Adding Fractions Calculator
Add two fractions with step-by-step LCD (Least Common Denominator) method. This calculator shows the simplified result as both a fraction and a decimal. See also our Dividing Fractions Calculator and Fractions Calculator.
How to Add Fractions
- Find the Least Common Denominator (LCD) of both fractions.
- Convert each fraction to an equivalent fraction with the LCD as the denominator.
- Add the numerators together, keeping the LCD as the denominator.
- Simplify the resulting fraction by dividing numerator and denominator by their GCD.
Formula
a/b + c/d = (a×(LCD/b) + c×(LCD/d)) / LCD
Where LCD = LCM(b, d)
Simplified: Divide result by GCD(numerator, denominator)Example
Add 1/4 + 2/3:
LCD of 4 and 3 = 12
1/4 = 3/12 (multiply by 3)
2/3 = 8/12 (multiply by 4)
3/12 + 8/12 = 11/12
Result: 11/12 (already simplified) = 0.916667
Common Fraction Addition Reference Table
| Fraction 1 | Fraction 2 | Sum | Decimal |
|---|---|---|---|
| 1/2 | 1/3 | 5/6 | 0.8333 |
| 1/4 | 1/4 | 1/2 | 0.5000 |
| 1/3 | 1/6 | 1/2 | 0.5000 |
| 2/5 | 1/10 | 1/2 | 0.5000 |
| 1/8 | 3/8 | 1/2 | 0.5000 |
| 3/4 | 1/8 | 7/8 | 0.8750 |
| 2/3 | 1/6 | 5/6 | 0.8333 |
| 1/5 | 2/5 | 3/5 | 0.6000 |
Frequently Asked Questions
What is the LCD method for adding fractions?
The LCD (Least Common Denominator) method finds the smallest number that both denominators divide into evenly. You convert each fraction to have this common denominator, then add the numerators.
Can I add fractions with different denominators directly?
No. You must first find a common denominator before adding. The LCD method is the most efficient way because it produces the smallest possible denominator.
How do I simplify the result?
Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. If the GCD is 1, the fraction is already in simplest form.
What if one fraction is negative?
Enter a negative numerator. The calculator handles negative fractions correctly, treating -a/b the same as a/(-b).
What is the difference between LCD and LCM?
LCD (Least Common Denominator) is the LCM (Least Common Multiple) of the denominators. They refer to the same calculation applied specifically to fraction denominators.