To rearrange the equation \( PV = nRT \) using the Division Property of Equality, we need to isolate one of the variables by dividing both sides of the equation by another expression.
Starting with the original equation:
\[ PV = nRT \]
- Isolating \(T\): If we divide both sides by \(nR\), we get:
\[ T = \frac{PV}{nR} \]
- Isolating \(R\): If we divide both sides by \(nT\), we obtain:
\[ R = \frac{PV}{nT} \]
- Isolating \(n\): If we divide both sides by \(RT\), we would have:
\[ n = \frac{PV}{RT} \]
- Attempting to isolate \(R\) again: Dividing both sides by \(PV\) will not yield a valid equation, as shown here:
\[ R = \frac{PV}{nT} \]
- Incorrect equation: The equation \(R = PV - nT\) does not represent a legitimate manipulation based on division since it doesn't maintain equality in a proportional sense.
Now let's examine the options given:
- Option \(T = \frac{PV}{nR}\): This rearrangement is incorrect due to inverting the \(R\).
- Option \(R = \frac{nT}{PV}\): This is not isolating \(R\) correctly.
- Option \(n = \frac{PV}{RT}\): This is a valid rearrangement isolating \(n\).
- Option \(R = PV - nT\): This is incorrect as it directly subtracts and doesn't follow from the equality.
Thus, the correct example of using the Division Property of Equality is:
\[ \boxed{n = \frac{PV}{RT}} \]