how can you use lcm to add or subtract fractions with different denominators

To add or subtract fractions with different denominators using the **Least Common Multiple (LCM)**, follow these steps:

### Steps to Add or Subtract Fractions Using LCM:
1. **Find the LCM of the denominators:**  
   The LCM is the smallest number that both denominators can divide into evenly.

2. **Rewrite the fractions with the LCM as the common denominator:**  
   For each fraction, divide the LCM by its denominator, then multiply both the numerator and denominator of the fraction by this result. This ensures both fractions have the same denominator (LCM).

3. **Add or subtract the numerators:**  
   Once the fractions have the same denominator, you can add or subtract the numerators directly. Keep the denominator (LCM) the same.

4. **Simplify the result if possible:**  
   Check if the resulting fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).

### Example:
Add \( \frac{3}{4} + \frac{5}{6} \).

1. **Find the LCM of 4 and 6:**  
   The multiples of 4: 4, 8, 12, 16...  
   The multiples of 6: 6, 12, 18...  
   The LCM of 4 and 6 is **12**.

2. **Rewrite the fractions with a denominator of 12:**  
   \( \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \)  
   \( \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \)

3. **Add the numerators:**  
   \( \frac{9}{12} + \frac{10}{12} = \frac{9 + 10}{12} = \frac{19}{12} \).

4. **Simplify the result if necessary:**  
   \( \frac{19}{12} \) is already in its simplest form, but it can be expressed as a mixed number:  
   \( 1 \frac{7}{12} \).

This same process applies for subtraction of fractions.

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Would you like more details or have any questions?

Here are 5 relative questions to further your understanding:
1. How do you find the LCM of more than two numbers?
2. What is the difference between LCM and GCD (Greatest Common Divisor)?
3. How can you apply the LCM method to improper fractions?
4. How does this method work when adding fractions with large denominators?
5. Can you explain how to convert between improper fractions and mixed numbers?

**Tip:** Always check if you can simplify your fractions at the end to make your answer easier to interpret!

Learn how to add or subtract fractions with different denominators by using the Least Common Multiple (LCM). Follow step-by-step instructions to find the LCM of denominators, convert fractions, and simplify the result. This method is suitable for students in Grades 5-7.

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