What is the difference between direct proportions and inverse proportions?

Answer 1

The easiest way to think about this is by example:

Direct Proportionality:

"A isproportionalto B"

That means A is equal to the product of B and some constant (usually denoted as k).

A = kB, where k is some constant

Simply put, if A goes up in value, than B goes up in value. If A goes down in value, B also goes down in value. They key here is A and B are either both in the numerator (top of a fraction) or the denominator (bottom).

(1/A) = k(1/B), where k is some constant

This time both A and B are in the denominator, but that's okay because they are BOTH in the denominator.

Inverse Proportionality:

"A is inversely proportional to B"

If A is in the numerator, B is in the denominator, and vice versa.

A = k(1/B)

(1/A) = kB

Simply put, if A goes up B goes down. If A goes down, B goes up.