Geoscience Reference
In-Depth Information
2
Basic Math Operations
Note everything that counts can be counted, and not everything that can be counted counts.
—Albert Einstein
2.1 INTRODUCTION
Most calculations required by wastewater operators and engineers (as with many others) start
with the basics, such as addition, subtraction, multiplication, division, and sequence of opera-
tions. Although many of the operations are fundamental tools within each operator's toolbox, it is
important to reuse these tools on a consistent basis to remain sharp in their use. Wastewater opera-
tors should master basic math definitions and the formation of problems; daily operations require
calculation of percentage, average, simple ratio, geometric dimensions, threshold odor number,
force, pressure, and head, and, at the higher levels of licensure, the use of dimensional analysis and
advanced math operations.
2.2 BASIC MATH TERMINOLOGY AND DEFINITIONS
The following basic definitions will aid in understanding the material that follows.
• An
integer
,
or an
integral number
,
is a whole number; thus, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
and 12 are the first 12 positive integers.
• A
factor
, or
divisor
, of a whole number is any other whole number that exactly divides it;
thus, 2 and 5 are factors of 10.
• A
prime number
in math is a number that has no factors except itself and 1; examples of
prime numbers are 1, 3, 5, 7, and 11.
• A
composite number
is a number that has factors other than itself and 1. Examples of com-
posite numbers are 4, 6, 8, 9, and 12.
• A
common factor
,
or
common divisor
,
of two or more numbers is a factor that will exactly
divide each of them. If this factor is the largest factor possible, it is called the
greatest
common divisor.
Thus, 3 is a common divisor of 9 and 27, but 9 is the greatest common
divisor of 9 and 27.
• A
multiple
of a given number is a number that is exactly divisible by the given number. If a
number is exactly divisible by two or more other numbers, it is a common multiple of them.
The least (smallest) such number is called the
lowest common multiple.
Thus, 36 and 72
are common multiples of 12, 9, and 4; however, 36 is the lowest common multiple.
• An
even number
is a number exactly divisible by 2; thus, 2, 4, 6, 8, 10, and 12 are even
integers.
• An
odd number
is an integer that is not exactly divisible by 2; thus, 1,3, 5, 7, 9, and 11 are
odd integers.
41
Search WWH ::
Custom Search