To determine if the equations \( \frac{3}{8}x = 1 \) and \( \frac{1}{3}x = \frac{1}{8} \) have the same solution, let's solve each equation step-by-step.
Solving the first equation:
\[ \frac{3}{8}x = 1 \]
To solve for \( x \), multiply both sides by the reciprocal of \( \frac{3}{8} \), which is \( \frac{8}{3} \):
\[ x = 1 \cdot \frac{8}{3} \] \[ x = \frac{8}{3} \]
Solving the second equation:
\[ \frac{1}{3}x = \frac{1}{8} \]
To solve for \( x \), multiply both sides by the reciprocal of \( \frac{1}{3} \), which is 3:
\[ x = \frac{1}{8} \cdot 3 \] \[ x = \frac{3}{8} \]
Comparing the solutions:
- The solution to the first equation is \( x = \frac{8}{3} \).
- The solution to the second equation is \( x = \frac{3}{8} \).
Since \( \frac{8}{3} \) is not equal to \( \frac{3}{8} \), the two equations do not have the same solution.
Conclusion:
The answer is no, \( \frac{3}{8}x = 1 \) does not have the same solution as \( \frac{1}{3}x = \frac{1}{8} \).