Basic Algebra

What's in this Basic Algebra Chapter?

1. Algebraic Addition and Subtraction, simplifying expressions like: -2[-3(x − 2y) + 4y].

2. Multiplication of algebra expressions, has examples like: Expand (2x + 3)(x² − x − 5).

3. Division of algebraic expressions, simplifying $\frac{{12a^2 b}}{{(3ab^2 )^2 }}$ .

4. Solving Equations, like 5 − (x + 2) = 5x.

5. Formulas and Literal Equations, which shows how to solve an equation for a particular variable.

6. Applied Verbal Problems shows why we are doing all this.

The 'Father of Algebra'

Abu Ja'far Muhammad ibn Musa al-Khwarizmi

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Al-Khwarizmi

Al-Khwarizmi lived in Baghdad, 780 to 850 AD. He was one of the first to write about algebra (using words, not letters).

Around 825 he wrote Al-jabr w’al muq abala, from which we get the word algebra (meaning 'restoration of broken parts'). This book included many word problems, especially to do with inheritance.

He was also influential in the establishment of Hindu-Arabic numbers (1, 2, 3, ...) which replaced Roman numerals (I, II, III, IV,...). The Hindu-Arabic system was much easier to use when performing mathematical operations, since it is a base-10 system. Ever tried to multiply using Roman numerals...?

From Al-Khwarizmi's name came the word "algorithm".

What is Algebra?

Algebra is the branch of mathematics that uses letters in place of some unknown numbers. Such letters are called "literal numbers".

You have been using algebra since your early schooling, when you learned formulas like the area of a rectangle, with width w, height h:

A = w × h

We may not have known the width or height, but we were using letters to stand for numbers. Once we had our values, we could substitute them in and find our area.

Another one you may have seen is the area of a square, with sides s:

A = s²

As soon as we know the length of the sides, we can find the area.

Literal numbers (letters) can either stand for variables (the value of the letter can change, like in the examples of the area of a rectangle and the area of a square) or constants (where the value does not change), for example e (which has a constant value of 2.781828...).

Why Do We Gotta Do This?

Algebra is a powerful tool for problem solving in science, engineering, economics, finance, architecture, ship-building and many other day-to-day tasks.

If we didn't use letters in place of numbers (and used words instead), we would be writing many pages for each problem and it would be much more confusing.

This section follows on from the earlier chapter on Numbers. If you find this basic algebra is difficult, it may be a good idea to go back and remind yourself about basic number properties.

Now, let's move on to: