Fraction Calculator
Add, subtract, multiply, and divide fractions with automatic simplification and step-by-step solutions
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What is a Fraction?
A fraction represents a part of a whole. It consists of two numbers: the numerator (top number) and the denominator (bottom number). The numerator indicates how many parts you have, while the denominator shows how many equal parts make up the whole. For example, in the fraction 3/4, you have 3 parts out of 4 total equal parts.
Adding and Subtracting Fractions
To add or subtract fractions, they must have the same denominator (common denominator). If they don't, you need to find the least common multiple (LCM) of the denominators and convert both fractions. Once the denominators match, you simply add or subtract the numerators while keeping the denominator the same.
For example: 1/4 + 1/6. The LCM of 4 and 6 is 12. Convert: 3/12 + 2/12 = 5/12.
Multiplying Fractions
Multiplying fractions is straightforward: multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Unlike addition and subtraction, you don't need a common denominator.
For example: 2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = 1/2 (simplified).
Dividing Fractions
To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second fraction. The reciprocal of a fraction is created by swapping the numerator and denominator. This "multiply by the reciprocal" rule makes fraction division much simpler.
For example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3 (simplified).
Simplifying Fractions
A fraction is simplified (or in lowest terms) when the numerator and denominator have no common factors other than 1. To simplify, find the greatest common divisor (GCD) of both numbers and divide both the numerator and denominator by it. Simplified fractions are easier to understand and work with.
For example: 12/18 can be simplified by dividing both by their GCD of 6, resulting in 2/3.
Mixed Numbers
A mixed number combines a whole number and a proper fraction, like 2 1/2. When a fraction's numerator is larger than its denominator (an improper fraction like 5/2), it can be converted to a mixed number. Divide the numerator by the denominator: the quotient becomes the whole number, and the remainder over the original denominator becomes the fraction part.