Algebra

Algebraic Notation

In order to learn about more manipulation rules, we need to be familiar with Algebraic notation.

First of all, instead of saying "3 multiplied by x", we say:

3x

This is because, if we used the multiplication symbol, it would like this:

3 × x

And that can confuse with

3xx

Which is completely different.

Instead of 2 × x --> 2x

Instead of y × x --> yx

Instead of x × 5 --> 5x

I hope you get the idea.

Question 5: Evaluate x + x + 5 + x + y + y.

Answer: we can rearrange this expression to this:

x + x + x + y + y + 5

And we know x + x + x is the same as 3 times x, and that y +y is the same as 2 times y. So we get:

3x + 2y + 5

And that means 3x + 2y + 5 is the final answer.

Another thing to keep in mind is how the division symbol is represented in Algebra. Instead of saying 3 ÷ x, we say 3/x.

Instead of x ÷ 9 --> x/9

Instead of 8 ÷ y --> 8/y

Instead of 6 × y ÷ 3 --> 6y/3

It is also important to know how to evaluate terms with division and multiplication. Like this term:

6y/3

You can translate this into:

(6/3)y

And that is equal to:

2y

Question 6: Evaluate (x + x)/2

Answer: we know that x + x is the same as 2 × x which is the same as 2x. So the expression simplifies to:

2x/2

Which is equal to:

(2/2)x

Which is equal to:

x

So the answer is x.