# Number Lines

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 picture or represent numbers on a line, i.e. using the number line.

## What is a 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 number and natural numbers. Just to recollect, the whole number is a set of numbers which include all counting numbers (1, 2, 3,4,5,6 …….) and zero (0), whereas the natural number is the set of all counting numbers i.e. 1, 2, 3, 4, 5, 6……..

### Numbers On a Number Line

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. In a number line, integers, fractions, and decimals can also be represented easily.

Representation of Numbers in a Number line
Representation Of Fraction On The Number Line Rational numbers on a number line
Representation Of Decimals On Number Line Represent Linear Inequalities In One Variable On Number Line

Important Notes:

• On a number line, a number on the left is always less than a number on the right.
• Similarly, a number on the right is always greater than a number on the left.

## Addition and Subtraction on Number Line

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 the right side if it is a negative number move to the left side of the first number for 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 the right side.

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

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

• 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 the left side.

For example, the addition of -2 and -3

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

### Subtraction of Numbers

• Positive numbers:

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

For example, subtract 5 from 2

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

• Negative numbers:

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

For example, subtract -4 from -2

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