# 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.

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

 Numbers Even and Odd Numbers

#### More on Integers from Fact Monster:

• number theory - number theory number theory, branch of mathematics concerned with the properties of the integers ...
• integer - integer: integer: see number; number theory.
• number - number number, entity describing the magnitude or position of a mathematical object or extensions ...
• number: The Integers and Rational Numbers - The Integers and Rational Numbers To the natural numbers one adjoins their negatives and zero to ...
• transfinite number - transfinite number transfinite number, cardinal or ordinal number designating the magnitude (power) ...