To eliminate the fractions in the equation \( \frac{x}{2} + \frac{x}{3} = \frac{25}{3} \), you can find the least common multiple (LCM) of the denominators.
The denominators are 2, 3, and 3. The LCM of these numbers is 6.
Now, let's multiply every term in the equation by 6:
\[ 6 \left(\frac{x}{2}\right) + 6 \left(\frac{x}{3}\right) = 6 \left(\frac{25}{3}\right) \]
This simplifies to:
\[ 3x + 2x = 50 \]
Thus, to eliminate the fractions, you should multiply the entire equation by 6.
So the answer is 6.