SELECTED TOPICS IN ALGEBRA

This chapter discusses some basic topics in algebra, such as the order of operations, evaluating algebraic expressions, solving equations, and solving simultaneous linear equations. The chapter focuses on the operations of addition, subtraction, multiplication, division, and groupings using parentheses. For arithmetic expressions those operations that are within parentheses are first performed. Then multiplication and division is performed from left to right. Finally, addition and subtraction are performed from left to right. When algebraic expressions are evaluated, the given numbers are substituted for the letters in the expression. To solve equations in one unknown, the rules of equality to manipulate the equation are used so as to isolate the unknown variable on one side of the equation; on the other side, the numerical terms are isolated. This chapter discusses two methods of solving simultaneous linear equations. The first method—the substitution method—involves solving for an unknown in one equation and substituting the resulting expression into the other equation, thereby eliminating one of the variables. This method is useful when one of the unknowns has a numerical coefficient of 1 or −1. The elimination by the addition method of solving simultaneous linear equations has the advantage in solving for both unknowns without having to encounter fractional expressions.