Why variables in directly proportinality are multipiled Why variables (RHS) in directly proportionality are always multiplied.
Suppose the Newton's 2nd law
$$F \propto m$$
$$F \propto a$$
$$F \propto m*a$$
Please don't give a rigorous proof. I just want to understand it intuitively.

Suppose you first increase mass $m$ by twice, that is $m\rightarrow2m$ thaen $F∝m$ implies that the force should also increase twice $F \rightarrow 2F$. After this let's increase the $a$ twice- this  implies that the force shoudl again become twice, that is $2F\rightarrow 4F$.
If we simultaneously increase mass and acceleration to double then the force should increase 4 times. Symbolically this can be written as:
$$F∝m \ \ and\ \ \  F∝a \implies F∝m∗a$$
