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A merchant keeps careful records. The same number can be written three ways — as a percentage, a decimal, or a fraction. Skilled bookkeepers can switch between the three without breaking stride.
31% as a decimal
31 ÷ 100 = 0.31
2.5% as a decimal
2.5 ÷ 100 = 0.025
63% as a fraction
63/100 (already simplest)
"What is 30% of $12?" A merchant tallying the day's taxes needs to find a portion of a total. Convert the percent to a decimal, then multiply.
Step 1 — convert: 30 ÷ 100 = 0.30
Step 2 — multiply: 0.30 × 12 = 3.60
30% of $12 = $3.60
0.072 × 90 = 6.48
The reverse question: the merchant spent 40c out of every $2 on salt. What percent is that?
Both amounts must be in the same unit. Convert $2 → 200c.
(40 ÷ 200) × 100 = 20%
(27 ÷ 93) × 100 ≈ 29.0%
A merchant marks up goods. The cheese costs him $85; he sells at a 20% increase. What does he charge?
$85 × 1.20 = $102
Check: 20% of $85 = $17. $85 + $17 = $102 ✓
The spring flood damages the warehouse. A rug worth $170 must be sold at a 40% discount. What's the new price?
$170 × 0.60 = $102
Check: 40% of $170 = $68. $170 − $68 = $102 ✓
A trader compares two prices. He bought rope for $40, sold it for $52. What was the percent change?
(52 − 40) ÷ 40 × 100
= 12 ÷ 40 × 100 = 30% increase
A negative result means a decrease. If rope drops from $40 to $30, the change is (30 − 40) ÷ 40 × 100 = −25%, i.e. a 25% decrease.
⚠ The Merchant's Trap. Most traders make a mistake here. Read carefully.
After a 15% discount, a fridge sells for $442. What was the original price?
Wrong: $442 + 15% of $442 = $508.30 ❌
This is wrong because 15% of the smaller number is not the same as 15% of the original.
Right: After a 15% discount, you paid 85% of the original. So $442 is 85% of the original.
Sale price is $442 after a 30% markup. The original cost was 100%; now it's 130%. So:
$442 ÷ 1.30 = $340
The merchant's craft is measured in profit. He buys at a cost price and sells at a sell price. The difference is profit (or loss) — expressed as a percent of what he paid.
Cost: $150. Sold for: $200.
Profit = 200 − 150 = $50
Fraction = 50/150 = 1/3
% = 50/150 × 100 ≈ 33.3% profit
A negative answer means a loss. If Hamish had sold for $120, the change is −30/150 × 100 = −20%, i.e. a 20% loss.
A merchant plans ahead. He bought the bicycle for $150 and wants a 50% profit. What should he charge?
$150 × 1.50 = $225 sell price
Check: profit = $225 − $150 = $75. $75 / $150 = 50% ✓
If the sell price is $442 and the merchant made a 30% profit, what did he pay?
cost = $442 ÷ 1.30 = $340
This is the same inverse technique you learned in Ledger VII.
The final test. Real merchants chain many operations together: discount → markup → find original price → calculate profit. You'll work through three connected scenarios using every skill you've learned.
You have worked through all ten ledgers of the Merchant's Guild.