ABSTRACT
This chapter investigates the reasons for the different methods readers use to perform operations on numbers. It describes the kinds of observations that led to the discovery of the commutative, associative, and distributive laws for whole numbers. The chapter discusses the definitions of addition and multiplication to rational numbers. It discusses decimal representations of numbers, and proves some of the basic theorems concerning decimal expansions of real numbers. The chapter explores the fascinating topic of cardinality, which link to the study of algebraic and transcendental numbers. It is a well-known fact that fractions are among the most confusing topics for elementary mathematics students. In fact, secondary school mathematics teachers claim that their students have extremely weak skills when it comes to fractions, and that this deficiency creates a major stumbling block when they are trying to learn algebra. The secondary school curriculum requires that students have facility using the laws of exponents.
