To add the fractions \( \frac{25}{82} + \frac{13}{?} \), we first need a common denominator. The denominator of the first fraction is 82, so we need to determine what the denominator of the second fraction should be in order to add them both.
If we denote the missing denominator of the second fraction as \( x \), we can set up the equation to find a suitable denominator. We want to have a common denominator, which means \( x \) should be equal to 82 or some multiple of 82.
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If we choose \( x = 82 \), then we can add the fractions as follows: \[ \frac{25}{82} + \frac{13}{82} = \frac{25 + 13}{82} = \frac{38}{82} \]
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If we wanted a different common denominator (like a multiple of 82), we could also choose something like 164, but the simplest solution is just to use the same denominator.
Thus, the missing denominator should be 82 in order to add the fractions successfully.
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