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

1. The denominators are 34 and 51.
2. The least common denominator (LCD) of 34 and 51 can be found by calculating the least common multiple (LCM) of these numbers. 

The prime factorizations are:
- \(34 = 2 \times 17\)
- \(51 = 3 \times 17\)

The LCM is \(2 \times 3 \times 17 = 102\).

Now, convert each fraction to have a denominator of 102:

\[
\frac{45}{34} = \frac{45 \times 3}{34 \times 3} = \frac{135}{102}
\]
\[
\frac{4}{51} = \frac{4 \times 2}{51 \times 2} = \frac{8}{102}
\]

Now, subtract the fractions:

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

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

Would you like to see the detailed steps? Also, here are some related questions:

1. How do you find the least common denominator (LCD)?
2. What is the process for subtracting fractions with different denominators?
3. How do you simplify fractions after performing arithmetic operations?
4. What are prime factorizations, and how are they used to find the LCM?
5. How can improper fractions be converted to mixed numbers?

**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 solve the fraction subtraction problem 45/34 - 4/51 by finding the least common denominator (LCD) and performing the subtraction step by step. This example covers the concepts of LCM, fraction conversion, and subtraction, suitable for students in Grades 5-7.

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