 4.25 as a decimal.

The calculator shows exactly these steps, so you can compare them with your own working line by line.

Common mistakes: adding denominators (1/2 + 1/3 is not 2/5), cancelling terms of a sum instead of factors ((2 + 3)/2 is not 3), forgetting to flip the divisor when dividing, and reading 2 3/4 as 2 × 3/4 instead of 2 + 3/4. Imperial measurements are a typical real-life use: 5/8″ + 3/16″ = 13/16″.