Placing Fractions on the Number Line

🏆Practice fraction on the numeric axis

Placing Fractions on the Number Line

To locate fractions on the number line, we will carry out several steps.

First Step Discovering the Value of Arcs

We will subtract two given numbers and keep the difference.
We will count the number of arcs between the numbers.
We will divide the subtraction result by the number of arcs to find out the measure of each arc.

Step Two – Placing the Numbers on the Number Line

Depending on the amount of arcs, the scale can be expanded or reduced.

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The number \( \frac{1}{4} \) is found?

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Fractions on the Number Line

In this article, we'll learn how to order fractions on the number line with ease, speed, and without any trouble.
Let's first look at the number line and analyze it.

let's look at the number line - Placing fractions on the number line

Here we see a number line from 00 to 55.
We notice that the line is divided into 55 sections, and each mark indicates an increase of 11.
However, if we look at this number line:

2 - Location of fractions on the number line

We'll see that each mark indicates an increase of 22.

To place fractions on the number line, the first thing we need to understand is how much we increase from one segment to the next.
The lines that mark the end of each segment on the number line are called points. It is also common to say that – represents the space between the two points.

The lines that mark the end of each segment on the number line are called points

Exercise Practice

Complete the missing numbers on the number line:

Complete the missing numbers on the number line

Solution:
To fill in the numbers, first let's mark, with an arc, the spaces that are between the dots of the two given numbers.

the number line - the spaces that are between the dots of the two given numbers

We will notice that there are 33 arcs between the number 2020 and 8080.
Remember, all the spaces are identical.
Let's subtract 8020=6080-20=60.
6060 is the total space.
Since there are 33 arcs, we will divide the 6060 by 33 to find the measure of each arc.
We will find that:
60÷3=2060 ÷ 3 = 20
Therefore, each arc measures 2020.
We will place marks on the number line so we can easily fill in the remaining numbers:


Now that we know a bit more about the number line and have learned how to find the distance between two points, we can move forward.

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Fractions on the Number Line

First Step

Finding the Measure of the Arc Between Two Points in the Following Way:
Subtract the two given numbers and keep the difference.
Count the number of arcs that are between the numbers.
Divide the result of the subtraction by the number of arcs to find out the measure of each arc.

Second step

Placing the Numbers: Reduction and expansion can be applied if necessary.


Let's continue learning with an example

Put the fractions 12 \frac{1}{2} and 112 1\frac{1}{2} on the number line.

Let's ask ourselves, what is the difference between the 22 given numbers?
For example, between 11 and 22?
The difference is 11.
How many arcs are there between 11 and 22?
44 arcs.
We will divide the difference we calculated by the number of arcs and we will get:
1:4=141:4=\frac{1}{4}
Each arc measures 141 \over 4.
Now let's think about where to place the 121 \over 2.
We can scale up the 121 \over 2 by 22 and we get 242 \over 4.
Therefore, 121 \over 2 will be placed here:

Now let's move on to 1121 \frac{1}{2}
We see that there is a whole number 1 in the fraction, so it will be located between 11 and 22
We saw that each segment measures 141 \over 4 and deduced that 121 \over 2 is equivalent to 242 \over 4.
Therefore, 1121 \frac{1}{2} will be located here:


Do you know what the answer is?

Another Exercise

Find the number that the arrow points to:

Solution:
First, let’s find out how much each segment represents.
Take the two given numbers 11 and 22
and count how many segments there are between them.
There are 77 segments between 11 and 22.
Subtract:
21=12-1=1
Now divide by 77
1÷7=171 \div 7=\frac{1}{7}
Each segment represents 171 \over 7.
Now, let's see how many segments we need to jump to reach the arrow:
The answer is 44, so the number will be 1471 \frac{4}{7}.
Make sure not to forget the whole number 11.

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