Last updated on July 4th, 2025
Rational numbers are the ratio of two whole numbers. In other words, rational numbers are written as fractions in the form of p/q where both p,q are integers and q is not equal to zero. In this section, we will learn how to represent rational numbers on a number line.
Rational numbers are numbers that can be expressed as the fraction p/q, where p and
q are integers and q is not equals to 0. This set includes terminating decimals, repeating decimals, integers, and fractions. Examples include 3, -5, 2/4, and 0.75. Rational numbers can be plotted on a number line and are useful in real-life applications such as measuring distances, handling finances, and analyzing data.
To represent rational numbers on a number line, we must follow the steps mentioned below:
Step 1: Draw a number line by marking 0 as the reference.
Step 2: Identify the integers between which the rational number lies and mark them. There will be two markings. For e.g., if the rational number is 3/4, then we have to mark 0 and 1 (two markings) as 3/4 lies between 0 and 1.
Step 3: Divide the space between the two 0 and 1 into four equal parts as the rational number’s denominator. According to the example given above, we need to divide the space between 0 and 1 into four equal parts because in our example 3/4, the denominator is 4.
Step 4: Starting from 0, move towards the right by counting the number of parts; the count should match the numerator of the rational number (in this case, 3). Once the count matches the value of the numerator, stop and mark the rational number that we need to represent.
Now, representing negative rational numbers on the number line is similar to the representation of positive rational numbers. However, only the direction of the movement is towards the left. All the steps described above remain the same. The only difference is they’re performed on the left side of the number line.
The rational numbers on a number line have numerous applications across various fields. Let us see how they are used in different areas:
Students tend to make mistakes while understanding the concept of rational numbers on a number line. Let us see some common mistakes and how to avoid them:
Plot the rational number ½ on a number line.
1/2 is located exactly midway between 0 and 1.
Draw the Number Line: Sketch a horizontal line and mark at least the integers 0 and 1.
Divide the Segment: Since the denominator is 2, divide the interval between 0 and 1 into 2 equal parts.
Locate the Fraction: The first mark (halfway) is ½.
Plot the rational number -¾ on a number line.
− ¾ is located three-fourths of the way from -1 to 0.
Draw the Number Line: Include negative values; mark -1, 0, and 1.
Divide the Segment: Divide the interval from -1 to 0 into 4 equal parts.
Locate the Fraction: Count three parts to the right of -1 (or three parts left of 0).
Find the distance between ⅓ and ⅔ on a number line
The distance is ⅓.
Plot Both Numbers: Divide the segment from 0 to 1 into 3 equal parts.
Identify the Points: ⅓ and ⅔ are consecutive marks.
Calculate the Distance: The distance between consecutive marks is ⅓.
Order the numbers -½, 0, ¾, and -¼ on a number line.
-½, -¼, 0, ¾,
Place 0 on the Number Line: Identify the central point.
Locate Negative Numbers: -½ is further than -¼.
Locate the Positive Number: ¾ is right of 0.
Order from least to greatest.
Which is greater, -⅗ or -⅖? Use a number line
-2/5 is greater than -⅗.
Understand Negative Values: On a number line, numbers further right are greater.
Compare Positions:
-⅗ is to the left of -⅖.
Conclusion: -⅖ is greater because it is closer to zero.
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.
: She loves to read number jokes and games.