We explain what a proportion is and some examples of this equality relationship. In addition, types of proportionality exist.
What is a proportion?
In mathematics, the equality relationship between two ratios, that is, between two comparisons between two determined quantities, is known as a proportion. If a/b is a ratio, then the equality a/b = c/d will be a proportion.
For example: if a business selling pizza 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 it costs this business $20 to make two pizzas (20/2 = 10), making four pizzas would cost $40 (40/4 = 10). If both ratios are expressed in a formula: 20/2 = 40/4. Here is a balance.
Theorizing about this type of relationship was developed in Greek antiquity and is attributed to Eudoxius of Cnidos, teacher of the famous Euclid of Alexandria, thanks to whom the teachings of his teacher survive, collected in book V of Euclid’s Elements.
Types of proportionality
We can say that a proportion occurs in mathematical situations where the values of two magnitudes depend directly on each other (direct proportionality). Thus, when one of the values of the relationship increases, the other will also necessarily do so, as is the relationship between temperature and energy; for example: the higher the temperature, the higher the power, and vice versa.
On the other hand, in a relationship where the increase of one of the terms leads to the decrease of the other, it is said that we face an inverse proportionality. This can be expressed as two terms being 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 shorter the time it will take to reach our destination, and vice versa.