Let's solve the expression:

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

First, we need to find a common denominator. The least common denominator (LCD) of 34 and 51 is 102, because:

\[
34 = 2 \times 17, \quad 51 = 3 \times 17
\]
Their least common multiple is \( 2 \times 3 \times 17 = 102 \).

Next, we rewrite the fractions with 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:

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

Thus, the result is:

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

This is already in its simplest form.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How do you find the least common denominator for fractions?
2. What is the process to simplify a fraction?
3. Can you convert \(\frac{127}{102}\) into a mixed number?
4. How do you add or subtract fractions with different denominators?
5. What is the decimal equivalent of \(\frac{127}{102}\)?

**Tip**: Always check if fractions can be simplified by finding the greatest common divisor of the numerator and denominator.

Learn how to subtract fractions with different denominators using the example 45/34 - 4/51. This solution explains how to find the least common denominator, rewrite the fractions, and perform the subtraction step-by-step. Ideal for students in Grades 6-8.

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