# What is an Integer in Mathematics

In mathematics integers are the set of whole numbers in which the numbers greater than zero are considered positive integers where as numbers lesser than zero are said to be negative integers and the number zero is neither positive nor negative. In simple language integers is nothing but number representation. The four main properties of whole numbers to operate integers are addition, subtraction, multiplication and division. But in integer there is no fraction and decimal.

## Positive Integers

The whole number is called as the positive integer and the symbol for positive integer is +. The positive integers are also combined with the negative integers. Here are some of the rules applied for addition and subtraction integers.

( + ) + ( + ) = ( + )

( + ) + ( - ) or ( - ) + ( + ) = The resultant value is based on large number sign. Take the numbers 4 and -2 and apply the addition operation as 4 + (-2) = 2.

Rules for multiplication:

( + ) x ( + ) = ( + )

( + ) x ( - ) = ( - )

( - ) x ( + ) = ( - )

Rules for division:

(+ ) / ( + ) = ( + )

( - ) / ( - ) = ( + )

## Negative Integers

The number value before the zero line is considered to be the negative integer and the symbol used for negative integer is -.

## Rules of Integer

The rules in integers give us the steps to be followed to solve a problem on integers. These rules are very important to perform any arithmetic operations in the field of integers. Rules are different depending on the sign of the integers. The integer rules are applied on arithmetic operations with integers like addition, subtraction, multiplication and division.

An example showing addition of integers:

Add the given two negative number -10, -23.

Therefore the rule of addition is applied to it. (-10) + (-23)

An example showing subtraction of integers:

Subtract the two integers -10 from -25.

Answer: The two numbers  given are negative numbers -25 and -10,

by  using the subtraction rules we get, (-25) - (-10), it  is written as -25 + 10  by Subtracting the above two numbers we get the  answer as  -15 ( while subtracting the larger value to the smaller value we must  put the larger value sign).

An example showing multiplication of integers:

Multiply 2 with -3.

Answer: In this sum  2 is a positive number and 3 is a negative number

Therefore multiply a positive number  with a negative number the result will be negative 2 x (-3) = -6

An example showing division of integers:

Divide 12 with 4

Answer: In this sum 12 and 4 are positive numbers.

When a positive number is divided by a positive number we get a positive result  12/4 = 3