Lovely Algebra!?


This is a pretty grim subject for most pupils but you WILL learn to become good at algebra after you've gone through these pages I hope!
When you come to try out the puzzles that I've set, you'll find them a lot easier than before and you'll be able to do them correctly with you skills in algebra!
Well, lets begin then!

Basics: Notations and Conventions (in other words rules)
When a number is unknown or if it can take any value, it is often expressed with another symbol i.e a letter in algebra.
  • ab means a � b. So if a=2 then 2b=2 � b. Note that this is also the same as ba.
  • a2 means a � a.
  • a3 means a � a � a.
  • 2a3 means 2 � (a3) which means 2 � a � a � a.
  • 5a - 2a means 5 lots of a minus 2 lots of a giving 3a. If you have something like 5a2 - 2a, then you leave it as it is. You'll see why later.
Index laws
What are those? Well, you'll need this to be able to express powers in short hand. It really isn't as hard as it sounds. Just try this exercise here and you'll then be able to work them out yourself instead of having me ramble on about them.

Simplifying Expressions using fruit salad algebra

What on Earth is she talkig about? You may have been taught how to simplify algebraic expressions involving a and b where a stands for apples and b stand for bananas.
It seems to work quite well for introducing this topic but I can't stress more stongly that a and b stand for numbers and NOT objects.
So lets say that a is the cost of one apple and b is the cost of a banana then the total cost of one apple and banana is a+b.
Normally you'd get something a little bit more complicated than that like: 3a+7b-2a+3b. You'll have to think about what this means.
  • 3a is the cost of 3 apples.
  • 7b is the cost of 7 bananas.
  • 2a is the cost of 2 apples and
  • 3b is the cost of 3 bananas
When we simplify the original expression, we put the cost of the apples together and the cost of the bananas together to get

(3a-2a)+(7b-3b)= a + 4b
(you don't need to put a 1 in front of the a)

"So where will we need this?" you ask. Here's a simple example using our old friend the rectangle.

a b

I'm sure you know how to write a simple expression for its perimeter, you should have
a + a + b + b which simplifies to
2a + 2b.

More on algebra

Home

1