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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.

In direct proportionality, the relationship between x and y remains the same. As a mathematical formula, this can be expressed as follows:

\frac{x}{y} = k

, where k is a constant

Direct proportionality can also be denoted as follows:

x \propto y

With the calculator on this site, you can easily perform calculations with things that are directly proportional. In these calculation tasks based on direct proportionality, three values are known and the fourth must be calculated.

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

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

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

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

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

Example: Price of apples

The total price of goods and their quantity are directly proportional to each other.

If a kilo of apples costs two euros, then four kilos of apples cost eight euros. The weight and price of apples are directly proportional to each other. In general, the quantity and price of products purchased from a store are directly proportional to each other. Of course, it is possible that the store has introduced a discount for those who buy more, in which case the quantity and price are no longer directly proportional.

The above example looks like the following as a calculation:

\frac{1}{2} = \frac{4}{8}

The relationship between the weight of apples and their price remains the same.

The numbers can also be entered the other way around, i.e.:

\frac{2}{1} = \frac{8}{4}

Three fields must be filled in in the calculator on the website.

Example: Price of strawberries

1.5 kilos of strawberries cost €10. How much does 2 kilos cost?

The calculator is filled in as follows, for example:


──────	=	──────

After the calculation, the result is:


──────	=	──────

So 2 kilos of strawberries cost €13.33.

Example: Image size changes

The calculator can also be used to change image sizes, for example. The width and height of the image are directly proportional to each other, if the aspect ratio is to be kept the same.

The size of the original image is 1200 x 628 px. If you want a new image whose width is not 1200 px but 500 px, you can get it by entering it in the calculator:


──────	=	──────

The final result is 261.67. The size of the converted image is therefore 500 x 262 px.

Example: Travel time

A person can cycle 7 kilometers in 30 minutes. How long does it take to cycle 10 kilometers?


──────	=	──────

The answer is 42.86 minutes.

Example: Hourly wage

The time spent working and the wage paid for it are directly proportional to each other.

A wage of €500 is paid for 12 hours of work. How much is paid for 67 hours of work?


──────	=	──────

The answer is: €2,791.67.

Author:

Arkikoodi

Published: 7.4.2025

proportionality

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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.