Partitive proportion describes the process by virtue of which a quantity is divided into two or more equal or unequal parts. Mathematically, the partitive proportion can be represented as a ratio of the different numbers of partitions such that a:b = n, where a and b represent the partitions and n is the totality of all the parts. Here, the constant of proportionality is not known and is considered to be an unknown variable. Partitive proportion is also known as a proportion by parts.

## Examples of Partitive Proportion

There exist a number of real-life situations that make use of partitive proportion, a few of them are listed below:

### 1. Planning Monthly Budget of a Household

One of the prominent examples of partitive proportionality can be observed while planning the monthly budget of a household. The expenses are firstly divided into various subcategories such as electricity bills, water bills, and food supplies. Then, the expenditure is represented by a corresponding ratio, say 1:2:4. Suppose, the total expenditure of the month of July is equal to INR 7000; therefore, the money required to pay the monthly electricity bill would be equal to INR 1000, water bill payment is equal to INR 2000, and food supplies cost a total of INR 4000.

### 2. Dividing Profit among Business Partners

Partitive proportion plays an important role in dividing profit amount among various business partners. Suppose three friends own a particular business. All of them agree to distribute profit among themselves in the ratio 1:2:3. Let us say that the amount of total profit procured in a month is equal to INR 6000. This means that according to partitive proportion the first friend would receive INR 1000, the second friend would get INR 2000, and the share of the third friend from the total profit would be equal to INR 3000.

### 3. Distribution of Goods among a group of People

Let us say, a family consists of 4 children and 3 adults. On the occasion of Christmas, the children are collectively given gift money equal to INR 1200. The distribution of money among the children is unequal and is required to be done according to the ratio 2:4:6:8. This means that the first child gets INR 120, while the second child would receive INR 240. Similarly, the third and the fourth child of the family would be provided with a total of INR 360 and INR 480 respectively. In this particular case, one can easily observe the application of partitive proportionality.

### 4. Gender Ratio in a Class

Suppose the total number of students studying in a particular class is equal to 120. A teacher wishes to know the exact number of individual girl and boy students studying in the class. The ratio of male and female students studying in the class is known to be equal to 2:4, hence it can be used to determine the exact number of girl and boy students. By applying the concept and mathematical relationship of partitive proportionality in this particular case, the number of girls comes out to be 40 and the number of boys comes out to be 80.

### 5. Donating Books to Libraries

To understand the concept of partitive proportion, let us take an example of a person who is willing to donate his books to three different libraries. He has a total of 1400 books and wishes to donate books in an unequal proportion. Suppose that he chooses to divide the books in the ratio of 2:4:8; therefore, the first library gets 200 books, the second library would be given 400 books, and the third library would receive a total of 800 books.

### 6. Dividing Party Expenses

Suppose a group of four friends go to a restaurant to celebrate an occasion. After the party, they plan to share the expenses in an unequal proportion. The ratio that they follow for dividing the party bill of INR 12000 is given as 1:2:3:6. This means that each of them is required to pay INR 1000, INR 2000, INR 3000, and INR 6000 respectively. So, next time when you go out with your friends or family, you may employ the concept of partitive proportion in real life to divide the bill.

### 7. Assigning Guides to a group of Tourists

To get a better understanding of the partitive proportionality, take an example of a group of tourists who visit a particular heritage site for sightseeing. Let the total number of tourists be equal to 45 and the total number of guides available is equal to 4. The subgroups of the tourists are formed randomly in the ratio 1:3:5:6. This means that the first guide would assist 3 tourists, while the second guide would have 9 tourists in his group. Likewise, the third and the fourth guides would have to assist groups that contain 15 and 18 tourists respectively.

### 8. Event Management

Suppose a team of 48 organizers is required to manage an event. The event manager divides the team into groups to handle specific sections of the function such as the decoration committee, boarding and lodging department, reception and hospitality staff, and catering committee. The groups so formed contain an unequal number of participants based on the ratio 2:3:5:6, hence the decoration committee has 6 people, the boarding and lodging department would have 9 people to perform all the relevant tasks, reception and hospitality staff contain 15 members, and the rest 18 people are assigned to the catering department. This means that one can easily apply the concept of partitive proportionality to divide a group of people and assign them to various departments while organizing a particular event.

### 9. Drafting a Question Paper

Suppose a teacher is required to draft a question paper for the midterm exams of a particular class. He refuses to disclose the exact number of questions chosen from various sections of the syllabus but tells the students that the number of questions selected from the four sections can be represented by a ratio of 2:3:4:6. The exam paper contains a total of 60 questions, therefore, the students are able to estimate that there would be a total of 8, 12, 16, and 24 questions from the respective four sections of the syllabus.

### 10. Setting up a Time Table

This particular example of partitive proportionality helps a person to effectively design a timetable. Let us say that a person divides his routine into 4 subcategories, namely hobbies and other activities, personal time, study time, and sleeping hours. The 24 hours of his day are unevenly distributed in the ratio 1:2:4:5. This means that he would devote 2 hours of his day to his interests and hobbies, 4 hours would be reserved for his personal activities, 8 hours would be spent studying, and 10 hours would be available for him to sleep and relax.

### 11. Surprise Gift Basket

Let us say a surprise basket contains 250 gift items. Four people are asked to pick gifts from the basket at random. It was found that the four participants picked up the gifts in a certain ratio given as 4:6:7:8, hence with the help of a partitive proportional relationship one can easily estimate that the first and second participants received a total of 40 and 60 gifts respectively. Similarly, the third participant got 70 gifts, whereas, the fourth person got a total of 80 gifts.