About the Fraction Calculator
This fraction calculator adds, subtracts, multiplies and divides two fractions or mixed numbers and gives the answer in lowest terms, as a mixed number and as a decimal. It also shows each step — the common denominator, the combined numerator and the greatest common divisor used to simplify — so you can follow the method rather than just copy the answer.
Enter a whole-number part for mixed numbers such as 2 3/4, or leave it at 0 for a simple fraction. Negative values work too: put the minus sign on the whole number or the numerator. It is useful for homework, recipe scaling, woodworking and sewing measurements, and anywhere you need exact answers instead of rounded decimals.
Addition and subtraction use the least common denominator, which keeps the numbers small; multiplication multiplies straight across; and division multiplies by the reciprocal of the second fraction. Division by a zero fraction is reported as undefined.
How to use the fraction calculator
- 1Enter the first fraction (add a whole number for a mixed number).
- 2Choose add, subtract, multiply or divide.
- 3Enter the second fraction.
- 4Read the simplified answer, mixed number and decimal.
- 5Follow the working to see the common denominator and simplification.
Formula and method
To add or subtract, rewrite both fractions over a common denominator. The calculator uses the least common denominator L = lcm(b, d), scales each numerator, then adds or subtracts. To multiply, multiply the numerators and the denominators. To divide, multiply by the reciprocal of the second fraction.
Mixed numbers are first converted to improper fractions (2 3/4 = 11/4). The result is simplified by dividing the numerator and denominator by their greatest common divisor, and then converted back to a mixed number and a decimal.
- a/b, c/d
- The two fractions (numerator over denominator)
- L
- Least common denominator, lcm(b, d)
- GCD
- Greatest common divisor used to reduce the answer
Worked examples
3/4 + 2/3
The least common denominator of 4 and 3 is 12, so 3/4 = 9/12 and 2/3 = 8/12. Adding gives 17/12, which is 1 5/12 or about 1.4167.
5/6 − 1/4
The LCD of 6 and 4 is 12: 10/12 − 3/12 = 7/12, which is already in lowest terms.
1 1/2 × 2/3
1 1/2 is 3/2. Multiplying 3/2 × 2/3 = 6/6, and dividing by the GCD of 6 gives exactly 1.
3/4 ÷ 1/8
Dividing by 1/8 is the same as multiplying by 8/1: 3/4 × 8 = 24/4 = 6. There are six eighths in three quarters.
Frequently asked questions
How do you add fractions with different denominators?+
Find a common denominator (ideally the least common multiple of the denominators), convert each fraction, then add the numerators. For 1/4 + 1/6, the LCD is 12: 3/12 + 2/12 = 5/12.
How do you multiply fractions?+
Multiply the numerators together and the denominators together, then simplify. For 2/3 × 3/5 = 6/15, which reduces to 2/5 by dividing both by 3.
How do you divide fractions?+
Keep the first fraction, change division to multiplication and flip the second fraction (keep, change, flip). So 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
How do you simplify a fraction?+
Divide the numerator and denominator by their greatest common divisor. For 18/24 the GCD is 6, so it simplifies to 3/4. A fraction is fully simplified when the GCD is 1.
How do I work with mixed numbers?+
Convert each mixed number to an improper fraction first: whole × denominator + numerator, over the denominator. So 2 1/3 = 7/3. Do the operation, then convert the answer back.