# Introduction

Arithmetic is the most elementary branch of mathematics, and is used by virtually everyone in their daily life, both at home and at work, and even whilst engaging in leisure activities! You will, for example, use arithmetic to check that you receive the correct change when making a purchase in a shop for cash. You may be counting the days remaining before your next holiday. You might even be calculating how many bottles of lemonade you will need for your next party! Although these are relatively trivial examples, they serve to illustrate the ubiquitous nature of arithmetic. There are very few human activities that do not involve arithmetic, directly or indirectly, in some way. For this reason, it is probably safe to say that everyone should have at least a basic knowledge of arithmetic. The definition of arithmetic can vary, depending on who is doing the defining. For the purposes of these pages however, we will concentrate on the basic elements of *addition*, *subtraction*, *multiplication* and *division* (sometimes referred to as the *four rules*).

As well as understanding the basic arithmetic operations, it is also necessary to have a grasp of the rules governing the *order* in which those operations must be carried out within complex expressions. Such expressions combine different types of operation, and frequently use brackets to indicate those parts of an expression that should be evaluated separately. The rules governing the order of evaluation are often referred to using the acronym BODMAS and we will look at what these letters stand for and how the rules work. We will also be looking at how the standard arithmetic operations are applied to fractions and numbers that have a fractional part. An understanding of factors, multiples and prime numbers is also useful when studying arithmetic, especially when dealing with multiplication and division. You will at some point undoubtedly need to apply arithmetic operations to numbers that are either very large or very small. A very large number can often be expressed as a smaller number multiplied by itself *n* number of times (i.e. it is said to be that number raised to the power of *n* + 1). The value *n* + 1 is often referred to as an *index* (or *exponent*). The index used is often a positive integer (whole number), but it can also be a negative number or fractional value. All of these topics will be examined in the general context of arithmetic.