Works back from a price with tax to the price before it: price ÷ (1 + rate/100). A price of 1100 at 10% tax was 1000 before tax — you do not simply subtract 10%.
This works backwards from a price including tax to the price before it.
A product costs 1100 including 10% tax.
The price before tax was 1000, and the tax is 100.
The standard mistake is to take 10% off the gross price.
Ten short of the correct 1000.
The reason is simple: the tax was charged on the net price. Ten per cent of 1000 is 100 — it was never ten per cent of 1100, which would be 110.
The two percentages are taken from different bases. The 10% you add and the 10% you would subtract are not the same 10%.
To undo a multiplication you divide. Something multiplied by 1.1 is returned by dividing by 1.1.
Where a reduced rate of 8% applies, as it does to food in Japan, divide by 1.08 instead.
Real invoices can differ by a unit because of rounding. Sellers are free to round down, round up or round to nearest, so a receipt that disagrees with this calculation by one is not necessarily wrong.