Ratios and Proportionality

The ratio of two numbers is simply the fraction obtained when one is divided by the other. The ratio of 3 and 4 is consequently 3/4 or 0.75 alternatively we may choose to use the ratio of 4/3 if this is more appropriate. 

The concept of proportionality will be familiar to most people. It is logical to expect that if we double the volume of a substance then its mass will also double. In this case we describe the relationship as direct proportionality. 

Mathematically, we define two quantities as being in direct proportion if their ratio is constant. This would be the case for the two quantities x and y which take the following values  

Here we see that the ratio y/x has a constant value of 1.5. This simple equation can be arranged to give y = 1.5x, where we call 1.5 the constant of proportionality. Another way of defining direct proportionality is to say that the two quantities must obey a relationship of the form y = kx. This can also be written using the proportionality symbol as y a x. 

Inverse proportionality may be less obvious, although it still frequently occurs in everyday life. A common example is the time taken to cover a fixed distance, which is inversely proportional to the speed of travel. 

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