# Integers

Integers include **positive whole numbers, negative whole numbers, and zero.**

The **“set of all integers”** is often shown like this:

Integers = {… -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …}

The dots at each end of the set mean that you can keep counting in either direction. The set can also be shown as a **number line:**

The arrows on each end of the number line mean that you can keep counting in either direction.

### Adding and Subtracting Integers

Looking at a number line can help you when you need to add or subtract integers.

Whether you are adding or subtracting two integers, **start by using the number line to find the first number.** Put your finger on it. Let's say the first number is 3.

- Then, if you are
**adding a positive number,** move your finger to the right as many places as the value of that number. For example, if you are adding 4, move your finger 4 places to the right.3 + 4 = 7

- If you are
**adding a negative number,** move your finger to the left as many places as the value of that number. For example, if you are adding -4, move your finger 4 places to the left.3 + -4 = -1

- If you are
**subtracting a positive number,** move your finger to the left as many places as the value of that number. For example, if you are subtracting 4, move your finger 4 places to the left.3 - 4 = -1

- If you are
**subtracting a negative number,** move your finger to the right as many places as the value of that number. For example, if you are subtracting -4, move your finger 4 places to the right.3 - -4 = 7

Here are two **rules to remember:**

- Adding a negative number is just like subtracting a positive number.
3 + -4 = 3 - 4

- Subtracting a negative number is just like adding a positive number. The two negatives cancel out each other.
3 + 4 = 3 - -4

### Multiplying and Dividing Integers

If you **multiply or divide two positive numbers,** the result will be positive.

6 x 2 = 12

6 / 2 = 3

If you **multiply or divide a positive number with a negative number,** the result will be negative.

6 x -2 = -12

6 / -2 = -3

If you **multiply or divide two negative numbers,** the result will be positive—the two negatives will cancel out each other.

-6 x -2 = 12

-6 / -2 = 3

### Is It an Integer?

**Integers are whole numbers and their negative opposites.** Therefore, these numbers can never be integers:

- fractions
- decimals
- percents