We explain what a proportion is and some examples of this relationship of equality. Furthermore, the types of proportionality that exist.
What is a proportion?
In mathematics, it is known as the proportion the relationship of equality that exists between two reasons that is, between two comparisons between two given quantities. That is to say: 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. Likewise, if it costs this business $20 to make two pizzas (20/2 = 10), so making four pizzas would cost $40 (40/4 = 10). If both ratios are expressed in a formula: 20/2 = 40/4. There is a proportion.
Theorization about this type of relationships was developed in Greek antiquity and it 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 in which the values of two magnitudes depend on each other directly (direct proportionality). So, When one of the values of the relationship increases, the other will necessarily do so as well such as the relationship between temperature and energy: the higher the temperature, the greater the energy recorded and vice versa.
On the other hand, in a relationship in which the increase of one of the terms leads to the decrease of the other, it is said that we are facing 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 higher the speed, the shorter the time it will take to reach our destination, and vice versa.
References
- EcuRed, Knowledge with everyone and for everyone.
- Colombia University.
