Online Calculators since 2009
In addition to the revision notes for Proportion on this page, you can also access the following Ratio and Proportion learning resources for Proportion
In these revision notes for Proportion, we cover the following key points:
If two quantities involved in a situation (we call them variables) are related in such a way that if one quantity changes, the other quantity changes at the same (or opposite) degree, we say these quantities are in proportion with (or proportional to) each other. In simpler words, a proportion indicates us how one thing changes in relation to another.
Any proportion includes two equal fractions, i.e. if
then a and c are proportional (as well as b and d).
In other words, if a/b and c/d are two equal ratios or rates, they are in proportion.
We can also write the above proportion in the form
where a is the first term, b is the second term, c is the third term and d is the fourth term of the proportion. The terms a and d are called outer terms or extremes, while b and c are called inner terms or means of the proportion.
There are two main types of proportion: direct and inverse proportion. In direct proportion, the quantities a and c change in the same way as well as b and d.
By definition, direct proportion is the relation between quantities whose ratio (or rate) is constant.
The graph representing a direct proportion is a straight (sloped) line that starts from the origin (otherwise it is not a direct proportion), where the slope is determined by the simplest form of the ratio or of the unit rate.
We can write a direct proportion as:
This method of expressing a proportion as equality of products is known as cross product. The cross product method of writing a proportion allows checking the veracity of proportion in an easier way, without involving rational numbers, simplifications or GCF calculations.
By definition, inverse (or indirect) proportion occurs when a decrease in one quantity or variable causes an increase by the same factor in another quantity or variable.
We can express an inverse proportion in symbols as
Two quantities involved in an inverse proportion have a relation of type a × b = constant, which we can write as
The graph of such a relation is called hyperbola, it is a curved line that approaches the axes without touching them with the increase in the values of a and b. To increase the accuracy of an inverse proportion graph, we must use as many points as possible.
Enjoy the "Proportion" revision notes? People who liked the "Proportion" revision notes found the following resources useful:
We hope you found this Math tutorial "Proportion" useful. If you did it would be great if you could spare the time to rate this math tutorial (simply click on the number of stars that match your assessment of this math learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of math and other disciplines.