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If A and B are in a proportional relationship then increasing A by a factor of 2 also increases B by the same factor.
If the relationship between A and B is inversely proportional then increasing A by a factor of 2 will decrease B by the same factor.
The 'inversely' comes from arithmetic. 1/2 is the inverse of 2, 1/5 is the inverse of 5, because we can express a whole number as itself over 1.... 4 = 4/1 and to invert something is to turn it upside down.
One of the best known instances of inverse proportionality is Boyle's Law, which concerns the relationship between the pressure and the volume of a gas. This states that the pressure, multiplied by the volume, gives a constant figure. That can only happen if one value decreases when the other increases, and the increase and decrease must be of the same magnitude.
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