- What is a ratio
- Types of ratio
- What is a proportion
- Types of proportions
Exam Connect
This concept is sure to come in any exam. Questions might not be asked directly from this concept, however, this concept will be mixed with some other concepts holding a good amount of marks. That’s why it is important to learn this concept, from an exam point of view.
Ratio
Ratio can be simply defined as a relationship between two quantities in which the relation of one quantity is shown with respect to the other quantity.
The ratio is denoted by ‘:’, which is also pronounced as “is to”. The two number that forms the ratio is known as terms. The first term is called antecedent and the second term is called the consequent. The ratio is generally given as p:q, which can be written as p/q. That is, 2:1 can be written as 2/1.
Types of Ratio
There are 5 types of ratio. It is important to know these 5 types because when a question comes based on Ratio and Proportions, you should be able to differentiate them with each other. This will make your work easier when it comes to solving the question. These 5 types of ratio are:
1. Duplicate Ratio
The square of a given ratio is known as duplicate ratio of the given ratio.
2. Sub-Duplicate Ratio
The square root of a given ratio is known as the sub-duplicate ratio of the given ratio.
3. Triplicate Ratio
The cube of a given ratio is known as triplicate ratio of the given ratio.
4. Sub-Triplicate Ratio
The cubic root of a given ratio is known as the sub-triplicate ratio of the given ratio.
5. Inverse Ratio
A self-explanatory term. Inverse of a ratio is the opposite of a given ratio.
[Note: Inverse can also be denoted as 1 divided by that particular number. That is, in the above example, the inverse of 5:8 can be given as 1/5:1/8 . Now, cross-multiplying, we get 8:5]
Proportions
Proportion can be defined as a statement that shows equality between two or more ratios. To put it in simple terms, proportion is a way to see if the given ratios are equal or not.
For example, if there are two ratios p:q and r:s and both of them are equal, then we can say p/q=r/s that is a proportion.
Equality in proportion is denoted as ‘::’, which is also pronounced as “is as”. So, the above example can be written as p:q::r:s
Types of Proportions
Proportion can be categorized into 3 types. Remembering these 3 types will help you analyse questions related with ratios in an easier way. Let’s go through these 3 types of proportions.
1. Third Proportional
Suppose there is a proportional defined as p:q = q:r, then ‘r’ is known as the third proportional to ‘p’ and ‘q’.
2. Fourth Proportional
Suppose there is a proportional defined as p:q = r:s, then ‘s’ is known as the fourth proportional to ‘p’, ‘q’ and ‘r’.
3. Mean Proportional
Suppose there is a ratio p:q, then the mean proportional of ‘p’ and ‘q’ will be square root of pq . It is also represented as p:r::r:q, where ‘r’ is the mean proportional.
