Fraction Calculator
Add, subtract, multiply, or divide two fractions. Results are simplified and shown both as a simplified fraction and as a decimal.
About this Calculator
Add, subtract, multiply, or divide two fractions. Results are simplified and shown both as a simplified fraction and as a decimal.
Formula & Calculations
Formula
a/b ± c/d = (ad ± bc)/bd, a/b × c/d = ac/bd, a/b ÷ c/d = ad/bcWhere:
- numerator=The top number of a fraction
- denominator=The bottom number of a fraction (cannot be zero)
- GCD=Greatest Common Divisor used to simplify fractions
Assumptions
- Denominators cannot be zero.
- Fractions are simplified to lowest terms using the Euclidean algorithm for GCD.
- Improper fractions are displayed as-is; mixed numbers are not converted.
Calculation Examples
Example 1
Find LCD of 2 and 3 = 6. Convert: 3/6 + 2/6 = 5/6.
Example 2
Multiply numerators (3×2=6) and denominators (4×5=20) → 6/20, simplified by GCD 2 to 3/10.
Example 3
Multiply by reciprocal: 7/8 × 4/3 = 28/24, simplified by GCD 4 to 7/6.
Frequently Asked Questions
How do you simplify a fraction?
Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by the GCD. For example, 8/12 → GCD is 4 → 2/3.
What is a common denominator?
When adding or subtracting fractions, you need a common denominator. The least common denominator (LCD) is the least common multiple of both denominators. Convert each fraction to an equivalent fraction with the LCD, then add/subtract the numerators.
How do you divide fractions?
To divide by a fraction, multiply by its reciprocal. For example, a/b ÷ c/d = a/b × d/c = ad/bc.