When an increase in the number of one item results in a proportionate drop in the other, and vice-versa, the product of the two quantities is said to be in inverse proportion. The product remains constant throughout the fluctuation.
You might not know but we are surrounded by various examples of inversely proportional relationships in our daily lives. While it is all around us, it is important to realize and make little ones understand the concept of inverse proportion through these examples.
Check out the helpful examples that depict real-life instances where inversely proportional relationships exist. These examples can help you clear the ambiguities that come along with this concept by observing and analyzing carefully.
Real-Life examples to understand inverse proportion
While it can be confusing to keep spotting inversely proportional relationships, these are the examples that help you comprehend the concept better. Discuss them with children and let them know how they are surrounded by multiple experiences and actions that are inversely proportional.
1. Task and Time Taken for Completion
The time it takes to complete a task depends inversely on how many people are working on it. More people generally take fewer hours to complete a task. Let’s assume it takes two friends to complete a school project in six hours. In accordance with the inverse proportion, a team of three friends can finish the same task in four hours, and a team of four friends only requires three hours. Here, the two variables—the number of friends and the number of hours have a product that is equal to 12 and is true throughout the variance.
2. Freshness of Vegetables and Time
Vegetables that have been picked from a department store and placed in a basket start to lose their freshness over time. Vegetables eventually start to rot as the number of days rises. This indicates that the relationship between time and the freshness of a vegetable is inverse. When one quantity’s value rises, the number of other entities typically decreases proportionately.
3. Number of Pipes for Baby Pool and the time taken
Let’s assume that a person can connect two water pipes to a swimming baby pool and fill it with water to the top in 2 hours. Now, if there are 4 pipes connected to the pool, the time needed to fill the pool will be cut in half to 1 hour. Here, the relationship between the number of pipes taken to fill the pool and the time is inverse.
4. Price and Quantity
Price and Quantity share an inversely proportional relationship and here is a classic example. Let’s assume a girl has $20 to purchase a beautiful diary for her journaling process. The diary costs $10 in the department store hence, she can purchase a maximum of 2 diaries. Next week, she again has a budget of $20 to purchase some new diaries. Now, the cost of a diary increases to $15 which allows her to purchase only 1 diary at the max. In this specific case, it is simple to see that the price and the number of items purchased have an inverse connection. When something’s cost rises, the ability to have more quantity decreases.
5. Modes of Traveling and Time Taken
Let’s now understand traveling and time taken to travel and negatively related to each other. Let’s assume a schoolboy takes 40 minutes to reach school if he chooses to walk the way. However, he takes 30 minutes to reach school if he chooses to ride a bicycle. However, it takes him only 15 minutes to reach the school via bus. In this case, the faster mode of traveling decreases the time taken to reach the destination.
6. Number of Toys and Free Space in the Room
Free space in the room and the number of toys are closely related. Usually, the amount of open space on a road is inverse to the number of toys present in the room. If the room is filled with multiple toys and games, there would be less room for empty space. Here, empty space in the room is inversely proportional to the number of toys spread across the room.
7. Expenses and Savings
The two financial concepts that are negatively related to one another are expenditure and savings. Let’s assume a person has $2000 in his savings account. He decides to spend $500 at the supermarket for groceries and utility items. Now, he is left with $1500. In this case, the more he spends the less he saves. Hence, expenses and savings are inversely proportional to each other.
8. Battery and Gadget Usage
A device’s battery life is inversely proportional to the amount of time it is utilized. Consider charging a device to 95 percent before using it. Let’s say that after using the device for an hour, the battery decreases to 83 percent, then reduces to 74 percent after two hours, then drops to 61 percent after three hours, and so on. In this instance, a large and proportional decline in the battery percentage is recognized with an increase in the amount of time the device is being utilized.
9. Hard Work and Age
Surprisingly, hard work and age are related in an inverse connection. Let’s assume a man aged 30 can work for 9 hours a day. Another man aged 45 can work 7 hours in a day. However, a man aged 60 might be able to put in effort for only 4-5 hours a day. Here, the amount of effort put in by the human body is inversely proportional to its age.
10. Rows and Columns
Let’s say a boy wants to arrange twelve chocolates into rows and columns. They can be arranged in this specific fashion in a variety of ways. Six rows would be included in a two-column configuration. If the number of rows drops to four, the number of columns increases to three. The same twelve chocolates can also be arranged in a pattern with four columns, three rows, and so forth. In this example, the number of rows and columns reaches a product of twelve and stays the same throughout. In other words, the number of columns changes in an inverse relationship to the number of rows.
11. Mistakes and Practice
Let’s assume that a boy has recently learned the drawing of a teddy bear. Initially, he makes several mistakes in shaping the bear’s ears, hands, and nose. After 2 days of practice, he makes mistakes in drawing the hands and nose while drawing the ears well. After practicing the same drawing for 5 days, he draws everything well as directed by the instructor. Here, the more he practices, the fewer mistakes he makes. Hence, the effort put into practice is inversely proportional to the number of mistakes.
12. See-saw and Height
A see-saw is a famous way to keep kids engaged at the park. The seats located on the board’s edges provide the simplest representation of inverse proportionality in real life. As the see-saw swings higher on one end, the other end descends. The slope of the relationship between the edges’ altitudes is inversely proportional. The height of one edge of the board tends to rise proportionately as the height of the opposite end of the board tends to fall.
13. Hunger and Food Consumption
The two facts are closely related and they show a clear case of inverse proportions. A lady consumes one apple for breakfast and starts feeling hungry within 2 hours of travel and office work. Another day, she consumes 2 apples and 1 banana for breakfast and starts feeling hungry after 3.5 hours of travel and work. On the third day, she chose to have bread, fruit juice, and an omelet for breakfast. With this breakfast, she starts feeling hungry after 5 hours of travel and office work. In this case, the quantity of food consumption is inversely proportional to hunger.
Summing up,
Inversely proportional relationships are everywhere around us. Such examples help teachers, parents, and adults to identify the relationship and teach the concept in a practical way. Additionally, when children are exposed to real-life situations and experiences, they are more likely to grasp the information and start spotting similar instances. Exposure to such examples inspires good observational skills, and concentration, and sharpens their memory. As children learn to identify various other instances, the other way round, they learn how directly proportional relationships work as well.
An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’,