To simplify the fraction $\frac{65}{55}$, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both by it.

1. Finding the GCD of 65 and 55:

   • The factors of 65 are 1, 5, 13, and 65.
   • The factors of 55 are 1, 5, 11, and 55.
   • The largest common factor is 5.

2. Divide both the numerator and the denominator by 5:

   $\frac{65}{55} = \frac{65 \div 5}{55 \div 5} = \frac{13}{11}$

3. Final Answer: $\frac{65}{55} = \frac{13}{11}$

The fraction simplifies to $\frac{13}{11}$.

Would you like more details on any part of this?

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1. What is the GCD and how is it used in simplification?
2. How do we know when a fraction is fully simplified?
3. Can we simplify improper fractions into mixed numbers?
4. Why does finding the GCD help in simplifying fractions?
5. How can you find the GCD quickly for larger numbers?

Tip: When simplifying fractions, always look for the GCD of the numerator and the denominator—it’s the quickest path to the simplest form.