Loading the lesson
Loading the lesson
Search AllRounder.ai
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Learn it your way
A short class with Sarah and her students. The other ways are under More.
Sign up free to listen. Transcripts are free to read.
Today, we are going to explore the concept of inverse proportion. Can anyone tell me what happens to one quantity when the other increases?
I think it decreases, right?
Exactly! That's correct. If one quantity increases, the other decreases. This relationship is very important in math and real life. For example, if we have a fixed amount of work, adding more workers will decrease the time taken. Let’s think of a formula. Can anyone remember what correlates their relationship?
Is it like xy = k?
Yes! Well done! So, if x is the number of workers and y is the time taken, their product remains constant. Remember this as we continue!
Let’s explore some real-life examples. For instance, if Zaheeda travels faster, how does her travel time change?
Her travel time would decrease!
Perfect! As we look at various cases, when speed increases, time decreases. Remember, if we double the speed, the time taken becomes half. What if we examine how it relates to buying books?
If the price of each book increases, the number of books you can buy goes down!
Exactly! So we can see this is again an example where one quantity's increase leads to the other’s decrease. Let’s think of a table we can create to show this.
Now, let’s put this concept into practice. If I have six pipes that can fill a tank in 80 minutes, how long would five pipes take?
We can set up the equation 80 * 6 = x * 5, right?
Yes, that's right! So we calculate. What are we solving for?
We’re looking for x, the time it would take with 5 pipes!
Correct! Let’s perform that multiplication, and what do we get?
We get 96 minutes!
Well done! Now you understand how to apply inverse proportions effectively.
Let's analyze more scenarios! If we keep a fixed amount of food for students and add more, what happens?
The food would run out faster!
Great observation! So we expect to see another case of inverse proportion here. Let's write this out. For 100 students, it lasts 20 days. If we have 125 students, what's the new number of days?
It would last only 16 days!
Excellent! You are really grasping the concept of how one quantity can affect another inversely.
To wrap up, can someone summarize what we learned about inverse proportions?
If one quantity increases, the other decreases, and their product remains constant.
That's right! Now, let’s have a quick quiz. If 15 workers can complete a task in 48 hours, how many are needed to finish in 30 hours?
That will be 24 workers!
Excellent job! Remember to keep practicing this concept as it comes up in various scenarios!
A relationship where one quantity increases while the other decreases.
Inverse proportionality implies a fixed product of two quantities.
The inverse of a relationship where increasing one quantity affects the other negatively.
If you hire more crew, the days will reduce, that’s inverse proportion, good to deduce.
Imagine a baker with just one oven. He can bake 12 pies in 3 hours. If he buys another oven, now he can bake 24 pies in the same time, making baking even faster!
RAP - Remember: As one rises, Another Plummets.
IP = Inverse Equals Increase and Decrease
Term
What is inverse proportion?
Click to flip
Term
What is the formula for inverse proportion?
Click to flip
Term
Example of inverse proportion?
Click to flip
A relationship between two quantities where an increase in one results in a decrease in the other, with their product remaining constant.
A fixed value in the equation xy = k that represents the relationship between two inversely proportional quantities.
The multiplicative inverse of a number; for a number x, its reciprocal is 1/x.
Inverse proportion describes the relationship between two quantities where an increase in one results in a decrease in the other, maintaining a constant product.
This section introduces the concept of inverse proportion, highlighting how two quantities vary together in opposite directions. Examples include how more workers reduce the time to complete a task, or how increasing the speed of a vehicle decreases the time taken for a journey. The key equation xy = k illustrates this relationship.
Inverse proportion describes a fundamental relationship between two quantities: when one quantity increases, the other decreases in such a way that the product of the two quantities remains constant. For example, if we consider the time taken to complete a job with respect to the number of workers, as more workers join a task, the time to finish decreases correspondingly. The inverse relationship can be expressed through the equation xy = k, where k is a constant.
This section builds upon the principles of direct proportion by contrasting them and enabling students to grasp the versatile nature of mathematical relationships.
There are 80 students in a dormitory. Food provisions for them is for 25 days. How long will these provisions last if 15 more students join the group?
Solution: Suppose the provisions last for days when the number of students is 95. We have the following table:
Note that the more the number of students, the sooner would the provisions exhaust. Therefore, this is a case of inverse proportion.
So,
Thus, the provisions will last for approximately 21 days if 15 more students join the dormitory.