What is Integer Number

In Maths, there are many types of numbers. But have we ever considered what an integer number is? An integer is a number which can be positive or negative or zero. The types of numbers could be any number such as natural numbers, whole numbers, real numbers and rational numbers.

Integers are numbers which cannot be decimals or fractions. They are either whole numbers or negative numbers. Some examples are: 2, 7, 0, -9, -12, etc.

Rules of Integers

The rules of integers are defined by the operations performed on them. Such as:

  • Adding of integers
  • Subtracting integers
  • Multiplication and division of integers

Adding integers

  • If we add two positive integers, then the sign of the resultant integers remains the same. Example: 5 + 7 = 12.
  • If we add two negative integers, then the sign of the resultant integer will be negative. Example: (-5)+(-7) = -5-7 = -12
  • If we add one positive integer and one negative integer, then the sign of the result will depend on the integer having greater value. Example: 5 + (-7) = -2

Subtracting Integers

  • If we subtract two positive integers, then the sign of the resultant integer will depend on the greater value. Example: 9 – 2 = 7
  • If we subtract two negative integers, then the sign of the second integer is changed to positive and the sign of output will be the sign of greater value. Example: (-5)-(-7) = -5+7 = 2

Multiplication and Division Rule

If the sign of the integers is the same, then multiplication and division of these integers produce positive value.

Example: (-5) x (-7) = 35 & 5 x 7 = 35

In case of division,

(-35)/(-5) = 7 & (35/5) = 7

If the signs are different, then the answer is always negative.

Example: (-5) x 7 = -35 & -35/5 = -7

Are negative numbers integers?

Negative numbers which are not fractions are all integers.

Or

All the numbers below value 0 and which are not fractions are also integers.

Examples: -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, …,-∞.

But numbers such as -½, -¾, -9.5, -10.5, etc. are not integers.

Is 0 an integer?

Yes, zero is an integer, apart from negative and positive real numbers. If we have to represent the integers as a whole with 0, then it can be done as:

……….,-10, -9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10…

Whole numbers and Integers

If we compare whole numbers and integers, then we can understand that all the whole numbers are integers but not all the integers are whole numbers. Since whole numbers start from value 0 and go till infinity, they do not consist of negative numbers. But, integers consist of negative numbers too.

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