Fraction Calculator: Complete Fraction Math Tool
Our fraction calculator handles all fraction operations with ease. Add, subtract, multiply, and divide fractions including mixed numbers, and get results automatically simplified to lowest terms. The visual representation helps you understand fractions intuitively, and step-by-step solutions show exactly how each calculation works.
Whether you're a student learning fractions, a teacher creating examples, or anyone who needs quick fraction math, this tool provides accurate results with clear explanations.
How Fraction Operations Work
Addition & Subtraction: Find a common denominator (LCM of both denominators), convert each fraction so they have the same denominator, then add or subtract the numerators. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Multiplication: Multiply the numerators together and the denominators together. Example: 2/3 × 3/4 = 6/12 = 1/2.
Division: Multiply by the reciprocal (flip the second fraction). Example: 2/3 ÷ 1/2 = 2/3 × 2/1 = 4/3 = 1 1/3.
Working with Mixed Numbers
A mixed number combines a whole number and a fraction (e.g., 2 1/2). To perform operations, first convert to an improper fraction: multiply the whole number by the denominator, add the numerator. So 2 1/2 = (2×2+1)/2 = 5/2.
After calculating, convert back to a mixed number by dividing the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator.
Simplifying Fractions
A fraction is in lowest terms when the numerator and denominator share no common factors other than 1. To simplify, find the GCD (Greatest Common Divisor) of both numbers and divide each by it. For example, 12/18: GCD(12,18) = 6, so 12/18 = 2/3.
FAQ
How do I convert a decimal to a fraction?
Use the decimal-to-fraction converter above. The algorithm finds the closest fraction with reasonable denominator. For example, 0.75 = 3/4, and 0.333... ≈ 1/3.
Why simplify fractions?
Simplified fractions are easier to understand and compare. 1/2 is clearer than 7/14, even though they represent the same value. Most math teachers require simplified answers.
What's an improper fraction?
A fraction where the numerator is larger than the denominator (e.g., 7/4). It represents a value greater than 1 and can be converted to a mixed number (7/4 = 1 3/4).