Basic Math Operations - Mathematics and Statistics for the Environment - page 40

• A product is the result of multiplying two or more numbers together; thus, 25 is the product
of 5 × 5. Also, 4 and 5 are factors of 20.
• A quotient is the result of dividing one number by another; for example, 5 is the quotient
of 20 ÷ 4.
• A dividend is a number to be divided, and a divisor is a number that divides; for example,
in 100 ÷ 20 = 5, 100 is the dividend, 20 is the divisor, and 5 is the quotient.
• Area is the area of an object, measured in square units.
• Base is a term used to identify the bottom leg of a triangle, measured in linear units.
• Circumference is the distance around an object, measured in linear units. When determined
for other than circles, it may be called the perimeter of the figure, object, or landscape.
• Cubic units are measurements used to express volume, cubic feet, cubic meters, etc.
• Depth is the vertical distance from the bottom of the tank to the top. This is normally
measured in terms of liquid depth and given in terms of sidewall depth (SWD), measured
in linear units.
• Diameter is the distance from one edge of a circle to the opposite edge passing through the
center, measured in linear units.
• Height is the vertical distance from the base or bottom of a unit to the top or surface.
• Linear units are measurements used to express distances: feet, inches, meters, yards, etc.
• Pi (π) is a number in calculations involving circles, spheres, or cones (π = 3.14).
• Radius is the distance from the center of a circle to the edge, measured in linear units.
• Sphere is a container shaped like a ball.
• Square units are measurements used to express area, square feet, square meters, acres, etc.
• Volume is the capacity of the unit (how much it will hold), measured in cubic units (cubic
feet, cubic meters) or in liquid volume units (gallons, liters, million gallons).
• Width is the distance from one side of the tank to the other, measured in linear units.
2.2.1 K eyWords
• Of means to multiply.
• And means to add.
• Per means to divide.
• Less than means to subtract.
2.3 SEQUENCE OF OPERATIONS
Mathematical operations such as addition, subtraction, multiplication, and division are usually per-
formed in a certain order or sequence. Typically, multiplication and division operations are done
prior to addition and subtraction operations. In addition, mathematical operations are also generally
performed from left to right using this hierarchy. The use of parentheses is also common to set apart
operations that should be performed in a particular sequence.
Consider the expression 2 + 3 × 4. You might answer 20 or, if you know the rules, you would
provide the correct answer of 14. The preceding expression may be written as 2 + (3 × 4), but the
brackets are unnecessary if you know the rules, as multiplication has precedence even without the
parentheses.
Note: It is assumed that the reader has a fundamental knowledge of basic arithmetic and math
operations. Thus, the purpose of the following section is to provide a brief review of the
mathematical concepts and applications frequently employed by environmental practitioners.