Arithmetic - Proportion

In mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio.

Inverse Proportion-
Two proportional variables are sometimes said to be directly proportional. This is done so as to contrast proportionality with inverse proportionality.

Two variables are inversely proportional (or varying inversely, or in inverse variation, or in inverse proportion or reciprocal proportion) if one of the variables is directly proportional with the multiplicative inverse (reciprocal)of the other, or equivalently if their product is a constant.

Direct Proportion-
Sometimes a change in one quantity causes a change, or is linked to a change, in another quantity. If these changes are related through equal factors, then the quantities are said to be in direct proportion.
For example, suppose that cans of soup at the store cost 50 cents, or $0.50, each.

Case #1:

Suppose that you buy 4 cans.You would pay $2.00.

Case#2:

You buy 8 cans. You would pay $4.00.

So, changing the number of cans that you buy will change the amount of money that you pay.Notice that the number of cans changed by a factor of 2, since4cans times2is8 cans.Also, notice that the amount of money that you must pay also changed by a factor of 2, since $2.00 times 2 is $4.00.Both the number of cans and the cost changed by the same factor, 2.When quantities are related this way we say that they are in direct proportion. That is, when two quantities both change by the same factor, they are in direct proportion.

In the above example the number of soup cans is in direct proportion to the cost of the soup cans. The number of soup cans is directly proportional to the cost of the soup cans.The formal definition of direct proportion:

Another example:

You had a container holding 6 quarts of a liquid, and that liquid weighed 3 pounds. If only 3 quarts remained, that liquid would now weigh 1.5 pounds. So, the volume of the liquid changed by a factor of 1/2, since it went from 6 to 3 quarts. The weight of the liquid also changed by a factor of 1/2 since it went from 3 to 1/5 pounds. Both the volume and the weight changed by the same factor, 1/2. So, in this example the weight and volume of the liquid are in direct proportion.

Acknowledgement:
http://en.wikipedia.org/wiki/Proportionality_(mathematics)
http://id.mind.net/~zona/mstm/physics/mechanics/forces/directProportion/directProportion.html