In an inverse proportion, when one quantity increases by a certain factor, the other quantity decreases by the same factor.
A good real-life example of inverse proportion is the speed you drive and the time it takes to travel a certain distance. Suppose you need to drive to a city that is located 200 miles away.
The following table shows the time it will take you to get to your destination based on the speed.
|Speed (miles per hour)
Did you make the following observations?
- 20 × 2 = 40 and 40 × 2 = 80
- 10 ÷ 2 = 5 and 5 ÷ 2 = 2.5
This means that every time you multiply the speed by 2, the time it takes is divided by 2 or multiplied by 1/2.
In general, with inverse proportion, when one quantity is multiplied by x, the other quantity is divided by x or multiplied by 1/x
Furthermore, notice the following:
20 × 10 = 200
40 × 5 = 200
80 × 2.5 = 200
200 is a constant, so let k = 200.
20, 40, or 80 is the independent variable, so let x = 20, 40, or 80
10, 5, or 2.5 is the dependent variable, so let y = 10, 5, or 2.5
We get x × y = 200 or y = 200/x
In general, with inverse proportion, y = k/x and we say that y is inversely proportional to x.
Other real-life examples of inverse proportion
- The number of people doing something and the time it takes to do it. As the number of people increases, the time it takes to finish decreases.
- Sharing a specific amount of money with a certain amount of people. As the number of people increases, the amount decreases.
- Suppose your income is constant. The money you save is inversely proportional to your expenses.
Jan 20, 20 01:57 PM
Top-notch information for those who want to become a high school math teacher. All important stuff that you need to know before making a move can be found right here on this website.
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.