Which of the following is an example of using the Division Property of Equality to rearrange the equation PV=nRT ?(1 point)

Responses

R=nTPV
upper R equals Start Fraction n upper T over upper P upper V End Fraction

n=PVRT
n equals Start Fraction upper P upper V over upper R upper T End Fraction

R=PV−nT
upper R equals upper P upper V minus n upper T

1 answer

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 \( PV = nRT \):

  1. 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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