Free Fraction Calculator
Enter any two fractions and choose an operation. Get the simplified result, decimal equivalent, and mixed number instantly. Ideal for students, teachers, and everyday math.
Operation Workbench
Configure your fractions and select an operator to synthesize the result.
FORMULA: Result = 1/2 + 1/4How It Works
Enter a numerator and denominator for each fraction, pick your operation (+, −, ×, ÷), and the result appears instantly. Every answer is automatically reduced to its simplest form using the Greatest Common Divisor (GCD) algorithm. If the result is an improper fraction, the mixed number form is shown too.
How Each Operation Works
Addition (+)
Find a common denominator, convert both fractions, then add the numerators.
Subtraction (−)
Same as addition — find a common denominator, then subtract the numerators.
Multiplication (×)
Multiply numerators together, and denominators together. Then simplify.
Division (÷)
Flip the second fraction (take its reciprocal), then multiply as normal.
Where Fractions Actually Come Up
What Is GCD Simplification?
After calculating the result, the tool divides both the numerator and denominator by their Greatest Common Divisor (GCD) — the largest number that divides both exactly. This guarantees the result is always in its lowest terms.
Accuracy & Limitations
This calculator is mathematically exact for all integer fractions. Decimal equivalents are displayed to 4 decimal places. For repeating decimals like 1/3 (0.3333…), the display is rounded — the fraction form is always the precise value. For further math work, try our Percentage Calculator, Ratio Calculator, or the Average Calculator.
Common Questions
Find the least common denominator (LCD) of both fractions. Convert each fraction to that denominator, then add the numerators. Our calculator does this automatically — just enter the fractions and hit +.
1/2 + 1/3 = 3/6 + 2/6 = 5/6. The common denominator is 6. Our tool calculates this in real time as you type.
To divide fractions, multiply the first fraction by the reciprocal of the second. For example, 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. This is called Keep, Change, Flip.
Simplifying means dividing both numerator and denominator by their Greatest Common Divisor (GCD) until no further reduction is possible. For example, 6/8 simplifies to 3/4.
A proper fraction has the numerator smaller than the denominator (e.g. 3/4). An improper fraction has the numerator equal to or larger than the denominator (e.g. 5/4). This tool shows both forms.
Yes. Every result includes the decimal equivalent automatically, accurate to 4 decimal places. For example, 1/3 shows as 0.3333.
A mixed number combines a whole number and a proper fraction, like 1 1/2. When a result is an improper fraction (e.g. 3/2), our tool also shows it as a mixed number for easier reading.