10.klasse

Proportional quantities mean that two things always increase or decrease in the same ratio. If one thing doubles, the other also doubles. If one is halved, the other is also halved. This ratio is constant. It can be generally expressed in this form, where $k$ is a constant.

Example:

Imagine you are baking cakes and each cake requires 2 eggs. If you want to make more cakes, you need more eggs. The ratio between the number of cakes and the number of eggs is always the same.

To find out if the ratio between cakes and eggs is proportional, you can divide the number of eggs by the number of cakes. If you get the same answer each time, the ratio is proportional. Let's try with the numbers in the table. For one cake, you need two eggs, which gives the fraction:

For two cakes, you need four eggs and can set up the fraction:

For three cakes, you need six eggs and can set up the fraction:

When you divide the number of eggs by the number of cakes, you get the same answer each time. 2 eggs per cake. The ratio between eggs and cakes is proportional, meaning constant. It can be expressed as:

Question:
How many eggs do you need to make 10 cakes?

Answer:
Use the ratio between eggs and cakes:

Substitute $x=10$ and calculate the answer:

You need 20 eggs to make 10 cakes.

Summary:
Proportional quantities follow a fixed ratio. You can use this ratio to create and solve equations to find unknown values.