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.