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

### Step 1: Find the Least Common Denominator (LCD)
- The denominators are 34 and 51.
- The least common multiple (LCM) of 34 and 51 is 102.

### Step 2: Convert each fraction to have the common denominator
- Convert \( \frac{45}{34} \) to have the denominator 102:
  \[
  \frac{45}{34} = \frac{45 \times 3}{34 \times 3} = \frac{135}{102}
  \]
- Convert \( \frac{4}{51} \) to have the denominator 102:
  \[
  \frac{4}{51} = \frac{4 \times 2}{51 \times 2} = \frac{8}{102}
  \]

### Step 3: Subtract the fractions
Now subtract the numerators:
\[
\frac{135}{102} - \frac{8}{102} = \frac{135 - 8}{102} = \frac{127}{102}
\]

### Step 4: Simplify the fraction (if possible)
Since 127 and 102 have no common factors other than 1, the fraction is already in its simplest form.

So, the result is \( \frac{127}{102} \).

Would you like more details or have any questions?

Here are some related questions:
1. How do you find the least common denominator?
2. Can you simplify the fraction \( \frac{135}{102} \)?
3. What is the difference between the greatest common divisor and the least common multiple?
4. How do you convert improper fractions to mixed numbers?
5. How would you subtract two fractions with different denominators using cross multiplication?

**Tip:** When working with fractions, always check if the result can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator.

Learn how to subtract fractions with different denominators using the problem 45/34 - 4/51. This step-by-step guide covers the concept of finding the least common denominator and applying it to subtract fractions. Suitable for students in Grades 6-8.

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