Let's simplify the expression:

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

To subtract fractions, we need a common denominator. The least common denominator (LCD) of 34 and 51 is 102.

### Step 1: Convert both fractions to have a denominator of 102

- For \(\frac{45}{34}\), multiply the numerator and denominator by 3:
  \[
  \frac{45 \times 3}{34 \times 3} = \frac{135}{102}
  \]

- For \(\frac{4}{51}\), multiply the numerator and denominator by 2:
  \[
  \frac{4 \times 2}{51 \times 2} = \frac{8}{102}
  \]

### Step 2: Subtract the numerators

\[
\frac{135}{102} - \frac{8}{102} = \frac{135 - 8}{102} = \frac{127}{102}
\]

### Final Answer:
\[
\frac{127}{102}
\]

This is the simplified form of the expression.

Would you like more details on any part of this? Here are some related questions to expand on this topic:

1. How do you find the least common denominator between two fractions?
2. How can you simplify complex fractions?
3. How do you convert improper fractions to mixed numbers?
4. What is the difference between subtracting fractions and adding them?
5. How do you check if your fraction is in its simplest form?

**Tip**: Always look for the least common denominator to simplify fraction operations efficiently.

Learn how to subtract fractions with different denominators using 45/34 - 4/51 as an example. This step-by-step guide explains finding the least common denominator, converting fractions, and subtracting the numerators. Suitable for students in Grades 6-8.

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