Four percentage questions.
The ones people actually need answered — including the reverse calculation almost everyone gets wrong.
What is X% of Y?
X is what percent of Y?
Percentage change
Take an added percentage back out
The mistake almost everyone makes
To take a percentage back off a total, you divide — you do not subtract the same percentage. An Ontario receipt for $113 including 13% HST is 113 ÷ 1.13 = $100.00, not 113 − 13% = $98.31. The gap is $1.69 on one receipt and a real bookkeeping problem across a year of them.
The same trap catches discounts. A price cut 20% and then raised 20% does not return to where it started — it lands 4% lower, because the second percentage applies to a smaller base.
Percentage points are not percent
If a mortgage rate moves from 4% to 5%, that is a rise of one percentage point — but a 25% increase in the rate. Coverage of interest rates and polling blurs the two constantly, usually in whichever direction makes the number sound better. When someone quotes a percentage change, ask what the base was.
Gains and losses are asymmetric for the same reason. A 50% loss needs a 100% gain to recover: a stock falling from $100 to $50 has to double, not rise 50%.
Canadian percentages worth memorising
| Situation | Percentage | On $100 |
|---|---|---|
| HST in Ontario | 13% | $113.00 |
| HST in Nova Scotia | 14% | $114.00 |
| HST in NB, NL and PEI | 15% | $115.00 |
| GST + PST in British Columbia | 12% | $112.00 |
| GST + QST in Quebec | 14.975% | $114.98 |
| GST only, Alberta and territories | 5% | $105.00 |
| Standard restaurant tip | 15% – 20% | $15.00 – $20.00 |
| Real estate commission, typical | 4% – 5% | $4.00 – $5.00 |
| RRSP contribution room | 18% of earned income | $18.00 |
| Capital gains inclusion rate | 50% | $50.00 |
Mental shortcuts
- 10% — move the decimal one place left.
- 5% — half of 10%. 20% — double it. 15% — 10% plus half again.
- 25% — divide by four. 331⁄3% — divide by three.
- Ontario HST — 10% plus a third of that again gets you to 13% within a cent or two.