MathsNumbersFractions on Number Line

Fractions on Number Line

Fractions on Number Line

Representing fractions on a number line signifies that fractions can be plotted on a number line, comparable to plotting whole numbers and integers. Fractions symbolize portions of a whole. Thus, fractions on the number line are represented by dividing a whole, i.e. 0 to 1, into equal parts, and the number of these equal parts corresponds to the fraction’s denominator. To represent 1/8 on the number line, for instance, we must divide 0 to 1 into eight equal parts and label the first portion as 1/8.

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How to Plot Fractions on Number Line?

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

  1. Draw a number line of the appropriate length.
  2. Mark the points 0 and 1 on the number line if the specified fraction is a correct fraction in Step 2. Or, if it is an improper fraction, convert it to a mixed fraction and then indicate the integers between which it resides. For example, to represent 3/2 or \(1 \frac{1}{2}\),
  3. Step 3: Draw a denominator-equivalent number of parts from the numbers marked in step 2.
  4. Step 4: Beginning at the leftmost point, count forward the number of fractional parts indicated by the denominator.
  5. Mark the point on the line in Step 5.
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Comparing Fractions on Number Line

On a number line, comparing fractions is simple. The number line represents values from left to right in ascending order. It indicates that the fraction marked on the left is less than the fraction marked on the right. As 1/5 is to the left of 3/5 in the image below, it is evident that 1/5 is greater than 3/5. This is how any two or more fractions can be compared on a number line.

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Representing Fractions on Number Line

Representing fractions on a number line can be comprehended in three distinct ways, namely:

  • Using a number line to depict equal fractions
  • Unacceptable fractions on a number line
  • Mixed fractions represented on a number line

Equivalent Fractions on Number Line

When reduced to their simplest form, fractions are equivalent if their values are identical. Fractions indicated with the same colour in the figure below are equivalent fractions. For example, 2/5 and 4/10 are equal because when 4/10 is simplified, it becomes 2/5. Consequently, they occupy the same location on the number line, regardless of the difference between their numerators and denominators.

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Mixed Fractions on Number Line

Mixed fractions consist of a whole number and an appropriate fraction. To plot mixed fractions on a number line, we must first mark two points: the whole number component on the left and its successor on the right. In the figure below, for instance, (2dfrac35) is displayed on a number line whose whole number component is 2. On the number line, we will therefore mark points 2 and 3. As the denominator of the above fraction is 5, the next step is to divide the interval between 2 and 3 into 5 equal parts. Now, last, we must make three hops to the right of two. On the number line, this point will represent the fraction  \(2\frac{3}{5}\)

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Improper Fractions on Number Line

The numerator of an improper fraction is either equal to or greater than the denominator. If the numerator equals the denominator, the result is a whole integer conveniently represented on a number line. In contrast, if the numerator is greater than the denominator, we can convert an improper fraction to a mixed number and then represent it on the number line using the same approach as described previously.

Example of Fraction on Number Line :

Represent 43/5 on the number line.


First, convert 43/5 into the mixed fraction.

\(\begin{array}{l}\frac{43}{5} = 8\frac{3}{5}\end{array} \)

Now, we start from 8 and divide the section between 8 and 9 into 5 equal parts (5 being the denominator). The third point, as shown in the figure, represents our required fraction.

Improper Fractions on Number Line

FAQs on Fractions on Number Line

Q.1 How to Explain Fractions on a Number Line?

A fraction on a number line is a way to show how fractions look in math. It is done by putting the fraction(s) given on a number line where the space between two integers is divided into equal parts that are equal to the fraction’s denominator. It is helpful to see how fractions add up, subtract, or compare.

Q.2 How to Represent Fractions on Number Line?

Follow these easy steps to show how fractions look on a number line:
Step 1: Draw a number line and mark where the fraction lies between two whole numbers.
Step 2: Split the section into two equal parts, which is the same number as the denominator.
Step 3: Start with the number on the left and jump as many times as the number in the fraction’s numerator.
Step 4: Circle or colour that point and write the fraction next to it.

Q.3 What are Equivalent Fractions on a Number Line?

On a number line, equivalent fractions are those that share the same spot, no matter what numbers are in their numerators and denominators. They are both worth the same.

Q.4 How to Order Fractions on a Number Line?

Left-side fractions are less significant than right-side fractions. The fraction printed on the leftmost side of a number line is the smallest fraction, the fraction written on the rightmost side is the greatest fraction, and all other fractions lie between these two based on their position from left to right.

Q.5 What is 1/4 on a number line?

To mark 1/4; move one part on the right-side of zero. To mark 7/4; move seven parts on the right-side of zero. To mark -3/4; move three parts on the left-side of zero. To mark -9/4; move nine parts on the left-side of zero.

Related Topics

Check these interesting articles related to the concept of fractions on a number line.

  • Rational Numbers on Number Line
  • Integers on Number Line
  • Representation of Real Numbers on Number Line
  • Decimals on Number Line
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