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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.
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.
4S - S = 3S
5 x T = 5T
4N + N - 3N = 2N
When working with Algebra and Numbers we have to work them out separately.
2 + N + 2 + 4N
= 2 + 2 + N + 4N
= 4 + 5N
5 - A - 3 + 2A
= 5 - 3 + 2A - A
= 2 + A
Remember that the usual Rules of Operations apply when working with algebra.