Many operations on real numbers are based on the commutative, associative, and distributive laws. The effective use of these laws is important. These laws will be stated in written form as well as algebraic form, where letters or symbols are used to represent an unknown number.

The commutative laws indicate that numbers can be added or multiplied in any order.

Commutative Law of Addition: a + b = b + a

Commutative Law of Multiplication: a(b) = b(a)

The associative laws state that in addition or multiplication, numbers can be grouped in any order.

Associative Law of Addition: a+(b+c) = (a+b)+c

Associative Law of Multiplication: a(bc) = (ab)c

The distributive laws involve both addition and multiplication and state the following. Distributive law: a(b + c) = ab + ac

Distributive law: (a + b)c = ac + be

The following list of axioms pertains to the real number system where a, b, and c represent any real numbers. These properties must be true for the algebraic laws to apply.

An equation is a statement of equality. For example, 4 + 3 = 7. An equation can also be written with one or more unknowns (or variables). The equation x + 7 = 9 is an equality only when the unknown x = 2. The number 2 is called the root or solution of this equation.

The end product of algebra is solving a mathematical equation(s). The operator normally will be involved in the solution of equations that are either linear, quadratic, or simultaneous in nature.

Summary

The important information in this chapter is summarized below.

Algebraic Laws Summary Commutative Law of Addition a + b = b + a

Commutative Law of Multiplication a(b) = b(a)

Associative Law of Addition a+(b+c) = (a+b)+c

Associative Law of Multiplication a(bc) = (ab)c

Distributive Law a(b + c) = ab + ac

LINEAR EQUATIONS

This chapter covers solving for unknowns using linear equations.

EO 1.2SOLVE for the unknown given a linear equation.

The rules for addition, subtraction, multiplication, and division described in previous lessons will apply when solving linear equations. Before continuing this course it may be worthwhile to review the basic math laws in Module 1 and the first chapter of this module.