Fraction Calculator
Add, subtract, multiply or divide fractions and mixed numbers. You get the simplified answer, the mixed number, decimal and percentage, plus every step of the working.
Leave the whole number empty for a plain fraction, or fill only the whole number for an integer. Put a minus sign on the whole number (or the numerator) for negatives.
= 13/6 = 2 1/6
Step-by-step working
- 1Convert 1 1/2 to an improper fraction: (1 × 2 + 1) / 2 = 3/2
- 2Find a common denominator: the LCM of 2 and 3 is 6
- 3Rewrite each fraction over 6: 3/2 = 9/6 (× 3), 2/3 = 4/6 (× 2)
- 4Add the numerators: 9/6 + 4/6 = 13/6
- 513/6 is already in simplest form (the GCD of 13 and 6 is 1)
- 6As a mixed number: 13/6 = 2 1/6
Fraction bars
To add or subtract fractions they need the same denominator. The calculator finds the least common multiple (LCM) of the two denominators, rewrites both fractions over it, then adds or subtracts the numerators.
Multiplying is simpler: multiply the tops and multiply the bottoms. Cancelling common factors across the two fractions first (cross-cancelling) keeps the numbers small. To divide, flip the second fraction upside down (its reciprocal) and multiply.
Every answer is simplified by dividing the top and bottom by their greatest common divisor (GCD). Mixed numbers like 1 1/2 are turned into improper fractions (3/2) before any working starts.
How each operation works
Add
Common denominator via the LCM, then add the numerators: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Subtract
Same as adding, but subtract the numerators: 3/4 − 1/6 = 9/12 − 2/12 = 7/12.
Multiply
Cross-cancel, then multiply straight across: 4/9 × 3/8 = 1/3 × 1/2 = 1/6.
Divide
Flip the second fraction and multiply: 3/4 ÷ 3/8 = 3/4 × 8/3 = 2.
Simplify
Divide top and bottom by their greatest common divisor: 6/8 ÷ 2 = 3/4.
Mixed numbers
Whole × denominator + numerator, over the denominator: 1 1/2 = 3/2.
How do I enter a mixed number like 2 3/4?
Type 2 in the whole box, 3 in the top box and 4 in the bottom box. For a plain fraction leave the whole box empty; for a whole number fill in only the whole box.
How do I enter a negative fraction?
Put the minus sign on the whole number for a mixed number (−1 1/2 means −1.5), or on the numerator for a plain fraction (−3/4).
Why can't the denominator be 0?
A fraction means top divided by bottom, and dividing by zero is undefined. The same goes for dividing by a fraction whose value is 0.
What is the difference between an improper fraction and a mixed number?
They are the same value written two ways. An improper fraction has a top bigger than its bottom (7/4); a mixed number splits out the wholes (1 3/4).
