Question about gas laws

[deleted647690]

I know this is simple math, but there is this question that asks,
"An ideal gas is placed in a 3.0 L container with a piston. The pressure of the gas is initially 850 torr. How much additional pressure must be exerted on the piston in order to lower the volume of the container to 1.0 L? Assume temperature doesn't change."

I realize that since the volume decreases by a factor of 3, the pressure must increase by 3x, so the new pressure would be 2550 torr, and thus the pressure added would be 1700 torr.

However, when I did this question, I saw the volume as decreasing by 2/3 (66%). Therefore, I assumed the new pressure would be 66% higher, so I calculated it as an additional 561 torr, which is totally wrong. Can someone explain why my reasoning was incorrect? I'm missing this fundamental math concept.

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[aldol16]

Decreasing by involves addition/subtraction, to which ratios do not apply. That is, x decreasing by 2/3 means x - 2/3*x = 1/3*x. In other words, instead of using the 1/3, which is the factor by which x decreases, you're using the 2/3, which is the absolute amount by which x decreases.

It's just like shopping where when you take 40% off $50, you take off $20 and pay $30. Yes, you paid $20 less, but your final amount paid is $30/$50 = 60% of the initial amount.