# "Triple fraction?"

### "Triple fraction?"

P1*V1/T1 = V2*P2/T2
How do we calculate in different way if one of these is unknown?
i.e. P2= P1*V1*T2/T1*V2
What is the formula?
/ is the division
* is the multiplication
Guest

### Re: "Triple fraction?"

$$]\frac{P_1V_1}{T_1}= \frac{P_2V_2}{T_2}$$

To solve for any one unknown "undo" whatever is done to it,
$$P_2$$ has been multiplied by $$V_2$$ and divided by $$T_2$$. To "undo" those divide both sides by $$V_2$$ and multiply by $$T_2$$. And, of course, do that to both sides:
$$P_2= \left(\frac{P_1V_1}{T_1}\right)\frac{T_2}{V_2}= \frac{P_1V_1T_2}{T_1V_2}$$ as you have.

Solving for $$T_2$$ is just a little more complicated because $$T_2$$ is in the denominator. To undo that invert the fraction: $$\frac{1}{\frac{1}{x}}= x$$. Inverting both sides $$\frac{T_2}{P_2V_2}= \frac{T_1}{P_1V_1}$$. Now multiply both sides by $$P_2V_2$$: $$T_2= \frac{T_1P_2V_2}{P_1V_1}$$.
Guest