Inverse proportionality describes a situation in which, when one term is multiplied by a certain number of times, the second term is decreased by the same number of times. This also occurs in reverse, if one term decreases by a certain number of times, the second term increases by the same number of times.

Let's see an example to illustrate this concept.

Given the following table:

We see two values, $X$ and $Y$. It can be very clearly seen that, when the value of $X$ increases by $2$, the value of $Y$ also decreases $2$ times. Therefore, it can be said that there is inverse proportionality here.

Imagine traveling in some vehicle while the roads are quite empty, without any traffic jams.

As you travel more kilometers and more time passes, the amount of gasoline decreases.

We can say that, as the distance increases the amount of gasoline decreases.

Let's see a graphical representation of inverse proportionality:

The function: $Y=\frac{a}{X}$

represents inverse proportionality.

As the $X$ increases the $Y$ decreases.

How can we check if there is inverse proportionality?

To find out if there is inverse proportionality, we will examine if, when one term is multiplied by a certain amount of times, the second term is decreased by the same amount of times.

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Question 1

In a box there are 28 balls, \( \frac{1}{4} \) of which are orange.