Fraction Calculator
Add, subtract, multiply, divide – result automatically reduced with decimal value
- Updated
Operation
Numerator on top, denominator below – whole numbers, negatives allowed.
Result (reduced)
5/6
5/61/2 + 1/3 = 5/6 (as a decimal 0.83333).
How this was calculated
Adding: bring both fractions to a common denominator (multiply the denominators), add the numerators, then reduce.
- Decimal value
- 0.83333
RZ-26 · headon.pro
Fraction arithmetic: basics and rules
Understanding the four basic operations with fractions
The arithmetic of fractions is a fundamental chapter of mathematics. A fraction consists of a numerator (top) and a denominator (bottom), separated by a fraction bar. The denominator indicates into how many equally sized parts a whole is divided; the numerator states how many of these parts are meant. So 3/4 represents three quarters of a whole.
When adding and subtracting fractions, you first need a common denominator: both fractions are expanded to the same denominator, after which the numerators can be added or subtracted. When multiplying, numerator is multiplied by numerator and denominator by denominator – no common denominator is needed. Division of fractions follows the rule: form the reciprocal of the second fraction and then multiply.
A result should always be fully reduced: the numerator and denominator are divided by their greatest common divisor (GCD). The result 6/8, for example, reduces to 3/4, because the GCD of 6 and 8 is 2. Our fraction calculator uses the Euclidean algorithm to efficiently determine the GCD and automatically reduce the result.
Calculation examples
- Common denominator
- 2 × 3 = 6
- Expanded 1st fraction
- 1/2 = 3/6
- Expanded 2nd fraction
- 1/3 = 2/6
- Sum (unreduced)
- 5/6
- Result (reduced)
- 5/6
- Reciprocal of 1/2
- 2/1
- Rearranged (×)
- 3/4 × 2/1
- Numerator: 3 × 2
- 6
- Denominator: 4 × 1
- 4
- Result (reduced)
- 3/2 = 1.5
- Numerator: 1 × 2
- 2
- Denominator: 2 × 3
- 6
- Unreduced
- 2/6
- GCD(2, 6)
- 2
- Result (reduced)
- 1/3
Frequently asked questions about the fraction calculator
Rules, examples and tips for fraction arithmetic
How do I add two fractions?
To add two fractions, you first need to find a common denominator. The simplest approach: expand both fractions to a common denominator equal to the product of the two denominators. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. After that, you can add the numerators while the denominator stays the same. Our fraction calculator does this automatically and reduces the result immediately.
What does it mean to reduce a fraction?
Reducing a fraction means dividing the numerator and denominator by their greatest common divisor (GCD) until no common divisors remain. Example: 4/6 can be reduced by 2 → 2/3. The GCD of 4 and 6 is 2. The result 2/3 is already fully reduced, since 2 and 3 are coprime. Our calculator automatically reduces all results using the Euclidean algorithm.
How do I divide fractions?
Dividing fractions works by multiplying by the reciprocal of the second fraction. Formula: a/b ÷ c/d = a/b × d/c = (a×d)/(b×c). Example: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2. Rule of thumb: "flip the second fraction and multiply." Our calculator converts the division automatically, so you only need to enter the starting values.
How do I convert a fraction to a decimal number?
To convert a fraction to a decimal number, simply divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Or: 1/3 = 1 ÷ 3 ≈ 0.33333… (repeating decimal). Our fraction calculator automatically shows the decimal value of the calculated result – accurate to up to 5 decimal places.
What is the greatest common divisor (GCD)?
The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without a remainder. It is needed to reduce fractions. Example: GCD(12, 8) = 4, because 4 divides both 12 and 8 – and there is no larger number that can do so. The most efficient way to calculate the GCD is the Euclidean algorithm, which our fraction calculator also uses internally.