Chapter 2

Exercise 2.1

1. 1. Proper fraction

   2. Mixed number

3. 1. Improper fraction

   2. Mixed number

5. 1. Mixed number

   2. Improper fraction

7. 1. [latex] \displaystyle{\frac{16}{7}} [/latex]

      
      

   2. [latex] \displaystyle{\frac{25}{8}} [/latex]

9. 1. [latex] \displaystyle{\frac{29}{5}} [/latex]

      
      

   2. [latex] \displaystyle{\frac{27}{4}} [/latex]

11. 1. [latex] \displaystyle{2\frac{5}{7}} [/latex]

       
       

    2. [latex] \displaystyle{5\frac{5}{8}} [/latex]

13. 1. [latex] \displaystyle{7\frac{2}{3}} [/latex]

    2. [latex] \displaystyle{5\frac{1}{6}} [/latex]

15. Not equivalent

17. Not equivalent

19. Equivalent

21. Equivalent

23. Not equivalent

25. Equivalent

27. Equivalent

29. Equivalent

31. 1. (i) [latex] \displaystyle{\frac{3}{2}} [/latex]   (ii) [latex] \displaystyle{\frac{2}{3}} [/latex]

       
       

    2. (i) [latex] \displaystyle{\frac{4}{7}} [/latex]   (ii) [latex] \displaystyle{\frac{7}{4}} [/latex]

33. 1. (i) [latex] \displaystyle{\frac{7}{6}} [/latex]   (ii) [latex] \displaystyle{\frac{6}{7}} [/latex]

       
       

    2. (i) [latex] 4 [/latex]   (ii) [latex] \displaystyle{\frac{1}{4}} [/latex]

35. 1. (i) [latex] \displaystyle{\frac{4}{7}} [/latex]   (ii) [latex] \displaystyle{\frac{7}{4}} [/latex]

       
       

    2. (i) [latex] \displaystyle{\frac{5}{8}} [/latex]   (ii) [latex] \displaystyle{\frac{8}{5}} [/latex]

37. Equivalent

39. Not equivalent

41. Not equivalent

43. Equivalent

45. 1. 12

    2. 45

47. 1. 24

    2. 3

49. 1. 8

    2. 18

51. [latex] \displaystyle{\frac{1}{3}} [/latex]

53. [latex] \displaystyle{\frac{3}{4}} [/latex]

55. [latex] \displaystyle{\frac{3}{4}} [/latex]

57. [latex] \displaystyle{\frac{149}{240}} [/latex]

Exercise 2.2

1. [latex] \displaystyle{\frac{2}{5}} [/latex]

3. [latex] \displaystyle{\frac{12}{15}} [/latex]

5. [latex] \displaystyle{\frac{8}{7}} [/latex]

7. [latex] \displaystyle{\frac{7}{9}} [/latex]

9. [latex] \displaystyle{\frac{5}{8}} [/latex], [latex] \displaystyle{\frac{3}{5}} [/latex]

11. 1. [latex] \displaystyle{1\frac{1}{2}} [/latex]

       
       

    2. [latex] \displaystyle{1\frac{1}{3}} [/latex]

13. 1. [latex] \displaystyle{2\frac{1}{6}} [/latex]

       
       

    2. [latex] \displaystyle{18\frac{1}{12}} [/latex]

15. 1. [latex] \displaystyle{15\frac{11}{12}} [/latex]

       
       

    2. [latex] \displaystyle{14\frac{5}{12}} [/latex]

17. 1. [latex] \displaystyle{\frac{309}{1000}} [/latex]

       
       

    2. [latex] \displaystyle{1\frac{9}{10}} [/latex]

19. 1. [latex] \displaystyle{\frac{5}{9}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{3}{20}} [/latex]

21. 1. [latex] \displaystyle{1\frac{7}{24}} [/latex]

       
       

    2. [latex] \displaystyle{14\frac{5}{8}} [/latex]

23. 1. [latex] \displaystyle{3\frac{1}{2}} [/latex]

       
       

    2. [latex] \displaystyle{2\frac{1}{10}} [/latex]

25. 1. [latex] \displaystyle{\frac{54}{125}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{11}{16}} [/latex]

27. 1. [latex] 4 [/latex]

       
       

    2. [latex] \displaystyle{2\frac{1}{3}} [/latex]

29. 1. [latex] \displaystyle{\frac{15}{88}} [/latex]

       
       

    2. [latex] \displaystyle{12\frac{1}{2}} [/latex]

31. 1. [latex] \displaystyle{\frac{1}{14}} [/latex]

       
       

    2. [latex] \displaystyle{3\frac{1}{3}} [/latex]

33. 1. [latex] \displaystyle{1\frac{1}{2}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{3}{32}} [/latex]

35. 1. [latex] \displaystyle{1\frac{5}{9}} [/latex]

       
       

    2. [latex] \displaystyle{2\frac{2}{3}} [/latex]

37. 1. [latex] \displaystyle{\frac{2}{5}} [/latex]

       
       

    2. [latex] \displaystyle{3\frac{3}{4}} [/latex]

39. 1. [latex] \displaystyle{\frac{4}{9}} [/latex]

       
       

    2. [latex] \displaystyle{12\frac{2}{3}} [/latex]

41. 1. [latex] \displaystyle{\frac{9}{25}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{36}{49}} [/latex]

43. 1. [latex] \displaystyle{\frac{27}{64}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{625}{81} = 7\frac{58}{81}} [/latex]

45. 1. [latex] \displaystyle{\frac{16}{9} = 1\frac{7}{9}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{625}{81} = 7\frac{58}{81}} [/latex]

47. 1. [latex] \displaystyle{\frac{1}{3}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{1}{7}} [/latex]

49. 1. [latex] \displaystyle{\frac{2}{2}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{9}{4} = 2\frac{1}{4}} [/latex]

51. 1. [latex] \displaystyle{\frac{7}{4} = 1\frac{3}{4}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{5}{2} = 2\frac{1}{2}} [/latex]

53. [latex] \displaystyle{\frac{2}{3}} [/latex]

55. [latex] \displaystyle{5\frac{7}{15}} [/latex] hours

57. [latex] \displaystyle{\frac{7}{8}} [/latex] pounds

59. [latex] \displaystyle{\frac{13}{28}} [/latex] kg

61. [latex] \displaystyle{\frac{1}{10}} [/latex]

63. 1,350 textbooks

65. [latex] \displaystyle{3\frac{1}{2}} [/latex] km

67. 14 pieces

69. 200 doses

71. 304 bulbs

73. [latex] \displaystyle{2\frac{2}{5}} [/latex]

Exercise 2.3

1. 1. 0.6

      
      

   2. 0.007

3. 1. 0.12

      
      

   2. 0.029

5. 1. 7.5

      
      

   2. 9.503

7. 1. 3.67

      
      

   2. 2.567

9. (i) 87.2   (ii) 80 + 7 + 0.2

11. (i) 3.04   (ii) 3 + 0.04

13. (i) 0.0401   (ii) 0.04 + 0.0001

15. (i) 89.0625

    (ii) 80 + 9 + 0.06 + 0.002 + 0.0005

17. (i) 1,787.025

    (ii) 1,000 + 700 + 80 + 7 + 0.02 + 0.005

19. (i) 412.65

    (ii) 400 + 10 + 2 + 0.6 + 0.05

21. (i) 1,600,000.02

    (ii) 1,000,000 + 600,000 + 0.02

23. (i) 23.5   (ii) 20 + 3 + 0.5

25. 1. Forty-two and fifty-five hundredths

       
       

    2. Seven hundred thirty-four and one hundred twenty-five thousandths

27. 1. Twenty-five hundredths

       
       

    2. Nine and five tenths

29. 1. Seven and seven hundredths

       
       

    2. Fifteen and two thousandths

31. 1. Sixty-two thousandths

       
       

    2. Fifty-four thousandths

33. 0.034, 0.043, 0.304, 0.403

35. 415.2

37. 264.2

39. 24.2

41. 10.4

43. 14.36

45. 181.13

47. $16.78

49. $9.99

Exercise 2.4

1. 1,716.045

3. 869.593

5. 479.444

7. 964.571

9. 240.922

11. 238.192

13. 15.88

15. 281.283

17. 229.668

19. 415.01

21. 744.606

23. 259.5571

25. 0.344

27. 319.4598

29. [latex] 7.53\overline{1} [/latex]

31. 91.575

33. [latex] 24.\overline{3} [/latex]

35. 12.4

37. 1. 0.001

       
       

    2. 0.09

39. 1. 0.16

       
       

    2. 0.000008

41. 1. 0.5

       
       

    2. 0.7

43. 1. 1.1

       
       

    2. 1.3

45. 1. 0.1

       
       

    2. 0.07

47. $378.64

    
    

49. $14.86

    
    

51. $76.38

    
    

53. $64.56

    
    

55. $1.54

    
    

57. $1,281.85

    
    

59. $187.86

    
    

61. $86.46

    
    

63. $44.21

    
    

65. $3,469.09

    
    

67. $54.45

    
    

69. 14 pieces

    
    

71. $2.55

    
    

Exercise 2.5

1. 1. [latex] \displaystyle{\frac{1}{5}} [/latex]

      
      

   2. [latex] 0.75 [/latex]

      
      

   3. [latex] \displaystyle{\frac{3}{50}} [/latex]

3. 1. [latex] 0.36 [/latex]

      
      

   2. [latex] \displaystyle{\frac{1}{250}} [/latex]

      
      

   3. [latex] 0.14 [/latex]

5. 1. [latex] 0.5 [/latex]

      
      

   2. [latex] \displaystyle{\frac{2}{5}} [/latex]

      
      

   3. [latex] 0.06 [/latex]

7. 1. [latex] \displaystyle{\frac{1}{200}} [/latex]

      
      

   2. [latex] 0.36 [/latex]

      
      

   3. [latex] \displaystyle{\frac{1}{100}} [/latex]

9. 1. [latex] \displaystyle{\frac{7}{2}} [/latex]

      
      

   2. [latex] 1.6 [/latex]

      
      

   3. [latex] \displaystyle{\frac{28}{5}} [/latex]

11. 1. [latex] 5.05 [/latex]

       
       

    2. [latex] \displaystyle{\frac{34}{5}} [/latex]

       
       

    3. [latex] 2.75 [/latex]

13. 1. [latex] \displaystyle{2\frac{1}{4}} [/latex]

       
       

    2. [latex] 1.75 [/latex]

       
       

    3. [latex] \displaystyle{4\frac{1}{50}} [/latex]

15. 1. [latex] 8.35 [/latex]

       
       

    2. [latex] \displaystyle{16\frac{1}{200}} [/latex]

       
       

    3. [latex] 15.5 [/latex]

17. 1. [latex] \displaystyle{\frac{2}{3}} [/latex]

       
       

    2. [latex] 0.2\overline{5} [/latex]

       
       

    3. [latex] \displaystyle{\frac{25}{99}} [/latex]

19. 1. [latex] 0.\overline{45} [/latex]

       
       

    2. [latex] \displaystyle{\frac{2}{9}} [/latex]

       
       

    3. [latex] 0.\overline{285714} [/latex]

21. 1. [latex] \displaystyle{\frac{8}{75}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{3}{256}} [/latex]

23. 1. [latex] \displaystyle{\frac{27}{128}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{9}{4} = 2\frac{1}{4}} [/latex]

25. 1. [latex] 1 [/latex]

       
       

    2. [latex] \displaystyle{\frac{5}{6}} [/latex]

27. 1. [latex] \displaystyle{\frac{2}{3}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{85}{44} = 1\frac{41}{44}} [/latex]

29. 1. [latex] \displaystyle{\frac{369}{25} = 14\frac{19}{25}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{707}{200} = 3\frac{107}{200}} [/latex]

31. 1. [latex] \displaystyle{\frac{55}{9} = 6\frac{1}{9}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{1}{1024}} [/latex]

33. 1. [latex] \displaystyle{\frac{169}{500} = 0.338} [/latex]

       
       

    2. [latex] \displaystyle{\frac{1}{100} = 0.01} [/latex]

35. [latex] \displaystyle{\frac{511}{192} = 2\frac{127}{192}} [/latex]

37. [latex] \displaystyle{\frac{12}{7} = 1\frac{5}{7}} [/latex]

39. [latex] \displaystyle{\frac{391}{100} = 3\frac{91}{100}} [/latex]

41. [latex] \displaystyle{\frac{2339}{70} = 33\frac{29}{70}} [/latex]

43. [latex] \displaystyle{\frac{1}{10} = 0.1} [/latex]

45. [latex] \displaystyle{\frac{3}{5} = 0.6} [/latex]

47. [latex] 79 [/latex]

49. [latex] \displaystyle{\frac{73}{20} = 3\frac{13}{20} = 3.65} [/latex]

51. [latex] \displaystyle{\frac{74}{25} = 2\frac{24}{25} = 2.96} [/latex]

Review Exercises 2

1. 1. 3, 48

      
      

   2. 4, 60

      
      

   3. 4, 15

      
      

   4. 27, 24

3. 1. [latex] \displaystyle{\frac{24}{21}} [/latex] < [latex] \displaystyle{\frac{11}{5}} [/latex]

      
      

   2. [latex] \displaystyle{\frac{20}{44}} [/latex] > [latex] \displaystyle{\frac{6}{15}} [/latex]

      
      

   3. [latex] \displaystyle{\frac{18}{45}} [/latex] < [latex] \displaystyle{\frac{16}{4}} [/latex]

      
      

   4. [latex] \displaystyle{\frac{15}{25} = \frac{63}{105}} [/latex]

5. 1. [latex] \displaystyle{1\frac{1}{2}} [/latex]

      
      

   2. [latex] \displaystyle{1\frac{1}{2}} [/latex]

      
      

   3. [latex] \displaystyle{7\frac{1}{3}} [/latex]

      
      

   4. [latex] \displaystyle{11\frac{1}{3}} [/latex]

7. 1. [latex] \displaystyle{\frac{5}{23}} [/latex]

      
      

   2. [latex] \displaystyle{\frac{31}{12}} [/latex]

      
      

   3. [latex] 5 [/latex]

      
      

   4. [latex] \displaystyle{\frac{4}{5}} [/latex]

9. 1. Five tenths

      
      

   2. Seven thousandths

      
      

   3. Twelve hundredths

      
      

   4. Twenty-nine thousandths

11. 1. Thirty-two and four hundredths

       
       

    2. Two hundred and two tenths

       
       

    3. Forty-five thousand, five and one thousandth

       
       

    4. One million, five thousand, seventy-one and twenty-five hundredths

13. 1. 564.667

       
       

    2. 40.103

       
       

    3. 79.3802

       
       

    4. 9.63625

15. 0.189

17. 1.996

19. 1. [latex] \displaystyle{\frac{1}{40}} [/latex]

       
       

    2. [latex] 0.625 [/latex]

       
       

    3. [latex] \displaystyle{\frac{2}{25}} [/latex]

       
       

    4. [latex] 0.28 [/latex]

       
       

    5. [latex] \displaystyle{\frac{1}{500}} [/latex]

    6. [latex] 0.78 [/latex]

21. [latex] \displaystyle{13\frac{13}{24}} [/latex] kg

23. [latex] \displaystyle{5\frac{5}{6}} [/latex] years

25. [latex] \displaystyle{376\frac{1}{5}} [/latex] km

27. Alisha: $360, Beyonce: $220

29. $2,201.40

31. $870.89

33. 96 girls

35. [latex] \displaystyle{15\frac{27}{125}} [/latex]

37. [latex] \displaystyle{1\frac{1}{4} = 1.25} [/latex]

39. [latex] \displaystyle{\frac{21}{625}} [/latex]

41. [latex] \displaystyle{\frac{5}{108}} [/latex]

43. [latex] \displaystyle{\frac{3}{4}} [/latex]

45. [latex] \displaystyle{1\frac{5}{1}} [/latex]

Self-Test Exercises 2

1. 1. 20, 24

      
      

   2. 11, 30

      
      

   3. 18, 96

      
      

   4. 66, 24

      
      

2. 1. [latex] \displaystyle{\frac{15}{2} = 7\frac{1}{2}} [/latex]

      
      

   2. [latex] \displaystyle{\frac{26}{3} = 8\frac{2}{3}} [/latex]

      
      

   3. [latex] \displaystyle{\frac{16}{9} = 1\frac{7}{9}} [/latex]

      
      

   4. [latex] \displaystyle{\frac{9}{55}} [/latex]

      
      

3. 1. [latex] \displaystyle{\frac{55}{4} = 13\frac{3}{4}} [/latex]

      
      

   2. [latex] \displaystyle{\frac{28}{15} = 1\frac{13}{15}} [/latex]

      
      

   3. [latex] \displaystyle{\frac{1}{2}} [/latex]

      
      

   4. [latex] 6 [/latex]

      
      

4. 1. [latex] 27.9028 [/latex]

      
      

   2. [latex] 8.133 [/latex]

      
      

   3. [latex] 2.13792 [/latex]

      
      

   4. [latex] 2.297\overline{6} [/latex]

      
      

5. 1. Four thousandths

      
      

   2. Six and five hundredths

      
      

   3. Three hundred and two hundredths

      
      

   4. Seven and seventy-one thousandths

      
      

6. 1. [latex] \displaystyle{\frac{5}{8}} [/latex]

      
      

   2. [latex] \displaystyle{\frac{16}{5} = 3\frac{1}{5}} [/latex]

      
      

   3. [latex] \displaystyle{\frac{8}{11}} [/latex]

      
      

   4. [latex] 0.35 [/latex]

      
      

   5. [latex] 1.8 [/latex]

      
      

   6. [latex] 1.0\overline{6} [/latex]

      
      

7. 593.75km; 37.8 cm

   
   

8. $1,500

   
   

9. 1. [latex] \displaystyle{25\frac{13}{40}} [/latex]

      
      

   2. [latex] \displaystyle{8\frac{3}{4}} [/latex]

      
      

   3. [latex] \displaystyle{12\frac{17}{24} = 12.708\overline{3}} [/latex]

      
      

10. 1. [latex] \displaystyle{8\frac{16}{19}} [/latex]

       
       

    2. [latex] \displaystyle{3\frac{91}{100}} [/latex]

       
       

    3. [latex] \displaystyle{4\frac{11}{270}} [/latex]

       
       

11. 13 deliveries

    
    

12. [latex] \displaystyle{\frac{1}{3}} [/latex]; $80

    
    

13. $242.69

    
    

14. [latex] \displaystyle{9\frac{1}{8}} [/latex] km