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Fractions on Number Line: Steps for How to Put Fractions on a Number Line.

fractions on number line

Plotting fractions on a number line is similar to Plotting integers and Whole numbers on the number line. We have learned how to Plot Whole numbers on the number line in primary classes. The concept is almost the same for plotting fractions on the number line. There is just a slight difference. But, nothing to worry about here! Representing a fraction on the number line is also easy as a pie. You have to understand a simple concept, and you are good to go. For this thing, we are here for you.

Now, let us know how to put fractions on the number line. 

Before diving deep into the core concept, let us first brush up on our understanding of a fraction and representing a fraction on a number line.

What is a Fraction?

In simple words, a fraction represents parts of a whole. It tells how many parts of a whole thing we are having. This whole can be a basket of fruits, a box of balls, a deck of cards, or anything. We can recognize a fraction by the slash between the two numbers. The number on the top is the numerator, and the number at the bottom is the denominator. 

For example, You are having a pack of three chocolates. Now, you ate 2 chocolates from it. So, we can represent the number of chocolates you ate from a whole of 3 chocolates as a fraction, i.e., 2/3. Here, 2 is the numerator, and 3 is the denominator.

Fractions diversify our number system ahead of the whole numbers and integers. By using fractions, we can easily denote any decimal number with accuracy. They help us to apportion and judge numbers effortlessly. It facilitates faster calculations. Here, plotting fractions on a number line is significant to understanding how fractions represent parts of a whole.

What is a Fraction Numbers Line?

In mathematics, fraction on the number line is a visual representation of fractions on a typical number line. We can represent a fraction on the number line by plotting the given fraction on a number line. We have to segregate the distance or the portion between two integers into equal parts. The number of parts should be equivalent to the denominator of a given fraction.

Now, let us dive into the core concept and understand how to put fractions on a number line.

How to Put Fractions On A Number Line?

As stated above, plotting fractions on a number line is similar to representing whole numbers and integers. Since fractions represent parts of a whole, we represent them by making equal parts of a whole, i.e., 0 to 1. The number of equal parts would be similar to the fraction’s denominator. For instance, to represent 1/5 on the number line, we must divide 0 to 1 into 5 equal parts and mark the first part as 1/5. 

Steps for how to put fractions on a number line

Let us learn how to correctly bifurcate a number line to represent fractions on a number line. The steps to represent fractions on the number line are as follows:

Step I: Draw a usual number line

First, you will have to draw a usual number line of a suitable length.

Step II: Mark the points

Next, you must mark the points between which you will locate the given fraction. If the given case is to plot a proper fraction, then you should mark points 0 and 1 on the number line. On the contrary, if the given case is an improper fraction, you should first convert it into a mixed fraction. Then mark two integers amid which the given fraction lies. For example: to represent 5/2 on the number line, first convert it into mixed fraction = 21/2. 21/2 will lie between points 2 and 3 on the number line. 

Step III: Mark equidistant sections 

Now, you have to draw an equal number of parts or sections of the numbers you have marked in Step II. Notably, these parts will be equal to the denominator of the fraction. 

Step IV: Count the sections and locate your fraction

Starting from the left side, count the number of parts per the numerator. As per our example, we will locate point 1.

Step V: Final Marking

Lastly, mark it on the number line after locating your fraction. In our example, we will mark 21/2 on the line.

Key Takeaways:

  • Our number line is a line with evenly spaced parts or sections that help to mark/spot the numbers.
  • To know how many even sections you should divide between the two points, you should refer to the denominator. It signifies how many parts or sections you have to mark.
  • To know which one part is your fraction among those marked parts, you should refer to the numerator. It signifies you have to mark your fraction on which part.

Reminder: Always remember to convert an improper fraction into the corresponding mixed fraction.

After this explanation, you must have gained clarity on the concept of fractions on a number line. Now, let us review how to represent equivalent fractions on a number line.

How to Find Equivalent Fractions on A Number Line

Here, we will discuss equivalent fractions and how to represent them with the help of a number line.

Equivalent fractions share the same position disregarding the numbers written in their numerators and denominators. They are equal in value. For example, 2/3, 4/6, 8/12 are equivalent fractions. All these share the same value, as on their simplification, 4/6 and 8/12 are also equivalent to 2/3.

Steps to Plot Equivalent Fractions On A Number Line

Let us explore how to bifurcate a number line to represent equivalent fractions. There are some definite steps that you should consider when calculating equivalent fractions on a number line. Recalling the statement above, the equivalent fractions are different ways to write the same fraction. On simplifying the successive equivalent fractions, you will get a fraction the same as the other one. To simplify, you have to divide both the numerator and the denominator. Consider a common factor to separate them.

We will begin with one example to find equivalent fractions, say 1/3. Now, follow these steps to find the equivalent fractions.

A Tip before you start – Try to make distant markings in the first step. In the next consecutive steps, the subsections will increase. So, it will be helpful to mark points clearly if you have good space.

Step I: Spot the original standard form of fractions on the number line.

First, you will need to locate the fraction on the number line. You will have to mark even sections on the number line. For example, to locate the fraction, our fraction is 1/3. You will need to mark points 0 and 1. 

You will have to divide the section between 0 to 1 mark into three equal parts. In the same way, if 1/4 is there, you will divide the space between the numbers 0 and 1) into four equal pieces. The denominator represents how many equal parts to divide in the corresponding section. At the same time, the numerator shows which one of those parts is your fraction. 

So, to locate 1/3, you will be dividing your first section of 0 to 1 into three even spaces. Put a small mark with a pen/pencil after finding the fraction. The numerator 1 represents that our fraction is the first part of the marked section of 0 to 1.

Step II: Divide each part of Step I into three equal parts or sections.

Next, to find the equivalent fractions, you will have to divide the parts you marked in Step I again into three even spaces. So, for your 3/9, you will divide the three divisions/parts marked in Step I into three equal sub-parts. You will now have nine similar spaces between your numbers 0 and 1.

Step III: Locate the equivalent fraction

To find the (next) equivalent fractions on a number line, you will have to read the newly created number line. Here, to read means to count. 

Remember that you had three equal separations for the initial fraction 1/3 between the numbers 0 and 1. But for this fraction, now your number line has nine equal separations. So this indicates that the denominator is now 9. Next, you have to count three points between 0 and 1. Starting from 0, count three points on the right and put a small mark. This is the numerator of your fraction, i.e., 3. So, 1/3 and 3/9 are equivalent fractions.

Step IV: Repeat Steps II and III

For finding more equivalent fractions on a number line, you have to repeat II and III Steps. 

So, your answer, i.e., the next equivalent fraction, is 3/9. Hence, an equivalent fraction to 1/3 is 3/9.

We hope today’s discussion of how to put fractions on a number line proves useful for you.

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