Before I even touch on to the basis of Algebra, I need to give you guys a feel for what equations and expressions are. I will assume that you already know the basics of arithmetic operations.
An expression refers to a collection of terms combined through the use of mathematical operations. I know this definition seems quite dodgy and incomprehensible, so I'll give a few examples of expressions:
7 + 9
7/3 + 8/3
9 x 8
89 - 7^2 + 91 x 45 (* When I say ^, I mean "raised to the power of". So 7^2 = 7 x 7 = 49)
I hope you guys get the idea of what it means. If you don't, please say, and I'll try to explain in more detail.
An equation is when two expressions are separated by a = symbol. The expressions have to be able to evaluate to be the same. Here's an example of a valid equation:
1 + 1 = 2
Because if we evaluate it, we get this:
1 = 1
And 1 is equal to 1. However, this is not a valid equation:
3 = 1 + 1
Because if we evaluate it, we get this:
3 = 2
And we know that 3 and 2 are completely different numbers.
A few heads up before I can show you to the world of Algebra, I'm going to be using some dodgy notation, so you're going to have to try and adapt to it.
1. Exponents
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Remember this? Instead of using that little two for "squared", I will have to use ^2. So that means that I will have to write equations like:
3^2 = 9 instead of "3 to the power of 2 is equal to 9"
7^2 = 49 instead of "7 squared is equal to 49"
2^3 = 3^2 - 1 instead of "2 cubed is equal to 3 squared minus 1"
I hope you guys get the idea.
2. Roots
Instead of saying "the square root of 4" I'll have to say sqrt(4).
sqrt(9) = 3 instead of "the square root of 9 is equal to 3"
sqrt(sqrt(9) + sqrt(16)) instead of "the square root of the sum of the square roots of 9 and 16"
At the end of every chapter, I'll give some questions to answer.
Question 1: Evaluate 3^2 + 2^3
Answer: Well, as I've said earlier, the "^2" means "squared". So I can evaluate like so:
3^2 + 2^3
= (3 x 3) + 2^3
= 9 + 2^3
And "^3" means cubed, so:
= 9 + (2 x 2 x 2)
= 9 + 8
= 17
So the answer is 17.
Question 2: Is this equation valid:
sqrt(9) = 4
Answer: Well, first, the question we have to ask ourselves is "what is the square root of 9". Prior to our knowledge, we should know that it is 3. So that means the equation evaluates to:
3 = 4
And we know 3 doesn't equal 4.
But of course, in Algebra we deal with valid equations.
