Categories: EDUCATION

Number Lines and Integers

Number Lines and Integers

The visual representation of different types of numbers on a horizontal straight line is called the number line. The direction of the movement is very important in the case of number lines. The values of numbers keep on increasing as we move in the right direction of the number line and the values of the numbers keep on decreasing as we move in the left direction of the number line. We generally mark the values of the integers on the number line and use it as a tool of comparison. In this article, we will discuss in detail the concepts of integers and the number line.

Procedure to Draw a Number Line

Let us now discuss the process to draw a number line:

  • Draw a straight horizontal line with arrows at both ends facing outwards.
  • Decide and choose the scale on the basis of the given numbers. For example: If you have to plot 60 and 80, you can choose a scale of either 10, 20, or 25. Deciding the scale depends upon the numbers given to the plot.
  • Different points should be marked at equal intervals.
  • Encircle the number that you want to plot on the number line.

What Do You Mean by Integers?

Mathematically speaking, integers are the subsets of real numbers. They are the numbers that are whole. Integers do not constitute fractions and decimals. Integers can be positive numbers as well as negative numbers. Some examples of integers are -13, -47, 15, 1, etc. The word integer has been originally derived from the Latin word, the meaning of which is ‘whole’. An important thing to note about integers is that all real numbers are not integers but all integers are real numbers. This is because rational numbers and irrational numbers are also included in the set of real numbers.

Universal Symbol for the Representation of Integers

The universally accepted notation of the integers is the alphabet ‘Z’. While listing down the set of integers, we write: Z = { 1, 2, 5, -6, -17, -24}

Subsets of Integers

There are different types of numbers that come under the category of integers. Let us discuss them in detail:

  • Whole Numbers: A set of numbers that start from the number 0 and extend up to infinity are called whole numbers.
  • Natural Numbers: Natural numbers are the same as the whole numbers except for one change. In the case of natural numbers, the number 0 is excluded. This means that natural numbers are the numbers that start from the number 1 and extend up to infinity.
  • Odd Integers: Odd integers are those integers that cannot be divided by the number 2 wholly. Examples of odd integers are -1, -57, 1, 57, etc.
  • Positive Integers: Positive integers are those integers that can be divided by the number 2 wholly. Examples of positive integers are 2, 25, -2, -25, etc.
  • Prime Numbers: Those numbers that have two factors only i.e. the number itself and the number 1 are called prime numbers. Some examples of prime numbers are 3, 11, 7, 13, 17, etc.
  • Composite Numbers: Composite numbers are the opposite of prime numbers. These are the numbers that have more than two factors. Some examples of composite numbers are 4, 46, 56, 21, etc.

Different Rules of Integers

  • The addition of two integers results in the formation of an integer.
  • The subtraction of two integers results in the formation of an integer.
  • The multiplication of two integers or more integers result in the formation of an integer.
  • The division of an integer with another integer result in the formation of an integer.

 

If you want to learn more about the concepts of number line and integers in detail and in a fun and interesting manner, visit Cuemath and learn and understand math, the Cuemath way.

Dinanath Singh: