In algebra, letters are used to stand for numbers.
The letters are often called variables or pronumerals.
It is necessary to be able to add, subtract, multipy and divide algebraic terms.
Definitions



e.g. { 2a, 4a, 6a } are like terms. { x, 3a^{2}, 6 } are unlike terms. 

e.g. 4x + 3y is an expression. 
Addition and Subtraction
An expression involving addition and subtraction can be simplified only if it contains like terms.
The like terms are collected together and then added or subtracted.
Simplify:


(a) 5a + 6a − 2a 
(a) 5a + 6a − 2a = 9a 
(b) 18pq − 10pq + 4pq 
(b) 18pq − 10pq + 4pq = 12pq 
(c) 3c + 4d^{2} + 5c − d^{2} 
(c) 3c + 4d^{2} + 5c − d^{2} = 8c + 3d^{2} 
(d) 4x^{2} + 10x^{2} − 3x^{2}  4x^{2} + 10x^{2} − 3x^{2} = 11x^{2} 
Multiplying
3xy means "3 multiplied by x multiplied by y ".
In terms of this type the number comes first and the variables are usually placed in alphabetical order.
e.g. 3q × 4p = 12pq
5c × 3e × 2d = 30cde
Note that numbers are multiplied first and letters (variables) are placed in alphabetical order.
Dividing
^{8xy}⁄_{4x} means " 8xy divided by 4x ".
This type of expression is simplified by cancelling.
e.g. 2y
Note Cancelling can only be done between numbers or letters on the top line and numbers or letters on the bottom line.
Words into Symbols
Many maths problems are written in words and these words often have to be changed into algebraic expressions.
3 is added to x 
x + 3 
5 is subtracted from y 
y − 5 
z is multiplied by 4 
4z 
w is divided by 10 
^{w}⁄_{10}

The product of x and y 
xy

The difference between a and 5 
a − 5

The sum of 7 and w 
7 + w 
p is muliplied by q and 5 is added 
pq + 5

6 multipied by c is equal to 30 
6c = 30
