To evaluate \( \frac{32}{34} \), you can simplify the fraction by finding the greatest common divisor (GCD) of the numerator (32) and the denominator (34).
The prime factorization of 32 is: \[ 32 = 2^5 \]
The prime factorization of 34 is: \[ 34 = 2 \times 17 \]
The GCD of 32 and 34 is \( 2 \).
Now, divide both the numerator and the denominator by their GCD: \[ \frac{32 \div 2}{34 \div 2} = \frac{16}{17} \]
Thus, the simplified form of \( \frac{32}{34} \) is: \[ \frac{16}{17} \]
Therefore, the final answer is: \[ \frac{16}{17} \]
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