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Last updated on July 4th, 2025

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Fractions on Number Line

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A portion of a whole number can be expressed in the form of fractions. These fractions can be visually represented by plotting on a number line. Fractions are used to represent accurate measurements, such as ½ cup of flour. In this topic, you’ll learn about how to plot fractions on a number line.

Fractions on Number Line for Filipino Students
Professor Greenline from BrightChamps

What are Fractions?

Fractions are expressions that represent parts of a whole. A fraction has two parts, the numerator and the denominator. It is expressed in the form a/b, where a is the numerator and b is the denominator and b ≠ 0. In other words, a fraction represents the portion occupied out of the whole.

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How to Plot Fractions on a Number Line

To plot fractions on a number line, use the steps listed below:

 

  • Draw a horizontal number line.
  • Determine whether the fraction is proper, improper, or mixed.
     

 

For proper fractions:

 

  • Draw a number line from 0 to 1 and divide it into as many parts to find out those proper fractions lying between 0 and 1.

 

For mixed fractions:

 

  • Start plotting from the whole number (quotient) part of the mixed fraction.

 

  • Then, divide the remaining part based on the denominator.

 

For improper fractions:

 

  • For converting the improper fraction into a mixed fraction, plot it on the number line.

 

  • Count from left to right on the number line and mark the points.
     
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How to Represent Fractions on Number Line

There are different ways to represent fractions on a number line based on their type:

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Equivalent Fractions on Number Line

To represent equivalent fractions on a number line, follow the steps below:

 

 

  • Express all the given fractions in their simplest form.

 

  • Check if the fractions have the same simplest form to confirm they are equivalent.

 

  • Now, we plot the fractions on the number line.

 

  • Equivalent fractions occupy the same position on the number line, even though they may look different.
     
Professor Greenline from BrightChamps

Proper Fractions on Number Line

Represent proper fractions on a number line using the following steps:

 

  • Since the numerator is less than the denominator, we represent it on a number line between 0 and 1.

 

  • Divide the section between 0 and 1into equal parts based on the denominator.

 

  • We now count to the numerator from the left to represent the proper fraction on the number line.
     
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Mixed Fractions on Number Line

Represent mixed fractions on a number line using the following steps:

 

 

  • Identify the fractional part and whole part of the mixed fraction.

 

  • The plotting should start from the whole number part of the mixed fraction.

 

  • Based on the denominator of the fractional part, divide the number line into equal parts.

 

  • Now, mark the given mixed fraction on the number line.
     
Professor Greenline from BrightChamps

Improper fractions on Number Line

Represent improper fractions on a number line using the following steps:

 

 

  • If the given fraction is an improper fraction, convert it into a mixed fraction.

 

  • Then, plot the mixed fraction on a number line.

 

  • Improper fractions have a numerator greater than or equal to the denominator.

 

  • If the numerator and denominator are equal, the fraction equals 1 and should be represented on the number line.

 

  • When the numerator is greater than the denominator, the fraction needs to be converted into its equivalent mixed fraction before plotting.
     
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Real-Life Applications of Fractions on Number Line

Fractions play an important role in our everyday life. Visualizing fractions on a number line helps us measure the accurate portion of a whole amount. Here, we will look at a few real-life examples of fractions:

 

 

  • While cooking, we use fractions to measure the quantity of ingredients, such as 1/2 cup of sugar.

 

  • We can use fractions to manage time by dividing it into sections. For example: 30 minutes = ½ of an hour.

 

  • With a fraction number line, students can determine the distance traveled and the distance remaining during a travel journey.

 

  • When shopping, we may come across discounts that involve fractions. For example: ½ off an item.

 

  • Fractions on a number line help us measure the remaining time or distance in a fitness routine. 
    For example: ¼ of the workout routine.
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Common Mistakes and How to Avoid Them in Fractions on Number Line

Students often make mistakes when plotting fractions on a number line, which can lead to wrong representations. Identifying these errors will help in preventing them. Here are a few common mistakes along with tips to avoid them:

Mistake 1

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Incorrectly Placing Fractions
 

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While plotting fractions incorrectly on a number line, it can lead to inaccurate calculations. Suppose, if it is an improper fraction, a student will make a mistake in plotting it over the number line.
Before marking the fractions, count the sections into which the number line is divided.
 

Mistake 2

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Confusion Between the Types
 

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There is a common confusion between improper and mixed fractions. For example, students mistakenly plot improper fractions instead of mixed fractions.
You can convert improper fractions into mixed fractions before marking on a number line to avoid confusion.
 

Mistake 3

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Mistakenly Counting backward
 

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Students count the fractions in the backward direction.
Always count the fractions from left to right on the number line.
 

Mistake 4

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Overlooking the Whole Number Part
 

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Some students might plot only the fractional part and ignore the whole number part.
To avoid this error, always start from the whole number part before dividing the fraction.
 

Mistake 5

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Unequal or inconsistent intervals on the number line 
 

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Dividing the number line into unequal or inconsistent scaling can lead to confusion.
Maintain equal spacing between each section on the number line.
 

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Solved examples of Fractions on Number Line

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Problem 1

Determine if 3/9 and 1/3 are equivalent fractions using a number line.

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3/9 and 1/3 are equivalent fractions.

Explanation

To determine that 3/9 and 1/3 are equivalent fractions, we plot both fractions on different number lines.
Since both fractions are marked at the same point on the number line, we can conclude that 3/9 and 1/3 are equivalent fractions.
 

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Problem 2

Represent 6/5 on a number line

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NA

Explanation

To represent the given fraction, first identify its type:
6/5 is an improper fraction because the numerator (6) is greater than the denominator (5))
We now convert the given improper fraction into a mixed fraction:
6 ÷ 5 = 1, remainder 1
So, 6/5 = 1 ⅕

 

  • Then, draw a horizontal number line by marking the points 0 to 2

 

  • Since the denominator is 5, we divide each whole-number section into 5 equal parts.

 

  • Now, count 1 part after 1 and mark 1 ⅕ on the number line
     

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Problem 3

A number line is given with 2 missing values labeled as A, B, C, D, and E. The number line is divided into equal parts, where each step represents 1/2. Find the missing values.

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C and D are 3/2 and 4/2
 

Explanation

Each segment on the number line represents 1/2. By adding 1/2 step by step.
A = 1/2
B = 2/2
C = 3/2
D = 4/2
E = 5/2
So, the values of points C and D are 3/2 and 4/2 respectively.
 

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Problem 4

Represent 4/7 on a number line

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NA

Explanation

We first identify the type of the given fraction:
If the numerator is smaller than the denominator, then it is a proper fraction.
Now, draw a horizontal number line from 0 to 1.
Divide the segment between 0 and 1 into 7 equal parts, since the denominator is 7.
To mark 4/7:

 

Start from 0 and count 4 parts towards 1.
This point on the line represents 4/7.
 

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FAQs on Fractions on Number Line

1.How can we identify a proper fraction from an improper fraction?

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2.Give an example of a mixed fraction.

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3.Can we compare fractions using a number line?

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4.How do we apply fractions in our everyday life?

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5.How can children in Philippines use numbers in everyday life to understand Fractions on Number Line?

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6.What are some fun ways kids in Philippines can practice Fractions on Number Line with numbers?

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7.What role do numbers and Fractions on Number Line play in helping children in Philippines develop problem-solving skills?

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8.How can families in Philippines create number-rich environments to improve Fractions on Number Line skills?

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

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Fun Fact

: She loves to read number jokes and games.

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