# Direct and Inversely Proportion

## Direct Proportion

Two variables are direct proportional if there is always a constant ratio between them.
(As one variable increases, the other also increases.)

$\frac{y}{x}=k$
$y=k·x\phantom{\rule{0ex}{0ex}}↓\begin{array}{ccc}a& & c\\ b& & d\end{array}↓\phantom{\rule{0ex}{0ex}}a:b=c:d\phantom{\rule{0ex}{0ex}}a·d=b·c$

(The direction of the arrows follows the growth of the variables.
When committing proportionality, follow the arrows direction!)

Example:
2 books cost 6 euros. How much do 10 books cost?
(direct proportion: more books - more money)

## Inversely Proportion

Two variables are inversely proportional if the product of those variables is a constant.
(As one variable increases, the other decreases.)

$y·x=k$
$y=\frac{k}{x}\phantom{\rule{0ex}{0ex}}↓\begin{array}{ccc}a& & c\\ b& & d\end{array}↑\phantom{\rule{0ex}{0ex}}a:b=d:c\phantom{\rule{0ex}{0ex}}a·c=b·d$

(The direction of the arrows follows the growth of the variables.
When committing proportionality, follow the arrows direction!)

Example:
20 workers finish a job in 20 days. In how many days will 5 workers finish the same job?
(inversely proportion: more workers - less days)

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