What is an
Integer in Maths?

An integer is a number which has no decimal or fractional part.  It has set of negative and positive numbers,
including zero.

Integer Examples:

-10, 0, 11, 25,
-8, 90, and 4587.

Integer Types:

Positive Integers: A number is greater than zero defined as positive Integers.
Positive Integer Example: 1, 2, 3 . . .

Negative
Integers: A number is  less than zero
defined as negative Integers.
Negative
integers Example: -1, -2, -3 . . .

Zero is
defined as neither negative nor positive integer. It is a whole number.

negative and positive number line

A number line which we represents integers on a straight line in a graphical
manner.  

Integer
Operations

We can perform
arithmetic operations on the integers. Most basic operations are

1. Adding Integers

2. Subtraction
Integers

3. multiplying
integers

4. divide
integers

1. Adding integers:  Adding integers,  we can find the sum of two or more integers. The
result of sum value will be increased or decreased depending on the integer
sign value i.e. , positive or negative value.

Example 1:  Find the sum of 3+6

Solution: 3
and 6 both positive integers and result will be 9.

Example 2:  Find the sum of 3+(-10)

Solution: An
expression has two different sign to the numbers. First number, 3 is positive number
and second, -10 is a negative number. When we do the sum, result will be -7.

Example3:  Find the sum of (-6)+(-20)
Solution: An expression that has same sign of numbers i.e., negative number,
perform addition on numbers, result value also we get as negative number that
is -26.

2. Subtraction Integers: Subtraction integers,  we can find the difference between two or more
integers. The result of difference value will be increased or decreased depending
on the integer sign value i.e. , positive or negative value.

Example :  Find the value of 5 – 8.
Solution: An expression that contain two numbers, first number is smallest number
than the second number.  In this case we
get result value has negative sign.  That
is -3. Generally 8-5 gives 3, because of First number larger than the second
number and differ value is 3.

3 Multiplying integers:
Multiply is nothing but a repetition process. We perform multiply on the number
and specify the  value how many times
repeat it. For example 5×3 is a mathematical expression, it gives 15 as result.
In that case 5 is a number and 3 is repeatation value. That means we are
counting the number 5 in three times i.e 5+5+5 (5 is repeating 3 times) that
will give 15.

The table shows product of signs and it result of sign value.   

4. Division Integers

Division of
integers means find out one number is determine how many times a number is
contained into another number.  This is opposite
to multiplication process. Example, 36 ÷ 6 that gives result is 6.   Here,
we are finding out how many times 6 is contained in 36. (i.e, 6+6+6+6+6+6 , 6
is repeated 6 times that gives 36.)

There are
few cases, we should know that is when we perform division operation on the sign of numbers result should we get as either positive or negative sign.
case 1: positive ÷ positive = positive
case 2: negative ÷ negative = positive
case 3: negative ÷ positive = negative
case 4: positive ÷ negative = negative  

Number System:Also Read: