How to Calculate Fractions
A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). This calculator handles all four basic operations: addition, subtraction, multiplication, and division of fractions and mixed numbers.
Adding and Subtracting Fractions
To add or subtract fractions, you need a common denominator. Find the least common denominator (LCD), convert each fraction, then add or subtract the numerators.
Example: 1/4 + 1/3 = 3/12 + 4/12 = 7/12
Multiplying Fractions
To multiply fractions, multiply the numerators together and the denominators together. Then simplify the result.
Example: 2/3 × 3/4 = 6/12 = 1/2
Dividing Fractions
To divide fractions, multiply by the reciprocal (flip the second fraction). This is often called "keep, change, flip."
Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2
Simplifying Fractions
To simplify a fraction, find the greatest common factor (GCF) of the numerator and denominator, then divide both by that number.
Example: 12/18 → GCF is 6 → 12÷6 / 18÷6 = 2/3
Mixed Numbers
A mixed number combines a whole number with a fraction (e.g., 2 1/3). To calculate with mixed numbers, first convert to an improper fraction: multiply the whole number by the denominator, add the numerator, and keep the same denominator.
Example: 2 1/3 = (2×3 + 1)/3 = 7/3
Frequently Asked Questions
What is an improper fraction? An improper fraction has a numerator larger than or equal to the denominator (e.g., 7/3). It can be converted to a mixed number: 7/3 = 2 1/3.
How do I convert a fraction to a decimal? Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75.
What is the LCD? The Least Common Denominator is the smallest number that both denominators divide into evenly. For 1/4 and 1/6, the LCD is 12.