Page 22 - Appplied Mathematics for the Petroleum and Other Industries, 5th Edition

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4

Principles of Algebra

OBJECTIVES

Upon completion of chapter 4, the student will be able to—
1. Use variables to represent an unknown quantity.
2. Solve an equation for an unknown quantity.
3. Convert a written problem into an equation and solve the equation.
4. Simplify an expression by removing the grouping symbols.
5. Add two or more algebraic expressions.
6. Add algebraic expressions containing a negative quantity.
7. Subtract one algebraic expression from another.
8. List the rules for multiplying algebraic expressions.
9. Multiply algebraic expressions containing exponents.
10. Divide one algebraic expression by another.
11. Transpose an equation to solve for a variable.
12. Use formulas to solve for quantities often used in industrial applications.

INTRODUCTION
In general, to calculate problems in simple arithmetic, only the numbers 0 through
9 (alone and in combination) and the signs +, –, ×, and ÷ are used. Algebra goes
a step further because it not only employs numbers and signs, but also letters
Petroleum Extension-The University of
as γ, α, and β.
The letters and symbols in algebra represent variables. A variable is an
unspecified or unknown quantity—a quantity that varies with a problem. A vari-
able may denote different values in different problems, but it always represents
the same value in a given problem. For instance, x may stand for gallons in one
problem and for feet in another, but, if it is selected to stand for gallons in a
problem, it must represent gallons throughout that problem.
Algebraic expressions—combinations of symbols, letters, and signs—are used
in formulas and equations. A formula is a symbolic expression of a general fact,
rule, or principle and is often stated as an equation. An equation is an expression
and symbols. For example, algebra uses the letters a through z and symbols such Texas at Austin
of equality between two quantities.

ALGEBRAIC EXPRESSIONS
An algebraic expression is a combination of algebraic symbols and signs. For
example, 2a + 3ab – 4c is an algebraic expression. The letters a, b, and c stand for
unknown quantities. Also, a and b are used together (ab, which means a × b) to
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