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Inverse proportionality

In inverse proportionality, as the value of one variable increases, the value of the other variable decreases in the same proportion. This can be applied to calculating speed and time, area calculations, resource allocation, calculating the number of employees, and many other practical matters. You can use the calculator on this website to calculate calculations based on inverse proportionality.

The variables x and y are inversely proportional if x and 1/y are directly proportional.

This can also be written as:

x \propto \frac{1}{y}

Inverse proportionality means that:

x \times y = k

, where k is a constant

With the calculator on this site, you can easily perform calculations with inversely proportional things. In these inversely proportional calculations, three values are known and the fourth must be calculated.

x_{1} \times y_{1} = x_{2} \times y_{2}

If, above, y₂ is unknown and the other numbers are known, y₂ can be calculated as follows:

x_{1} \times y_{1} = x_{2} \times y_{2} | \div x_{2}

y_{2} = \frac{x_{1} \times y_{1}}{x_{2}}

Example: Speed and time

Speed and time are inversely proportional if the distance traveled remains the same.

You ride a bicycle at a speed of 15 km/h for two hours. (The distance is therefore 30 km.) How fast should you ride to go the distance traveled in 1.5 hours?

For example, fill in the calculator as follows:

* = *

And the final result is:

* = *

To go the distance in 1.5 hours, you should ride at 20 km/h.

Example: Area

The sides of a rectangle are inversely proportional if the area of the rectangle remains the same.

The sides of the rectangle are 4m and 3m. (The area of the rectangle is therefore 12m².). If one side is 5m, what must the other side be for the area to remain the same?

* = *

The other side of the rectangle is therefore 2.4m.

Example: Sharing the cake

The number of pieces of cake given to the guests is inversely proportional to the number of guests.

The cake is divided into sixteen pieces. If there are eight guests, two pieces of cake will be enough for each. How many pieces will each person get if there are twelve guests?

* = *

Each of the twelve guests will get 1.33 pieces of cake.

Example: Number of employees

The number of employees is inversely proportional to the time it takes to do the work.

Six employees do the work in ten hours. How many employees are needed to do the same work in six hours?

* = *

To do the work in six hours, 10 employees are needed.

Author:

Arkikoodi

Published: 8.4.2025

proportionality

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Direct Proportionality
In direct proportionality, the relationship between two variables remains the same. This can be applied to pricing, estimating distance and time, image size changes, and many other practical matters. The calculator on the page makes it easy to perform calculations based on direct proportionality.

Inverse proportionality

Example: Speed ​​and time

Example: Area

Example: Sharing the cake

Example: Number of employees

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Example: Speed and time