Let's simplify the expression:

\[
\frac{45}{34} - \frac{4}{51}
\]

To subtract these fractions, we need to find a common denominator. The least common denominator (LCD) of 34 and 51 is 102, because the least common multiple of 34 and 51 is 102.

Now, let's rewrite both fractions with a denominator of 102:

1. Convert \(\frac{45}{34}\) to have a denominator of 102:
   \[
   \frac{45}{34} = \frac{45 \times 3}{34 \times 3} = \frac{135}{102}
   \]

2. Convert \(\frac{4}{51}\) to have a denominator of 102:
   \[
   \frac{4}{51} = \frac{4 \times 2}{51 \times 2} = \frac{8}{102}
   \]

Now subtract the two fractions:
\[
\frac{135}{102} - \frac{8}{102} = \frac{135 - 8}{102} = \frac{127}{102}
\]

The simplified result is:

\[
\frac{127}{102}
\]

This fraction is in its simplest form.

Would you like more details on how to find the LCD or how I simplified the fraction?

---

Here are some related questions to expand on this:

1. How do you find the least common denominator (LCD) for two fractions?
2. Can you explain how to simplify a fraction to its lowest terms?
3. What are some real-world applications of subtracting fractions?
4. How do you handle mixed numbers when subtracting fractions?
5. What is the method for adding or subtracting fractions with different denominators?

**Tip:** Always simplify the fractions before performing operations; it can make calculations easier.

Learn how to subtract fractions with different denominators using the example 45/34 - 4/51. This guide walks you through finding the least common denominator (LCD), simplifying fractions, and performing subtraction. Ideal for students in Grades 6-8.

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