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.

Solutions:

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

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