Chapter 9 - Real estate mathematics - Mathematical Basics, Units, Percentages, Fractions, and Core Calculations

Sep 29, 2026

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Chapter 9 focuses on the mathematical skills needed for the California DRE salesperson and broker licensing examinations. It explains how exam math is limited in scope and how calculator-assisted computations rely on basic formulas. The chapter reviews land measurement units (township through square yard/acre), then covers converting percentages and decimals, interpreting fractions, and calculating rectangle area. It also introduces commission/percentage fee formulas, property taxes under California rules, transfer tax mechanics, and value-estimation concepts such as GRM.

LanguageEnglish

CategoryExam

FormatPDF

Pages10

Reading Time25 min

AccessFree to download

Chapter 9: Real estate mathematics

Mathematical Basics

Land Measurements

Percentages

Fractions

Calculating the Area of Property

Commission

Property Taxes

Transfer Tax

Income Approach, Gross Rent Multiplier (GRM)

California Real Estate License Exam Prep: Unlocking the DRE Salesperson and Broker Exam ANSWER SHEET INSTRUCTIONS: The exam consists of multiple choice questions. Multiple choice questions are answered by selecting A, B, C, or D. You may use pen or pencil. Chapter 9: Real estate mathematics 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. A o o o o o o o o o o B o o o o o o o o o o C o o o o o o o o o o D o o o o o o o o o o Chapter 9: Real estate mathematics 149 | | | --- | | Chapter 9: Real estate mathematics | | | MATHEMATICAL BASICS A very small proportion of the Department of Real Estate (DRE) salesperson and broker licensing examination consist of math questions. An examinee could miss or skip every math question and still successfully pass the exam. Most math questions are solved with basic formulas using a nonprogrammable calculator. Anonprogrammable calculator is provided during both licensing exams. The examinee is well advised to use the calculator supplied to ensure their accuracy on the exam questions. A grasp of mathematical basics is helpful when dealing with: • land measurements; • percentages; • fractions; • area; • commissions; • loans; • investments/cost analysis; and • capitalization rates (cap rates) . LAND MEASUREMENTS Here is a review of basic units of land measurement: • Township = 36 sq. mi. broken up into 36 sections; • Section = 640 acres and 1 sq. mi.; • Half section = 320 acres (quarter section = 160 acres; quarter of a quarter = 40 acres); 150 Unlocking the DRE Salesperson and Broker Exam, Sixth Edition • Acre = 43,560 sq. ft.; • Mile = 5,280 ft.; • Square mile = 27,878,400 sq. ft. (5,280 ft. x 5,280 ft.) or 640 acres (27,878,400 sq. ft. / 43,560 sq. ft.); • Square acre = approximately 209 ft. x 209 ft.; • 1 yard = 3 ft.; • 1 square yard = 9 sq. ft. (3 ft. x 3 ft.); • 1 mile = 320 rods, 5,280 ft.; and • 1 rod = 16.5 ft. or 5.5 yards (16.5 ft. / 3 ft.) . PERCENTAGES A percentage needs to be converted to a decimal before any mathematical computations may be completed. When converting percentages to decimals, the basic rule to follow is to move the decimal point two spaces to the left. Examples: 50% = 0.5 3% = 0.03 115% = 1.15 Conversely, to convert a decimal to a percentage, move the decimal point two spaces to the right. Examples: 1.43 = 143% 0.03 = 3% 0.5 = 50% As the use of a calculator is allowed while taking the licensing exam, it is beneficial to convert all fractions to decimals and then use the calculator to complete the remaining computations. FRACTIONS To understand fractions, it is helpful to understand their basic mechanics. A fraction is composed of a numerator and a denominator. The number on the top of the fraction is the numerator and the number on the bottom is the denominator. When converting a fraction into a decimal, divide the numerator by the denominator. Examples: 4/5 = 0.8 1/2 = 0.5 3/4 = 0.75 3/100 = 0.03 667/100 = 6.67 Chapter 9: Real estate mathematics 151 CALCULATING THE AREA OF PROPERTY The formula for the area of a rectangle is most often used in land measurement. The area of a rectangle equals its length multiplied by its width, the result being the number of square feet within the parcel. A = L x W COMMISSION The percentage formula is a basic calculation used in real estate mathematics. It is typically used to determine the amount of a broker’s fee (commission) earned on a transaction. As compensation for services rendered, a broker is entitled to a broker’s fee typically stated as a percentage of the: • sales price; • loan amount; or • total rents. The percentage formula is easily converted to suit a variety of situations. Usually, two of the three variables will be provided in the question, leaving the third variable in the example tobe determined. Understanding the basic formula makes

FAQs

How much of the DRE salesperson and broker exam involves math questions?

Only a very small proportion of the licensing examination consists of math questions, and an examinee could miss or skip all math questions and still pass.

What is the rule for converting percentages to decimals and back?

Move the decimal point two spaces left to convert a percentage to a decimal, and move it two spaces right to convert a decimal to a percentage.

How are commission fees calculated using the percentage formula?

Use Fee = Percent (%) × Principal (P). Determine the fee by multiplying P × %, the rate by dividing Fee / P, or the principal by dividing Fee / %.

Sep 29, 2026

Upload by Grenda