The register's one move
The till has exactly one trick and it plays it on every purchase: (read aloud: T equals P times one-plus-r). is the price before tax, is the tax rate as a decimal, and is the total the register asks for — that last one is what you are solving for. The 1 in the bracket is your price, kept whole; the is the government's slice, stacked on top. In Ontario the sales tax is 13%, so and every dollar of price becomes at the register — which is why a $100 pair of shoes quietly asks for $113.
The one non-negotiable step: the percent must become a decimal BEFORE it enters the bracket. 13 stays a percent on the sign; is what does the math. Skip the ÷100 and the formula cheerfully charges you thirteen extra copies of the price — the arithmetic never argues, it just obeys.