To solve \(7 \frac{5}{12} - 5 \frac{7}{9}\), we can break it down step by step:

1. **Convert the mixed numbers to improper fractions:**
   - \(7 \frac{5}{12} = \frac{7 \times 12 + 5}{12} = \frac{84 + 5}{12} = \frac{89}{12}\)
   - \(5 \frac{7}{9} = \frac{5 \times 9 + 7}{9} = \frac{45 + 7}{9} = \frac{52}{9}\)

2. **Find a common denominator:**
   - The denominators are 12 and 9. The least common denominator (LCD) of 12 and 9 is 36.

3. **Convert both fractions to have the same denominator:**
   - \(\frac{89}{12} = \frac{89 \times 3}{12 \times 3} = \frac{267}{36}\)
   - \(\frac{52}{9} = \frac{52 \times 4}{9 \times 4} = \frac{208}{36}\)

4. **Subtract the fractions:**
   \[
   \frac{267}{36} - \frac{208}{36} = \frac{267 - 208}{36} = \frac{59}{36}
   \]

5. **Convert the improper fraction back to a mixed number:**
   \[
   \frac{59}{36} = 1 \frac{23}{36}
   \]

Thus, \(7 \frac{5}{12} - 5 \frac{7}{9} = 1 \frac{23}{36}\).

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How do you add mixed numbers?
2. What is the least common denominator and how do you find it?
3. How do you convert improper fractions back to mixed numbers?
4. How can you simplify fractions?
5. How do you multiply mixed numbers?

**Tip:** When working with mixed numbers, converting them to improper fractions first often simplifies operations like addition or subtraction.

Learn how to subtract mixed numbers like 7 5/12 - 5 7/9 with this step-by-step guide. This solution covers converting mixed numbers to improper fractions, finding the least common denominator, and simplifying the result. Suitable for students in Grades 6-8.

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