Learning Objectives

• Translate fractions, decimals, and percentages accurately.
• Use the part–whole–rate relationship to solve for any missing value.
• Calculate square footage, square yardage, acreage, frontage value, and unit price.
• Distinguish linear, square, and cubic measurements.
• Calculate total commission, brokerage shares, affiliated-broker shares, and seller proceeds before other costs.
• Organize multistep problems so that each percentage is applied to the correct base.
• Estimate and check whether a result is reasonable before selecting an exam answer.
• Separate national math principles from Indiana compensation rules awaiting current-authority verification.

Key Vocabulary

Term	Meaning
Base / Whole	The total amount to which a percentage is applied.
Part	The amount produced when a rate is applied to a whole.
Rate	A percentage written as a decimal for calculation.
Decimal	A number expressed through place value, such as 0.075.
Fraction	A number representing part of a whole, such as 3/8.
Linear Foot	A one-dimensional measurement of length.
Square Foot	A two-dimensional unit of area.
Cubic Foot	A three-dimensional unit of volume.
Acre	43,560 square feet.
Front Foot	A unit based on the width of a parcel along a street, waterway, or other boundary.
Commission Rate	The negotiated percentage or other compensation basis stated in an agreement.
Commission Split	Allocation of earned compensation between brokerages or between a brokerage and an affiliated broker.
Gross Commission Income	Commission produced before internal splits and business expenses.
Net to Seller	Amount remaining for the seller after subtracting specified charges from the sale price.

Chapter Opening

Real estate math is not advanced mathematics. It is disciplined reading. The arithmetic is usually multiplication, division, addition, or subtraction; the challenge is deciding which number is the whole, which rate applies, and what the question actually asks.

A strong student does not begin by pressing calculator keys. The student labels the facts, writes the relationship, converts the rate, calculates in steps, and performs a reasonableness check. That same habit protects a broker when estimating acreage, presenting a commission illustration, or reviewing a settlement figure.

Core Lesson

1. Read the Question Before Choosing the Formula

Underline the requested result and label every number with a unit: dollars, feet, square feet, acres, or percent. A number without a label invites mistakes. If the problem gives unnecessary facts, ignore them. If it asks for one brokerage's share, do not stop after calculating the total commission.

2. Fractions, Decimals, and Percentages

To change a percent to a decimal, move the decimal point two places left: 7% = 0.07 and 2.5% = 0.025. To change a decimal to a percent, move it two places right: 0.375 = 37.5%. To convert a fraction to a decimal, divide the numerator by the denominator: 3 ÷ 8 = 0.375.

Form	Equivalent	Operation
6%	0.06	Move two places left
0.42	42%	Move two places right
5/8	0.625 or 62.5%	5 ÷ 8

3. Part = Whole × Rate

The central percentage relationship is Part = Whole × Rate. If the part is unknown, multiply. If the whole or rate is unknown, divide.

4. Percentage Increase and Decrease

A percentage change is applied to the original amount, not the final amount. A $240,000 value increasing 8% rises by $19,200 and becomes $259,200. A 10% decrease from $300,000 is $30,000, leaving $270,000. Increasing by 10% and then decreasing by 10% does not return to the starting point because the second rate applies to a different base.

5. Linear, Square, and Cubic Measure

Length is one-dimensional. Area is two-dimensional. Volume is three-dimensional. A fence is commonly measured in linear feet; a floor in square feet; concrete or interior space may be measured in cubic units. Units must match before numbers are combined.

6. Rectangle, Triangle, and Irregular Parcels

A 120-foot by 180-foot rectangular parcel contains 21,600 square feet. A triangular parcel with a 100-foot base and 80-foot perpendicular height contains 4,000 square feet. For an irregular tract, divide the sketch into familiar shapes, calculate each area, then add or subtract as the diagram requires. Use perpendicular height—not a sloping side—for a triangle.

7. Square Feet, Square Yards, and Acres

One square yard contains nine square feet because it is three feet by three feet. Divide square feet by 9 to find square yards. One acre contains 43,560 square feet. Divide square feet by 43,560 to find acres; multiply acres by 43,560 to find square feet.

Do not confuse 43,560 with 4,356 or 435,600. The current Pearson VUE handbook tells Indiana candidates to memorize 43,560 square feet per acre and 5,280 feet per mile.

8. Frontage and Unit Pricing

If land is priced per front foot, multiply the frontage by the price per front foot. Depth may matter to actual value, but it is not multiplied unless the problem instructs you to calculate area or uses another pricing method. Unit price is total price divided by the number of units—square feet, acres, apartments, or front feet.

9. Commission Is Negotiated Compensation

Commission problems use stated assumptions for math practice. In actual brokerage, compensation is negotiable and must be handled through lawful agreements and brokerage procedures. Never describe a particular percentage as standard, fixed, required, or approved by a trade group.

Total commission is commonly calculated as sale price multiplied by the negotiated rate. If two brokerages share the commission, apply the inter-brokerage split to the total commission. If an affiliated broker then receives a percentage from the broker's own firm, apply that internal split to the firm's share—not to the sale price unless the agreement expressly says otherwise.

10. A Three-Level Commission Waterfall

The most common error is applying 70% directly to $24,000. That skips the brokerage split. Draw a waterfall: sale price → total commission → brokerage share → affiliated-broker share.

11. Seller Proceeds and Missing Values

If a problem asks for proceeds before other closing costs, subtract the stated commission from the sale price. If it also gives a mortgage payoff or other seller debit, subtract each stated amount. Do not invent expenses not provided in the question.

12. Estimation and Reasonableness

Estimate before calculating. Five percent of $400,000 is about $20,000, so an answer of $200,000 signals a misplaced decimal. A 100-by-200-foot parcel is under half an acre because 20,000 is less than half of 43,560. Reasonableness catches key-entry and unit errors.

Learn It

1. Write the unit requested.
2. Convert every percentage to a decimal.
3. Identify part, whole, and rate.
4. Write the formula before substituting numbers.
5. Keep multistep splits on separate lines.
6. Round only at the end unless the problem directs otherwise.
7. Compare the result with a quick estimate.

Live It

Pass It

On the exam, label the base before multiplying by a rate. “Sixty percent of the commission” uses commission as the base. “Six percent of the price” uses price as the base. For area, draw the shape and write the unit. For acreage, divide square feet by 43,560. If the requested answer is an affiliated broker's amount, follow every split.

Indiana Law Spotlight

The mathematical principles in this chapter are national. Indiana compensation and brokerage practice are governed by current agreements, statutes, rules, managing-broker procedures, and federal competition law. Compensation is negotiable; students and licensees should never imply that Indiana, the Commission, an MLS, or an association sets a standard commission.

Partially verified Indiana rules: A qualifying broker-owned business entity may receive compensation directly from the broker company under IC 25-34.1-3-4.5, but only within that statute's ownership and purpose conditions. Under IC 25-34.1-10-13, payment of compensation does not by itself create agency, and parties must be advised whether compensation will be shared with broker companies representing different or adverse interests. Current 876 IAC 8-1-9 routes an offered cooperative commission to the selling broker—not directly to an affiliated broker working under that selling broker.

An unlicensed assistant may not negotiate a commission, commission split, management fee, or referral fee for a broker. A broker company using a referral service needs a written client agreement and a written fee agreement with cooperating brokers. An inducement or rebate used to obtain a listing or induce a sale requires full written disclosure to all parties when offered or accepted, and compensation may not be paid to an unlicensed person for services that require a license. The managing broker remains responsible for company direction and supervision.

Practical brokerage application: Never invent a payment route or promise a rebate, credit, referral fee, or split from a personal account. Confirm the recipient's status, the service performed, the written agreement, every required disclosure, federal RESPA implications, and the firm's approved procedure before money is offered or paid.

Remaining Indiana legal verification queue: Exact agreement terms, when compensation is earned, procuring-cause and post-termination issues, teams and nonstandard entities, every rebate and referral scenario, advertising and MLS representations, records, tax treatment, out-of-state cooperation, RESPA, discipline, antitrust fact patterns, and controlling decisions remain queued. No universal rate, split, rebate, referral-payment, or earned-commission outcome is stated.

National Exam Alert

• Memorize 43,560 square feet per acre and 5,280 feet per mile.
• Convert percentages to decimals before multiplying or dividing.
• The phrase “of” usually signals multiplication.
• Use perpendicular height for triangle area.
• A brokerage split is applied after total commission is calculated.
• Commission rates are negotiable; antitrust principles reject fixed or “standard” rates.

Common Exam Trap

• Decimal trap: 6% is 0.06, not 0.6.
• Unit trap: divide square feet by 9—not 3—to obtain square yards.
• Acre trap: divide square feet by 43,560 when converting to acres.
• Triangle trap: forgetting the one-half factor doubles the answer.
• Split trap: applying an affiliated-broker split to the sale price or total commission instead of the firm's share.
• Question trap: calculating total commission when the question asks for seller proceeds.

PASS FIRST Memory Trick

Broker Insight

Math builds trust only when its assumptions are transparent. Put estimates in writing, show the source of dimensions or rates, identify excluded costs, and distinguish “approximately” from a verified figure. Never guarantee dimensions from public records or marketing data. Never describe compensation as standard. A clean worksheet is both a communication tool and a risk-control record.

Tables & Comparison Charts

Problem	Relationship	Quality check
Find a percentage amount	Part = Whole × Rate	Part should be proportionate to whole
Find the original whole	Whole = Part ÷ Rate	Whole usually exceeds part when rate is under 100%
Rectangle area	Length × Width	Answer in square units
Triangle area	½ × Base × Height	Use perpendicular height
Square feet to acres	Square feet ÷ 43,560	43,560 sq. ft. = 1 acre
Total commission	Price × Rate	Use negotiated problem rate
Affiliated-broker share	Firm share × Internal split	Follow every stage
Seller proceeds	Price − stated seller charges	Do not invent missing charges

Chapter Summary

• Most real estate percentage problems use Part = Whole × Rate.
• Convert a percent to a decimal before calculating.
• Area uses square units; volume uses cubic units.
• A rectangle is length times width; a triangle is one-half base times perpendicular height.
• One square yard is nine square feet; one acre is 43,560 square feet.
• Front-foot pricing uses frontage, while unit pricing divides total price by the stated unit count.
• Commission calculations move from price to total commission to brokerage and affiliated-broker shares.
• Compensation is negotiable and should never be described as fixed or standard.
• Indiana payment channels, written disclosures, unlicensed-assistant limits, referral-service agreements, and managing-broker supervision are partially verified; fact-specific compensation and antitrust issues remain queued.
• Estimation, unit labels, and separate calculation steps prevent most errors.

Quick Review

• 7.5% = 0.075.
• 3/8 = 0.375 = 37.5%.
• Part = Whole × Rate.
• Square feet ÷ 9 = square yards.
• Square feet ÷ 43,560 = acres.
• Acres × 43,560 = square feet.
• Rectangle area = length × width.
• Triangle area = ½ × base × height.
• Total commission = price × negotiated rate.
• Follow each split in order and calculate only what the question asks.

Practice Questions

1. What is 6.25% written as a decimal?
   1. 0.625
   2. 0.0625
   3. 0.00625
   4. 6.25
2. A property worth $320,000 increases by 7%. What is the new value?
   1. $322,240
   2. $337,400
   3. $342,400
   4. $344,000
3. A rectangular lot is 125 feet wide and 180 feet deep. What is its area?
   1. 22,500 square feet
   2. 15,250 square feet
   3. 30,500 square feet
   4. 45,000 square feet
4. A triangular parcel has a 160-foot base and a perpendicular height of 90 feet. What is its area?
   1. 14,400 square feet
   2. 8,000 square feet
   3. 28,800 square feet
   4. 7,200 square feet
5. A tract contains 130,680 square feet. How many acres does it contain?
   1. 2 acres
   2. 3 acres
   3. 4 acres
   4. 5 acres
6. A home sells for $415,000 with a hypothetical 5.2% commission. What is the total commission?
   1. $20,750
   2. $22,100
   3. $21,580
   4. $23,240
7. A $30,000 total commission is shared 60% to the listing brokerage and 40% to the cooperating brokerage. How much does the listing brokerage receive?
   1. $18,000
   2. $12,000
   3. $20,000
   4. $24,000
8. A listing brokerage receives $18,000 and pays its affiliated broker 70% of that amount. What does the affiliated broker receive?
   1. $5,400
   2. $18,000
   3. $25,714
   4. $12,600
9. A lot has 92 feet of street frontage and is priced at $1,350 per front foot. What is the indicated price?
   1. $121,500
   2. $124,200
   3. $135,000
   4. $148,500
10. A 2,700-square-foot floor contains how many square yards?
    1. 900
    2. 270
    3. 300
    4. 30
11. A $16,500 commission represents 5% of the sale price. What was the sale price?
    1. $330,000
    2. $82,500
    3. $313,500
    4. $346,500
12. A seller closes at $500,000. The hypothetical commission is 4.8%, and the mortgage payoff is $281,000. Ignoring other costs, what remains for the seller?
    1. $194,000
    2. $205,000
    3. $219,000
    4. $195,000
13. Which calculation correctly converts 6 acres to square feet?
    1. 6 ÷ 43,560
    2. 6 × 43,560
    3. 43,560 ÷ 6
    4. 6 × 5,280
14. A property price decreases from $450,000 to $414,000. What is the percentage decrease?
    1. 7%
    2. 9%
    3. 8%
    4. 12%
15. A $24,000 commission is split equally between two brokerages. An affiliated broker receives 65% of one brokerage's share. What does that broker receive?
    1. $7,800
    2. $12,000
    3. $15,600
    4. $8,400
16. Which statement about actual brokerage compensation is most accurate?
    1. State law fixes one commission rate for residential sales.
    2. Every MLS establishes the rate a seller must pay.
    3. Rates become standard when most firms use them.
    4. Compensation is negotiable and should be documented in lawful agreements.
17. An irregular parcel can be separated into a 100-by-150-foot rectangle and a triangle with a 40-foot base and 50-foot perpendicular height. What is the total area?
    1. 16,000 square feet
    2. 15,500 square feet
    3. 17,000 square feet
    4. 20,000 square feet
18. A buyer pays $288,000 for 4 acres. What is the price per acre?
    1. $68,000
    2. $74,000
    3. $72,000
    4. $76,000
19. Why should a student estimate before completing an exact calculation?
    1. It eliminates the need to know the formula.
    2. It identifies unreasonable results caused by unit or decimal errors.
    3. It permits the student to ignore all stated facts.
    4. It makes rounding directions unnecessary.
20. A broker estimates acreage from unverified marketing dimensions. What is the safest practical response?
    1. Guarantee the figure if the arithmetic is correct.
    2. Replace the legal description with the estimate.
    3. Advertise the figure without identifying its source.
    4. Label it as an estimate, identify the source and limitation, and recommend appropriate verification.

Detailed Answer Explanations

1. B. Move the decimal point two places left: 6.25% = 0.0625. Choice A is 62.5%, and choice C is 0.625%.
2. C. Increase = $320,000 × 0.07 = $22,400. New value = $320,000 + $22,400 = $342,400.
3. A. Rectangle area = 125 × 180 = 22,500 square feet. The answer must use square units.
4. D. Triangle area = ½ × 160 × 90 = 7,200 square feet. Choice A omits the one-half factor.
5. B. 130,680 ÷ 43,560 = 3 acres. Divide square feet by 43,560 when converting to acres.
6. C. $415,000 × 0.052 = $21,580. The stated rate is a math assumption, not a standard commission.
7. A. $30,000 × 0.60 = $18,000. The 40% cooperating share would be $12,000.
8. D. $18,000 × 0.70 = $12,600. Apply the internal split to the brokerage's share.
9. B. 92 front feet × $1,350 = $124,200. Depth is not part of this stated pricing method.
10. C. 2,700 ÷ 9 = 300 square yards. One square yard is nine square feet.
11. A. Whole = Part ÷ Rate: $16,500 ÷ 0.05 = $330,000.
12. D. Commission = $500,000 × 0.048 = $24,000. $500,000 − $24,000 − $281,000 = $195,000. Do not subtract charges that the problem does not provide.
13. B. Acres grow to square feet through multiplication: 6 × 43,560 = 261,360 square feet.
14. C. Decrease = $36,000. Rate = $36,000 ÷ $450,000 = 0.08, or 8%.
15. A. One brokerage receives $24,000 ÷ 2 = $12,000. The affiliated broker receives $12,000 × 0.65 = $7,800.
16. D. Compensation is negotiable and belongs in lawful agreements. A government, MLS, association, or pattern of local practice does not create a mandatory standard rate.
17. A. Rectangle = 100 × 150 = 15,000. Triangle = ½ × 40 × 50 = 1,000. Total = 16,000 square feet.
18. C. $288,000 ÷ 4 = $72,000 per acre.
19. B. Estimation exposes misplaced decimals, wrong units, and answers that are too large or small. It does not replace the exact work.
20. D. Accurate arithmetic cannot verify the source dimensions. The broker should label the estimate, disclose its limits, and recommend a survey or other appropriate verification.

Mastery Checklist

• I can convert among fractions, decimals, and percentages.
• I can identify the part, whole, and rate in a word problem.
• I can solve for any missing value using Part = Whole × Rate.
• I can distinguish linear, square, and cubic measure.
• I can calculate rectangle and triangle area.
• I can convert between square feet, square yards, and acres.
• I can calculate front-foot and per-unit pricing.
• I can calculate total commission and follow multiple commission splits in order.
• I can calculate seller proceeds using only the charges stated.
• I can explain why real-world compensation is negotiable rather than standard.
• I can separate national calculations from Indiana compensation rules awaiting verification.
• I can label assumptions and refer uncertain measurements for professional verification.
• I can answer at least 80% of this chapter's assessment and explain the reasoning behind each answer.