Fractions and decimals represent part of a whole and are also part of our numbers apart from other numbers like whole numbers and integers. A number line is an effective way of visualizing numbers. You can represent fractions and decimals also on a number line in the same way as you represent whole numbers and integers.
In this article, you’ll learn how to represent fractions on number line.
How To Represent Fraction On Number Line?
You have used number lines to represent natural numbers and whole numbers. In the case of natural numbers, the number line is represented by a ray starting from $1$ and moving on to $2$, $3$, $4$, and so on. Similarly, the number line of whole numbers starts from $0$ and moves on to $1$, $2$, $3$, and so on.
Representing fractions on a number line is very much similar to the representation of decimals. The gaps between each of the numbers ($0$, $1$, $2$, …) are divided into the required number of divisions representing the fractional part of the fraction.
The denominator of a fraction denotes the number of equal partitions that you make between each of the numbers.
For example, to represent fractions like $\frac {1}{2}$, $\frac {3}{2}$, $\frac {4}{2}$, $\frac {9}{2}$, the distance between each of the adjacent numbers is divided into $2$ equal parts.
Similarly, to represent fractions like $\frac {1}{8}$, $\frac {2}{8}$, $\frac {5}{8}$, $\frac {17}{8}$, the distance between each of the adjacent numbers is divided into $8$ equal parts.
Representing Proper Fractions On Number Line
To represent proper fractions on a number line, the first step is to draw a normal number line like the one you do to represent whole numbers.
The next step is to divide equally the distances between the adjacent numbers. The number of divisions between two adjacent numbers will be equal to the denominator of a fraction.
For example, the number line shown below will be used to represent fractions like $\frac {1}{2}$, $\frac {3}{2}$, $\frac {7}{2}$, and so on.
The distance between each adjacent whole number in the line shown above is divided into $2$ equal parts.
The number line shown below will be used to represent fractions like $\frac {1}{4}$, $\frac {3}{4}$, $\frac {5}{4}$, $\frac {11}{4}$ and so on.
The distance between each adjacent whole number in the line shown above is divided into $4$ equal parts.
The number line shown below will be used to represent fractions like $\frac {1}{8}$, $\frac {2}{8}$, $\frac {9}{8}$, $\frac {15}{8}$ and so on.
The distance between each adjacent whole number in the line shown above is divided into $8$ equal parts.
The number line shown below will be used to represent fractions like $\frac {1}{3}$, $\frac {2}{3}$, $\frac {11}{3}$, $\frac {16}{3}$ and so on.
The distance between each adjacent whole number in the line shown above is divided into $3$ equal parts.
The number line shown below will be used to represent fractions like $\frac {1}{6}$, $\frac {2}{6}$, $\frac {5}{6}$, $\frac {7}{6}$, $\frac {19}{6}$ and so on.
The distance between each adjacent whole number in the line shown above is divided into $6$ equal parts.
The number line shown below will be used to represent fractions like $\frac {1}{12}$, $\frac {2}{12}$, $\frac {7}{12}$, $\frac {17}{12}$, $\frac {26}{12}$ and so on.
The distance between each adjacent whole number in the line shown above is divided into $12$ equal parts.
Examples
Ex 1: Locate $\frac {2}{3}$ on a number line.
The denominator of a fraction is $3$, so divide the distance between each number on a number into $3$ equal parts.
Now, starting from $0$ move to position $2$. This point represents $\frac {2}{3}$.
Ex 2: Locate $\frac {6}{8}$ on a number line.
The denominator of a fraction is $8$, so divide the distance between each number on a number into $8$ equal parts.
Now, starting from $0$ move to position $6$. This point represents $\frac {6}{8}$.
Note: In both these examples, the point lies before $1$. It’s because proper fractions are less than $1$.
Representing Mixed Fractions On Number Line
To represent a mixed fraction on a number line, first of all, note down the whole part. After that starting from $0$ move to the number equal to the whole part of the mixed fraction. Now, taking that number as the initial position, count up to the number equal to the numerator of the fraction. This point represents the given mixed fraction on the number line.
Examples
Ex 1: Locate $1\frac {2}{6}$ on a number line.
The denominator of a fraction is $6$, so divide the distance between each number on a number into $6$ equal parts.
The whole part is $1$. So, start from the point $1$.
The numerator of the fractional part is $2$, so move $2$ steps. This point represents $1\frac {2}{6}$.
Ex 2: Locate $2\frac {1}{2}$ on a number line.
The denominator of a fraction is $2$, so divide the distance between each number on a number into $2$ equal parts.
The whole part is $2$. So, start from the point $2$.
The numerator of the fractional part is $1$, so starting from $2$, move $1$ step. This point represents $2\frac {1}{2}$.
Note: In both these examples, the point lies after $1$. It’s because mixed fractions are greater than $1$.
Representing Improper Fractions On Number Line
To represent an improper fraction on a number line is the same as locating a proper fraction. Divide the distance between each number equal to the denominator of the fraction on the number line. Now starting from $0$, count the number of points equal to the numerator of the fraction.
Examples
Ex 1: Locate $\frac {13}{6}$ on a number line.
The denominator of a fraction is $6$, so divide the distance between each number on a number into $6$ equal parts.
Since, the numerator part of the fraction is $13$, so starting $0$, move $13$ steps. The point represents $\frac {13}{6}$.
Ex 2: Locate $\frac {5}{3}$ on a number line.
The denominator of a fraction is $3$, so divide the distance between each number on a number into $3$ equal parts.
Since, the numerator part of the fraction is $5$, so starting $0$, move $5$ steps. The point represents $\frac {5}{3}$.
Conclusion
The procedure for representing fractions on a number line is the same as that of decimal numbers. In the case of fractions, the space between two adjacent whole numbers is divided into a number of partitions equal to that of the denominator of the fraction.
Problems
Represent the following decimals on a number line.
- $\frac {1}{5}$
- $\frac {5}{7}$
- $\frac {9}{12}$
- $\frac {7}{8}$
- $\frac {5}{2}$
- $\frac {11}{3}$
- $\frac {13}{6}$
- $2\frac {1}{2}$
- $1\frac {4}{5}$
- $3\frac {3}{4}$
- $1\frac {9}{12}$
Recommended Reading
- Decimals On Number Line – Representation & Examples(With Pictures)
- Improper Fractions(Definition, Conversions & Examples)
- Mixed Fractions – Definition & Operations (With Examples)
FAQs
How do you find a proper fraction on a number line?
First of all, draw a number line similar to the natural number or whole number line. Let’s consider the proper fraction $\frac {3}{5}.
Observe the denominator of a fraction and divide the space between each of the adjacent numbers on the number line by that many numbers of spaces. For example, if the denominator of the fraction is $5$, then divide the space between each number into $5$ spaces.
Now starting from $0$ move the number of spaces equal to the numerator of the fraction. For example, if the numerator is $3$, move three spaces from $0$ towards the right. This point represents $\frac {3}{5}$.
How do you find a mixed fraction on a number line?
First of all, draw a number line similar to the natural number or whole number line. Let’s consider the proper fraction $2\frac {3}{4}$.
Observe the denominator of a fraction and divide the space between each of the adjacent numbers on the number line by that many numbers of spaces. For example, if the denominator of the fraction is $4$, then divide the space between each number into $4$ spaces.
Now, move to the point $2$ (the whole part of the mixed fraction) on the number line and then move to $3^{rd}$ point between $2$ and $3$ on the number line. This point represents $2 \frac {3}{4}$.
How do you find an improper fraction on a number line?
First of all, draw a number line similar to the natural number or whole number line. Let’s consider the proper fraction $\frac {17}{3}$.
Observe the denominator of a fraction and divide the space between each of the adjacent numbers on the number line by that many numbers of spaces. For example, if the denominator of the fraction is $3$, then divide the space between each number into $3$ spaces.
Convert the fraction to a mixed fraction. $\frac {17}{3} = 5 \frac {2}{3}$.
Now, move to the point $5$ (the whole part of the mixed fraction) on the number line and then move to $2^{nd}$ point between $5$ and $6$ on the number line. This point represents $5 \frac {2}{3}$ or $\frac {17}{3}$.
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.
