**Square Measure**

144 sq inches= 1sq ft

9 sq ft = 1 sq yd

43,560 sq ft = 1 acre

**Cubic Measure**

27 cubic feet = 1 cubic yard

**Tax Valuation**

**X Dollars ***Per $100 *AV = X/1*00 = Tax Rate*

Divide the AV by 100, then multiply by X Dollars

*X Mils** Per $1 *AV

Divide the AV by 1000,

then multiply by X Mils

**Area Formulas**

Formula for rectangles: Area = length x width

Formula for square: Area = side x side

Formula for triangle: Area = base x height x 0.5

**MATHEMATICS Percentages**

To use a percentage in an arithmetic calculation, change the percentage to its decimal equivalent. The rule for changing a percentage to a decimal is to remove the percent sign and move the decimal point two places to the left (or divide the percentage by 100). Examples of converting a percentage to a decimal are:

98% = 0.98 | 1 1/2% = 1.5% = 0.015 |

1.42% = 0.0142 | 1 1/4% = 1.25% = 0.0125 |

0.092% = 0.00092 | 3/4% = 0.75% = 0.0075 |

To change a decimal or a fraction to a percentage, simply reverse the procedure. Move the decimal point two places to the right and add the percent sign (or multiply by 100). Some examples of this operation are:

1.00 = 100% | 1/2 = 1 ÷ 2 = 0.5 = 50% |

0.90 = 90% | 3/8 = 3 ÷ 8 = 0.375 = 37.5% |

0.0075 = 0.75% | 2/3 = 2 ÷ 3 = 0.667 = 66.7% |

**Commission Problems**

Problems involving commissions are readily solved by the Formula: **sales price X rate of commission = total commission**

**Sales**

- A real estate broker sells a property for $90,000. Her rate of commission is 7%. What is the amount of commission in dollars?

**Product Missing = multiply**

**Solution Step 1 – sales price x rate = commission**

Calculation

**$90,000 x 0.07 = $6,300**

**Answer:**$6,300 commission

- A real estate broker earns a commission of $6,000 in the sale of a residential property. His rate of commission is 6%. What is the selling price?

**Factor Missing = Divide**

**Solution Step 1 – sales price = commission dollars divided by commission rate**

Calculation

$6000/.06 = $100,000

**Answer:**$100,000 sales price

- A real estate broker earns a commission of $3,000 in the sale of property for $50,000. What is her rate of commission?

**Factor missing = divide**

**Solution Step 1 – commission dollars divided by sales price = rate of commission**

Calculation

$3,000/50,000 = 6%

**Answer =**6% commission rate

**Rentals**

- A real estate salesperson is the property manager for the owner of a local shopping center. The center has five units, each renting for $24,000 per year. The center has an annual vacancy factor of 4.5%. The commission for rental of the units is 9% of the gross rental income. What is the commission for the year?

**Solution Step 1 — Actual Occupancy Rate = 100% – Vacancy Rate**Calculation – 100% – 4.5 % = 95.5% = Actual Occupancy Rate

**Solution Step 2 — Actual Rent Dollars = Potential Gross Rent x Occupancy Rate**Calculation = $120,000 x 95.5% = $114,600

**Solution Step 3 – Actual Rent x Commission Rate = Commission Dollars**Calculation — $114,600 x 9% = $10,314 = Commission Dollars

**Answer:**$10,314 commission

**Commission Splits**

- A real estate broker sells a property for $65,000. The commission on this sale to the real estate firm with whom the broker is associated is 7%. The broker receives 60% of the total commission paid to the real estate firm. What is the firm’s share of the
__commission in____dollars?__

**Solution Step 1 Selling Price x Commission Rate = Commission Dollars**Calculation – $65,000 x 7% = $4,550

**Solution Step 2 — Total Commission x Firm Share Percentage = Firm Share Dollars**Calculation – $4,550 x 40% = $1,820

**Answer: $1,820**

**Estimating Partial Sales of Land**

- A subdivision contains 400 lots. If a broker has sold 25% of the lots and his sales staff has sold 50% of the remaining lots, how many lots are still unsold?

**Solution Step 1 — Original Number of Lots x Percentage Sold by Broker = Number of Lots ****Remaining**Calculation — 400 x 25% = 100 lots. 400 Lots minus 100 Lots = 300 Lots

**Solution Step 2 — Remaining Lots x % Sold by Sales Force = Number of lots Sold by Agents**Calculation — 300 x 50 % = 150 Lots

**Solution Step 3 Add the number of lots sold**Calculation — 100 + 150 = 250

**Solution Step 4 — Original Number of Lots less the Number of Lots Sold = Number of Lots ****Remaining**Calculation — 400 — 250 = 150

**Answer:**150 lots still unsold

**Profit/Loss on Sale of Real Estate**

The formula for profit is: investment X percent of profit = dollars in profit

The formula for loss is: investment X percent of loss = dollars lost

- Mr. Wong buys a house for investment purposes for $48,000. He sells it six months later for $54,000 with no expenditures for fix-up or repair. What is Mr. Wong’s percentage of profit?

**Solution Step 1 — Sales Price less Original investment = Profit Dollars**Calculation = $54,000 – $48,000 = $6,000

**Solution Second Step — Profit Dollars divided by Original Investment Dollars = % Profit**Calculation = $6,000/$48,000 = 12.5%

**Answer:**12.5% Profit

- Ms. Clary purchases some property in 1987 for $35,000. She makes improvements in 1988 costing her $15,500. In 1990 she sells the property for $46,000. What is her percentage of loss?

**Solution Step 1 — Purchase Price Plus Improvements = Current Investment**Calculation = $35,000 + $15,500 = $50,500

**Solution Step 2 — Investment less Selling Price = Loss**Calculation = $50,500 – $46,000 = $4,500 loss

**Solution Step 3 = Loss divided by Investment = Percent Loss**Calculation = $4,500/$50,500 = 8.91%

**Answer:**8.91%