P02 · Lesson 1 of 10 · 10 min · 4 hands-on tasks
Percentages Without Panic
Percent of, percent change, and the two traps that fool even experienced managers: going up then down, and points vs percent.
🎥 Watch it (2 min)
🎬 Situation
Priya just opened Crumb, a small bakery-café. Within a week she's drowning in percentages: a supplier's "price adjustment", a delivery app's "commission", a website "conversion rate", a bank's "interest".
She's always felt a little shaky with percentages. Today, that ends.
🎮 Play
Trap 1: up, then down. Priya's croissant price goes up, then a discount takes it down. Do equal percentages cancel?
Same percent up and down, yet you end lower. The discount was taken from a bigger price.
Trap 2: points vs percent. More of Priya's website visitors start ordering. How do you describe the change?
"Up 1 point" and "up 50%" can describe the same change. Headlines love the bigger-sounding one.
🏷️ Name it
| Idea | Formula | Priya's example |
|---|---|---|
| Percent of | number × percent | 15% of $40 = $6 |
| Percent change | (new − old) ÷ old | $80 → $100 is +25% |
| Percentage points | new rate − old rate | 2% → 3% is +1 point |
| Up then down | × (1 + up) × (1 − down) | +50% then −50% = −25% |
Percent change = (new − old) ÷ old
Two quick mental tricks:
- 10% is easy: move the decimal point one place ($40 → $4). Build everything else from it: 5% is half, 15% is 10% + 5%, 20% is double.
- Percents flip: 8% of 50 = 50% of 8 = 4. Pick whichever order is easier.
🖍️ Like you're five: you have 10 stickers. A friend gives you half as many again (5 more, now 15). Then you give away half (7½ gone). You end with 7½, not 10. Halving a bigger pile takes away more.
Real life: "Sales up 300%!" might mean 1 sale became 4. "Risk doubles!" might mean 1 in a million became 2 in a million. Businesses, news and adverts all pick the most exciting way to say a number. Asking "percent of what?" is the quickest way to see what's really going on.
🔨 Do it: 4 tasks
0 / 4 doneTask 1 of 4 · Percent of
Priya's café takes a 15% service charge on a $40 catering order.
How much is the service charge?
Task 2 of 4 · Percent change
Priya's flour supplier raises a sack from $80 to $100. By what percent did the price rise?
Task 3 of 4 · Up, then down
A $100 coffee machine goes up 50% in price. Then it's put on sale at 50% off.
What does it cost now?
Task 4 of 4 · Points vs percent
Last month 2% of Priya's website visitors ordered. This month it's 3%.
By what percent did the order rate grow?
🧩 Case: The supplier's offer
⭐ VIPPriya buys $2,000 of butter a month. Her supplier calls: "Prices are going up 20% next month. But because you're loyal, we'll give you 20% off after that. So it evens out."
Does it even out?
What would you do? VIP members make the call, see what happens next across 2 decisions, and get the expert debrief.
🔁 Remember it
Sales went from $200 to $150. The percent change is...
A share price falls 50%. How much must it rise to get back to where it started?
Interest rates rise from 4% to 5%. Which is correct?
Percent change = (new − old) ÷ old. Always ask "percent of what?". Up 50% then down 50% leaves you 25% lower, and a rate going from 2% to 3% is up 1 point but up 50%.
📅 Use it Monday
Find one percentage in a report or email at work this week. Ask: percent of what? How many dollars (or people) is that? If it compares two rates, check whether it means points or percent.
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