# Addtion of fractions with different denominators

- Example:

- Analysis:
- The denominator of the first fraction is 2, the numerator of the first fraction is 1
- The denominator of the second fraction is 3, the numerator of the second fraction is 2
- The denominator of the third fraction is 4, the numerator of the third fraction is 3
- To find the least common denominator (LCD) of a set of fractions, we need to follow these steps:
- Step 1. factor each denominator into a product of prime numbers.
- Step 2. List each prime factor with the largest exponent it has in any factored denominator.
- Step 3. LCD is the product of the factors.
- Since 2 = 1 × 2, 3 = 1 × 3, 4 = 1 × 2
^{2}, so the least common denominator (LCD) is:
- LCD = 2 × 3 × 2 = 12

- Solution:
- Rule of adding fractions with different denominators:
- Step 1: Find the least common denominator(LCD).
- Step 2: Use the least common denominator to make each fraction has the same denominator.
- Step 3: Adding the fractions with the same denominator together.

- Note:
- The denominators of the fractions can not be zero.

- Formula to add fractions:
- a/b + c/d = (ad + cb)/bd, in which the denominators b and d can not be zero