In general, we say that proportional reasoning is a type of mathematical reasoning which involves a sense of multiple comparisons, co-variation and the ability to store and process pieces of information mentally. This is also concerned with prediction and inference and also involves both quantitative and qualitative thought methods.

Events like exchanging money, making scaled diagrams, speed, decay rates, growth rates calculation, changing units of measurement etc. are all common real life examples of the use of methods of proportional reasoning.

We can compare quantities or objects in multiplicative way rather than in an additive way. The comparison is explained by making use of terms like double, half, two thirds greater, by three times, smaller than etc.

We can also say that, proportions are same as talking about equivalent fractions, that is, the fractions that are same once they are reduced to their simplest forms or the fractions that comes out to be same by either means of multiplying or dividing.

The various proportions we deal with are:

Continuous proportion is the one similar to geometric mean. We have three quantities here such that $\frac{a}{b}$ = $\frac{b}{c}$. Here ‘b’ is the geometric mean of the given continuous proportion.

**Direct proportion** is the one in which two quantities or objects are related to each other directly. For example distance is directly related to speed as well as time;work is directly related to wages as in more work will get you more wages etc.

**Inverse proportion** is the one in which two quantities or objects are related to each other inversely. For example, the increase in number of persons employed for doing a work will decrease the time taken to complete the work; speed and time are also inversely proportional as when speed is more time taken is less and vice versa.