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# What is a proportion?

We explain what a proportion is and some examples of this relationship of equality. In addition, the types of proportionality that exist.

1. ### What is a proportion?

In mathematics , it is known as a proportion to the relationship of equality that exists between two reasons , that is, between two comparisons between two determined quantities. That is: if a / b is a reason, then the equality a / b = c / d will be a proportion.

For example: if a pizza sale business has a profit of \$ 15,000 and an expense of \$ 5,000, we can say that the company has a ratio of 3. Similarly, if this business costs \$ 20 to make two pizzas (20/2 = 10), so making four pizzas would cost \$ 40 (40/4 = 10). If both reasons are expressed in a formula: 20/2 = 40/4. There is a proportion.

Theorizing about this type of relationship was elaborated in Greek antiquity , and is attributed to Eudoxio de Cnidos, master of the famous Euclid of Alexandria, thanks to those who survive the teachings of their teacher, collected in Book V of the Elements of Euclid .

Types of proportionality

We can say that a proportion occurs in mathematical situations in which the values ​​of two magnitudes depend on each other directly (direct proportionality). Thus, when one of the values ​​of the relationship increases, the other will also necessarily do so , such as the relationship between temperature and energy: at higher temperatures, more energy is recorded and vice versa.

On the other hand, in a relationship in which the increase of one of the terms entails the decrease of the other, it is said that we are facing an inverse proportionality. This can be expressed as two terms are inversely proportional: when one goes up the other goes down, and vice versa. Such is the relationship between speed and time : the faster the speed, the less time it will take to reach our destination, and vice versa.