► WHAT ARE THE PARTS OF A FRACTION?
The denominator shows the number of equal parts in the whole or total (The denominator is the bottom number). The numerator, which is the top number, shows the number of those parts with which you are working. It is very common to see the "numerator" written to the left and the "denominator" to the right of a "slash" In the example below, the whole or total has been divided into eight equal parts, and you have seven of those equal parts.
 7              Numerator              (Top Number)
 8            Denominator       (Bottom Number)

In the fraction 7/8 the 7 is the Numerator and the 8 is the Denominator separated by a “slash”. The fraction is read “Seven Eighths”.

► WHAT IS MEANT BY A "PROPER FRACTION"?
7/8 is an example of a proper fraction. In a proper fraction the numerator, which when printed in line is on the left, is less than the whole or less than 1. In this case 7 (the numerator) is less than the whole which is 8 (the denominator).

► WHAT IS AN "IMPROPER FRACTION"?
11/8 is an example of an improper fraction. In an improper fraction, the numerator is greater than the whole or greater than 1. In this case 11 (the numerator) is more than the whole which is 8 (the denominator).

► WHAT IS A MIXED NUMBER?
11 1/2 is a mixed number. You have a whole number (11)  plus a fraction (1/2).  A mixed number is greater than the whole or greater than 1.

► HOW DO I MULTIPLY FRACTIONS?
When multiplying fractions, the numerator is multiplied by the numerator, and the denominator by the denominator. Let's start with an easy question. What is 1/2 x 3/4?  First multiply the numerators (top numbers) 1 x 3 = 3; then the denominators (bottom numbers) 2 x 4 = 8. Thus, 1/2 x 3/4 = 3/8

For me, an easier way to approach any fraction and to understand the mathematical answer to a problem is to convert the fraction to decimal. In the fraction multiplication above (1/2 x 3/4 = 3/8) the numbers become .50 x .75 = .38 when the fraction’s numerator is divided by the denominator for example: 1 is divided by 2 which equals .50.
Likewise, 2/3 is equal to 2 ÷ 3 or .67.
                  5/8 is equal to 5 ÷ 8 or .625.
                  3/4 is equal to 3 ÷ 4 or .75

Whenever working with fractions or decimals equivalents, the answers will be very close but often not necessarily exact.

► HOW DO I DIVIDE BY FRACTIONS?
Dividing by fractions is a two step process.  For example what is 3/4 ÷ 1/4?
First, invert the 1/4 to 4/1. Then, multiply 3/4 x 4/1 = 12/4. Finally, 12 ÷ 4 = 3.

You may and you should convert fractions to a decimal using a calculator to divide them. Using the example above of what is 3/4 ÷ 1/4? Firstly convert the fractions to a decimal (we’ll look closely at doing that below) 3/4 is converted to the decimal .75 and 1/4 to the decimal .25.

.75 ÷ .25 = 3. (There are three .25 in .75.) You most likely realized that there are 3 “1/4” in “3/4” but a more difficult fraction could be a challenge and there is no point when calculators are available and should be used.

► HOW DO I CONVERT FRACTIONS TO DECIMALS?
Finally, we get to the section that makes sense; converting fractions to decimals. Calculators are abundant, very sophisticated and for the most part, there is no reason for you as a real estate agent to do math using fractions. In fact, there is no reason for a realestate agent to do any more that to properly put numbers into a computer program or a calculator.  Fractions will sometimes be used in real estate problems and on the real estate test. Since calculators may be used on the licensing examination, it is best to convert fractions to decimals.

To convert a fraction to a decimal, the top number, called the numerator, is divided by the bottom number, called the denominator.

For example:  7/8=7÷8=0.875   and  11/8=11÷8=1.375

In the case of a mixed number, the whole number is just carried over to the answer. For Example:  11 ½ =1÷2=0.5 + 11=11.5

Once fractions have been converted to decimals, other calculations can be easily completed using the calculator. Note that many calculators automatically add the zero before the decimal point. And all calculators will correctly place the decimal point into the number.

► HOW DO I ADD OR SUBTRACT DECIMALS?
Line up the decimals, add or subtract, and bring the decimal down in the answer. You may add zeros if necessary, as place holders. For example, 0.5 is the same as 0.50, or .5.

When you use a calculator, the decimal will be in the correct place in the answer.  For Example: 0.5 + 3.25 = 3.75, and 8.2 - 0.75 = 7.45

► HOW DO I MULTIPLY DECIMALS?
Multiply the numbers, then count the number of decimal places in each number. Next, start with the last number on the right and move the decimal the total number of decimal places to the left in the answer.

Multiply as you normally would to get the 1,500, then count the four decimal places in the numbers (.20 and .75). In the 1,500, start at the last zero on the right, and count four decimal places to the left. The decimal is placed to the left of the 1.

Again Note: When you use a calculator, the decimal will be in the correct place in the answer (0.2 x 0.75 = 0.15).

► HOW DO I DIVIDE DECIMALS?
Divide the dividend (the number being divided) by the divisor (the number you are dividing by) and bring the decimal in the dividend straight up in the quotient (answer). If the divisor has a decimal, move the decimal to the right of the divisor and move the decimal the same number of places to the right in the dividend. Now divide as stated above.

The truth of the matter is twofold: One, you will not likely be dividing decimals on the real estate exam, and secondly it is unlikely that you will ever be required to divide a decimal in the real estate business. You are allowed a simple calculator in the exam room and that is all you need to divide a decimal. When you use a calculator, you can have a decimal in the divisor and the decimal will be in the correct place in the answer.

For Example: 1.5 ÷ 2 = 0.75, and 15.5÷0.5=31

►  BRINGING A CALCULATOR TO YOUR PSI REAL ESTATE EXAMINATION
Calculators on cell phones cannot be used as cell phones are not allowed in the examination center. You do need to bring a calculator but you need to use caustion considering a calculator. In previous years, I bought a new solar power calculator to take to any import examination with math. Only non-programmable calculators that are silent, battery-operated, do not have paper tape printing capabilities. The calculator keyboard cannot contain the alphabet. While programable calculators will not be allowed in the examination site, you should have one that has a % key on it that will easyly solve precentage  problems..

As mentioned, I prefer a calculator that is also solar powered as they will operate from the lights as a power source. I also like larger keys/buttons, large display and a percentage button which is allowed.

► WHAT IS A PERCENTAGE?
Percent (%) means per hundred or per hundred parts. The whole or total always represents 100 percent.
     5% = 5 parts of 100 parts, or 5 ÷ 100 = 0.05 or 1/20
     75% = 75 parts of 100 parts, or 75 ÷ 100 = 0.75 or 3/4
     120% = 120 parts of 100 parts, or 120 ÷ 100 = 1.2 or 1 1/5

►  HOW CAN I CONVERT A PERCENTAGE TO A DECIMAL?
Move the decimal two places to the left and drop (eliminate) the % sign.
      20% which is calculated as 20 ÷ 100 = 0.20 or 0.2
      1% which is calculated by dividing 1 by 100 as such 1÷100=0.01

► HOW CAN I CONVERT A DECIMAL TO A PERCENTAGE?
Move the decimal two places to the right and add the % sign.
     0.25 = 25%
     0.9 = 90%
     0.0875 = 8.75% or 8 3/4%

► HOW DO I MULTIPLY BY PERCENTAGES?
     500 x 25% = 500 x 25/100 =12,500/100= 125
          or
     500 x 25% = 125, or 500 x .25 = 125

► HOW DO I DIVIDE BY PERCENTAGES?
     100 ÷ 5% = 100 ÷ 5/100 = 100 x 100/5 = 10,000/5 = 2,000
        or
    100 ÷ 5% = 2,000, or 100 ÷ .05 = 2,000

►  HOW TO SOLVE PERCENTAGE PROBLEMS?
The following three formulas are important for solving all percentage problems:
        TOTAL x RATE = PART
        PART ÷ RATE = TOTAL
        PART ÷ TOTAL = RATE
There is a simple way to remember how to use these formulas:
         MULTIPLY when PART (top)  is UNKNOWN.
         DIVIDE when PART  (top) is KNOWN.
         When you divide, always enter PART into the calculator first.

► WHAT IS THE "T-BAR" METHOD?
The T -Bar is another tool to use to solve percentage problems. For some people, the "three-formula method" is more difficult to remember than the visual image of a T.

            ÷ PART ÷              
  TOTAL x │ x RATE

►  HOW DO I USE THE T-BAR?
The procedure for using the T -Bar is as follows:
     1. Enter the two known items in the correct places.
     2. If the line between the two items is vertical, you multiply to equal the missing item.

VIDEO UNDERSTANDING THE T BAR

            ÷ PART ÷             
   TOTAL x │ x RATE

Divide Using the T-Bar. If the line between the two items is horizontal (straight across) you divide discover the missing item. When you divide, the top (Part) always goes into the calculator first and is divided by the bottom (Total or Rate).

The math used to solve precentage problems is something you have been dealing with since the forth grade. I would like you to watch this short video which should help you grasp the information about the the T-Bar method in resolving precentage problems.