Question

What are direct and inverse proportions?

Answer 1

Determine the direct and inverse proportions.

Direct proportion

If two quantities, $aandb$, rise or decrease concurrently, they are said to be in direct proportion. In other words, the proportion of their respective values remains constant. This indicates that

$\frac{a}{b}=k$

$aandb$are said to fluctuate directly when $k$ is a positive value.

In this situation, if the values $b_1,b_2$ of $b$ correspond to the values $a_1,a_2$of $a$, it becomes;

$\frac{a_1}{b_1}=\frac{a_2}{b_2}$

Inverse proportion

Two quantities $aandb$are said to be in inverse proportion if an increase in quantity $a$, there will be a decrease in quantity $b$, and vice-versa. In other words, the product of their corresponding values should remain constant.

If $ab=k$, then $aandb$are said to vary inversely.

Hence, the direct and inverse proportion may be used to demonstrate how the quantities and amounts are connected. It is sometimes referred to as directly proportional or inversely proportional. The proportionality sign is $\text{'}\alpha \text{'}$.