Algebra is the part of mathematics that is used to help to solve problems. It provides a way for a problem and its solution to be written down.
In algebra, letters or symbols are used to represent numbers.
The letters are often called variables or pronumerals. In a problem the variable often stands for the unknown thing we are trying to find.
Most people would work out this problem in their head but algebra like this allows us to work out much more difficult problems.
First of all, the meanings of some of the words used in algebra are given below;
Words into Symbols
Many mathematics problems are written in words and these words often have to be changed into algebraic expressions using letters and symbols.
We need to be able to write down mathematical operations using algebra:
In this section on algebra, six topics will be used to introduce the following algebraic ideas:
Indices or Exponents
When 3 is multiplied by 3, this can be written as 32. In algebra if x is multiplied by x this can be written as x2. The two is called an index or exponent.
Often in algebra, expressions can be simplified. For example, 2x + 3x can be simplified to 5x.
Expanding and Factorising
If an expression such as 2x + 3 is multiplied by 5, this can be written 5(2x + 3). This is said to be in factorised form and if these factors are expanded this gives 10x + 15. The 5 is multiplied by each of the terms inside the brackets.
A variable in algebra can be given a value. For example if p is given the value of 4 then a term like 6p becomes 6 x 4 = 24. This is called substituting or evaluating the term.
Equations and Formulae
When solving a problem using algebra an equation is often formed. For example if 6 bananas are bought and the total cost is $4.20 then an equation can be formed to find the cost of each banana. The equation would be 6x = 4.20
Patterns, Sequences and Graphs
Solving problems is often helped by looking for a pattern, finding a missing term in a sequenceor drawing a graph. This topic looks at how this can be done.