# Rule of Three

## Calculator

 Type of proportions: Direct (If one magnitude increases, the other one also increases, in the same proportion) Inverse (If one magnitude increases, the other one decreases, in the same proportion)

If the quantity:
corresponds to:
Then, the following quantity:
corresponds to:

## Theory

A rule of three is a method to find the fourth term of a proportion when three terms are given.
There two type of rule of three, direct and inverse.

### Direct rule of three

If one magnitude increases, the other one also increases, in the same proportion.
a/b=c/d
a, b, and c are known. To calculate d:
d= c x b/a

Example: It takes 2 hours (a) to travel 200km (b). But, what happens if our travel last 4 hours (c), what is the distance (d)? Note that this is a direct rule of three because if the number of hours increases, the distance also increases.
Solution: d = c x b/a = 4 x 200 / 2 = 400 km

### Inverse rule of three

If one magnitude increases, the other one decreases, in the same proportion.
a x b = c x d

a, b, and c are known. To calculate d:
d= a x b/c

Example: Ten workers (a) are able to finish the job in 2 days (b). If now we have 20 workers (c), how many days (d) will be required? Note that this is an inverse rule of three: if the number of workers increases, the number of days decreases.

Solution: d = a x b/c = 10 x 2/20 = 1 day.