Worksheet on Comparison between Rational Numbers

Comparison of rational numbers or fractions can be easily done by following some steps as mentioned below:

1. A positive integer is always greater than zero.

2. A negative integer is always less than zero.

3. A positive integer is always greater than a negative integer.

4. In case of fractions, remember to make the denominator of the fraction to be positive. If not, make it positive by multiplying both numerator and denominator by (-1).

5. For like fractions (i.e., same denominators) comparison is just done by comparing the numerators of the fractions and the one having higher numerator will be greater of the two fractions.

6. For unlike fractions (i.e., different denominators) first of all denominators are made same by taking the L.C.M. of the denominators and then comparing them as in case of like fractions.

Based on above mentioned steps try to solve some questions:

1. (i) Compare \(\frac{2}{3}\) and \(\frac{7}{3}\).

(ii) Compare \(\frac{4}{5}\) and \(\frac{3}{-5}\)

(iii) Compare \(\frac{8}{11}\) and \(\frac{9}{22}\).

(iv) Compare \(\frac{-23}{45}\) and \(\frac{-3}{9}\).

(v) Compare \(\frac{13}{-24}\) and \(\frac{9}{-4}\)

2. Arrange the following in ascending order:

(i) \(\frac{2}{5}\), \(\frac{6}{5}\), \(\frac{1}{5}\), \(\frac{13}{5}\), \(\frac{9}{5}\).

(ii) \(\frac{19}{25}\), \(\frac{16}{25}\), \(\frac{27}{25}\), \(\frac{7}{5}\).

(iii) \(\frac{-2}{9}\), \(\frac{11}{3}\), \(\frac{-3}{27}\), \(\frac{13}{-9}\).

(iv) \(\frac{4}{5}\), \(\frac{6}{16}\), \(\frac{9}{20}\), \(\frac{13}{5}\).

(v) \(\frac{-21}{105}\), \(\frac{12}{21}\), \(\frac{16}{5}\), \(\frac{20}{105}\).

3. Arrange the following in descending order:

(i) \(\frac{7}{16}\), \(\frac{9}{16}\), \(\frac{21}{16}\), \(\frac{12}{16}\)

(ii) \(\frac{3}{17}\), \(\frac{12}{17}\), \(\frac{21}{34}\), \(\frac{13}{-34}\)

(iii) \(\frac{5}{15}\), \(\frac{-16}{40}\), \(\frac{24}{5}\), \(\frac{18}{-25}\)

(iv) \(\frac{14}{21}\), \(\frac{1}{7}\), \(\frac{-17}{21}\), \(\frac{-19}{21}\)

4. Aman and Suraj are taxi drivers. Aman started his journey at 8:30 a.m. and stopped at 9:30 a.m. by covering a distance of 20 km. on the other hand, Suraj travelled 50 km in 2 hours. Assuming that they travel at constant speed, compare the distances travelled by them in first hour of their journey.

5. Find the largest and the smallest rational numbers among the following.

(i) \(\frac{4}{7}\), - \(\frac{4}{7}\) and - \(\frac{7}{15}\) 

(ii) 0, - \(\frac{5}{6}\), \(\frac{2}{3}\) and \(\frac{- 13}{14}\)

6. (i) Arrange \(\frac{3}{5}\), - \(\frac{2}{3}\), - \(\frac{4}{5}\) and \(\frac{5}{6}\) in ascending order.

(ii) Write - \(\frac{10}{9}\), \(\frac{2}{9}\), \(\frac{5}{12}\) and \(\frac{7}{18}\) in descending order.


1. (i) \(\frac{7}{3}\) > \(\frac{2}{3}\)

(ii) \(\frac{4}{5}\) > \(\frac{3}{-5}\)

(iii) \(\frac{8}{11}\) > \(\frac{9}{22}\)

(iv) \(\frac{-23}{45}\) < \(\frac{-3}{9}\)

(v) \(\frac{13}{-24}\) > \(\frac{9}{-4}\)

2. (i) \(\frac{1}{5}\), \(\frac{2}{5}\), \(\frac{6}{5}\), \(\frac{9}{5}\), \(\frac{13}{5}\).

(ii) \(\frac{16}{25}\), \(\frac{19}{25}\), \(\frac{27}{25}\), \(\frac{7}{5}\).

(iii) \(\frac{13}{-9}\), \(\frac{-2}{9}\), \(\frac{-3}{27}\), \(\frac{11}{3}\).

(iv) \(\frac{6}{16}\), \(\frac{9}{20}\), \(\frac{4}{5}\), \(\frac{13}{5}\).

(v) \(\frac{-21}{105}\), \(\frac{20}{105}\), \(\frac{12}{21}\), \(\frac{16}{5}\).

3. (i) \(\frac{21}{16}\), \(\frac{12}{16}\), \(\frac{9}{16}\), \(\frac{7}{16}\).

(ii) \(\frac{12}{17}\), \(\frac{21}{34}\), \(\frac{3}{17}\), \(\frac{13}{-34}\).

(iii) \(\frac{24}{5}\), \(\frac{5}{15}\), \(\frac{-16}{40}\), \(\frac{18}{-25}\).

(iv) \(\frac{14}{21}\), \(\frac{1}{7}\), \(\frac{-17}{21}\), \(\frac{-19}{21}\)

4. Suraj travelled more than Aman.

5. (i) Largest = \(\frac{4}{7}\), smallest = - \(\frac{4}{7}\)

(ii) Largest = \(\frac{2}{3}\), smallest = - \(\frac{-13}{14}\)

6. (i) - \(\frac{4}{5}\) < - \(\frac{2}{3}\) < \(\frac{3}{5}\) < \(\frac{5}{6}\)

(ii) \(\frac{5}{12}\) > \(\frac{7}{18}\) > \(\frac{2}{9}\) > \(\frac{-10}{9}\)

Rational Numbers

Rational Numbers

Decimal Representation of Rational Numbers

Rational Numbers in Terminating and Non-Terminating Decimals

Recurring Decimals as Rational Numbers

Laws of Algebra for Rational Numbers

Comparison between Two Rational Numbers

Rational Numbers Between Two Unequal Rational Numbers

Representation of Rational Numbers on Number Line

Problems on Rational numbers as Decimal Numbers

Problems Based On Recurring Decimals as Rational Numbers

Problems on Comparison Between Rational Numbers

Problems on Representation of Rational Numbers on Number Line

Worksheet on Comparison between Rational Numbers

Worksheet on Representation of Rational Numbers on the Number Line

9th Grade Math

From Worksheet on Comparison between Rational Numbers to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?

Recent Articles

  1. Relation between Diameter Radius and Circumference |Problems |Examples

    Apr 22, 24 05:19 PM

    Relation between Radius and Diameter of a Circle
    Relation between diameter radius and circumference are discussed here. Relation between Diameter and Radius: What is the relation between diameter and radius? Solution: Diameter of a circle is twice

    Read More

  2. Circle Math | Terms Related to the Circle | Symbol of Circle O | Math

    Apr 22, 24 01:35 PM

    Circle using a Compass
    In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We…

    Read More

  3. Preschool Math Activities | Colorful Preschool Worksheets | Lesson

    Apr 21, 24 10:57 AM

    Preschool Math Activities
    Preschool math activities are designed to help the preschoolers to recognize the numbers and the beginning of counting. We believe that young children learn through play and from engaging

    Read More

  4. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Apr 20, 24 05:39 PM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  5. What are Parallel Lines in Geometry? | Two Parallel Lines | Examples

    Apr 20, 24 05:29 PM

    Examples of Parallel Lines
    In parallel lines when two lines do not intersect each other at any point even if they are extended to infinity. What are parallel lines in geometry? Two lines which do not intersect each other

    Read More