The number line is better understood as a two dimensional way of representing positive and negative digits in a particular interface in relation with each other. The positive integers are placed to the right hand side of zero on the number line which is also considered as the origin and the negative integers to the left hand side of zero on the number line. The origin or zero is considered as neither positive nor negative.

## What is a Number Line?

The set of Integers consists of all natural numbers and their opposites and also includes zero. We can represent integers on a number line. A standard number line is a horizontal line. Zero is called as the origin. The numbers to the right of zero are positive and the numbers to the left of zero are negative numbers. The numbers plotted on the number line are called as the coordinates. Usually we finish the number line on either side with arrows to show that the line can be extended in either direction.

## Number Line Template

Number line templates are nothing but standard models of number lines which are used for demonstration and to maintain uniformity in all drawings involving the number line plot.

The original point is taken as zero, to the left of which are all negative integers while the right of the origin are used for all positive integers.
The use of the number line template makes it easier for anyone to maintain the standard and also draw and plot easily without bothering about the uniformity of plots and graphs.

## Features of Number Line

Here are a few key features of the Number line

1. The number line is a graphical representation of integers on a straight line.
2. The positive numbers are greater than zero and are represented on the right side of the origin which is zero.
3. Zero is neither positive nor negative.
4. The negative numbers are lesser than zero and are represented on the left of zero.
5. Each number is located on a number line by its distance with respect to the origin.
6. The distance of any integer a and -a from zero is the same except the direction of measurement of the distance.
7. Number lines are very useful to compare two numbers. We use > symbol to say that a number is greater than the other, < symbol to say a number is lesser than the other, = symbol to say a number is equal to the other.
8. As we move right from zero, the value of the number increases and as we move to the left, the value of the number decreases.
9. Number lines can also be used to represent the number and the number after it has been increased or decreased.
10. Number line can also be used to find the absolute value of an integer. Absolute value of an integer is its distance from zero. Absolute value of any number a is denoted as |a|.

## Operations using Number Line

The arithmetic operation involving Addition, Subtraction, Multiplication and Division can be demonstrated using a number line. On a number line Positive and Negative numbers are marked on either side with zero in the middle. To mark a positive integer, starting from 0 the counting is done towards the right and for a negative integer towards the left.

Add 1 + 4 on a Number line.

1 is marked starting from zero and moving one unit towards the right. As 4 a positive quantity is added, four units are counted from 1 towards the right landing on 5. For adding a negative quantity the move is made towards the left.

Subtraction

Subtract 7 from 5

Subtracting a number is same as adding its additive inverse. Subtracting 7 is equivalent to adding -7.Starting from 5, seven units are moved towards the left to get the answer as -2.

Skip Counting:

The number line can be used for skip counting to get a sequence of numbers with equal difference between two consecutive numbers. The diagram illustrates how odd numbers are counted skipping two.

Multiplication

Multiplication is nothing but repeated addition. This operation is done on a number line using the method of skip counting.

Division

Just as multiplication is repeated addition, division is repeated subtraction. Starting from the dividend, the divisor is skip counted towards the left. The counting is stopped when a number less than the divisor is reached. The number of skips gives the quotient while the number where the counting stops is the remainder.

## Integers Number Line

Integers plotted on the number line mainly consist of numbers on the right and left of the origin. These numbers can either be positive or negative depending upon the position of these numbers on the number line.

All the related operations of integers are also completed keeping in view the due position of these integers on the number line.

Add the integers on a number line (+4) + (-6)

+ 4 - 6 = -2

## Decimal Number Line

A number line that gets divided into hundredths can be used in a manner which will show how one can round hundredths to tenths or to the nearest whole numbers.

To round a decimal hundredth to tenths, we have to apply a rule similar to rounding tenths to whole numbers.

Example: we can round 0.57 to 0.60 and once this is done, we can easily plot this on the number line.
The decimal fraction 1.23 could be rounded to 1.2 and then plotted on number line.

## Number Line Addition

The number line can be used for showing the addition of numbers which are signed. There can be an addition between numbers of like signs and numbers of unlike signs. Adding numbers of like signs can be between two positive signs or negative signs.

Let us take an example of addition between like signed numbers.

Let us do (+4) + (+2). In these three positive signs, two signs belong to numbers and one sign belongs to the operation.

= 4 + 2 = 6

Similarly, when we take two negative signed numbers (-2) + (-3), the positive sign here shows the sign of operations and the two negative signs signify the signs of numbers.

(-2) + (-3) = -2 - 3 = -5

## Number Line Subtraction

The number line can be used for showing subtraction of numbers which are carrying signs.
As in addition, there can be subtraction between numbers of like signs and numbers of unlike signs.

In case there is an operation for numbers like (-2) – (-7) then out of all the three negative signs, two belong to the numbers and one to the operation.

(-2) – (-7) = -2 + 7 = 5

Similarly, in (+3) – (+9) only one negative sign belongs to the operation while the rest belongs to the numbers.

(+3) – (+9) = +3 - 9 = -6

## Examples on Number Lines

Given below are examples based on the number line

Example 1: Compare -3 and -7. Place the correct inequality symbol.

Solution:

Step 1: Draw the number line.
Step 2: Plot -3 and -7 on the number line.
Step 3: The number that is on the right side is the larger number

-3 is to the right of -7 and hence, -3 is the larger integer.

-7 < -3 OR -3 > -7

Example 2: What is the absolute value of -5 and the absolute value of 5?

Solution:

Step 1: Plot the given values, -5 and 5 on the number line.
Step 2: Measure the distance -5 from zero and that of 5 from zero. All the measurements are taken with respect to zero which is the origin. -5 is at a distance of 5 units from zero and 5 is also at a distance of 5 units from zero.
Step 3: This distance is the absolute value of the number. The absolute value of -5 is 5 and the absolute value of 5 is also 5.

Hence, |-5| = |5| = 5

MCQ

Use the number line shown above wherever necessary.