The mistake you are making is modulus in PSI is pounds per square inch, not pounds times square inches.
When you multiply PSI by inch squared in the denominator the inch squares cancel leaving just pounds. So the numerator is inch pounds and the denominator pounds giving a result which is just inches.
When you multiply PSI by inch squared in the denominator the inch squares cancel leaving just pounds. So the numerator is inch pounds and the denominator pounds giving a result which is just inches.