How to Represent Fractions on a Number Line? (Plotting Fractions, Examples) - BYJUS

Finding Fractions using a Number Line and Strips

Fractions are numbers that exist between two whole numbers. We can use mathematical models like the fraction strip and number line to represent fractions. Learn about some special types of fractions using these mathematical models....Read MoreRead Less

What are Fractions?

A fraction is a portion of a whole or, more broadly, a set of equal parts. In everyday language, a fraction denotes the number of parts of a specific size, such as one-half, eight-tenth, or two-quarters. The picture below shows the fraction in every circle.

Models to Represent Fractions

• Fraction Strips

Fraction strips can be used to investigate equivalency, fraction comparison, fraction ordering, and fraction number operations. If you’re buying commercially made strips, go for the ones that aren’t labelled as it can help you learn more.

The fraction strip is a block diagram that represents the value of the fraction.

How to model a fraction strip for a given fraction?

The steps for modelling a fraction strip are:

Step 1: Create the fraction strip based on the denominator of the fraction.

Step 2: Now, color the strips that represent the numerator.

Example : Create a fraction strip model for $$\frac{1}{3}$$.

How can we find a fraction using a given fraction strip model?

In the fraction strip, the total boxes represent the denominator and the coloured boxes represent the numerator.

Example : Use the given diagram and write the fraction.

As there are two boxes, the denominator is 2 and one of them is colored, so the numerator will be 1.

Fraction $$=\frac{1}{2}$$

How do we compare fractions using fraction strips?

Students use fraction strips to learn how to divide a whole number into fractions, in this case, a strip of paper. Students should compare the strips by placing them next to one another. Notice that the four pieces representing fourths are equal when placed next to the entire strip.

Represent Mixed Fraction on Fraction Strip

There are two parts to mixed fractions: one whole number and one proper fraction. On a fraction strip, we must first mark two strips: the whole number part on the top and its successor on the bottom in order to represent mixed fractions.

How can we represent improper fractions on a fraction strip?

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 number that can be represented on a fraction strip. However, if the numerator is greater than the denominator, we can convert the improper fraction to a mixed number and then represent it on a fraction strip.

Equivalent Fractions

Equivalent fractions are those that have the same value regardless of their numerators and denominators.

How to Plot a Fraction on a Number Line?

The number line is an important linear model for students to use because it reinforces the fact that between two fractions, there is always one more fraction to be found.

How can we plot fractions on a number line?

Follow the steps below to plot fractions on a number line:

Step 1: Draw a number line of suitable length .

Step 2: Mark points 0 and 1 on the number line if it is a proper fraction. Alternatively, if the fraction is an improper fraction, convert it to a mixed fraction first, and then mark the two integers between which the given fraction lies. Mark points 1 and 2 on the number line to represent 3/2 or 1/2, for example.

Step 3: Make an equal number of parts of the numbers marked in Step 2 that equal the fraction’s denominator.

Step 4: Count forward from the left point the number of parts indicated by the numerator.

Step 5: Mark the point on the line.

Example  : The image below shows an example of $$\frac{4}{5}$$ to help you understand how to plot fractions on number lines step by step.

How do we compare fractions on a number line?

On a number line, comparing fractions is simple. From left to right, the number line represents values in an ascending order. It indicates that the fraction on the left side is smaller than the fraction on the right.

Example  : $$\frac{1}{7}$$ and $$\frac{4}{7}$$ is clearly visible in the image below, as $$\frac{1}{7}$$ is to the left of $$\frac{4}{7}$$. On the number line, this is how you can compare any two or more fractions.

How can we represent mixed fractions on a number line?

There are two parts to mixed fractions: one whole number and one proper fraction. On a number line, we must first mark two points: the whole number part on the left and its successor on the right, in order to represent mixed fractions.

How do we represent improper fractions on the 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 number that can be represented on a number line. However, if the numerator is greater than the denominator, we can convert the improper fraction to a mixed number and then represent it on a number line.

How can we represent equivalent fractions on a number line?

When reduced to their simplest form, equivalent fractions have the same value. Fractions of the same colour are equivalent fractions in the image below.

Solved Examples on Plotting a Fraction using Number line

Example 1 : Find a fraction with a denominator of 36 that is equivalent to $$\frac{5}{6}$$ using the multiplication rule.

To find equivalent fractions, multiply the numerator and denominator by the same number, so the denominator of five by six must be multiplied by a number that equals 36. We can find an equivalent fraction by multiplying both the numerator and denominator by 6 because 6 multiplied by 6 equals 36.

$$\frac{5\times 6}{6\times 6}=\frac{30}{36}$$

So, $$\frac{30}{36}$$ is an equivalent fraction to $$\frac{5}{6}$$

Example 2: Find an equivalent fraction of $$\frac{35}{14}$$ with a numerator of 5 using the division rule.

To find equivalent fractions, divide the numerator and denominator by the same number, so 35 must be divided by a number that equals 5. We can find an equivalent fraction by dividing both the numerator and denominator by 7 because 35 divided by 7 equals 5.

$$\frac{35\div7}{14\div7}=\frac{5}{2}$$

So, $$\frac{5}{2}$$ is an equivalent fraction to $$\frac{35}{14}$$

Unit Fractions

A unit fraction has a numerator of 1. It represents one shaded part of the whole, made up of all the equal parts.