For example, suppose I make a purchase that is $\$5.36$. Now there is tax added. So my total price is actually $$(5.36 + (5.36 * 0.13))=\$6.06$$
But really, I can just do this and get the same answer:
Why does the second way work? Why does it make sense?
As mentioned in the answers section, this is very easily mathematically shown (factoring and such), but I am looking for the actual "intuition" behind it. How would you explain it to someone without using math?