The Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the two sides remain equal.
In the equation \( PV = nRT \):
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To isolate \( R \), you could divide both sides by \( nT \):
\[ R = \frac{PV}{nT} \]
This corresponds to the second response you provided:
- n = PVRT
- R = \frac{nT}{PV}
- R = \frac{PV}{nT}
None of the provided options directly represent this calculation, but the option you referenced as "R=PV−nT" is incorrect since it implies subtraction rather than division.
So the correct answer representing the use of the Division Property of Equality to isolate \( R \) would technically be:
- upper R equals Start Fraction n upper T over upper P upper V End Fraction is not correct.
Thus, the closest rearrangement using the Division Property of Equality to rearrange the equation \( PV = nRT \) is:
- n = \frac{PV}{RT} which is missing in the provided options.
None of the options fully represent using the Division Property to isolate \( R \) correctly, but if we're looking for the one corresponding closer to the rearrangement of one variable using division within the provided options, the second option \( n = \frac{PV}{RT} \) is correct as an example though it does not directly solve for \( R \).
To conclude, please note that the correct use of the Division Property to rearrange would ideally be \( R = \frac{PV}{nT} \).
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