Real Estate Exam Math Practice Test — with a worked solution for every problem

The complete free guide to real estate exam math

Last reviewed · Written by the Toolskia study team · Independent study material — not affiliated with any real estate commission, school or testing provider.

Ask anyone who has sat a real estate licensing exam what they were most nervous about, and the answer is almost always the same: the math. It is a curious thing, because the arithmetic itself is simple — multiplication, division and a few percentages — and there are only about a dozen formulas to know. Yet math sinks more candidates than any other section. The reason is not difficulty; it is avoidance. People happily reread the chapters on agency and contracts, then quietly skip the math, hoping the handful of questions will not matter. On exam day the panic arrives, the formula will not come, and easy points slip away. This guide and the practice test above are built to remove that fear completely, by turning the math into a small set of patterns you have seen so many times that the right setup is automatic.

The one idea behind almost every problem

If you learn nothing else, learn this: most real estate math is a single relationship wearing different costumes. That relationship is Part = Whole × Rate. A commission is a part of the sale price (the whole) at a commission rate. Interest is a part of a loan at an interest rate. Property tax is a part of a value at a tax rate. Appreciation is a part of an original price at a growth rate. Once you see that these are the same problem, you only have to remember how to rearrange three values. If you know the whole and the rate, multiply to get the part. If you know the part and the rate, divide the part by the rate to get the whole. If you know the part and the whole, divide the part by the whole to get the rate. Teachers often draw this as a "T" with the part on top and the whole and rate underneath; cover the value you want and the T shows you whether to multiply or divide. Every percentage question on the exam yields to this one tool.

Commission and brokerage splits

Commission is the most common math on the exam and the easiest points once you have the pattern. The total commission is simply the sale price times the commission rate: a $420,000 home at 6% earns $420,000 × 0.06 = $25,200. The twist examiners love is the split. A total commission is usually shared between the listing brokerage and the selling brokerage, and each brokerage then shares with its own agent. The rule is to apply each split in order. Suppose a $360,000 sale carries a 5% commission, the two brokerages split it 50/50, and the selling brokerage gives its agent 60%. First the total: $360,000 × 0.05 = $18,000. Then the brokerage's half: $9,000. Then the agent's 60% of that half: $9,000 × 0.60 = $5,400. The classic trap answer is $9,000 — the brokerage's share before the agent's split. Read the question to see exactly whose money you are being asked for. To run the formula backwards, divide: a broker who received $14,250 at a 4.75% rate sold a property worth $14,250 ÷ 0.0475 = $300,000.

Proration at closing

Proration is the topic that produces the most careless errors, because it has two small decisions hidden inside it. The idea is fair: a yearly expense such as property tax or homeowners-association dues is divided between buyer and seller according to how many days each one owns the property during the period. The method never changes — find the daily rate by dividing the annual amount by the number of days in the year, then multiply by the days that party is responsible for. The first decision is which day count to use: a 360-day "banker's" year of twelve 30-day months, or the actual 365-day calendar year. The question will tell you; use what it says. The second decision is whether the item was prepaid (the seller already paid the whole year, so the buyer reimburses the seller for the days after closing) or paid in arrears (not yet paid, so the seller owes the buyer for the days before closing). Take annual taxes of $2,400 paid in arrears, a 360-day year, and a closing 90 days into the year. The daily rate is $2,400 ÷ 360 = $6.6667, and the seller's 90 days give a $600 charge to the seller. Slow down on the prepaid-versus-arrears wording and proration becomes free points instead of lost ones.

Area, lot size and land measurement

Area questions reward two memorised facts. The first is that one acre is 43,560 square feet; the second is that a section of land is one square mile and contains 640 acres. With those, the rest is rectangles. A lot 150 feet by 200 feet covers 30,000 square feet, which is 30,000 ÷ 43,560 = 0.69 acre. To value land sold by the square foot, convert acres first: a 2-acre parcel is 2 × 43,560 = 87,120 square feet, so at $8 per square foot it is worth $696,960. Interior problems work the same way — a room 12 feet by 15 feet is 180 square feet, so carpet at $4.50 a foot costs $810. Land-description math uses the section: a quarter-section is 640 ÷ 4 = 160 acres, and a quarter of that quarter (a "quarter-quarter") is 40 acres. Draw the rectangle, label the sides, and never multiply before you have converted every measurement to the same units.

Loans, points and interest

Finance questions look intimidating and are usually the simplest of all. Loan-to-value (LTV) is the loan as a percentage of value, so a $250,000 home at 80% LTV carries a $200,000 loan, leaving a $50,000 down payment. A discount point is always 1% of the loan amount — never the sale price — so two points on a $180,000 loan cost 2% × $180,000 = $3,600. Simple interest for a period is the balance times the annual rate, then divided down to the period you need: a $240,000 loan at 6.5% generates $15,600 of interest a year, which is $1,300 in a single month. An interest-only monthly payment is just that monthly interest: $150,000 at 7% is $10,500 a year, or $875 a month. The recurring mistakes are taking points on the price instead of the loan, and forgetting to divide an annual interest figure by twelve.

Investment maths: GRM and cap rate

Two measures let buyers compare income property. The gross rent multiplier (GRM) is price divided by gross annual rent, written as a plain number. A property renting for $2,000 a month earns $24,000 a year, so a $336,000 price gives a GRM of 14. Watch the units — dividing by the monthly rent by mistake gives 168. The capitalisation rate is more complete because it uses net operating income (rent after operating expenses) and is written as a percentage: cap rate = NOI ÷ value. A property with $36,000 of NOI and a $450,000 value has an 8% cap rate. The same formula values a property when you rearrange it: at an 8% cap rate, an income of $48,000 implies a value of $48,000 ÷ 0.08 = $600,000. Cap rate up means price down for the same income, and vice versa — a relationship examiners like to test in words.

Appreciation, depreciation and the seller's net

Appreciation adds a percentage to a starting value, and the fastest method is to multiply by one plus the rate: a $300,000 home that appreciates 15% is worth $300,000 × 1.15 = $345,000. To work backwards from a grown value, divide: if a home sold for $364,000 after appreciating 4%, the original was $364,000 ÷ 1.04 = $350,000 — not $364,000 minus 4%, because the percentage was based on the smaller original. Straight-line depreciation spreads a cost evenly: a $500,000 building over a 25-year life depreciates $20,000 a year. The most famous trap of all is the seller's net. A seller who wants to keep $200,000 after a 6% commission does not simply add 6%, because the commission is charged on the final price, not the net. The price is the net divided by one minus the rate: $200,000 ÷ 0.94 = $212,765.96. The tempting wrong answer, $212,000, comes from adding 6% to the net and is the single most common slip on the whole exam.

Property tax and mill rates

Property tax math hinges on understanding a mill. A mill is one-thousandth of a dollar, so one mill is $1 of tax per $1,000 of taxable value, or 0.001 as a decimal. A rate of 25 mills is therefore 0.025, and on an assessed value of $180,000 the tax is $180,000 × 0.025 = $4,500. Run it backwards to find a value: a $3,300 tax bill at 22 mills (0.022) implies an assessed value of $3,300 ÷ 0.022 = $150,000. Some questions add an assessment ratio — the taxable value is only a fraction of market value. Apply that first: a $400,000 home assessed at 40% has a $160,000 taxable value, and at 30 mills the tax is $160,000 × 0.030 = $4,800. The trick is simply to convert mills to a decimal correctly; once the rate is 0.0xx the rest is multiplication. Transfer taxes follow a related "per increment" pattern: at $0.75 per $500 of price, a $350,000 sale has 700 increments and a $525 transfer tax.

How to use the practice test on this page

1. Begin in Practice mode. It reveals the correct answer and the full worked solution the instant you choose, so you learn the setup for every problem type. Read the working even when you were right — it often shows a faster route.
2. Pick how many questions — a quick 10, a representative 15-question math section, or all of the problems in one sitting to drill the whole bank.
3. Answer by tapping or with the keyboard. Tap an option on a phone, or press A, B, C or D on a computer, use the left and right arrows to move, and press F to bookmark a tricky one.
4. Switch to Mock mode when a type feels familiar. It hides the solution and runs a timer at about 90 seconds per question, training the speed you need to finish multi-step problems on the real exam.
5. Use the smart review tools. On the results screen, check your readiness meter and topic breakdown, then tap "Review incorrect only" to redo just your misses, "Retry weak topic" to drill your lowest family, or "Retry bookmarked" to revisit flagged problems.

The daily 5-question challenge — your three-minute habit

Cramming the night before is the worst way to learn real estate math; spaced, repeated practice is the best. That is why this page has a daily 5-question challenge at the top. Each day the tool automatically selects five problems — the same five for everyone that day, a fresh set the next — so you can build a streak with a short, low-effort session that takes about three minutes. The point is not the five questions themselves but the habit: returning every day keeps the dozen formulas active in memory so they are instantly available on exam day, rather than something you half-remember under pressure. Your challenge streak is counted separately from your overall practice streak and, like everything here, lives only in your own browser. Miss a day and the streak resets to one, which is the gentle nudge that turns five minutes of daily drilling into a genuinely prepared candidate. Do the daily five, then spend ten more minutes on whichever topic the breakdown marks as your weakest, and your readiness meter will climb steadily week over week.

A deep bank built for repetition without memorising

This test now draws on a bank of 37 original problems spread across all six formula families, which matters more than it sounds. A small bank trains recall of specific answers; a deeper one trains the method, because you keep meeting the same formula dressed in different numbers and contexts — a commission split one run, a seller's-net problem the next, a proration in a 360-day year and then a 365-day year. That is exactly the skill the real exam tests, where every figure is new. Mixing the quick ten, the full fifteen-question math section, the extended twenty and the complete all-problems set, together with the shuffle on every run, means you almost never see the same sequence twice. Drill until you are reaching for the right setup automatically, and the worked solution after each answer turns every miss into a lesson rather than a guess.

A quick formula cheat-sheet

A short, calm study plan

• Day 1 — Percentages and commission. Master Part = Whole × Rate, then run commission and split problems in Practice mode until every step is automatic.
• Day 2 — Proration and tax. Drill the daily-rate method and the prepaid-versus-arrears decision, then mill rates and assessment ratios.
• Day 3 — Area and finance. Memorise 43,560 and 640, then practise LTV, points, interest, GRM and cap rate.
• Day 4 — Appreciation and the seller's net. Focus on the net-price trap until you reach for "divide by (1 − rate)" instinctively.
• Day 5 — Timed mocks. Switch to Mock mode and run full timed sets until your score sits comfortably above 70% and the readiness meter is green.

Common mistakes to avoid

Why these problems are free and original

All real estate math rests on the same public, standard formulas — the relationship between price, rate and commission, the definition of an acre, the way a mill works. None of that is anyone's private property; it is the shared language of the profession. What we have done is write our own original problems and our own plain-English worked solutions on top of those public formulas. We do not copy any test provider's confidential question bank, and we do not need to: practising fresh problems on the same formulas teaches the method far better than memorising leaked questions, and it keeps everything fully legal. The tool, the explanations and this guide are our own work; we are an independent study resource with no connection to any commission, school or testing company.

Authoritative sources to confirm everything

This guide and tool are for study only. Real estate rules, tax practices and rounding conventions vary by state, so always confirm specifics with official sources:

• Your state's real estate commission — the exam content outline, the official pass mark and any state-specific rules.
• Your approved pre-licensing school — the math conventions (such as 360 vs 365 day counts) your course and exam use.
• Your county assessor — how assessment ratios and mill rates are applied where you live.

Frequently asked questions

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