Basic Algebra

Algebra involves the use of letters in mathematics. These letters are unknowns and can represent either a single unknown number or a range of unknown numbers

Sometimes algebraic expressions can be simplified – this means that we collect all the similar terms together. We would never say in conversation “I have 3 apples plus 2 apples”. Instead we would say, “I have 5 apples”. Similarly in algebra we can say:

3  + 2  = 5 

However, if I had 5 bananas and 2 apples, it would be impossible to write this in a simpler way.

In algebra:

5  + 2  = 5  + 2 

This cannot be written in a simpler way. When simplifying using addition or subtraction, it is helpful to think of different letters as being completely different things – much like bananas and apples. It is important to note that 5  means '5 lots of ' or '5 × '.

Here are some more examples of how we can simplify:

7  - 4  = 3 

12  + 4 - 3  = 4 + 9 

2  + 3  - 7  + 6  = 9  - 5 

3  + 2  + 7 = 7 + 3  + 2 

• • There are four things to note about the above examples:
• the sign (+ or -) belongs to the term that comes after it.
• when giving our simplified answer we always give it in alphabetical order
• a term containing, for example , cannot be added to terms with an  or terms with a  but must instead be kept separate
• numbers on their own cannot be added to terms containing a letter