Converting fractions to decimals Some real estate math problems will contain fractions. While it is possible to solve the problem using fractions, it s typically easier to convert the fraction to a decimal and then solve for the answer. A fraction contains two numbers. The top number is the numerator; the bottom number if the denominator. Formula to convert a fraction to a decimal: So, to convert the fraction into a decimal, divide the bottom number (numerator) into the top number (denominator). What is ¼ as a decimal? 1
Converting decimals to percentages Quickly converting decimals to percentages and vice-versa is a very important skill to learn as many student errors are caused by incorrectly converting percentages to decimals. Converting a decimal to percentage: Decimal number x 100 = Percentage number 0.022 x 100 = 2.2% Converting a percentage to a decimal: Helpful hint! An easy way to convert a percentage to a decimal is to simply move the decimal point two spaces to the left: If given 5% in a question, just imagine there is a decimal point between the 5 and the percent sign and move it two spaces to the left: When using a calculator, the answer will be in a decimal and it will need to be converted back to a percentage. To convert a decimal to a percentage, move the decimal point to the right two spaces. 2
Multiplying by percentages Dividing by percentages 3
The T-bar Method The T method is a simple method for solving math questions that uses the three keys parts of a math question to answer the problem. Many real estate math problems have formulas that fit into the T-bar method. This is the basic set up of the T-bar: The math problem will always provide two of the three parts of the T-bar needed to solve the problem. Some problems will require two T s to solve the problem. How does the T-bar work? There are two ways to use the T-bar. 1. If the math problem provides the top number and either bottom number, divide the bottom number into the top number. 50 is what percentage of 200? 2. If the math problem provides the two bottom numbers, multiply those two numbers across to get the top number. What is 25% of 200? 4
Area of a Square or Rectangle Area is the measurement of a flat surface and is expressed in square feet (SF, sq/ft). So, square footage is how large a lot or parcel is (how much area it contains). When a rectangular lot is described using its dimensions, such as 150 feet by 300 feet, the first dimension is the width of the lot and second dimension is the depth of the lot. Depth means how far back the lot goes if one is standing in front of it. Area of a Rectangle or Square= Width x Depth/Length (Horizontal) or Width x Height (Vertical) Width= Area Depth/Length (Height) Depth/Length (Height)= Area Width T-Bar Area of a Rectangle or Square Area in Sq/Ft Width X Depth/Length/Height When using the T-bar, it doesn t matter which side you place the width and depth/length on as long as they are always on the bottom. The square footage is always on the top of the T-bar. 5
Area of a Triangle Example What is the area of this triangle? 6 B x 10 H = 60 SF / 2 = 30 SF 6
Area of a Trapezoid Trapezoids are shapes like rectangles but have uneven sides. Area = (L + L / 2) x H What is the area of this trapezoid? 1. 8 Length + 12 Length = 20 2. 20 / 2 = 10 new Length (after adding the 2 lengths, always divide the answer by 2) 3. 10 Length x 6 Height = 60 SF 7
Area of a Trapezoid Trapezoids are shapes like rectangles but have uneven sides. Area = (L + L / 2) x H What is the area of this trapezoid? 1. 12 Length+ 18 Length = 30 2. 30 / 2 = 15 new Length (after adding the 2 lengths, always divide the answer by 2) 3. 15 Length x 10 Height = 150 SF 8
1 Acre = 43,560 SF Square Feet to Acres conversion This is a very important number to remember. It is used in many real estate math calculations. Acres = Total SF / 43,560 T-bar Formula for SF to Acres conversion: Total Square Footage 43,560 SF # of Acres Example #1: If a lot contains 152,460 total SF, how large is the lot in acres? 152,560 / 43,560 = 3.5 Acres Example #2: If a man purchases 4 acres of land, how large is the lot in square feet? 43,560 x 4 = 174,120 Total SF Example #3: If a man purchases a lot that measured 600 x 363 and costs $650 per acre, what was the total cost of the lot? 1. Calculate the size of the lot in acres: 600 x 363 = 217,800 SF 2. Calculate the number of acres in the lot: 217,800 / 43,560 = 5 Acres 3. Calculate the price of the lot: 4. $650 per acre x 5 acres = $3,250 total cost of the lot 9
Front Footage Front footage is the width of the lot and the expanse of road exposure that a lot offers. It is typically used to describe commercial lots and parcels. Remember that when a rectangular lot is described using its dimensions, such as 150 feet by 300 feet, the first dimension is the width of the lot and second dimension is the depth of the lot. Depth means how far back the lot goes if you were standing in front of it. T-Bar Formula for Front Footage: Width Cost of Lot Price per Foot If the EZ Sales car lot is valued at $150,00 and is 300 wide, how much is it worth per front foot? $150,000 300 = $500 per front foot 10
Gross Living Area Gross Living Area, or GLA, the heated and cooled square footage of a structure that is measured using the outside dimensions. When calculating GLA: Only include areas that are heated and cooled. Items excluded from the GLA typically include garages, carports, decks, and patios. What is the GLA of this home? 1. Don t include the garage and the screened porch in the calculation because each is not heated or cooled. 2. Calculate the dimensions of the house: 60 wide and 40 deep. Add the depth of the garage, 30, and the remaining depth of the house, 10, to get a total of 40 in depth: 60 width x 40 depth = 2,400 SF GLA 11
Setbacks Setbacks are the amount of space local zoning regulations require between the property line and any improvements. The setback line is the boundary line that delineates the setback area. To calculate the remaining area of the lot that can be built on, subtract the setbacks from the dimensions: The front yard and back yard setbacks are subtracted from the depth. The side yard setbacks are subtracted from the width. On a residential lot that measures 70 feet by 100 feet, the side-yard building setbacks are 10 feet, the front-yard setback is 25 feet, and the rear-yard setback is 20 feet. What would the maximum possible area for a one-story structure be for this lot? 1. Subtract the front yard and back yard setbacks from the depth: 100 25 20 = 55 new depth 2. Subtract the side yard setbacks from the width: 70 10 10 = 50 new width 3. Multiply new depth by new width: 55 depth x 50 width = 2,750 SF maximum possible area 12
Calculating Section Size The Rectangular/Government Survey is type of legal description that describe a parcel of land using a set of fractions and the corresponding section, township and range numbers. While legal descriptions will be covered in detail in the National Appraisal chapter, students must learn how to calculate the size of the parcel described using this method. A section is a square tract of land used in the Rectangular/Government Survey method. A section: Is 1 mile wide and 1 mile deep. Contains 640 Acres How many acres are there in the S ½ of the SE ¼ of the SW ¼ of section 24, township 32 north, range 18 east? 1. Ignore the text section 24, township 32 north, range 18 east. It doesn t affect the answer. 2. Multiply all denominators together (the bottom number of the fraction), 2 x 4 x 4 = 32. 3. Divide 640 by that answer, 640 32 = 20 acres. 13
Volume Measurement Volume is the amount of something that a container can hold. For example, the amount of water required to fill a swimming pool is the volume of water that the swimming pool can hold. Volume is expressed in CUBIC feet (not in square feet like area). Volume = Height (or Depth) x Width x Length If a homeowner wishes to fill in an old, outdated swimming pool that measures 20 in length, 10 in width and is 6 in depth with dirt, how much dirt will he need to buy in cubic feet? H (or D) x W X L 6 x 10 x 20 = 1,200 Cu/Ft 14