Indirect Proportion

Indirect proportion can be defined as the establishment of a relationship between two different quantities where an increase of a quantity leads to a decrease of the other quantity. It occurs when there is an inverse type of relationship present between two different quantities.  It means that when one quantity is increased to a certain extent, then the other quantity will decrease to the same extent. By the end of the assessment, a comprehension of the indirect proportion formula and the features of indirect proportion could be found.

Indirect proportion features

The features of indirect proportion are given in the following points.

• Indirect proportion or inverse proportion occurs when the value of one quantity increases and the value of another quantity decrease. 
• The increase in the percentage of one quantity is the same as the decrease in the percentage of the other quantity present in the relationship.
• The two quantities present in the relationship behave oppositely.

What is the indirect proportion in Mathematics?

Indirect proportion exists in mathematics when there is the presence of two variables that has an inverse relationship. It has been explained by using examples of two variables. When there is a presence of two variables such as “a” and “b”, there is an inverse relationship between these two variables, where, a = 1/b. It means that variable “a” is indirectly proportional to variable “b”. In this equation, there exists a proportionality constant variable k. The equation can be written as a ∝ 1/b, which means variable “a” is inversely proportional to “b”. Then the equation can be written as a = k/b, where k has been defined as the proportionality constant. 

This means when variable a increases to a certain extent, then variable b will decrease to the same extent. In the case of indirect proportion, the products of the two different quantities that are present in the relationship are the same for any sort of value. 

Explanation of indirect proportion formula

The determination of indirect proportion using the indirect proportion formula includes the following steps. 

Step 1: At first, the proportional relationship that exists between the variables needs to be written down.

Step 2: in this step, the equation is needed to be written down by using the constant of proportionality.

Step 3: In this step, the value of the proportionality constant needs to be found out by the use of the given values of the variables.

Step 4: In the last step, the value of the proportionality constant needed to be substituted in the equation. 

The formula has been explained using an example in the next instances. For instance, there are two variables such as m and n and there is the presence of an indirectly proportional relationship between these two variables. Then the inverse proportion or indirect proportion between these two variables can be explained as m = 1/n. This equation can also be written as n=k/m, where k is the proportionality constant present in the equation. The product of the two different entities, which are present in the equation of indirect proportion, is equal for any kind of value. The indirect proportion has been explained using some numerical examples of mathematics. 

For instance, 7 days can be taken by 10 laborers for the harvesting of coffee in a coffee plantation. However, if the number of laborers is increased then the total number of days required for the completion of the task will decrease. Therefore, it can be seen that there exists an indirect proportion relationship between the total number of laborers required for the completion of the task and the total number of days. It has been observed that when the total number of laborers is increased, the total number of days for the completion of the entire task has been decreased. 

Another numerical example has been given in the context of indirect proportion.  For instance, five taps are required for the complete filling of a tank within 2 hours. Now, when the total number of taps is increased then the total time for filling the tank will decrease. This is because when the total number of taps is increased the total time for filling up the tank is decreased. 

Conclusion

It can be concluded that there exists an inverse form of relationship between two variables when for the increase of a variable there is the decrease of another variable. A constant variable is present in the equation of the indirect proportion. Thus, it can be summarized that this variable is known as the proportionality constant.