Page 30 - Standard Handbook Of Petroleum & Natural Gas Engineering

Algebra 19

1. Exponentiation
2. Multiplication or division
3. Addition or subtraction
from left to right unless this order is changed by the insertion of parentheses.
For example:

a + b c - d3/e
will be operated upon (calculated) as if it were written

a + (b c) - [(ds)/e]
The symbol I a I means “the absolute value of a,” or the numerical value of a
regardless of sign, so that
1-21 = 121 = 2
n! means “n factorial” (where n is a whole number) and is the product of
the whole numbers 1 to n inclusive, so that
4! = 1 2 3 4 = 24

The notation for the sum of any real numbers a,, a2, . . . , an is

and for their product

The notation ‘‘x = y” is read “x varies directly with y” or ‘‘x is directly
proportional to y,” meaning x = ky where k is some constant. If x = l/y, then
x is inversely proportional to y and x = k/y.

Rules of Addition
a+b=b+a

(a + b) + c = a + (b + c)
a - (-b) = a + b and

a - (x - y + z) =a - x + y - z
(i.e., a minus sign preceding a pair of parentheses operates to reverse the signs
of each term within, if the parentheses are removed)