Direct proportionality occurs when two quantities are multiplied or divided by the same number. By dividing any value of the second magnitude by its corresponding value of the first magnitude, the same (constant) value is always obtained, this constant is called the direct proportionality ratio. Direct proportionality occurs when two quantities are multiplied or divided by the same number.
Proportionality is a relationship between measurable quantities. It is one of the few mathematical concepts widely disseminated in the population. This is because it is largely intuitive and very common to use. Direct proportionality can be seen as a particular case of linear variations. We can use the constant factor of proportionality to express the relationships between the quantities.
The easiest way to understand this concept is through a simple, everyday example. Imagine going shopping and proposing to buy some sweets. Since you like them very much, you may be tempted to buy many.
A kilo of candy is worth $ 24. So you ask, how much will 3 kg, 6 kg, 10 kg and 12 kg cost? The most common way to think about this answer is usually the following:
If a kilo is worth $ 24, then 3 kg will be worth 3 times $ 24, mathematically it would be 3 * 24 = 72
By applying the same reasoning and similar operation for the other cases. They will soon realize that the simplest thing is to build a box where you write down each quantity and its price, so that you quickly realize something.
The relationship between the quantities is called the constant of proportionality and is generally denoted by the letter k.
In the example above k = 3.
If one magnitude increases and the other increases, or vice versa, will it always be a direct proportionality relationship?
It is important to analyze the following situations and draw your conclusions:
- SITUATION I: A child weighs 3.5 kg per month of birth, at two months it will have 7 kg, at 3 months it weighs 10.5 kg?
- SITUATION II: In a supermarket, the package of rice costs $ 34.50. The offer of the week is "Take 3 packages are paid $ 69".
Therefore, a long list of situations can be continued, although not all can be technically defined as magnitudes. In any case, what matters here is that you fully understand what you are talking about when you say that two things are directly proportionally related, or that the proportionality between them is direct.
