Everything in arithmetic starts with whole numbers. These are the numbers you first learned to count with: 0, 1, 2, 3, and so on. They are simple, complete units without any fractional or decimal parts.

You can think of whole numbers arranged on a number line. Zero is in the middle. Positive numbers stretch endlessly to the right, and negative numbers (like -1, -2, -3) stretch endlessly to the left. Together, the positive whole numbers, negative whole numbers, and zero are called integers.

The two most basic operations in arithmetic are addition and subtraction. Addition is simply combining values. If you have 3 apples and you get 2 more, you add them together to find the total.

Subtraction is the opposite. It's about taking away one value from another, or finding the difference between them. If you start with 5 apples and eat 2, you subtract to see how many are left.

Addition and subtraction are inverse operations. One undoes the other. If you add 2 to 3 to get 5, you can subtract 2 from 5 to get right back to 3.

Multiplication is a shortcut for repeated addition. Instead of adding 4 + 4 + 4, you can just multiply. This is useful when you have several groups of the same size.

Division is the inverse of multiplication. It’s the process of splitting a number into equal groups. If you have 12 cookies to share among 3 friends, you divide to find out how many cookies each friend gets.

Sometimes, numbers don't divide perfectly. If you had 13 cookies for 3 friends, each would get 4, but there would be 1 cookie left over. This leftover part is called the remainder.

Not everything comes in whole numbers. We often need to work with parts of a whole, which is where fractions, decimals, and percentages come in. They are just different ways of expressing the same idea.

A fraction shows a part of a whole, like a slice of pizza. It's written as one number over another. The top number (the numerator) tells you how many parts you have. The bottom number (the denominator) tells you how many parts the whole is divided into.

A decimal is another way to write a fraction. Specifically, it's a fraction where the denominator is a power of 10 (like 10, 100, 1000). The decimal point separates the whole number part from the fractional part.

Finally, a percentage is a way of expressing a number as a fraction of 100. The word "percent" literally means "per hundred." So, 75% is just another way of saying 75 out of 100.

Understanding how to switch between these forms is a key skill. If you know a value as a fraction, you can find its decimal form by dividing the numerator by the denominator. To turn a decimal into a percentage, you just multiply by 100.

Let's test your understanding of these core concepts.

Mastering these operations and concepts is the first step. They are the foundation for almost every other area of math you will encounter.