Number Line

Did you know that the number line was invented by Ancient Egyptians with a rope to measure lengths? This was done 2500 years ago, and with it, they were able to carry out number line addition and number line subtraction.

Over millennia, philosophers, scientists, and mathematicians discovered interactive number lines, negative number lines, number line integers, and with their help, we will try and solve some number line examples.

Ancient Egyptians: number line rope

You can check out the interactive simulations to know more about this lesson and try your hand at solving a few interesting practice questions at the end of the page.

Lesson Plan

What Is a Number Line?

A number line is a visual representation of numbers on a straight line.

This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.

Rainbow number line, less and more marked


Integers on a Number Line

On a number line, integers are marked on equal intervals.

Positive Number Line and Negative Number Line

If we observe the given number line, we find that the origin is \(0\) (zero), which stands in the middle.

To the right, there are positive numbers and to the left, there are negative numbers.

Hence, this number line represents integers which include positive and negative numbers.

These extend endlessly in both directions and that is why the arrows are marked at both ends to show that the line is infinite.

Positive and negative Number line

The numbers increase and decrease as we change directions

Any number to the left is always less than the number to its right.

For example:

\(2\) is less than \(4\)

-\(3\) is less than -\(1\)

Similarly, any number to the right is always more than the number to its left.

For example:

\(5\) is greater than \(3\)

-\(1\) is greater than -\(3\)


Use of Number Lines

In math, number line has applications for the understanding of number operations, which are considered as basics or foundation of math.

Number Line Addition

Let's assume that you have \(2\) flowers. Your friend gave you \(3\) more.

Find the number of flowers you have now.

How will you solve it using a number line?

Use of Number Line-addition example

We know that the numbers increase as we go to the right.

Starting from \(2\), take \(3\) steps to the right to get the answer!

Now you have \(5\) flowers!

Number Line Subtraction

Let's say, you have \(7\) oranges and you give \(3\) to your friend.

Find the number of oranges you have now.

How will you solve this using a number line?

Number line subtraction example

We know that the numbers decrease as we go to the left.

Starting from \(7\), take \(3\) steps to the left to get the answer!

Now you have \(4\) oranges left!

Solving Negative Numbers

Number lines help us understand negative numbers and solve questions like the following.

What is \(3\) more than -\(1\)?

Solution:

Let us represent this on a number line.

This helps us understand the position of -\(1\), and where it reaches after moving \(3\) steps to its right.

Number line with plus 3

We move \(3\) steps to the right of -\(1\) (A Number to the right is always greater than the number to the left).

Thus, the answer is \(2\)


Interactive Number Lines

Try this interactive number line to observe number line addition and subtraction.


Reset, Enter the answer and Check!

 
important notes to remember
Important Notes
  1. We can represent various numbers on the number line, according to our requirement. For example, they can be only positive numbers, or integers between -\(4\) and \(3\), or even fractions between -\(2\) and \(2\).
  2. Number lines can help us in real-life situations. For example, they read the altitude (height) which is shown on a GPS device's screen and can tell you how high or low you are below sea level!

Solved Examples

Here are a few number line examples. Let's have a look!

Example 1

 

 

A diver wants to click a photograph of a fish that he spotted while swimming in the sea.

He is at -\(2\) and needs to go to the number which is \(4\) more than -\(2\)

Can you find the exact location of the fish?

Solution

If he starts from -\(2\), he needs to move \(4\) steps to the right.

\(4\) more than -\(2\) can also be understood as :  \(4 + (-2) = 2\)

Diver with fish shown on a number line

Hence, the fish is located at number \(2\) and the diver should go to number \(2\)

\(\therefore\) The fish is located at number \(2\)
Example 2

 

 

A flower is hidden behind an integer which is at a position \(7\) less than the spot where the butterfly is placed.

Can you find the integer?

Number line with butterfly shown at 4

Solution

From the above figure, it is clear that the butterfly is placed at \(4\)

Number line with flower and butterfly

\(7\) steps less than \(4\) means: \(7\) steps to the left of \(4\) will take the butterfly to the flower.

This can also be understood as:  \( +  4 - 7 = -3\)

This brings us to -\(3\)

Thus, the flower is hidden behind -\(3\)

\(\therefore\) The integer is -\(3\)
Example 3

 

 

Arrange the numbers shown on these trees in ascending order with the help of a number line.

5 trees with numbers marked on them

Solution

Let us mark the given numbers \(7\), -\(3\), \(0\), \(1\), \(5\) on the number line.

Number line example

We see that  -\(3\) < \(0\) < \(1\) < \(5\) < \(7\)

Hence, -\(3\), \(0\), \(1\), \(5\), \(7\) are in ascending order.

\(\therefore\) -\(3\), \(0\), \(1\), \(5\), \(7\) are in ascending order.
Example 4

 

 

How many steps should the rabbit jump to reach the carrot on the given number line?

Rabbit is at -5 position on the number line

Solution

The rabbit, which is at -\(5\), starts jumping to reach the carrot which is at \(1\)

The rabbit will have to jump \(6\) steps to the right.

Number line - Rabbit and carrot example

\(\therefore\) The rabbit will jump \(6\) steps.
Example 5

 

 

A group of ducklings has been given numbers.

They need to be arranged in descending order based on these numbers.

Arrange them with the help of a number line.

Ducklings with numbers marked on them.

Solution

The numbers on the ducklings are -\(6\), \(7\), -\(2\), \(3\) and \(0\)

Let's mark them on the number line.

Number line example

We see that  \(7\) > \(3\) > \(0\) > -\(2\) > -\(6\)

Hence, \(7\), \(3\), \(0\), -\(2\), -\(6\) are in descending order.

\(\therefore\) 7 ,3 ,0 ,2 ,6 are in descending order.
 
tips and tricks
Tips and Tricks
  1. Positive Numbers: If a number does not have a sign, it is a positive number. For example, \(7\) is actually +\(7\)
  2. The value of numbers decreases as we move to the left of a number line, whereas, the value increases as we move to the right.

Try this interactive number line to compare numbers.

 

Reset, place the sign, and check your answer!

 


Interactive Questions

Try these Questions based on the Number Line in the worksheet given below.

Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 

 
 

Let's Summarize

We hope you enjoyed learning about the number line with the simulations and practice questions. Now you will be able to easily solve problems on number lines, number line addition, interactive number lines, negative number lines, number line integers, number line examples, and number line with negatives.

About Cuemath

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Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we at Cuemath believe in.


Frequently Asked Questions (FAQs)

1. How do you write a number line?

A number line usually has its origin with the number \(0\) (zero) located in the middle.

The positive numbers are marked to its right, whereas negative numbers are plotted to its left, in an order where each number is placed at equal intervals.

2. What is the definition of the number line?

A number line is a visual representation of numbers on a straight line.

3. What is a number line model?

A number line model is a representation of numbers plotted on an infinite line which extends at both ends.

  
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