What is Algebra?

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Algebra is about using pictures or letters to represent numbers. It is about stating a relationship between different numbers. 

For example, if N represents a number, then N + 9 is the number that is 9 greater than N. 

So if N represents the number 3, then N + 9 is the number 12.

If N represents the number 7, then N + 9 is the number 16.

Here are 2 important terms for you to understand: Algebraic Expression and Algebraic Equation.

In the previous example, N + 9 is called an algebraic expression because N can represent any number.


If we write it this way:  N + 9 = 12, we are writing an algebraic equation. 

In an equation, N represents a specific number, not any number.

N + 9 = 12 means N is a number which, when added to 9, must give the answer 12.

So N can only be the number 3 because only 3 + 9 is equal to 12.


An algebraic expression tells us the relationship between numbers.

An algebraic equation tells us a specific number that gives a specific result.

Working with Algebra

Since the letters used in algebra are numbers, we can work with them in the same way that we work with numbers.

Example:  M + M = 2M   or 1M + 1M = 2M

This means that a number added to itself gives an answer that is twice of the number.

If you are not sure, just substitute actual numbers as M:

2 + 2 = 4 [M is 2, and 4 is twice of 2]

3 + 3 = 6 [M is 3, and 6 is twice of 3]

It does not matter what number you chose for M, the result will still be twice of that number.

Thus 2M means 2 groups of M. 

2 groups of M can also mean 2 x M.  Thus 2 x M = 2M is also true.

Similarly, 5 x H = 5H, and so on.


Just make sure that the letter used in algebra is the same.

Thus:   R + R + 3R = 5R  is true

but R + T = 2RT is not true because R and T represents two different numbers.



More Examples:

4S - S = 3S

5 x T = 5T

4N + N - 3N = 2N

When working with Algebra and Numbers we have to work them out separately.

Example 1

   2 + N + 2 + 4N

= 2 + 2 + N + 4N

= 4 + 5N


Example 2

   5 - A - 3 + 2A

= 5 - 3 + 2A - A

= 2 + A

Remember that the usual Rules of Operations apply when working with algebra.

Try out these algebra questions.

Go to Negative Numbers.