Chapter 1

Basic Algebra: some reminders of how it works

Chapter description
In many areas of science and engineering, information can be made clearer and more helpful if it is thought of in a mathematical way. Because this is so, algebra is extremely important since it gives you a powerful and concise way of handling information to solve problems. This means that you need to be confident and comfortable with the various techniques for handling expressions and equations.
The chapter is divided up into the following sections.

1. Handling unknown quantities
   1. Where do you start? Self-Test (1)
   2. A mind-reading explained
   3. Some basic rules
   4. Working out in the right order
   5. Using negative numbers
   6. Putting into brackets, or factorising

2. Multiplications and factorising: the next stage
   1. Self-Test (2)
   2. Multiplying out two brackets
   3. More factorisation: putting things back into brackets

3. Using Fractions
   1. Equivalent fractions and cancelling down
   2. Tidying up more complicated fractions
   3. Adding fractions in arithmetic and algebra
   4. Repeated factors in adding fractions
   5. Subtracting fractions
   6. Multiplying fractions
   7. Dividing fractions

4. The three rules for working with powers
   1. Handling powers which are whole numbers
   2. Some special cases

5. The different kinds of numbers
   1. The counting numbers and zero
   2. Including negative numbers: the set of integers
   3. Including fractions: the set of rational numbers
   4. Including everything on the number line: the set of real numbers
   5. Complex numbers: a very brief forwards look

6. Working with different kinds of number: some examples
   1. Other number bases: the binary system
   2. Prime numbers and factors
   3. A useful application ... simplifying square roots
   4. Simplifying fractions with square root signs underneath

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