Fraction Calculator
Add, subtract, multiply, or divide any two fractions or mixed numbers. Enter whole number parts optionally for mixed numbers. The calculator shows the complete step-by-step working — LCD, conversion, operation, and simplification — so students can learn the method.
How It Works
Fraction arithmetic follows four distinct procedures depending on the operation.
Addition and Subtraction:
1. Convert mixed numbers to improper fractions: whole × denominator + numerator, over denominator.
2. Find the Least Common Denominator (LCD) using LCM of the two denominators.
3. Convert each fraction to the common denominator by multiplying numerator and denominator.
4. Add or subtract the numerators; keep the common denominator.
5. Simplify by dividing numerator and denominator by their GCD.
6. Convert back to mixed number if the result is an improper fraction.
Example: 1½ + 2⅓
Convert: 3/2 + 7/3
LCD = 6
= 9/6 + 14/6 = 23/6
GCD(23, 6) = 1, so already simplified
Convert: 3 and 5/6
Multiplication:
1. Convert mixed numbers to improper fractions.
2. Multiply numerators together and denominators together.
3. Simplify the result.
Division:
1. Convert mixed numbers to improper fractions.
2. Multiply the first fraction by the reciprocal of the second.
3. Simplify the result.
Frequently Asked Questions
What is a mixed number?
A mixed number combines a whole number and a proper fraction, like 2¾ (two and three-quarters). To convert to an improper fraction: 2¾ = (2×4 + 3)/4 = 11/4.
What is the LCD?
LCD stands for Least Common Denominator — the smallest number that is a multiple of both denominators. For fractions with denominators 4 and 6, the LCD is 12. Finding the LCD is the key step in adding and subtracting fractions.
How does GCD simplification work?
To simplify a fraction, divide both numerator and denominator by their Greatest Common Divisor (GCD). For 12/18, GCD(12,18) = 6, so 12÷6 / 18÷6 = 2/3. The calculator uses the Euclidean algorithm to find the GCD efficiently.
Can I enter just a fraction without a whole number?
Yes. Leave the whole number field blank (or enter 0) and just fill in the numerator and denominator. Mixed numbers are optional.