Fraction Decimal Math - Junior आधुनिक विद्या निकेतन ट्यूशन सेंटर Visit: avnlearn.com

1. Fractional Numbers

1. Write the fraction representing the shaded portion:

   1. 

   2. 

   3. 

   4. 

   5. 

   6. 

2. Shade the figures to show the fractions written below them.

   1. 

   2. 

3. Write a fraction for each of the following:
   1. three-fourths
   2. four-sevenths
   3. two-fifths
   4. three-tenths
   5. one-eighth
   6. five-sixths
   7. eight-ninths
   8. seven-twelfths
4. Write down the fractional number for each of the following:
   1. \(\frac{2}{3}\)
   2. \(\frac{4}{9}\)
   3. \(\frac{2}{5}\)
   4. \(\frac{7}{10}\)
   5. \(\frac{1}{3}\)
   6. \(\frac{3}{4}\)
5. Write the numerators and the denominators of the following fractional numbers:
   1. \(\frac{3}{5}\)
   2. \(\frac{4}{7}\)
   3. \(\frac{12}{17}\)
   4. \(\frac{23}{35}\)
   5. \(\frac{57}{61}\)
6. Write down the fraction in which
   1. Numerator = 5, Denominator = 12
   2. Numerator = 8, Denominator = 15
7. Represent each of the following fractions on the number line:
   1. \(\frac{3}{8}\)
   2. \(\frac{5}{9}\)
   3. \(\frac{4}{7}\)
   4. \(\frac{2}{5}\)
   5. \(\frac{1}{4}\)
8. Ring all the like fractions:
   1. \(\frac{1}{10}\), \(\frac{3}{10}\), \(\frac{7}{10}\), \(\frac{10}{7}\)
   2. \(\frac{19}{11}\), \(\frac{11}{19}\), \(\frac{15}{19}\), \(\frac{16}{19}\)
9. Which of the following are proper fractions, improper fractions and mixed fractions?
   \(\frac{1}{2}\), \(\frac{7}{4}\), 2, \(\frac{15}{8}\), \(\frac{16}{16}\), 3\(\frac{6}{17}\), \(\frac{23}{10}\), \(\frac{3}{2}\), \(\frac{5}{6}\), \(\frac{9}{4}\), \(\frac{8}{8}\), 3, \(\frac{27}{16}\), \(\frac{23}{31}\), \(\frac{10}{13}\), \(\frac{26}{26}\), 3\(\frac{1}{4}\), 1\(\frac{1}{2}\), \(\frac{4}{5}\), 7\(\frac{1}{4}\), \(\frac{12}{1}\), 9\(\frac{1}{3}\), \(\frac{12}{17}\), 21\(\frac{1}{12}\), 29\(\frac{3}{4}\)
10. Ring the unit fractions: \(\frac{7}{1}\), \(\frac{1}{2}\), \(\frac{1}{7}\), \(\frac{8}{1}\), \(\frac{8}{9}\), \(\frac{1}{9}\)
11. Write each of the following divisions as fractions:
    1. 3 ÷ 5
    2. 5 ÷ 3
    3. 7 ÷ 9
    4. 9 ÷ 1
12. Write each of the following fractions in the form of division:
    1. \(\frac{7}{9}\)
    2. \(\frac{8}{11}\)
    3. 2\(\frac{1}{4}\)
    4. \(\frac{8}{8}\)
    5. \(\frac{6}{1}\)
13. Express each of the following as a mixed fraction or a whole number:
    1. \(\frac{20}{3}\)
    2. \(\frac{11}{5}\)
    3. \(\frac{17}{7}\)
    4. \(\frac{28}{5}\)
    5. \(\frac{19}{6}\)
    6. \(\frac{35}{9}\)
14. Express the following as improper fractions :
    1. \(7\frac{3}{4}\)
    2. \(2\frac{5}{6}\)
    3. \(10\frac{3}{5}\)
    4. \(8\frac{4}{9}\)
    5. 1\(\frac{1}{2}\)
15. Write the integral part and the fractional part of the following mixed frachons:
    1. 2\(\frac{3}{4}\)
    2. 4\(\frac{5}{7}\)
    3. 9\(\frac{1}{2}\)
    4. 10\(\frac{7}{8}\)
16. Fill in the blanks:
    1. \(\frac{2}{3}\) = \(\frac{\cdots}{12}\)
    2. \(\frac{3}{4}\) = \(\frac{9}{\cdots}\)
    3. \(\frac{4}{7}\) = \(\frac{20}{\cdots}\)
    4. \(\frac{29}{32}\) = \(\frac{\cdots}{64}\)
    5. \(\frac{\cdots}{5}\) = \(\frac{6}{15}\)
    6. \(\frac{1}{2}\) = \(\frac{\cdots}{4}\)
17. Fill in the blanks so that the fractions may be equivalent:
    1. \(\frac{2}{3}\) = \(\frac{2 \times 2}{3 \times \cdots}\) = \(\frac{2 \times \cdots}{3 \times 3}\) = \(\frac{2 \times 5}{3 \times \cdots}\) = \(\frac{2 \times \cdots}{3 \times 6}\)
    2. \(\frac{3}{5}\) = \(\frac{3 \times 2}{5 \times \cdots}\) = \(\frac{3 \times 3}{5 \times \cdots}\) = \(\frac{3 \times \cdots}{5 \times 4}\) = \(\frac{3 \times \cdots}{5 \times 5}\)
    3. \(\frac{5}{8}\) = \(\frac{5 \times 2}{8 \times \cdots}\) = \(\frac{5 \times 3}{8 \times \cdots}\) = \(\frac{5 \times \cdots}{8 \times 7}\) = \(\frac{5 \times \cdots}{8 \times 9}\)
    4. \(\frac{2}{7}\) = \(\frac{2 \times 6}{7 \times \cdots}\) = \(\frac{2 \times 8}{7 \times \cdots}\) = \(\frac{2 \times \cdots}{7 \times 9}\) = \(\frac{2 \times \cdots}{7 \times 10}\)
18. 1. Write two equivalent fractions of \(\frac{1}{4}\).
    2. Write three equivalent fractons of \(\frac{3}{4}\).
    3. Write four equivalent fractions of \(\frac{2}{5}\).
    4. Write five equivalent fractions of \(\frac{1}{2}\).
19. Change each of the following fractions to equivalent fractions having the denominator 32:
    1. \(\frac{1}{2}\)
    2. \(\frac{1}{4}\)
    3. \(\frac{3}{8}\)
    4. \(\frac{5}{16}\)
20. Change each of the following fractions to equivalent fractions having the numerator 48:
    1. \(\frac{2}{3}\)
    2. \(\frac{3}{4}\)
    3. \(\frac{4}{3}\)
    4. \(\frac{8}{19}\)
21. Are the following fractions equivalent? Write ‘Yes’ or ’No:
    1. \(\frac{1}{2}\) = \(\frac{5}{10}\)
    2. \(\frac{2}{4}\) = \(\frac{6}{7}\)
    3. \(\frac{3}{6}\) = \(\frac{12}{24}\)
    4. \(\frac{4}{9}\) = \(\frac{36}{81}\)
    5. \(\frac{3}{4}\) = \(\frac{3 + 4}{4 + 4}\)
    6. \(\frac{11}{17}\) = \(\frac{11 - 2}{17 - 2}\)
22. Write ‘True’ or ‘False’:
    1. \(\frac{4}{7}\) = \(\frac{12}{21}\)
    2. \(\frac{3}{5}\) = \(\frac{21}{35}\)
    3. \(\frac{4}{7}\) = \(\frac{24}{42}\)
    4. \(\frac{4}{9}\) = \(\frac{9}{14}\)
23. 1. Express 6 as a fracton with 5 as the denominator.
    2. Express 3 as a fraction with 8 as the denominator.
24. Change the following fractions to like fractions:
    1. \(\frac{1}{6}\), \(\frac{1}{9}\)
    2. \(\frac{3}{4}\), \(\frac{5}{12}\)
    3. \(\frac{7}{12}\), \(\frac{8}{15}\)
    4. \(\frac{7}{16}\), \(\frac{11}{24}\)
    5. \(\frac{2}{5}\), \(\frac{3}{10}\), \(\frac{4}{15}\)
    6. \(\frac{1}{8}\), \(\frac{5}{16}\), \(\frac{9}{32}\)

25. 1. \(\frac{9}{10}\) □ \(\frac{7}{10}\)
    2. \(\frac{3}{7}\) □ \(\frac{6}{7}\)
    3. \(\frac{6}{11}\) □ \(\frac{5}{11}\)
26. 1. \(\frac{7}{8}\) □ \(\frac{7}{10}\)
    2. \(\frac{4}{11}\) □ \(\frac{4}{9}\)
    3. \(\frac{11}{14}\) □ \(\frac{11}{15}\)
27. 1. \(\frac{2}{3}\) □ \(\frac{3}{4}\)
    2. \(\frac{1}{2}\) □ \(\frac{1}{3}\)
    3. \(\frac{2}{5}\) □ \(\frac{6}{11}\)
    4. \(\frac{7}{12}\) □ \(\frac{2}{5}\)
    5. \(\frac{3}{7}\) □ \(\frac{4}{5}\)
    6. \(\frac{5}{16}\) □ \(\frac{4}{17}\)
28. 1. 2\(\frac{1}{2}\) □ \(\frac{3}{2}\)
    2. \(\frac{4}{3}\) □ 4\(\frac{1}{3}\)
    3. 3\(\frac{2}{3}\) □ \(\frac{11}{3}\)

29. 1. \(\frac{5}{11}\), \(\frac{9}{11}\), \(\frac{7}{11}\), \(\frac{4}{11}\)
    2. \(\frac{11}{12}\), \(\frac{5}{12}\), \(\frac{7}{12}\), \(\frac{1}{12}\)
30. 1. \(\frac{15}{17}\), \(\frac{15}{19}\), \(\frac{15}{18}\), \(\frac{15}{31}\)
    2. \(\frac{31}{37}\), \(\frac{31}{49}\), \(\frac{31}{36}\), \(\frac{31}{45}\)
31. 1. \(\frac{1}{4}\), \(\frac{3}{4}\), \(\frac{1}{6}\), \(\frac{7}{10}\)
    2. \(\frac{1}{5}\), \(\frac{2}{15}\), \(\frac{3}{10}\), \(\frac{7}{20}\)
    3. \(\frac{2}{3}\), \(\frac{4}{9}\), \(\frac{5}{12}\), \(\frac{5}{6}\)
    4. \(\frac{2}{7}\), \(\frac{3}{14}\), \(\frac{5}{28}\), \(\frac{4}{21}\)
32. Find out if the following fractions are in the lowest terms:
    1. \(\frac{6}{9}\)
    2. \(\frac{4}{15}\)
    3. \(\frac{14}{21}\)
    4. \(\frac{72}{77}\)
    5. \(\frac{51}{85}\)
    6. \(\frac{88}{91}\)
33. Which of the following fractions are not in the lowest terms?
    1. \(\frac{6}{9}\)
    2. \(\frac{7}{9}\)
    3. \(\frac{10}{70}\)
    4. \(\frac{85}{91}\)
    5. \(\frac{88}{117}\)
    6. \(\frac{108}{135}\)
34. Reduce to the lowest terms:
    1. \(\frac{2}{4}\)
    2. \(\frac{4}{8}\)
    3. \(\frac{5}{10}\)
    4. \(\frac{6}{8}\)
    5. \(\frac{2}{10}\)
    6. \(\frac{3}{12}\)
    7. \(\frac{4}{12}\)
    8. \(\frac{8}{12}\)
    9. \(\frac{2}{12}\)
    10. \(\frac{7}{14}\)
    11. \(\frac{9}{15}\)
    12. \(\frac{4}{16}\)
    13. \(\frac{8}{20}\)
    14. \(\frac{9}{24}\)
    15. \(\frac{16}{12}\)
    16. \(\frac{54}{12}\)
    17. \(\frac{24}{20}\)
    18. \(\frac{56}{40}\)
35. Add together:
    1. \(\frac{5}{17}\), \(\frac{2}{17}\)
    2. \(\frac{1}{12}\), \(\frac{4}{12}\)
    3. \(\frac{4}{19}\), \(\frac{15}{19}\)
    4. \(\frac{7}{22}\), \(\frac{25}{22}\)

36. 1. \(\frac{2}{5}\) + \(\frac{1}{5}\)
    2. \(\frac{4}{10}\) + \(\frac{3}{10}\)
    3. \(\frac{5}{17}\) + \(\frac{2}{17}\)
    4. \(\frac{4}{18}\) + \(\frac{3}{18}\)
    5. \(\frac{2}{13}\) + \(\frac{4}{13}\)
    6. \(\frac{4}{19}\) + \(\frac{15}{19}\)
37. 1. \(\frac{4}{19}\) + \(\frac{7}{19}\) + \(\frac{9}{19}\)
    2. \(\frac{5}{12}\) + \(\frac{7}{12}\) + \(\frac{1}{12}\)
    3. \(\frac{15}{8}\) + \(\frac{7}{8}\) + \(\frac{1}{8}\)
    4. \(\frac{13}{10}\) + \(\frac{3}{10}\) + \(\frac{19}{10}\)
38. 1. \(\frac{3}{4}\) + \(\frac{5}{8}\)
    2. \(\frac{2}{5}\) + \(\frac{4}{15}\)
    3. \(\frac{2}{5}\) + \(\frac{1}{4}\)
    4. \(\frac{3}{7}\) + \(\frac{2}{3}\)
    5. \(\frac{2}{3}\) + \(\frac{4}{21}\)
    6. \(\frac{3}{10}\) + \(\frac{7}{20}\)
    7. \(\frac{3}{8}\) + \(\frac{25}{24}\)
    8. \(\frac{4}{15}\) + \(\frac{7}{30}\)
    9. \(\frac{3}{16}\) + \(\frac{35}{32}\)
39. 1. \(\frac{1}{2}\) + \(\frac{3}{4}\) + \(\frac{5}{8}\)
    2. \(\frac{3}{4}\) + \(\frac{5}{6}\) + \(\frac{7}{12}\)
    3. \(\frac{2}{5}\) + \(\frac{13}{10}\) + \(\frac{7}{15}\)
    4. \(\frac{3}{5}\) + \(\frac{7}{10}\) + \(\frac{31}{20}\)
    5. \(\frac{1}{2}\) + \(\frac{5}{6}\) + \(\frac{27}{12}\)
    6. \(\frac{2}{13}\) + \(\frac{1}{26}\) + \(\frac{4}{39}\)
    7. \(\frac{1}{2}\) + \(\frac{3}{4}\) + \(\frac{5}{8}\) + \(\frac{7}{16}\)
    8. \(\frac{2}{3}\) + \(\frac{3}{5}\) + \(\frac{1}{15}\) + \(\frac{4}{5}\)
    9. \(\frac{1}{2}\) + \(\frac{1}{3}\) + \(\frac{1}{4}\) + \(\frac{1}{5}\)
    10. \(\frac{5}{12}\) + \(\frac{2}{3}\) + \(\frac{3}{4}\) + \(\frac{5}{6}\)
40. 1. 5 + \(\frac{3}{11}\)
    2. 4 + \(\frac{6}{13}\)
    3. 7 + \(\frac{11}{4}\)
    4. \(\frac{11}{15}\) + 0
41. 1. 5\(\frac{2}{9}\) + 2\(\frac{4}{9}\)
    2. 2\(\frac{1}{2}\) + 3\(\frac{1}{2}\) + 4\(\frac{1}{4}\)
    3. 2\(\frac{1}{6}\) + 3\(\frac{5}{6}\) + 10\(\frac{1}{6}\)
    4. 3\(\frac{1}{13}\) + 1\(\frac{4}{13}\) + 2\(\frac{3}{13}\)
42. 1. 2\(\frac{1}{2}\) + 1\(\frac{2}{3}\)
    2. 3\(\frac{1}{3}\) + 2\(\frac{2}{9}\)
    3. 4\(\frac{3}{4}\) + 3\(\frac{1}{8}\)
    4. 6\(\frac{3}{8}\) + 10\(\frac{1}{16}\)
    5. 3\(\frac{5}{8}\) + 2\(\frac{7}{12}\)
    6. 2\(\frac{2}{15}\) + 1\(\frac{9}{20}\)
43. 1. 2\(\frac{5}{8}\) + 2\(\frac{3}{4}\) + 2\(\frac{1}{2}\)
    2. 3\(\frac{3}{4}\) + 5\(\frac{1}{8}\) + 1\(\frac{3}{16}\)
    3. 3\(\frac{1}{3}\) + 4\(\frac{5}{9}\) + 2\(\frac{5}{6}\)
    4. 4\(\frac{2}{7}\) + 1\(\frac{10}{21}\) + 5\(\frac{2}{3}\)
    5. 1\(\frac{5}{8}\) + 2\(\frac{7}{12}\) + 3\(\frac{3}{4}\)
    6. 2\(\frac{1}{16}\) + 3\(\frac{5}{12}\) + 4\(\frac{1}{4}\)
44. 1. \(\frac{11}{8}\) + 2\(\frac{3}{16}\)
    2. 1\(\frac{3}{10}\) + \(\frac{7}{10}\)
    3. 2 + \(\frac{6}{21}\) + 3\(\frac{4}{7}\)
    4. 4\(\frac{3}{4}\) + 3 + 3\(\frac{1}{12}\)
45. 1. \(\frac{7}{9}\) − \(\frac{4}{9}\)
    2. \(\frac{7}{12}\) − \(\frac{6}{12}\)
    3. \(\frac{25}{36}\) − \(\frac{11}{36}\)
    4. \(\frac{20}{51}\) − \(\frac{16}{51}\)
    5. \(\frac{79}{89}\) − \(\frac{47}{89}\)
    6. \(\frac{15}{92}\) − \(\frac{13}{92}\)
46. 1. \(\frac{3}{8}\) − \(\frac{1}{4}\)
    2. \(\frac{23}{40}\) − \(\frac{1}{8}\)
    3. \(\frac{11}{12}\) − \(\frac{5}{16}\)
    4. \(\frac{7}{16}\) − \(\frac{5}{24}\)
    5. \(\frac{8}{15}\) − \(\frac{3}{20}\)
    6. \(\frac{7}{24}\) − \(\frac{5}{36}\)
47. 1. 12\(\frac{3}{4}\) − \(\frac{1}{2}\)
    2. 7\(\frac{7}{9}\) − \(\frac{1}{3}\)
    3. 4\(\frac{3}{7}\) − \(\frac{1}{14}\)
48. 1. 6\(\frac{3}{4}\) − 4\(\frac{1}{4}\)
    2. 7\(\frac{8}{9}\) − 5\(\frac{2}{3}\)
    3. 8\(\frac{9}{10}\) − 3\(\frac{3}{5}\)
    4. 3\(\frac{2}{16}\) − 1\(\frac{3}{8}\)
    5. 4\(\frac{5}{18}\) − 2\(\frac{4}{9}\)
    6. 5\(\frac{3}{8}\) − 1\(\frac{1}{24}\)
49. 1. 3 − \(\frac{2}{11}\)
    2. 6 − \(\frac{5}{12}\)
    3. 8 − 3\(\frac{2}{5}\)
50. 1. \(\frac{3}{10}\) − 0
    2. \(\frac{15}{8}\) − 0
    3. 2\(\frac{1}{3}\) − 0
    4. \(\frac{2}{9}\) − \(\frac{2}{9}\)
    5. \(\frac{10}{3}\) − \(\frac{10}{3}\)
    6. 3\(\frac{4}{9}\) − 3\(\frac{4}{9}\)
51. Use repeated addition to find the following:
    1. 3 × \(\frac{1}{4}\)
    2. 6 × \(\frac{3}{5}\)
    3. 2 × \(\frac{4}{7}\)
    4. 4 × \(\frac{2}{3}\)

52. 1. \(\frac{7}{2}\) of 6
    2. \(\frac{5}{12}\) of 60
    3. \(\frac{8}{3}\) of 9
    4. \(\frac{2}{15}\) of 75
53. 1. \(\frac{5}{11}\) of ₹ 220
    2. \(\frac{4}{9}\) of 54 metres
    3. \(\frac{6}{7}\) of 35 litres
    4. \(\frac{1}{6}\) of an hour
    5. \(\frac{5}{6}\) of an year
    6. \(\frac{7}{20}\) of a kg
    7. \(\frac{9}{20}\) of a metre
    8. \(\frac{7}{8}\) of a day
    9. \(\frac{3}{7}\) of a week
    10. \(\frac{7}{50}\) of a litre
54. 1. How much is 4 times \(\frac{1}{8}\)?
    2. How much is 5 times \(\frac{3}{20}\)?

55. 1. 7 × \(\frac{2}{11}\)
    2. 8 × \(\frac{7}{9}\)
    3. 9 × \(\frac{4}{11}\)
    4. \(\frac{5}{12}\) × 11
    5. \(\frac{17}{11}\) × 12
    6. \(\frac{1}{13}\) × 28
56. 1. 3\(\frac{1}{4}\) × 5
    2. 4\(\frac{1}{3}\) × 7
    3. 9\(\frac{1}{2}\) × 3
    4. 2\(\frac{1}{3}\) × 8
    5. 3\(\frac{1}{2}\) × 9
    6. 4\(\frac{1}{2}\) × 7
    7. 10 × 6\(\frac{1}{3}\)
    8. 11 × 2\(\frac{1}{3}\)
    9. 17 × 1\(\frac{1}{2}\)
57. 1. \(\frac{2}{3}\) × \(\frac{2}{7}\)
    2. \(\frac{4}{7}\) × \(\frac{2}{5}\)
    3. \(\frac{6}{13}\) × \(\frac{2}{5}\)
    4. \(\frac{7}{15}\) × \(\frac{5}{8}\)
    5. \(\frac{9}{16}\) × \(\frac{4}{9}\)
    6. \(\frac{8}{13}\) × \(\frac{7}{12}\)
58. 1. 1\(\frac{1}{2}\) × \(\frac{5}{7}\)
    2. 1\(\frac{1}{3}\) × \(\frac{7}{8}\)
    3. 2\(\frac{1}{2}\) × \(\frac{3}{8}\)
    4. \(\frac{9}{11}\) × 2\(\frac{1}{4}\)
    5. \(\frac{6}{13}\) × 3\(\frac{2}{5}\)
    6. \(\frac{4}{7}\) × 5\(\frac{1}{3}\)
59. 1. 4\(\frac{1}{4}\) × 1\(\frac{1}{3}\)
    2. 9\(\frac{1}{12}\) × 2\(\frac{2}{5}\)
    3. 5\(\frac{1}{3}\) × 5\(\frac{1}{4}\)
60. 1. 2\(\frac{2}{3}\) × \(\frac{5}{12}\)
    2. 1\(\frac{3}{4}\) × \(\frac{8}{15}\)
    3. \(\frac{12}{25}\) × 6\(\frac{2}{3}\)
    4. 20 × 3\(\frac{1}{5}\)
    5. 1\(\frac{1}{4}\) × 2\(\frac{2}{5}\)
    6. 3\(\frac{3}{8}\) × 5\(\frac{1}{9}\)
    7. 5\(\frac{1}{7}\) × 5\(\frac{1}{9}\)
    8. 8\(\frac{1}{8}\) × 28
61. 1. 5 times 1\(\frac{4}{15}\)
    2. 12 times 2\(\frac{5}{24}\)
62. Fill in the blanks:
    1. \(\frac{1}{4}\) of a rupee = □ paise
    2. \(\frac{3}{8}\) of two rupees = □ paise
    3. \(\frac{3}{5}\) of fifty rupees = □ rupees
    4. \(\frac{7}{10}\) of four rupees = □ paise
63. Fill in the blanks:
    1. \(\frac{2}{5}\) of a kg = □ g
    2. \(\frac{1}{100}\) of 30 kg = □ g
64. Write the reciprocals (multiplicative inverses) of the following:
    1. \(\frac{1}{2}\)
    2. \(\frac{1}{3}\)
    3. \(\frac{1}{4}\)
    4. 7
    5. 11
    6. 45
    7. \(\frac{4}{5}\)
    8. \(\frac{6}{7}\)
    9. \(\frac{9}{11}\)
    10. 1\(\frac{4}{5}\)
    11. 2\(\frac{3}{7}\)
    12. 3\(\frac{4}{5}\)

65. 1. 3 by 1\(\frac{1}{2}\)
    2. 5 by 2\(\frac{1}{2}\)
    3. 4 by 3\(\frac{1}{3}\)
    4. 1\(\frac{1}{2}\) by 3
    5. 2\(\frac{1}{2}\) by 5
    6. 4\(\frac{2}{3}\) by 6
    7. \(\frac{2}{7}\) by 5
    8. \(\frac{12}{7}\) by 14
    9. 15 by \(\frac{3}{10}\)
    10. \(\frac{4}{7}\) by \(\frac{2}{3}\)
    11. \(\frac{3}{11}\) by \(\frac{2}{7}\)
    12. \(\frac{7}{6}\) by \(\frac{2}{21}\)
    13. \(\frac{3}{4}\) by 3
    14. \(\frac{8}{5}\) by 4
    15. \(\frac{14}{25}\) by 7
    16. \(\frac{1}{2}\) by 3
    17. \(\frac{3}{16}\) by 3
    18. \(\frac{14}{15}\) by 7
    19. \(\frac{1}{6}\) by \(\frac{1}{3}\)
    20. \(\frac{2}{15}\) by \(\frac{1}{15}\)
    21. \(\frac{1}{5}\) by \(\frac{2}{25}\)
    22. \(\frac{7}{9}\) by \(\frac{28}{45}\)
    23. \(\frac{11}{12}\) by \(\frac{33}{24}\)
    24. \(\frac{15}{16}\) by \(\frac{75}{128}\)

66. 1. 1\(\frac{1}{2}\) ÷ 3
    2. 1\(\frac{1}{3}\) ÷ 4
    3. 2\(\frac{1}{5}\) ÷ 11
    4. 3\(\frac{2}{7}\) ÷ 92
    5. 63 ÷ 2\(\frac{1}{4}\)
    6. 72 ÷ 9\(\frac{1}{7}\)
67. 1. \(\frac{1}{2}\) ÷ 2
    2. \(\frac{1}{4}\) ÷ 2
    3. \(\frac{1}{2}\) ÷ 4
    4. \(\frac{1}{3}\) ÷ 3
    5. \(\frac{1}{5}\) ÷ 4
    6. \(\frac{1}{6}\) ÷ 5
68. 1. 2\(\frac{1}{3}\) ÷ 7
    2. 3\(\frac{1}{4}\) ÷ 26
    3. 5\(\frac{1}{4}\) ÷ 42
    4. 7\(\frac{2}{3}\) ÷ 46
    5. 11\(\frac{2}{5}\) ÷ 57
    6. 12\(\frac{3}{4}\) ÷ 102
69. 1. 4 ÷ \(\frac{4}{5}\)
    2. 13 ÷ \(\frac{1}{6}\)
    3. 15 ÷ \(\frac{1}{8}\)
70. 1. 16 ÷ \(\frac{8}{3}\)
    2. 21 ÷ 3\(\frac{1}{2}\)
    3. 25 ÷ 7\(\frac{1}{2}\)
    4. 35 ÷ 3\(\frac{3}{4}\)
    5. 67 ÷ 9\(\frac{4}{7}\)
    6. 99 ÷ 2\(\frac{5}{47}\)
71. 1. \(\frac{12}{49}\) ÷ \(\frac{3}{7}\)
    2. \(\frac{25}{39}\) ÷ \(\frac{10}{13}\)
    3. \(\frac{16}{63}\) ÷ \(\frac{4}{27}\)
    4. \(\frac{4}{7}\) ÷ \(\frac{2}{21}\)
    5. \(\frac{5}{48}\) ÷ \(\frac{5}{24}\)
    6. \(\frac{3}{28}\) ÷ \(\frac{5}{14}\)
72. 1. 1\(\frac{1}{4}\) ÷ \(\frac{5}{8}\)
    2. \(\frac{12}{49}\) ÷ \(\frac{11}{15}\)
    3. \(\frac{12}{49}\) ÷ \(\frac{27}{50}\)
    4. 1\(\frac{2}{3}\) ÷ 6\(\frac{1}{4}\)
    5. 3\(\frac{3}{10}\) ÷ 5\(\frac{1}{2}\)
    6. 10\(\frac{1}{2}\) ÷ 4\(\frac{2}{3}\)
73. 1. 3\(\frac{1}{4}\) ÷ \(\frac{1}{8}\)
    2. 5\(\frac{2}{3}\) ÷ \(\frac{1}{6}\)
    3. 16\(\frac{3}{5}\) ÷ \(\frac{1}{25}\)
    4. \(\frac{1}{5}\) ÷ 1\(\frac{1}{10}\)
    5. \(\frac{2}{7}\) ÷ 2\(\frac{3}{14}\)
    6. \(\frac{3}{8}\) ÷ 2\(\frac{3}{16}\)
    7. 6\(\frac{2}{3}\) ÷ 2\(\frac{2}{9}\)
    8. 11\(\frac{2}{5}\) ÷ 3\(\frac{3}{4}\)
    9. 6\(\frac{2}{3}\) ÷ 13\(\frac{1}{3}\)

74. 1. \(\frac{11}{12}\) − \(\frac{5}{12}\) + \(\frac{1}{12}\)
    2. \(\frac{10}{13}\) + \(\frac{5}{13}\) − \(\frac{3}{13}\)
    3. \(\frac{16}{23}\) − \(\frac{3}{23}\) − \(\frac{11}{23}\)
    4. \(\frac{21}{25}\) − \(\frac{7}{25}\) + \(\frac{11}{25}\)
75. 1. \(\frac{8}{9}\) + \(\frac{1}{9}\) − \(\frac{7}{9}\) + \(\frac{4}{9}\)
    2. \(\frac{8}{17}\) + \(\frac{3}{17}\) + \(\frac{1}{17}\) − \(\frac{11}{17}\)
76. 1. \(\frac{7}{8}\) − \(\frac{3}{4}\) + \(\frac{1}{2}\)
    2. \(\frac{5}{12}\) + \(\frac{5}{8}\) − \(\frac{5}{16}\)
    3. 3 − \(\frac{11}{12}\) + \(\frac{5}{8}\)
    4. 11 + \(\frac{7}{9}\) − \(\frac{5}{6}\)
77. 1. 3\(\frac{6}{7}\) − 1\(\frac{2}{3}\) − \(\frac{20}{21}\)
    2. 1\(\frac{1}{15}\) − 2\(\frac{3}{5}\) + 5\(\frac{7}{10}\)
    3. 4 + 1\(\frac{5}{6}\) − 2\(\frac{3}{8}\)
    4. 5 − 2\(\frac{1}{7}\) − 1\(\frac{3}{5}\)
78. 1. \(\frac{42}{65}\) × \(\frac{39}{59}\) × \(\frac{24}{27}\)
    2. 6\(\frac{7}{8}\) × 6\(\frac{2}{11}\) × \(\frac{3}{10}\)
    3. 2\(\frac{1}{9}\) × \(\frac{5}{38}\) × 2\(\frac{1}{5}\)
    4. 4\(\frac{5}{8}\) × \(\frac{27}{35}\) × 7 × 1\(\frac{3}{37}\)
    5. \(\frac{5}{21}\) × \(\frac{7}{15}\) × 2\(\frac{1}{4}\) × \(\frac{12}{35}\) × 23\(\frac{1}{3}\)
79. 1. \(\frac{4}{5}\) ÷ \(\frac{7}{15}\) of \(\frac{8}{9}\)
    2. \(\frac{4}{5}\) ÷ \(\frac{7}{15}\) × \(\frac{8}{9}\)
    3. 5\(\frac{1}{4}\) ÷ \(\frac{3}{7}\) × \(\frac{1}{2}\)
    4. 5\(\frac{1}{4}\) ÷ \(\frac{3}{7}\) of \(\frac{1}{2}\)
    5. \(\frac{7}{8}\) + 2\(\frac{5}{6}\) − \(\frac{11}{12}\) × 3\(\frac{3}{11}\)
    6. 3\(\frac{3}{4}\) ÷ \(\frac{7}{8}\) × 4\(\frac{1}{6}\) × 1\(\frac{13}{15}\)
    7. \(\frac{1}{2}\) + 1\(\frac{1}{2}\) ÷ 1\(\frac{1}{2}\) × \(\frac{2}{3}\) − \(\frac{1}{4}\)
    8. 1\(\frac{4}{5}\) − 2\(\frac{3}{4}\) of \(\frac{8}{11}\) + \(\frac{3}{8}\) ÷ \(\frac{9}{10}\)
    9. 9\(\frac{1}{3}\) ÷ \(\frac{3}{5}\) of \(\frac{7}{9}\) × \(\frac{4}{5}\)
    10. \(\frac{3}{5}\) of 1\(\frac{3}{7}\) ÷ \(\frac{2}{5}\) − \(\frac{1}{2}\) + \(\frac{2}{3}\) × \(\frac{6}{7}\)
    11. 7\(\frac{1}{3}\) ÷ 3\(\frac{2}{3}\) of 2 + 4\(\frac{1}{2}\) ÷ 2\(\frac{1}{4}\) − 2\(\frac{1}{2}\)
    12. 25 of \(\frac{3}{5}\) ÷ 1\(\frac{2}{3}\) + 3 of \(\frac{1}{3}\) ÷ 10
80. 1. \(\Big(\frac{4}{9} + \frac{7}{9}\Big) \times 2\frac{1}{4}\)
    2. \(\frac{3}{8} \div \Big(1\frac{7}{8} - \frac{3}{4}\Big)\)
    3. \(6 + \Big\lbrace 1 + \frac{1}{2} + \Big(\frac{3}{4} - \frac{1}{2}\Big)\Big\rbrace\)
    4. \(\Big\lbrace \Big(13\frac{1}{3} - 12\frac{1}{2}\Big) \div \frac{5}{6} \Big\rbrace \text{ of } \frac{3}{8}\)
    5. \(2\frac{1}{2} - \Big\lbrace \frac{13}{4} - \Big(3\frac{1}{2} - 1\frac{3}{4}\Big)\Big\rbrace\)
    6. 140 - [4 + {12 × (7 − 5)}]
    7. \(4\frac{1}{2} - \Big[1 + \Big\lbrace 2\frac{1}{2} - \Big(\frac{1}{3} - \frac{1}{4}\Big)\Big\rbrace\Big]\)
    8. \(3\frac{1}{12} - \Big[1\frac{3}{4} + \Big\lbrace 2\frac{1}{2} - \Big(1\frac{1}{2} - \frac{1}{3}\Big)\Big\rbrace\Big]\)
    9. \(3\frac{1}{3} \text{ of } \frac{1}{2} + 2 \div \Big[2 \times \Big\lbrace 2 - \Big( 2 - \frac{1}{5} \Big) \Big\rbrace\Big]\)
    10. \(5\frac{1}{2} - \Big[2\frac{1}{3} \div \Big\lbrace \frac{3}{4} - \frac{1}{2} \times \Big(\frac{2}{3} - \frac{1}{24}\Big)\Big\rbrace\Big]\)
    11. \(\Big[2 + 5 \times \Big\lbrace 1\frac{1}{2} + \Big(\frac{3}{4} - \frac{1}{10}\Big)\Big\rbrace\Big] + 1\frac{1}{2}\)

2. Decimals

1. Write each of the following in figures:
   1. Fifty-eight point six three
   2. One hundred twenty-four point four two five
   3. Seven point seven six
   4. Nineteen point eight
   5. Four hundred four point zero four four
   6. Point one seven three
   7. Point zero one five
2. Read each of the following decimal fractions:
   1. 2.3
   2. 15.67
   3. 278.789
   4. 1234.5678
3. Write the integral parts of the following decimal fractions:
   1. 7.1
   2. 12.651
   3. 167.4
   4. 2345.678
4. Write the fractional parts of the following decimal fractions:
   1. 6.5
   2. 27.34
   3. 175.678
   4. 2929.38387
5. Write the place value of each digit in each of the following decimals:
   1. 275.269
   2. 46.075
   3. 5370.34
   4. 186.209
6. Write each of the following decimals in expanded form:
   1. 24.675
   2. 0.294
   3. 8.006
   4. 4615.72
7. Write each of the following in decimal form:
   1. 40 + 6 + \(\frac{7}{10}\) + \(\frac{9}{100}\)
   2. 600 + 5 + \(\frac{7}{10}\) + \(\frac{9}{100}\)
   3. 800 + 5 + \(\frac{8}{10}\) + \(\frac{6}{100}\)
   4. 30 + 9 + \(\frac{4}{10}\) + \(\frac{8}{100}\)
   5. 700 + 30 + 1 + \(\frac{8}{10}\) + \(\frac{4}{100}\)
   6. 500 + 70 + 8 + \(\frac{3}{10}\) + \(\frac{1}{100}\) + \(\frac{6}{1000}\)
8. Fill in the blanks with >,< or =.
   1. 0.1 □ 0.01
   2. 2.32 □ 1.99
   3. 16.123 □ 16.12300
   4. 252.9111 □ 252.099
   5. 13.99 □ 14
   6. 8.431 □ 8.413
9. Arrange the following decimals in ascending order:
   1. 5.8. 7.2. 5.69. 7.14, 5.06
   2. 0.6, 6.6, 6.06, 66.6, 0.06
   3. 6.54. 6.45, 6.4, 6.5, 6.05
   4. 3.3, 3.303, 3.033, 0.33, 3.003
10. Arrange the following decimals in descending order:
    1. 7.3. 8.73. 73.03. 7.33. 8.073
    2. 3.3, 3.03, 30.3, 30.03, 3.003
    3. 2.7. 7.2. 2.27. 2.72, 2.02, 2.007
    4. 8.88, 8.088, 88.8, 88.08, 8.008
11. Write the following fractional numbers as decimal fractions:
    1. \(\frac{9}{10}\)
    2. \(\frac{11}{100}\)
    3. \(\frac{17}{1000}\)
    4. \(\frac{31}{10000}\)
    5. 3\(\frac{19}{100}\)
12. Convert each of the following into a fraction in its simplest form:
    1. .9
    2. 0.6
    3. .08
    4. 0.15
    5. 0.48
    6. .053
    7. 0.125
    8. .224
    9. 0.23
    10. 0.357
    11. 5.4567
    12. 12.05
13. Convert each of the following as a mixed fraction:
    1. 6.4
    2. 16.5
    3. 8.36
    4. 4.275
    5. 25.06
    6. 7.004
    7. 2.052
    8. 3.108
14. Convert each of the following into a decimal:
    1. \(\frac{23}{10}\)
    2. \(\frac{167}{100}\)
    3. \(\frac{1589}{100}\)
    4. \(\frac{5413}{1000}\)
    5. \(\frac{21415}{1000}\)
    6. \(\frac{25}{4}\)
    7. \(3\frac{3}{5}\)
    8. \(1\frac{4}{25}\)
    9. \(\frac{37}{50}\)
    10. \(\frac{107}{250}\)
    11. \(\frac{3}{40}\)
    12. \(\frac{7}{8}\)
    13. 1\(\frac{1}{25}\)
    14. 7\(\frac{7}{8}\)
    15. 10\(\frac{1}{20}\)

15. 1. 8 kg 640 g in kilograms
    2. 9 kg 37 g in kilograms
    3. 540 g in kilograms
16. 1. 4 km 365 m in kilometres
    2. 5 km 87 m in kilometres
    3. 270 m in kilometres
    4. 35 m in kilometres
17. 1. ₹ 18 and 25 paise in rupees
    2. ₹ 9 and 8 paise in rupees
    3. 32 paise tn rupees
    4. 5 paise in rupees
18. Add:
    1. 0.275 and 0.425
    2. 0.001, 2.9 and 0.0002
    3. 39.101, 0.064 and 47 1.98
    4. 11.146, 0.2567, 9.23865 and 256
    5. 9.6, 14.8, 37 and 5.9
    6. 23.7, 106.94, 68.9 and 29.5
    7. 72.8, 7.68, 16.23 and 0.7
    8. 18.6, 84.75. 8.345 and 9.7
    9. 8.236, 16.064, 63.8 and 27.53
    10. 28.9, 19.64, 123.697 and 0.354
    11. 4.37, 9.638, 17.007 and 6.8
    12. 14.5, 0.038, 118.573 and 6.84

19. 1. Rs 3.45 + Rs 15.50 + Rs 3.05
    2. 7.25 m + 2.45 m + 12.75 m
    3. 35.280 l + 42.500 l + 8.700 l + 15 l
    4. 90.250 kg + 186.450 kg + 1001.750 kg + 98 kg
20. 1. 9.0005 − 7.462
    2. 10 − 0.0002
    3. Rs 5.50 − Rs 4.80
    4. 36.50 km − 10.85 km
    5. 13 m − 10.400 m
    6. 87.1251 − 16.250 1
    7. 400 kg − 1 50.650 kg
    8. 25 kg − 18.950 kg
21. Subtract:
    1. 27.86 from 53.74
    2. 59.63 from 92.4
    3. 56.8 from 204
    4. 127.38 from 216.2
    5. 39.875 from 70.68
    6. 348.237 from 523.12
    7. 458.573 from 600
    8. 0.612 from 3.4

22. 1. 0.2 × 4
    2. 0.4 × 12
    3. 9.1 × 11
    4. 13.5 × 17
    5. 0.12 × 62
    6. 4.32 × 51
    7. 2.007 × 36
    8. 3.125 × 86
    9. 4.028 × 234
23. 1. 2.34 × 10
    2. 89.015 × 10
    3. 134.2 × 10
    4. 4.34 × 100
    5. 1.325 × 100
    6. 8.7 × 100
24. 1. 1.67895 × 1000
    2. 76.2583 × 10000
    3. 0.125 × 100000
    4. 19.35 × 10000
    5. 0.00045 × 100000
    6. 20.012 × 10000
25. 1. 0.1 × 0.2
    2. 0.5 × 10.5
    3. 1.3 × 0.4
    4. 0.01 × 0.6
    5. 3.3 × 3.3
    6. 7.5 × 5.7
26. 1. 0.235 × 0.48
    2. 0.427 × 0.235
    3. 2.4327 × 4.23
    4. 1.0003 × 0.53
    5. 0.009 × 2.12
    6. 3.00704 × 4.0205
27. 1. 1 × 5.4
    2. 732.001 × 1
    3. 51.8 × 0
28. 1. 0.2 × 0.2 × 0.2
    2. 0.4 × 7.6 × 0.55
    3. 0.407 × 4.36 × 0.06
    4. 1.01 × 4.1 × 0.001
    5. 0.52 × 0.07 × 4.3 × 0.02
29. 1. 3.9 ÷ 3
    2. 18.9 ÷ 9
    3. 25.5 ÷ 5
    4. 80.8 ÷ 8
    5. 1.4 ÷ 7
    6. 4.8 ÷ 8
30. 1. 60.72 ÷ 12
    2. 55.55 ÷ 11
    3. 128.48 ÷ 16
    4. 9.09 ÷ 15
    5. 0.175 ÷ 25
    6. 0.0455 ÷ 35
31. 1. 617.313 ÷ 15
    2. 527.34 ÷ 85
    3. 426.478 ÷ 16
    4. 0.07849782 ÷ 72
    5. 0.00463 ÷ 50
    6. 1.2 ÷ 25
    7. 0.0042 ÷ 125
    8. 773.682 ÷ 169
    9. 2078.61 ÷ 579
    10. 00.00019517 ÷ 673
    11. 2.4 ÷ 625
    12. 0.217 ÷ 1250
    13. 431.376 ÷ 8170
    14. 0.001007 ÷ 47500
32. 1. 14.23 ÷ 10
    2. 0.456 ÷ 10
    3. 237.56 ÷ 100
    4. 8.12 ÷ 100
    5. 0.623 ÷ 100
    6. 8123.5 ÷ 1000
    7. 425.67 ÷ 1000
    8. 0.76 ÷ 1000
33. 1. 7.1 ÷ 100
    2. 23.45 ÷ 1000
    3. 6.14 ÷ 10000
    4. 100.23 ÷ 10000
    5. 9.2 ÷ 10000
    6. 0.3 ÷ 100000

34. 1. 36.48 by 20
    2. 458.5 by 50
    3. 374.96 80
    4. 12.04 by 400
    5. 545.1 by 600
    6. 21.07 by 7000
35. 1. 1.5 ÷ 0.3
    2. 6.4 ÷ 0.4
    3. 4.94 ÷ 0.7
    4. 1.296 ÷ 0.108
    5. 44.1 ÷ 2.1
    6. 2.52 ÷ 1.2
    7. 0.625 ÷ 0.025
    8. 31.5 ÷ 1.5
    9. 9.69 ÷ 1.9
    10. 0.00169 ÷ 1.3
    11. 2.05 ÷ 2.5
    12. 7.45 ÷ 0.32
    13. 108.997 ÷ 2.3
36. 1. 1 ÷ 0.5
    2. 16 ÷ 0.08
    3. 148 ÷ 0.074
    4. 210 ÷ 1.25
    5. 1032 ÷ 2.064
    6. 9894 ÷ 3.88
37. 1. 2 ÷ 5
    2. 3 ÷ 8
    3. 16 ÷ 64
    4. 56 ÷ 224
    5. 12 ÷ 8
    6. 1500 ÷ 6000
38. 1. 3 ÷ 0.8
    2. 11 ÷ 0.4
    3. 7 ÷ 1.25
39. Simplify:
    1. 37.6 + 72.85 − 58.678 − 6.09
    2. 75.3 − 104.645 + 178.96 − 47.9
    3. 213.4 − 56.84 − 1 1.87 − 16.087
    4. 76.3 − 7.666 − 6.77
    5. 5 − 0.005 − 0.05 + 0.5