Real estate arithmetic: area, percentages, and commissions

Start with units and the requested amount

Real estate arithmetic becomes manageable when you identify the unknown, label the units, and choose the correct base. Area measures surface; perimeter measures boundary length. A rectangular parcel's area equals length times width. A 120-foot by 80-foot lot contains 120 × 80 = 9,600 square feet; its perimeter is 2 × (120 + 80) = 400 feet. A triangle's area is one-half times base times perpendicular height. Divide irregular parcels into nonoverlapping shapes and add their areas, or subtract a missing piece.

Convert before calculating

One acre contains 43,560 square feet. Divide square feet by 43,560 to obtain acres; multiply acres by 43,560 to obtain square feet. Thus 87,120 ÷ 43,560 = 2 acres. One mile equals 5,280 feet; one square mile equals 640 acres. Convert linear measurements to the same unit before multiplying them.

Find the percentage base

Convert a percent to a decimal by dividing by 100. The basic relationship is part = whole × rate. Rearrange it: rate = part ÷ whole; whole = part ÷ rate. Multiply a decimal rate by 100 to express a percentage. A 15% down payment on $400,000 is $400,000 × 0.15 = $60,000. A percentage change uses the original amount as its base: a rise from $400,000 to $440,000 is $40,000 ÷ $400,000 = 0.10, or 10%. To recover a price before a 10% increase, divide the new price by 1.10.

Follow each commission split

Commission examples use assumed agreements: commission rates and splits are negotiated, not fixed by law. Use the rate and allocation stated in the problem. On a $500,000 sale with a stated total commission of 4%, total commission is $500,000 × 0.04 = $20,000. If a brokerage receives 60% of that total, its share is $20,000 × 0.60 = $12,000. If its salesperson receives 70% of that share, the salesperson receives $12,000 × 0.70 = $8,400. Do not add those percentages.

To recover sale price from a $20,000 total commission at 4%, divide $20,000 by 0.04 to get $500,000. If commission is the sole selling expense, a seller retains 96% of the price at that rate; a desired net of $480,000 therefore requires $480,000 ÷ 0.96 = $500,000. Carry precision through intermediate steps and round money at the end as directed.