Fraction Calculator
Free online fraction calculator for addition, subtraction, multiplication, division, simplification, and conversion.
Basic Fraction Calculator
📚 Understanding Fractions
A fraction represents a part of a whole. It consists of two numbers: a numerator (top number) and a denominator (bottom number). For example, in the fraction 3/8:
- Numerator (3): Represents the number of parts you have
- Denominator (8): Represents the total number of equal parts that make up the whole
Example: If you have a pie cut into 8 slices and you eat 3 slices, you've eaten 3/8 of the pie. The remaining portion would be 5/8.
🧮 Fraction Operations
Example: 1/4 + 1/6 = (1×6 + 4×1) / (4×6) = 10/24 = 5/12
Find a common denominator by multiplying denominators together, then add the adjusted numerators.
Example: 3/4 - 1/6 = (3×6 - 4×1) / (4×6) = 14/24 = 7/12
Example: 2/3 × 3/4 = (2×3) / (3×4) = 6/12 = 1/2
Multiply the numerators together and the denominators together, then simplify.
Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
Multiply by the reciprocal: flip the second fraction and multiply.
Example: 24/36 → GCD(24,36) = 12 → 24÷12 / 36÷12 = 2/3
Find the Greatest Common Divisor (GCD) and divide both numerator and denominator by it.
Fraction Operations, Simplification, and Mixed Numbers
Find a common denominator (usually by multiplying the denominators), adjust the numerators accordingly, then add them. Example: 1/4 + 1/3 = 3/12 + 4/12 = 7/12.
An improper fraction is where the numerator is greater than or equal to the denominator (e.g., 7/4). It can be converted to a mixed number (1 3/4).
Find the Greatest Common Divisor (GCD) of both numerator and denominator, then divide both by the GCD. Example: 12/18 → GCD=6 → 2/3.
No, the denominator cannot be zero as division by zero is undefined in mathematics.
Count the decimal places, use that power of 10 as the denominator, and the digits as the numerator. Example: 0.75 = 75/100 = 3/4. Then simplify if possible.
A mixed number combines a whole number with a fraction (e.g., 2 1/3). It represents the same value as an improper fraction but is often easier to understand.
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