Introduction to algebra

Algebra is an ancient part of maths that originated thousands of years ago! Here we'll explain the amazing story of Algebra and the concept of variables and equations.


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Where did algebra come from

It's origins can be traced back to ancient Babylonia sometime around 2000 BC. This is almost as far back to the time when Egyptians were building pyramids. It's amazing that this maths you're about to learn is so ancient and so useful today thousands of years later.

The city of Babylon all those years ago is now known as present day Baghdad - say whaaaat!

 

After Babylon kicked things off a bloke called Al-Khwarizm took the next big step a few thousand years later. He was a Persian mathematician whose writings revolutionized math in the Western world. The word algebra comes from the title of a book he wrote called al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābala (The Compendious Book on Calculation by Completion and Balancing),

Here is a timeline showing you the gist of these events:

What is algebra

Algebra is about solving for an unknown. Often with real world problems we're able to write down the information we do know in the form of algebra - and then use the rules of algebra to find out the information we do not know.

As you can imagine this is a powerful tool to have which is why algebra is the basis of many other branches of maths as well as  science and modern technology.

Variables

In order to do this algebra introduces a new element called variables which take the place of unknowns in our problem. Variables are written as letters and they represent numbers that we don't know yet.

Why do we use letters and not something else? Because:

  • It's easier than drawing pictures or writing a word.
  • There could be more than one unknown so we might have the need to use more than one letter.
  • Letters can stand for something. E.g. the area of a rectangle is written as A = w × h.

Why are they called variables? Because the number they represent can vary.

Equations

Now in Algebra when we put numbers and variables together this way and we use an equals sign (=) we call that thing an algebraic equation (or just equation for short).

Why are they called equations? Because they have an equals sign.

Solving an equation

So after being given a problem and writing that problem in the form of an equation with numbers and a variable (unknown) we now get to solve the equation to get the value of the variable and hence the answer to our problem.

This involves the process of simplifying the equation and getting the variable on it's own. This is quite fun and a lot like solving a puzzle. There are rules to follow that give you an answer at the end.

The idea of the game is:

  • Try and get the variable by itself (which gives us the answer)
  • Always keep the equation balanced