Fractions on Number Line

Representing fractions on a number line means that we can plot fractions on a number line, which is similar to plotting whole numbers and integers. Fractions represent parts of a whole. So, fractions on the number line are represented by making equal parts of a whole i.e. 0 to 1, and the number of those equal parts would be the same as the number written in the denominator of the fraction. For example, to represent 1/8 on the number line, we have to divide 0 to 1 into 8 equal parts and mark the first part as 1/8.

To plot fractions on the number line, follow the steps given below:

• Step 1: Draw a number line of a suitable length.
• Step 2: If the given fraction is a proper fraction, then mark points 0 and 1 on the number line. Or, if it is an improper fraction, then first convert it into a mixed fraction, and then mark two integers between those the given fraction lies. For example, to represent 3/2 or \(1 \dfrac{1}{2}\), mark points 1 and 2 on the number line.
• Step 3: Draw an equal number of parts of the numbers marked in step 2 which will be equal to the denominator of the fraction.
• Step 4: Starting from the left point, count forward the number of parts shown by the numerator.
• Step 5: Mark the point on the line.

An example of 3/7 is shown in the image below to help you understand how to plot fractions on a number line step-wise.

It is easy to compare fractions on a number line. The number line represents values in ascending order from left to right. It means that the fraction which is marked on the left side is lesser than the fraction on its right. For example, in the image below, it is clear that 1/5<3/5, as 1/5 is on the left of 3/5. This is how you can compare any two or more fractions on the number line.

Representing fractions on a number line can be understood in three different ways, which are:

• Representing equivalent fractions on a number line
• Improper fractions on a number line
• Mixed fractions on a number line

Equivalent Fractions on Number Line

Equivalent fractions are those that have the same value when reduced to the simplest form. In the image below, fractions marked in the same color are equivalent fractions. For example, 2/5 and 4/10 are equivalent, as when we reduce 4/10 to its simplest form we get 2/5. That is why, they are at the same position on the number line, irrespective of the difference in numerators and denominators.

Mixed Fractions on Number Line

Mixed fractions have two parts, one whole number and one proper fraction. To represent mixed fractions on a number line, first, we have to mark two points: the whole number part on the left and its successor on the right. For example, in the image given below, \(2\dfrac{3}{5}\) is shown on the number line whose whole number part is 2. So, we will mark points 2 and 3 on the number line. The next step is to divide the section between 2 and 3 into 5 equal parts, as the denominator of the given fraction is 5. Now, at last, we will have to make 3 jumps to the right of 2. This point will be the representation of the fraction \(2\dfrac{3}{5}\) on the number line.

Improper Fractions on Number Line

Improper fractions are those whose numerator is either equal to or greater than the denominator. If numerator = denominator, then it will become a whole number that can be easily represented on a number line. But if, numerator>denominator, then we can first convert an improper fraction to a mixed number, and then represent it on the number line using the same procedure as discussed above.

Fractions on a Number Line Worksheet PDFs

Download fractions on a number line worksheets with answers to practice questions on this topic.

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

How to Explain Fractions on a Number Line?

Fraction on a number line is a visual mathematical representation of fractions. It is done by plotting the given fraction(s) on the number line where the section or the distance between two integers is divided into equal parts which are equal to the denominator of the given fraction. It is useful to add/subtract or to compare fractions visually.

How to Represent Fractions on Number Line?

Fractions can be represented on a number line by following these simple steps:

• Step 1: Draw a number line and mark two integers between which the fraction lies.
• Step 2: Divide the section between the two integers in an equal number of parts which is equal to the denominator.
• Step 3: Start from the integer on the left side and make as many jumps as the number written in the numerator of the fraction.
• Step 4: Mark that point with a color or a circle and write the fraction beside it.

What are Equivalent Fractions on a Number Line?

Equivalent fractions on a number line are those fractions that share the same position irrespective of the numbers written in their numerators and denominators. They are equal in value.

How to Order Fractions on a Number Line?

Fractions that lie on the left side are smaller than the ones that are on their right side. To order fractions on a number line, the fraction written on the leftmost side is the smallest, the fraction written on the rightmost side is the largest fraction, and all other fractions will lie between these two depending on their position from left to right.

How to Add Fractions on Number Line?

We can easily add like fractions on the number line by plotting any one fraction first, and then take as many jumps to the right as the numerator of the second fraction. For example, to add 3/4 and 5/4, we can first plot 5/4 on the number line, and then take three jumps to the right. We will reach at 8/4 or 2 and that is the required answer because 3/4 + 5/4 = 8/4 = 2.