Fraction Calculator
Add, subtract, multiply, and divide fractions and mixed numbers with automatic simplification, common denominators, and decimal conversion.
About the Fraction Calculator
The Fraction Calculator provides complete step-by-step solutions for adding, subtracting, multiplying, and dividing mathematical fractions. It handles proper fractions (numerator < denominator), improper fractions (numerator > denominator), and mixed numbers.
Whether you are checking homework, scaling culinary recipes, or computing engineering measurements, this tool reduces results to their simplest irreducible form and displays the decimal equivalent.
How to Calculate Fraction
Enter the numerator and denominator for your first fraction.
Select the arithmetic operation: Addition (+), Subtraction (-), Multiplication (×), or Division (÷).
Enter the numerator and denominator for your second fraction.
Click Calculate to see the simplified fraction, mixed number, and decimal representation.
Fraction Arithmetic Rules
Addition: (a/b) + (c/d) = (ad + bc) / bd Subtraction: (a/b) - (c/d) = (ad - bc) / bd Multiplication: (a/b) × (c/d) = (ac) / (bd) Division: (a/b) ÷ (c/d) = (ad) / (bc)
For addition and subtraction, convert to a common denominator before combining numerators. For multiplication, multiply across. For division, multiply by the reciprocal of the second fraction.
Variable Descriptions
- a & c
- Numerators (top numbers of the fractions)
- b & d
- Denominators (bottom numbers, must not equal zero)
Worked Example
Important Considerations & Tips
- A denominator can never be zero because division by zero is mathematically undefined.
- Negative fractions are standardized with the minus sign in the numerator (e.g., -3/4).
- The calculator automatically finds the Greatest Common Divisor to reduce outputs to simplest form.
Frequently Asked Questions
How do you add fractions with different denominators?
Find a common denominator (often by multiplying the two denominators), adjust both numerators accordingly, add the numerators together, and simplify the resulting fraction.
How do you divide two fractions?
To divide fractions, multiply the first fraction by the reciprocal (the inverted form) of the second fraction. For example, (1/2) ÷ (3/4) = (1/2) × (4/3) = 4/6 = 2/3.
What is a mixed number?
A mixed number consists of a whole number combined with a proper fraction, such as 2 1/2, which represents 2 + 1/2 (or 5/2 as an improper fraction).
Related Calculators
Percentage Calculator
Free online percentage calculator. Calculate percentage of a number, percentage change, increase, decrease, and percentage differences instantly with formulas.
Ratio Calculator
Free online ratio calculator. Simplify ratios to lowest terms, find missing terms in proportions (A:B = C:D), and calculate scaling factors instantly.
GPA Calculator
Free online GPA calculator. Calculate your semester and cumulative Grade Point Average on a 4.0 scale with credit weights and letter grades.
Grade Calculator
Free online grade calculator. Calculate current weighted course grades and find what score you need on your final exam to earn your target class grade.