Basic Algebra

What's in this Basic Algebra Chapter?

1. Algebraic Addition and Subtraction, shows you how to do problems like:
Simplify: -2[-3(x − 2y) + 4y].

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

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

4. Solving Equations, like this one: 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.

What is Algebra?

Algebra is the branch of mathematics that uses letters in place of some unknown numbers.

You've 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 used letters to stand for numbers. Once we knew the width and height, we could substitute them into the formula 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 (the letters used in algebra) 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...).

And as my students constantly ask...

Why Do We Have to 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 elementary algebra chapter follows on from the earlier chapter on Numbers.Do you find basic algebra is difficult? It may be a good idea to go back and remind yourself about basic number properties first.

OK, let's move on to the first section in Basic Algebra:

1. Addition and Subtraction of Algebraic Expressions »

The 'Father of Algebra'

Abu Ja'far Muhammad ibn Musa al-Khwarizmi

math image
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 dealing 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".

The IntMath Newsletter

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!