Adding Fractions
To add fractions, you must first find a common denominator, then add the numerators and simplify the result.
Formula
a/b + c/d = (ad + bc) / bd
Steps
- Find a common denominator (often the product of both denominators)
- Convert each fraction to equivalent fractions with the common denominator
- Add the numerators
- Keep the common denominator
- Simplify if possible
Examples
Example 1: 1/3 + 1/4
Common denominator: 12
4/12 + 3/12 = 7/12
Example 2: 1/2 + 1/6
Common denominator: 6
3/6 + 1/6 = 4/6 = 2/3
Same Denominator?
If fractions already have the same denominator, just add the numerators and keep the denominator.
Common Mistakes
- Adding denominators (wrong!)
- Forgetting to simplify
- Not finding common denominator first
Quick Tips
- Double-check your inputs for accurate results
- Use parentheses to clarify order of operations
- Results are rounded — consider significant figures
Frequently Asked Questions
Find a common denominator, convert both fractions, then add numerators.
No, never add the denominators together.
1/2 + 1/4 = 2/4 + 1/4 = 3/4
Yes, except when denominators are already the same.
Multiply the two denominators, though a smaller LCM may exist.