Sales Tax and Total Price

Adding tax is easy: multiply by $1 + r$. A $100 job at 13% HST totals $113. Taking tax back out of a tax-included figure is where people go wrong, because the instinct is to subtract 13% of the total. Do that to $113 and you get $98.31, which is not the price you started from. The correct move is to divide: $113/1.13 = 100$.

The reason is that the tax was calculated on the smaller number, not the larger one. This matters whenever you quote all-in prices to residential customers and then have to report the pre-tax revenue, and it matters at every reconciliation between a cash drawer and a return. The shortcut worth memorising is that backing out a 13% tax means dividing by 1.13, or equivalently multiplying by 0.885.