To solve the expression \( \frac{45}{34} - \frac{4}{51} \), we need to find a common denominator.

1. **Finding the common denominator**: The denominators are 34 and 51. We find the least common denominator (LCD) by calculating the least common multiple (LCM) of 34 and 51.

   - \( 34 = 2 \times 17 \)
   - \( 51 = 3 \times 17 \)
   - The LCM of 34 and 51 is \( 2 \times 3 \times 17 = 102 \).

2. **Rewrite the fractions** with the common denominator:
   \[
   \frac{45}{34} = \frac{45 \times 3}{34 \times 3} = \frac{135}{102}
   \]
   \[
   \frac{4}{51} = \frac{4 \times 2}{51 \times 2} = \frac{8}{102}
   \]

3. **Subtract the fractions**:
   \[
   \frac{135}{102} - \frac{8}{102} = \frac{135 - 8}{102} = \frac{127}{102}
   \]

So, \( \frac{45}{34} - \frac{4}{51} = \frac{127}{102} \).

The result can also be left as an improper fraction or converted to a mixed number if needed.

Would you like more details or have any questions?

Here are some related questions:

1. How do you convert an improper fraction to a mixed number?
2. What is the process for finding the least common multiple (LCM) of two numbers?
3. How can you simplify a fraction?
4. What are some real-life applications of subtracting fractions?
5. How do you add fractions with different denominators?

**Tip:** Always find the least common denominator to make operations with fractions easier!

Learn how to subtract fractions with different denominators by solving 45/34 - 4/51. This problem explains key concepts such as finding the least common denominator (LCD) and applying subtraction to fractions, suitable for students in Grades 6-8.

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