To find the total fractional portion of parks that have flagpoles after installing more, we start with the given information:
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Initially, \( \frac{1}{3} \) of the parks have flagpoles.
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The city plans to install flagpoles in another \( \frac{1}{3} \) of the parks.
To calculate the new total portion of parks with flagpoles, we add the two fractions:
\[ \text{Initial portion with flagpoles} + \text{Portion to have flagpoles installed} = \frac{1}{3} + \frac{1}{3} \]
Adding these fractions:
\[ \frac{1}{3} + \frac{1}{3} = \frac{2}{3} \]
So, after installing flagpoles in another \( \frac{1}{3} \) of the parks, the total fractional portion of parks that have flagpoles will be:
\[ \frac{2}{3} \]
Thus, the answer is \( \frac{2}{3} \).