Units of Measure
The units of measure used in real estate math calculations can be varied. Lot sizes and building sizes use feet, or more precisely, square feet as a basic unit of measure. If we take a storage shed measuring 6 feet by 6 feet, its area would be 6 feet x 6 feet = 36 feet2 or 36 square feet. Notice that both the 6 is squared and the unit of measure, or feet, is squared. You will see both lot sizes and building sizes described in number of square feet, which is a measure of size for the area of a lot or building.
Some basic units of measure that are used in real estate include:
1 foot = 12 inches 1 yard = 3 feet 1 acre = 43,560 square feet 1 section = 640 acres = 1 square mile 1 township = 36 sections 1 mile = 5,280 feet 1 mile = 8 furlongs
As a subset of feet, we may look at inches, for smaller-sized objects. Surface area calculations result in answers with units of measure stated in square feet, square yards, or square inches. In the case of a rectangle you take the length times the width to get the area. If you are measuring the area of a square, as in the previous paragraph, you also take the length times the width, it just so happens these lengths are both the same. By definition the length and the width are the same in the case of a square.
When measuring volume, the unit of measure is not square feet, square inches, or square yards, but rather it is cubic feet, cubic inches, or cubic yards. That is because in order to calculate the volume of a three-dimensional object, you take the length times the width times the height. If our cube is 6 inches by 6 inches by 6 inches, the calculation becomes 6 inches x 6 inches x 6 inches = 216 inches3 or 216 cubic inches.
Other units of measure that we may come across in real estate would include acres. One acre is equal to 43,560 square feet. Regarding the government survey system of legal descriptions, one township is made up of 36 sections of land. One section is 1 square mile and is made up of 640 acres of land. If that is the case, how many square feet are there in one section?
Equation 1.1
640 x 43,560 square feet = 27,878,400 square feet
So there are 27,878,400 square feet in one section of land. Then how many square feet are there in a township?
Equation 1.2
36 x 640 x 43,560 square feet = 1,003,622,400 square feet It appears that there are over 1 billion square feet in one township.
An equation is a mathematical statement that includes an equal sign. The values on either side of the equal sign must be equivalent to each other. If they are not equivalent, then the statement is not true. The following statement is not true: 35 = 5 x 6. That is, 35 is not the same as 5 x 6. When you take 5 x 6, you do not get an answer of 35; you get an answer of 30. In order to make the statement true, you would need to write 30 = 5 x 6, or you could write 35 = 5 x 7. In either case, the statement being made is true, so they are both valid equations. Thirty is equivalent to 5 x 6 and 35 is equivalent to 5 x 7.
Equations are the tools that are used to solve problems. The problem may be a long complex word problem, or it could be a short straightforward calculation. In either case an equation can be used to solve the question at hand.
In algebra we learned that an equation can be altered, and as long as we do the same thing to both sides of the equation, it will still be an equation. If we are using the equation from the first part of this section:
Equation 1.3
and we divide both sides of the equation by 5, the result is:
Equation 1.4
so our equation is still a true statement.
Some of these types of problems are addressed in this book. If algebra scares you, don't worry. That word will not be mentioned again ... too much.
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