Everything in math starts with numbers. But what kind of numbers are there? For most of what we do, we use the real number system. Think of it as a giant toolkit containing all the numbers you can imagine on a number line.

This number line includes a few key groups:

• Natural Numbers: The numbers you count with: 1, 2, 3, and so on.
• Whole Numbers: Just the natural numbers plus zero: 0, 1, 2, 3...
• Integers: All the whole numbers and their opposites (negatives): ...-3, -2, -1, 0, 1, 2, 3...
• Rational Numbers: Any number that can be written as a fraction, like $1/2$ or $-7/3$. This includes all integers (since 4 is just $4/1$) and decimals that end or repeat, like 0.75 or 0.333...
• Irrational Numbers: Numbers that can't be written as a simple fraction. Their decimal forms go on forever without repeating. The most famous is $\pi$ (pi).

Arithmetic is built on four fundamental operations. They're the actions we perform on numbers.

When you have a calculation with multiple operations, the order you do them in matters. To keep things consistent, we follow a rule called the order of operations. A common way to remember it is with the acronym PEMDAS.

Sometimes we need to work with numbers that aren't whole. That's where fractions, decimals, and percentages come in. They are all different ways of representing parts of a whole.

A fraction like $3/4$ means you have 3 parts out of 4 total parts. The top number is the numerator and the bottom is the denominator.

Decimals are just another way to write fractions. Specifically, they represent fractions where the denominator is a power of 10 (like 10, 100, 1000, etc.).

Percentages are even simpler. The word "percent" means "per hundred." So, a percentage is just a fraction with a denominator of 100.

Finally, we use ratios to compare two quantities. If a recipe calls for 2 cups of flour and 1 cup of sugar, the ratio of flour to sugar is 2 to 1. We can write this as 2:1 or as the fraction $2/1$. Notice how these concepts are all related.

Mastering these fundamental ideas is the first and most important step in your mathematical journey. They form the foundation for everything that comes next.