Number Lines: Representation And Significance

Mathematics is a subject which has introduced numbers to us. We began with counting, types of numbers, followed by addition, subtraction, and other arithmetic operations. We started to know the value of numbers and compared them. Recently, we have also learnt about the ways to picturize or represent numbers on a line, i.e. using number line. Here, we will learn about the ways to do arithmetic operations of numbers on a number line.

Numbers On Number Line:

A number line is a pictorial representation of numbers on a straight line. It’s a reference for comparing and ordering numbers. It can be used to represent any real number that includes every whole numbers and natural numbers. Just to recollect, Whole number is a set of numbers which include all counting numbers (1, 2, 3,4,5,6 …….) and zero (0), whereas Natural number is the set of all counting numbers i.e. 1, 2, 3, 4, 5, 6……..

Arithmetic operations of numbers can be better explained on a number line. To begin with, one must know to locate numbers on a number line. Zero is the middle point of a number line. All (natural numbers) positive numbers occupy the right side of the zero whereas negative numbers occupy the left side of zero on the number line. As we move on to the left side value of a number decreases. For example, 1 is greater than -2.

Number Line

Addition and Subtraction

Whether it is addition or subtraction of two numbers, begin with the first number. Locate the first number on the number line. The first number lets us know where to begin. The second number lets know the direction of movement. If the second number is a positive number move to right side, if it is a negative number move to left side of the first number for addition.

Addition

Positive numbers: When we add two positive numbers, the result will always be a positive number. Hence, on adding positive numbers direction of movement will always be to right side.

For example, addition of 1 and 5 (1 + 5 = 6)

Here the first number is 1 and second number is 5; both are positive. First, locate 1 on number line. Then move 5 places to right will give 6.

Adding 5 to 1

Negative numbers: When we add two negative numbers, the result will always be a negative number. Hence, on adding negative numbers direction of movement will always be to left side.

For example, addition of -2 and -3

Here, first number is -2 and second number is -3; both are negative. Locate -2 on number line. Then move 3 places to left will give -5.

Adding -3 to -2

Subtraction

Positive numbers: When we subtract two positive numbers, move to the left as far as the value of second number.

For example, subtract 5 from 2

Here the first number is 2 and second number is 5; both are positive. First, locate 2 on number line. Then move 5 places to the left will give -3.

Subtracting 5 from 2

Negative numbers: When we subtract two negative numbers, move to the right as far as the value of second number.

For example, subtract -4 from -2

First, locate -2 on number line. Then move 4 places to the right will give 2.

Subtracting (-4) from -2

To solve more problems and to watch interactive videos on the topic, download BYJU’S – The Learning App. Also, take free tests to practice for exams.


Practise This Question

On a real number line, x1=4 and x2=14. What is the distance between these two points?