## Basic Algebra

Now here's the part that you've all been waiting for. Let's get into some math formulas and calculations! I tried to include the more serious math sections as far back in the book as I could to "break it to you gently". **When you read the Cash Equivalency Example #3 you'll see how all the following math sections relate to an actual appraisal report. **So don't get bored and put this book on the shelf to collect dust. Instead of looking at the math with a negative attitude, try to be like Dorothy from the Wizard of Oz and keep repeating to yourself over and over:

*"There's no place like math class. There's no place like math class. There's no place like math class."*If you do it with your eyes closed while you click your heels, then you might start to believe what you're saying! Just use your computer to handle most of the math calculations which takes the tedious work out of the process. I will round out the numbers when there are more than two decimal places. So please don't worry if you get answers with more than two decimal places and they don't appear to

*exactly*match the numbers in the book.

We'll start off with some simple algebra. In algebra you always multiply and divide before you do any other calculations in a formula, unless there are parentheses around part of the formula. Anything inside the parenthesis is always calculated first. To solve the equation 5/7 + 6/11 you have to first make the *denominator* (lower figure) equal for both sets of numbers. You do this by multiplying each number by the opposite number's denominator. For example, the *numerator* (top figure) and the denominator in 5/7 would be multiplied by 11 to give you:

5/7 x 11 = 55/77

The numerator and the denominator in 6/11 would then be multiplied by 7:

6/11 x 7 = 42/77

This leaves us with:

55/77 + 42/77 = 97/77

The *reciprocal* of a number is that number turned upside down. For example:

- The reciprocal of X = 1/X
- The reciprocal of 4 = 1/4
- The reciprocal of 6/11 = 11/6

The *complement* of a number is 1 minus that number. For example:

- The complement of X = 1 - X
- The complement of 4 = 1 - 4
- The complement of 75% = 1 - .75

Let's try to solve the equation:

(8X - 4) 2 = 3 (14 - 3X)

First we'll multiply the numbers that are located inside the parenthesis:

16X - 8 = 42 - 9X

Then we'll add 8 to each side of the equation to eliminate the non-X number on one side:

16X = 50 - 9X

Then we'll add 9X to each side of the equation to eliminate the X number on one side:

25X = 50

Then we'll divide each side of the equation by 25 to find the X value. This will give us our answer:

X = 2