# Basic Algebra

Introduction to Algebra

### What is algebra?

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

Algebra is a very powerful tool for solving real-world problems.

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 = s^{2}

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.

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