*This is the second of three episodes in our new real estate mathematics series. Here, we apply percentages and fractions to California real estate principles. *

*The prior episode covers land measurements and provides actionable guidance to aspiring agents and brokers preparing for the State Exam. *

## Percentages

A **percentage** needs to be converted to a decimal before any mathematical computations can be completed. This is a conversion financial calculators are preprogrammed to make.

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

Alternatively, 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%

## Fractions converted

As the use of a calculator is allowed while taking the DRE state licensing exam, it is beneficial to convert all fractions to decimals and then use the calculator to complete the computations.

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 (the number on top) by the denominator (the number on the bottom).

**Examples:**

4/5 = 0.8

1/2 = 0.5

3/4 = 0.75

3/100 = 0.03

667/100 = 6.67

## Basic formulas for area

The formula for an **area** of a rectangle is most often used in *land measurement*. The area of a rectangle equals *length* multiplied by *width*, the result being the number of square feet within the parcel.

**A = L x W**

Another critical formula is the area of a **triangle**. This formula is used when determining the area of a *triangular* shaped lot.

The area of a triangle equals its base multiplied by its height divided by two.

**A = (B x H) / 2 **

## Percentage formula

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** on a transaction.

As compensation for services, 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. On the state licensing exam, usually two of the three variables will be known, leaving the third to be determined.

Understanding the basic formula makes solving problems a question of mechanics.

The percentage formula is as follows:

**Fee = Percent (%) x Principal**

Percent (%) = the rate charged.

Principal (P) = the dollar amount of the price, loan or rents.

Given the basic formula and two of the three variables, solutions are determined as follows:

- To determine the
*fee*, multiply the principal by the rate (**P x %**). - To determine the
*rate*, divide the fee by the principal (**Fee / P**). - To determine the
*principal*, divide the fee by the rate (**Fee / %**).

*Editor’s note – Stay tuned. A new episode of this series will release each week.*