Chapter 1: The Basics

Adding

Adding is the operation in which you increase the size of the number. But not literally.
Examples:

Subtracting

Subtracting is the opposite of adding. It is the operation in which you decrease the size of a number. But not literally.
Examples:

Multiplying

Multiplying is adding a number to itself multiple times. Pretty self-explanatory.
Examples:

Division

Division is the operation where you split numbers into x groups.
Examples:

Exponents

Basically, it is just the operation of making a number multiply by itself x times.
Examples:

The Order of Operations

• PEMDAS
This is the order that most people would use. It stands for Parentheses, Exponent, Multiplication, Division, Addition, and Subtraction. This is actually similar to BODMAS

Example:

[7 * 2 + (8 - 6 / 3) + (6 - 2)² ] / 6 Firstly, you must do the parenthesis first. Remember to always apply the PEMDAS. In the first parenthesis, you must divide 6 by 3 before you subtract 8 from the quotient.
= [7 * 2 + (8 - 2) + (6 - 2)² ] / 6
P.S.: You might notice that there are two brackets: the round brackets or what we call as parenthesis, and the square brackets. The square brackets are actually not needed. You can replace them with the normal parenthesis but these are in for sightreadability.
Then calcuate them.
= (7 * 2 + 6 + 4² ) / 6
Next up is to calcuate the result of 4² , since it is next in the order.
= (7 * 2 + 6 + 16) / 6
The next step is to calcuate 7 * 2, with Multiplication in the next order.
= (14 + 6 + 16) / 6
The next steps are pretty straightforward.
= (20 + 16) / 6
= 36 / 6
= 6

Fractions

These are quotients that represent values. There are two parts of a fraction: the numerator and a denominator.
Example:
$$\frac{\mathrm{numerator}-->2}{3<--\mathrm{denominator}}$$