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A percent literally means "per hundred". To convert a percent to a decimal, divide by 100 — equivalently, shift the decimal point two places to the left.
"What is X% of Y?" asks for a portion of a total — a tax on a price, a tip on a bill, a discount off a tag. The rule: convert the percent to a decimal (divide by 100), then multiply by the amount.
"What percent is the part of the whole?" The rule: divide the part by the whole, then multiply by 100. That fraction ÷ operation gives the decimal form; multiplying by 100 turns it into a percent.
A +X% increase means: new = old × (1 + X/100). The "1 +" is the original (100%); the "X/100" is the extra. E.g. +20% → 1 + 0.20 = 1.20. Finding this multiplier is the first step.
A −X% decrease means: new = old × (1 − X/100). The "1 −" is the original (100%) minus what\'s taken away. E.g. −40% → 1 − 0.40 = 0.60. The multiplier is BELOW 1 — that\'s the mirror of Ledger IV.
Given a before-value (old) and an after-value (new), the percent change is: % change = (new − old) ÷ old × 100. A positive answer means an increase; a negative answer means a decrease. The key move: always divide by the old value.
Given the new (discounted) price, find the original. Do NOT add the percent back. The rule is: original = new ÷ multiplier. To undo a multiplication, divide. E.g. 20% off means × 0.80 forward → ÷ 0.80 to reverse.
A merchant buys at a cost price and sells at a sell price. Profit percentage is just the percent change from cost to sell: profit % = (sell − cost) ÷ cost × 100. Same formula as Ledger VI — with "cost" playing the role of "old".
A merchant pays the cost and wants to sell for a percent margin above cost. This is Ledger IV in business vocabulary: sell = cost × (1 + margin/100). A 50% margin means multiply by 1.50. The multiplier includes the original plus the extra.
Real merchants apply many percentage operations in sequence: buy at a discount, mark it up to sell, compare to an original. Multipliers chain by multiplication. Two operations at once = multiply the two multipliers. E.g. a 20% discount then a 50% markup: 0.80 × 1.50 = 1.20 — the final price is 20% above the original, not 30%.
You have worked through all ten ledgers of the Merchant's Guild.