Real estate math: percentages, area, and profit and loss

Start with the base

Percentage problems connect a whole, a rate, and a part: part = whole × decimal rate. Divide a percent by 100 before multiplying. To find the rate, divide part by whole; to find the whole, divide part by decimal rate. A $24,000 down payment on a $160,000 price is $24,000 ÷ $160,000 = 0.15 = 15%. A $12,000 commission at a stated 4% rate implies $12,000 ÷ 0.04 = $300,000 in sales price. Commission rates in examples are given assumptions, not legally fixed rates.

For sequential percentages, follow the money. A $300,000 sale at a stated 4% commission produces $300,000 × 0.04 = $12,000. If a brokerage receives 50% and its associate receives 60% of that share, calculate $12,000 × 0.50 = $6,000, then $6,000 × 0.60 = $3,600.

Measure area, not boundary

A rectangle's area is length × width; its perimeter is 2 × (length + width). A triangle's area is base × perpendicular height ÷ 2. Convert dimensions to the same unit before multiplying. Divide a composite parcel into nonoverlapping shapes and add their areas; subtract an excluded area when appropriate.

One acre equals 43,560 square feet. One mile equals 5,280 feet, and one square mile, or standard survey section, equals 640 acres. A 150-foot by 290-foot lot contains 150 × 290 = 43,500 square feet; 43,500 ÷ 43,560 ≈ 0.9986 acre. For a price per square foot, divide price by square footage; multiply area by unit price to find total price.

Profit, loss, and reverse percentages

For a simple resale problem, profit equals selling price minus cost; a loss equals cost minus selling price. Profit or loss percentage on cost uses cost as the denominator. Buying for $200,000 and selling for $230,000 gives $230,000 − $200,000 = $30,000 profit; $30,000 ÷ $200,000 = 15%. A margin on selling price instead equals $30,000 ÷ $230,000 ≈ 13.04%.

To recover cost from a resale at a 15% profit on cost, divide resale price by 1.15: $230,000 ÷ 1.15 = $200,000. For a 10% loss on cost, resale price is 90% of cost, so divide by 0.90. Include acquisition, improvement, and selling expenses when the problem specifies them. Loan payoff affects cash proceeds, but repaying principal is not itself a profit-calculation expense. Keep intermediate precision and round the final answer as requested.

Florida application

Florida Statutes section 475.705(1)(e) permits a commercial real estate commission notice to express the claimed commission as a dollar amount or a formula, such as a percentage of sales price. The formula still requires identifying the correct base and rate.