⁵⁵Recall from algebra that we may perform any arithmetic operation we wish to any equation, so long as we apply that operation equally to both sides of the equation. Dividing one equation by another equation obeys this principle, because both sides of the second equation are equal. In other words, we could divide both sides of the first equation by P_AV _A (although that would not give us the solution we are looking for), but dividing the left side by P_AV _A and the right side by nRT_A is really doing the same thing, since nRT_A is identical in value to P_AV _A.