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Real estate math practice, with the working shown.

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Reviewed September 7, 2026 by the Pass Texas editorial team. Original teaching questions for Texas exam candidates, not official or recalled exam items.

How should you approach a real estate math question?

Write down the quantity the question asks for. Choose the formula, identify the base and units, then calculate without rounding early. Use the rates and day-count assumptions supplied in the problem. Finally, check whether the size and direction of the answer make sense. The worked examples below follow that sequence.

Choose a topic. Work it out. Check the steps.

Use scratch paper and a calculator if helpful. There is no timer. Pick an answer before checking it, or reveal the steps without earning a point.

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One question from each topic, with the topic name hidden until you check. Work out which formula fits before calculating.

Question 1 of 110 checked

In a simplified tax problem, one taxing unit uses a $310,000 value before exemptions and a stated $140,000 exemption. No other value limit applies. At $2.20 per $100 of taxable value, what annual tax does this unit levy?

Choose one answer$3,740$1,700$4,400$6,820

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The formulas behind the questions.

Start here if you need the setup. Follow a topic link to its worked answers, or use the matching calculator to try your own numbers.

Eleven study topics, not eleven official exam sections
Topic	Formula cue	Practice tool
Property tax	Taxable value ÷ 100 × rate per $100	Property tax calculator
Proration	Period amount ÷ period days × ownership days	Proration calculator
Commission split	Sale price × commission rate × side split × agent split − fees	Commission split calculator
LTV and down payment	Loan amount ÷ applicable property value × 100	LTV and down payment calculator
Mortgage ratios	Monthly obligations ÷ gross monthly income × 100	Mortgage ratios calculator
Cap rate and NOI	Cap rate (decimal) = annual NOI ÷ value; value = annual NOI ÷ cap rate	Cap rate and NOI calculator
GRM	Value = gross rent × GRM	GRM calculator
Area and acreage	1 acre = 43,560 sq ft; 1 section = 640 acres	Area and acreage calculator
Comparable adjustment	Comparable sale price ± feature adjustments	Comparable adjustment calculator
Seller net	Sale price − payoff − commission − seller costs − credits	Seller net calculator
Equity	Current market value − debt secured by the property	Equity calculator

For the printable reference, use the real estate math formula cheat sheet. For additional problem types, explore all real estate calculators.

All 33 questions and worked solutions.

Open one topic at a time. These examples use supplied values, not current market prices, a real tax estimate, or a lending decision.

Property tax: 3 worked questions

Property tax

Use the taxable value for the taxing unit in the problem. If you must calculate it, apply the stated exemptions and any value limits first.

1. In a simplified tax problem, one taxing unit uses a $310,000 value before exemptions and a stated $140,000 exemption. No other value limit applies. At $2.20 per $100 of taxable value, what annual tax does this unit levy?

Answer: $3,740

First move: Subtract the stated exemption before touching the tax rate.

Taxable value ÷ 100 × rate per $100

Work: ($310,000 − $140,000) ÷ 100 × $2.20 = 1,700 × $2.20 = $3,740

The taxable value is $170,000. Applying this unit's stated rate gives $3,740. These are supplied study assumptions, not a claim that every Texas taxing unit allows this exemption or charges this rate.

Watch for: Applying the rate to the full appraised value produces the $6,820 distractor.

2. A property has a taxable value of $264,000. The combined tax rate is $2.05 per $100 of value. What is the annual property tax?

Answer: $5,412

First move: Convert the taxable value into $100 units.

Taxable value ÷ 100 × rate per $100

Work: $264,000 ÷ 100 × $2.05 = 2,640 × $2.05 = $5,412

The stated rate applies once to each $100 of taxable value.

Watch for: The taxable value has already been supplied. Do not subtract an exemption again or forget the per-$100 conversion.

3. For one taxing unit, a classroom problem supplies a $420,000 value before exemptions, a $140,000 exemption, and no other value limit. Its rate is $1.85 per $100 of taxable value. What is the annual tax for that unit?

Answer: $5,180

First move: Build the $280,000 taxable base first.

(Supplied value before exemptions − applicable exemption) ÷ 100 × rate

Work: ($420,000 − $140,000) ÷ 100 × $1.85 = 2,800 × $1.85 = $5,180

Exemptions reduce the taxable base. They are not subtracted from the final tax bill.

Watch for: Subtracting $140,000 after calculating tax has no mathematical or tax meaning.

Use the property tax calculator Topic source: Texas Comptroller property-tax guidance

Proration: 3 worked questions

Proration

Identify the period, day-count method, ownership days, and debit-credit direction before calculating.

1. Unpaid annual property taxes are $4,380, which the buyer will pay after closing. Closing is September 12, 2026, and the seller owns closing day. Use actual calendar days and a 365-day year. What credit does the buyer receive for the seller's share?

Answer: $3,060

First move: Count seller ownership through September 12 because the seller owns closing day.

Annual amount ÷ 365 × seller days

Work: $4,380 ÷ 365 = $12 per day; 255 seller days × $12 = $3,060

January through August contributes 243 days, and September 1 through 12 adds 12, for 255 seller days.

Watch for: Stopping at September 11 removes one day and creates a close distractor.

2. Annual property taxes are $3,600. Closing is April 15, 2026, and the buyer owns closing day. Using actual calendar days and a 365-day year, what is the seller's tax share, rounded to cents?

Answer: $1,025.75

First move: Count only January 1 through April 14 for the seller.

Annual amount ÷ 365 × seller days

Work: $3,600 ÷ 365 × 104 days = $1,025.75

The seller owns 104 days. Keep the daily rate unrounded until the final answer.

Watch for: Including April 15 gives the seller a day the problem assigns to the buyer.

3. Annual taxes are $7,200. Closing is June 18 and the seller owns closing day. Use a 30/360 method: each month has 30 days and the year has 360. What is the seller's share?

Answer: $3,360

First move: Use the 30-day months and 360-day year expressly stated in the problem.

Annual amount ÷ 360 × seller days

Work: $7,200 ÷ 360 = $20 per day; (5 × 30 + 18) × $20 = 168 × $20 = $3,360

A banker's year treats each full month as 30 days for this classroom setup.

Watch for: A 360-day denominator alone does not tell you the numerator's day-count method. This question explicitly requires 30-day months, not actual calendar days.

Use the proration calculator Topic source: Pearson VUE Texas Real Estate Content Outlines

Commission split: 3 worked questions

Commission split

Move through the money in order: total commission, brokerage side, agent split, then stated fees.

1. A home sells for $390,000 with an agreed 6% total commission. The listing side receives half. The sales agent gets 70% of that side and pays a $295 transaction fee. What does the agent keep before taxes?

Answer: $7,895

First move: Calculate the total commission before applying either split.

Sale price × rate × side split × agent split − fee

Work: $390,000 × 6% = $23,400; × 50% = $11,700; × 70% = $8,190; − $295 = $7,895

Each percentage applies to the amount produced by the prior step. The rate and splits are supplied assumptions, not standard or required commission terms.

Watch for: Stopping at total commission, brokerage-side commission, or pre-fee agent share matches three different distractors.

2. A $525,000 sale has an agreed 5% total commission. The buyer brokerage receives 40% of the total, and the sales agent receives 75% of that brokerage share. What is the agent's gross commission?

Answer: $7,875

First move: Respect the stated 40% side split instead of assuming 50/50.

Sale price × total rate × brokerage share × agent share

Work: $525,000 × 5% × 40% × 75% = $7,875

The problem gives two separate splits after total commission.

Watch for: A brokerage split is not automatically equal. Use the percentage supplied in the question.

3. A brokerage side earns $9,000. The agent receives 65% of that side, then keeps 80% after a team split. What amount reaches the agent before taxes?

Answer: $4,680

First move: Apply the broker split, then the team split, to the shrinking balance.

Brokerage-side commission × agent split × retained team share

Work: $9,000 × 65% × 80% = $4,680

The agent first receives $5,850 from the brokerage split and then retains 80% of that amount.

Watch for: Adding 65% and 80% or applying both percentages to the original sale price is incorrect.

Use the commission split calculator Topic source: Pearson VUE Texas Real Estate Content Outlines

LTV and down payment: 3 worked questions

LTV and down payment

Divide the loan by the property value the problem specifies. These purchase examples expressly use the lower of price or appraisal.

1. A buyer pays $365,000 for a property appraised at $350,000 and borrows $280,000. For this problem, use the lower of price or appraisal as the LTV base. What is the LTV?

Answer: 80%

First move: Use the $350,000 appraisal because it is lower than the price.

Loan amount ÷ applicable property value × 100

Work: $280,000 ÷ $350,000 × 100 = 80%

The question tells you to use the lower of price or appraisal. Dividing by that $350,000 base gives an 80% LTV.

Watch for: Dividing by the $365,000 sale price produces the 76.7% distractor.

2. A property sells for $320,000 and appraises for $335,000. The stated loan limit is 85% of the lower of price or appraisal. What is the maximum loan amount under that limit?

Answer: $272,000

First move: Choose the lower $320,000 purchase price as the base.

Applicable property value × LTV rate

Work: $320,000 × 85% = $272,000

An 85% loan on the lower value leaves $48,000 between price and loan before closing costs.

Watch for: Using the higher appraisal produces $284,750 and overstates the loan in this purchase setup.

3. A borrower requests a $247,500 loan on a property valued at $330,000. What is the LTV?

Answer: 75%

First move: Put the loan in the numerator and the property value in the denominator.

Loan amount ÷ property value × 100

Work: $247,500 ÷ $330,000 × 100 = 75%

LTV measures the financed amount as a share of property value.

Watch for: Reversing numerator and denominator produces a value over 100%.

Use the ltv and down payment calculator Topic source: Consumer Financial Protection Bureau, loan-to-value ratio

Mortgage ratios: 3 worked questions

Mortgage ratios

Use gross monthly income. Housing ratio uses housing expense, while total DTI adds the recurring debts stated in the problem.

1. A buyer has $9,200 gross monthly income, $2,576 in monthly principal, interest, taxes, and insurance (PITI), and $625 in other recurring monthly debt. No other obligations apply. What is the total DTI, rounded to one decimal place?

Answer: 34.8%

First move: Add housing and other recurring debt before dividing by gross income.

Total monthly obligations ÷ gross monthly income × 100

Work: ($2,576 + $625) ÷ $9,200 × 100 = 34.8%

Total DTI includes the stated housing payment and other recurring monthly obligations.

Watch for: Using housing alone gives 28%, which is the housing ratio, not total DTI.

2. A buyer earns $8,500 in gross monthly income and has a proposed $2,210 monthly housing expense. What is the housing expense ratio?

Answer: 26%

First move: Use housing expense only because the question asks for the housing ratio.

Monthly housing expense ÷ gross monthly income × 100

Work: $2,210 ÷ $8,500 × 100 = 26%

The denominator is gross income before taxes and deductions.

Watch for: Do not use take-home pay or add debts that the question did not ask you to include.

3. A classroom problem gives 28% housing and 36% total-DTI limits. Gross monthly income is $10,000 and other monthly debt is $1,000. What maximum housing payment satisfies both limits?

Answer: $2,600

First move: Calculate both limits and use the lower housing result.

Lower of housing limit or total-DTI room after other debt

Work: $10,000 × 28% = $2,800; $10,000 × 36% − $1,000 = $2,600; use $2,600

Both stated limits must hold. The total-DTI calculation is the tighter constraint here.

Watch for: The 28/36 figures are supplied classroom assumptions, not universal approval limits for every lender or loan product.

Use the mortgage ratios calculator Topic source: Consumer Financial Protection Bureau, debt-to-income ratio

Cap rate and NOI: 3 worked questions

Cap rate and NOI

Build NOI from property income and operating expenses, then keep financing and owner income taxes outside NOI.

1. An income property has $96,000 annual net operating income (NOI). Using the stated 8% capitalization rate, what is the indicated value?

Answer: $1,200,000

First move: Solve the income triangle for value by dividing NOI by the rate.

Value = NOI ÷ cap rate

Work: $96,000 ÷ 0.08 = $1,200,000

The cap rate must be written as a decimal before division.

Watch for: Multiplying NOI by 8% produces $7,680, which is not a property value.

2. A property's annual figures are $120,000 potential rent, 5% vacancy and collection loss on that rent, $4,000 other income, and $46,000 total operating expenses. What is its annual NOI?

Answer: $72,000

First move: Build effective gross income before subtracting operating expenses.

Potential income − vacancy loss + other income − operating expenses

Work: $120,000 − $6,000 + $4,000 − $46,000 = $72,000

Five percent vacancy on $120,000 is $6,000. Debt service and depreciation are not part of this NOI calculation.

Watch for: Subtract vacancy before adding the other income. Do not deduct debt service or depreciation as operating expenses when calculating NOI.

3. An investment property is valued at $750,000 and produces $67,500 annual NOI. What is the cap rate?

Answer: 9%

First move: Put NOI over value.

Cap rate = NOI ÷ value × 100

Work: $67,500 ÷ $750,000 × 100 = 9%

Cap rate expresses annual NOI as a percentage of value.

Watch for: Reversing value and NOI produces 11.1 before percentage interpretation and is the wrong relationship.

Use the cap rate and noi calculator Topic source: Pearson VUE Texas Real Estate Content Outlines

GRM: 3 worked questions

GRM

Match the rent period to the multiplier. Monthly rent needs monthly GRM, and annual rent needs annual GRM.

1. A rental property's gross rent is $2,500 per month. Comparable annual GRM is 11. What is the estimated value?

Answer: $330,000

First move: Convert monthly rent to annual rent because the multiplier is annual.

Annual gross rent × annual GRM

Work: $2,500 × 12 × 11 = $330,000

Annual rent is $30,000, and $30,000 multiplied by 11 produces $330,000.

Watch for: Multiplying the monthly rent directly by an annual GRM produces $27,500.

2. A comparable monthly GRM is 140 and the subject's monthly gross rent is $2,400. What value is indicated?

Answer: $336,000

First move: Keep the rent monthly because the GRM is monthly.

Monthly gross rent × monthly GRM

Work: $2,400 × 140 = $336,000

The rent period and multiplier period already match, so no annual conversion is needed.

Watch for: Multiplying by 12 again mixes periods and overstates value.

3. A comparable property sold for $480,000 and rents for $3,200 per month. What is its monthly GRM?

Answer: 150

First move: Divide sale price by monthly gross rent.

Monthly GRM = sale price ÷ monthly gross rent

Work: $480,000 ÷ $3,200 = 150

GRM is a multiplier, not a percentage, so the answer is 150 without a percent sign.

Watch for: Converting rent to annual before using a monthly GRM formula produces 12.5, a different-period measure.

Use the grm calculator Topic source: Pearson VUE Texas Real Estate Content Outlines

Area and acreage: 3 worked questions

Area and acreage

Name the shape or land fraction, find square feet or section acreage, then convert only once.

1. A rectangular parcel measures 220 feet by 198 feet. How many acres is the parcel?

Answer: 1 acre

First move: Find rectangle area in square feet, then divide by 43,560.

Length × width ÷ 43,560

Work: 220 × 198 = 43,560 sq ft; 43,560 ÷ 43,560 = 1 acre

Pearson identifies 43,560 square feet per acre as a figure candidates should memorize.

Watch for: Convert square feet to acres after finding the area. Dividing just one side length by 43,560 does not convert the parcel's area.

2. A triangular tract has a 300-foot base and a perpendicular height of 180 feet. Approximately how many acres does it contain?

Answer: 0.62 acres

First move: Use one-half base times perpendicular height.

Base × height ÷ 2 ÷ 43,560

Work: 300 × 180 ÷ 2 = 27,000 sq ft; 27,000 ÷ 43,560 = 0.62 acres

A triangle is half the rectangle created by the same base and perpendicular height.

Watch for: Using base times height without dividing by two produces the 1.24-acre distractor.

3. In the standard government survey model, how many acres are in the NE 1/4 of the SW 1/4 of one section?

Answer: 40 acres

First move: Multiply the nested fractions, then apply them to 640 acres.

1/4 × 1/4 × 640 acres

Work: 1/16 × 640 = 40 acres

A quarter-quarter section is one-sixteenth of a standard 640-acre section. This is the national government-survey model, not a claim that Texas land generally uses that survey system.

Watch for: Adding the fractions or stopping after the first quarter produces an oversized tract.

Use the area and acreage calculator Topic source: Pearson VUE Texas Real Estate Content Outlines

Comparable adjustment: 3 worked questions

Comparable adjustment

Adjust the comparable toward the subject: add when the comparable is inferior and subtract when it is superior.

1. A comparable sold for $410,000. The comp lacks a garage that the subject has, worth $18,000. The comp has a newer roof than the subject, worth $7,000. What is the adjusted comp value?

Answer: $421,000

First move: Adjust the comparable, adding for its missing garage and subtracting for its superior roof.

Comparable price + inferior features − superior features

Work: $410,000 + $18,000 − $7,000 = $421,000

The adjustments move the comparable toward the subject's feature set.

Watch for: Reversing both signs produces $399,000.

2. A comparable sold for $350,000. It has a pool the subject lacks, worth $25,000, but its kitchen is inferior to the subject's by $15,000. What is the adjusted comp value?

Answer: $340,000

First move: Subtract for the comp's superior pool, then add for its inferior kitchen.

Comparable price − superior feature + inferior feature

Work: $350,000 − $25,000 + $15,000 = $340,000

Each sign comes from the comparable's relationship to the subject, not from whether the feature sounds desirable.

Watch for: A pool is not always an addition. It is subtracted here because only the comparable has it.

3. A comparable sold for $500,000. It is 200 square feet smaller than the subject. Use a supplied market-supported adjustment of $150 per square foot and subtract $20,000 for its superior view. What is the adjusted comp value?

Answer: $510,000

First move: Turn the size difference into dollars before combining adjustments.

Comparable price + size deficiency − superior feature

Work: $500,000 + (200 × $150) − $20,000 = $510,000

The comp is inferior in size by $30,000 and superior in view by $20,000.

Watch for: Adjusting the subject or applying both adjustments in the same direction misses the comparison logic.

Use the comparable adjustment calculator Topic source: Pearson VUE Texas Real Estate Content Outlines

Seller net: 3 worked questions

Seller net

Separate equity from proceeds. Seller net subtracts the payoff and every stated seller cost from the sale price.

1. A seller closes at $425,000 with a $298,000 loan payoff, 6% commission, and $3,200 in other seller costs. What is the seller net?

Answer: $98,300

First move: Calculate commission, then subtract every seller-side outflow once.

Sale price − payoff − commission − other seller costs

Work: $425,000 − $298,000 − $25,500 − $3,200 = $98,300

The result is the cash remaining after all charges supplied in this problem. It is not an estimate of every possible cost in a real closing.

Watch for: Equity is not seller net because selling costs still reduce proceeds.

2. A seller wants $200,000 after a $150,000 payoff, $5,000 in fixed seller costs, and a 6% commission. Approximately what sale price is required?

Answer: $377,660

First move: Put percentage costs on the sale-price side of the equation.

Required price = (desired net + payoff + fixed costs) ÷ (1 − commission rate)

Work: ($200,000 + $150,000 + $5,000) ÷ 0.94 = $377,659.57, or about $377,660

The commission depends on the unknown sale price, so simply adding 6% to the required cash understates the price.

Watch for: Adding $355,000 and 6% produces $376,300, but 6% of that new price is larger than the amount added.

3. A home sells for $600,000. Seller charges are a $390,000 payoff, 5.5% commission, $8,500 other costs, and a $7,500 buyer credit. What is the seller net?

Answer: $161,000

First move: Treat the buyer credit as another reduction to seller proceeds.

Sale price − payoff − commission − costs − seller credit

Work: $600,000 − $390,000 − $33,000 − $8,500 − $7,500 = $161,000

Every listed seller obligation reduces the cash remaining at closing.

Watch for: Leaving out the buyer credit produces the $168,500 distractor.

Use the seller net calculator Topic source: Pearson VUE Texas Real Estate Content Outlines

Equity: 3 worked questions

Equity

Equity is the value left after debt. It is not automatically the same as profit or cash at closing.

1. A property is worth $470,000 and the remaining mortgage balance is $318,000. What is the owner's equity before selling costs?

Answer: $152,000

First move: Subtract secured debt from current market value.

Current value − mortgage balance

Work: $470,000 − $318,000 = $152,000

Equity is the ownership value left after the debt balance.

Watch for: Selling costs affect net proceeds, not this basic equity calculation.

2. A property was bought for $360,000, is now worth $450,000, and has a $300,000 loan balance. What is the current equity?

Answer: $150,000

First move: Use current value and current debt. The old purchase price answers a different question.

Current market value − current debt

Work: $450,000 − $300,000 = $150,000

The $90,000 increase from purchase price is appreciation, not total equity.

Watch for: Confusing appreciation with equity ignores the owner's original and repaid principal position.

3. A property that once was worth $400,000 is now worth $360,000. The remaining loan balance is $275,000. What is the current equity?

Answer: $85,000

First move: Use today's value, not the prior value or the amount of depreciation.

Current market value − current debt

Work: $360,000 − $275,000 = $85,000

The $40,000 value decline and the $85,000 current equity are separate measures.

Watch for: A decline in value reduces equity but does not replace the equity formula.

Use the equity calculator Topic source: Pearson VUE Texas Real Estate Content Outlines

What this drill covers, and what it does not.

The Pearson VUE national salespersons outline assigns seven scored items to Real Estate Math Calculations. Related numerical concepts also appear in valuation and financing. Our 11 topics are a teaching arrangement, not the official exam's section names or weighting.

This bank gives you repeated practice with common setups. It does not cover every math skill: interest, discount points, amortization, investment returns, and property-management calculations need further practice. Use the free real estate math questions and full formula guide alongside it.

National principles, Texas context

Area, valuation, equity, ratios, and proration are general real estate math. Tax examples use expressly supplied assumptions. The government-survey question uses a standard section model, not a claim about how all Texas parcels are described.

Read the assumptions

Rates and commission splits are supplied study figures, not required terms. Tax exemptions depend on the taxing unit and property. Loan limits vary by product and lender. Use the numbers and method specified in each question.

Use the right units

Match annual NOI to an annual cap rate and monthly rent to a monthly multiplier. For proration, check the year basis and who owns closing day. Keep intermediate calculations precise, then round the final result as instructed.

Turn one tricky setup into something you understand.

If you missed a question, rebuild it with the calculator before trying a new one. If the setup now feels clear, move on to more free math questions or the timed practice exam.

Before your next drill.

Are all 33 questions free?

Yes. All questions, explanations, calculators linked here, and the formula reference can be used without an account. The web and mobile study app offers selected free content and an optional full-access purchase.

Does a perfect score mean I am ready for the exam?

No. Three questions on a topic or one question per topic cannot establish mastery or predict a pass. A repeat uses the same 33-question bank, even when the order changes. Check your understanding with unfamiliar questions and review non-math topics too.

Does the mixed drill generate unlimited new questions?

No. It selects one question from each of the 11 topics. Rotating the set changes the selection and order within the same bank. A focused drill always uses the same three questions for that topic, with their order and answer positions rotated on retry.

Can I save this score to my account?

Not from this drill. Its completed best score stays in this browser when storage is available; clearing browser data removes it. To carry a website test result into an account, use the separate practice exam and its save-result option. Practice completed inside the study app is separate.

Should I use a calculator while practicing?

You can use one here, but write the setup first so the calculator does not hide a wrong base or unit. Pearson's outline says to memorize 43,560 square feet per acre and 5,280 feet per mile. For test-day device rules, check the Texas exam calculator guide.

Sources and calculation checks.

Reviewed September 7, 2026. Pearson's outline establishes topic coverage and exam conventions. CFPB explains LTV and DTI; the Texas Comptroller provides property-tax context. The scenarios and worked calculations are our teaching examples, not questions supplied or endorsed by these organizations.

All 33 correct choices were independently recalculated and covered by automated checks. These exercises are educational, not tax, lending, appraisal, or legal advice for a transaction.