Fraction Calculator

How to use the fraction calculator

1. Type the First fraction and the Second fraction. You can write proper fractions (3/4), negative fractions (-5/6), mixed numbers with a space (1 1/2), whole numbers (7) or decimals (0.25 or 0,25).
2. Choose the Operation: Add, Subtract, Multiply or Divide.
3. The result updates as you type; you can also press Calculate. It is shown three ways: Result (simplified) as a fraction in lowest terms, Mixed number when the fraction is larger than 1, and Decimal.
4. Read Step by step to see the common denominator, the converted fractions and the simplification. Copy copies the simplified fraction.

To reduce a single fraction, use Simplify a fraction further down: type something like 18/24 and read the Simplified fraction and the greatest common divisor used.

How each operation works

Adding and subtracting. Fractions can only be added when they share a denominator. The tool finds the least common denominator (LCD), rewrites each fraction with it, then adds or subtracts the numerators:

1/2 + 1/3 → LCD(2, 3) = 6 → 3/6 + 2/6 = 5/6

Multiplying. Multiply the numerators together and the denominators together, then simplify: 2/3 × 3/4 = 6/12 = 1/2.

Dividing. Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down): 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6. Dividing by zero is impossible, and the tool says so.

Simplifying. A fraction is in lowest terms when the numerator and the denominator have no common factor other than 1. The tool computes their greatest common divisor (GCD) and divides both by it: GCD(18, 24) = 6, so 18/24 = 3/4.

Mixed numbers and decimals

A mixed number such as 1 3/4 means 1 + 3/4, which is the improper fraction 7/4. The tool converts mixed numbers and decimals to fractions before calculating, and shows that conversion as the first step (1 1/2 = 3/2, 0.25 = 1/4). The answer is then given back both as an improper fraction and as a mixed number.

Every calculation is exact: numerators and denominators are whole numbers of any size, so there is no rounding until the decimal display. When the decimal needs more than ten places, as with 1/3, it is rounded and marked with “≈”. To see the full repeating decimal, use the fraction to decimal converter.

Tips

• A minus sign can go in front of the fraction (-3/4) or of the mixed number (-1 1/2); the sign applies to the whole number.
• Negative operands are shown in brackets in the steps, for example 1/2 − (−1/4), to avoid confusion.
• If you get a result like 12/8 in your own working, it is correct but not simplified: the tool always reduces to lowest terms.