Ratio: The comparing of two related quantitative terms. Usually expressed in the form a/b or a:b
E.g. 2/3, 2:3
Rate: The relationship between two measurements, often with different units or a comparison of two different quantities.
E.g. 2 km per hour, $300 per day
Direct Proportion: a change in two quantities that have same factors. Two quantities, A and B, are in direct proportion if by whatever factor A changes, B changes by the same factor.
E.g. A cans are $2B. I buy 3A cans so I pay the cashier $6B.
Inverse Proportion: The relation between two quantitative terms that have reciprocal factors, such as 5 and 1/5. Two quantitative terms, A and B, are in inverse proportion if by whatever factor A changes, B changes by the reciprocal of it.
E.g. I have driven for 340km. If I took 1 hour to achieve it, my average speed would be 340km/hr. If I took 4 hours to complete it, my average speed would be 85km/hr. Thus, the number of hours I drive will affect my average speed.
The two quantities, in this case Time and Average Speed, was changed by reciprocal factors. Time was changed by a factor of 4( 85km/hr multiplied by 4hr) whilst speed was changed by a factor of 1/4 ( 340km/hr multiplied by 1/4).
Sources: http://en.wikipedia.org/wiki/Ratio,library.thinkquest.org/04apr/00265/ratesandspeed.htm,http://id.mind.net/~zona/mstm/physics/mechanics/forces/directProportion/directProportion.html, http://id.mind.net/~zona/mstm/physics/mechanics/forces/inverseProportion/inverseProportion.html
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