What is an Integer?

What is an integer? An integer is any number including 0, positive numbers, and negative numbers. It should be noted that an integer can never be a fraction, a decimal or a per cent. Some examples of integers include 1, 3, 4, 8, 99, 108, -43, -556, etc. Also, check Integers.

All About Integers

Integers are a set of counting numbers that can be written without a fractional component. As mentioned above, an integer can be either positive, negative or zero. The integers can be represented as:

Z = {……., -3, -2, -1, 0, 1, 2, 3, ……….}

Examples and Types of Integers

An integer can be of two types:

  • Positive Numbers
  • Negative Integer
  • 0

Some examples of a positive integer are 2, 3, 4, etc. while a few examples of negative integers are -2, -3, -5, etc.

In the number system, there are various types of numbers that come under the integer category. Some numbers which are integers are:

  • Odd Numbers
  • Even Numbers
  • Prime Numbers
  • Composite Numbers

Integer Rules

Addition rule: If the sign of both the integers is the same, then they are added such as:

  • (+) + (+) = +
  • (-) + (-) = –

Example:

  • 5 + 9 = 14
  • -5 + (-9) = -14

But if one of the numbers has a different sign, then it will lead to subtraction and output will contain a sign of the larger number. Let us understand with the help of examples.

  • (-10)+(2) = -10 + 2 = -8
  • (-2)+(10) = -2+10 = 8

Subtraction Rule: The sign of the first number stays the same, change subtraction to addition and change the sign of the second number. Once you have applied this rule, follow the rules for adding integers

  • (+) – (+) = (+) + (-); consider the sign of greater number
  • (-) – (-) = (-) + (+); consider the sign of greater number
  • (+) – (‐) = (+) + (+); answer will be positive
  • (‐) – (+) = (‐) + (‐); answer will be negative

Examples:

  • 9 – 6 = 3
  • -9 – (-6) = -9 + 6 = -3
  • 9 – (-6) = 9 + 6 = 15
  • -9 – (6) = -15

Multiplication and Division rules: If the signs are the same, multiply or divide and the answer is always positive.

  • (+) x (+) = + and (+) ÷ (+) = +
  • (‐) x (‐) = + and (‐) ÷ (‐) = +

If the signs are different, multiply or divide and the answer is always negative.

  • (+) x (‐) = – and (+) ÷ (‐) = ‐
  • (‐) x (+) = – and (‐) ÷ (+) = ‐

Examples: 

  • 4 x 2 = 8 and 4 ÷ 2 = 2
  • (-4) x (-2) = 8 and (-4) ÷ (-2) = 2
  • (4) x (-2) = -8 and 4 ÷ (-2) = -2
  • (-4) x (2) = -8 and (-4) ÷ (2) = -2 

Frequently Asked Questions on Integers

How is an integer represented?

An integer is represented using the alphabet “Z”. For integers, Z = {…, -2, -1. 0. 1, 2, ……}

Are odd and even numbers integers?

Yes, odd and even numbers fall under the category of integers. Even whole numbers, prime numbers, and composite numbers are all integers.

What are the main properties of integers?

There are 5 main properties of integers which are:

  • Property 1: Closure property
  • Property 2: Commutative property
  • Property 3: Associative property
  • Property 4: Distributive property
  • Property 5: Identity Property

Learn more about the properties of integers here.