Answer Key – Chapter 2

Exercise 2.1

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 2.2

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 2.3

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 2.4

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{8}{9}}[/latex]

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

11. 1. [latex]\displaystyle{2\frac{1}{6}}[/latex]
    2. [latex]\displaystyle{18\frac{1}{12}}[/latex]

13. 1. [latex]\displaystyle{15\frac{11}{12}}[/latex]
    2. [latex]\displaystyle{14\frac{5}{12}}[/latex]

15. 1. [latex]\displaystyle{\frac{309}{1000}}[/latex]
    2. [latex]\displaystyle{1\frac{9}{10}}[/latex]

17. 1. [latex]\displaystyle{\frac{5}{9}}[/latex]
    2. [latex]\displaystyle{\frac{3}{20}}[/latex]

19. 1. [latex]\displaystyle{1\frac{7}{24}}[/latex]
    2. [latex]\displaystyle{14\frac{5}{8}}[/latex]

21. 1. [latex]\displaystyle{3\frac{1}{2}}[/latex]
    2. [latex]\displaystyle{2\frac{1}{10}}[/latex]

23. 1. [latex]\displaystyle{\frac{54}{125}}[/latex]
    2. [latex]\displaystyle{\frac{11}{16}}[/latex]

25. 1. [latex]4[/latex]
    2. [latex]\displaystyle{2\frac{1}{3}}[/latex]

27. 1. [latex]\displaystyle{\frac{15}{88}}[/latex]
    2. [latex]\displaystyle{12\frac{1}{2}}[/latex]

29. 1. [latex]\displaystyle{\frac{1}{14}}[/latex]
    2. [latex]\displaystyle{3\frac{1}{3}}[/latex]

31. 1. [latex]\displaystyle{1\frac{1}{2}}[/latex]
    2. [latex]\displaystyle{\frac{3}{32}}[/latex]

33. 1. [latex]\displaystyle{1\frac{5}{9}}[/latex]
    2. [latex]\displaystyle{2\frac{2}{3}}[/latex]

35. 1. [latex]\displaystyle{\frac{2}{5}}[/latex]
    2. [latex]\displaystyle{3\frac{3}{4}}[/latex]

37. 1. [latex]\displaystyle{\frac{4}{9}}[/latex]
    2. [latex]\displaystyle{12\frac{2}{3}}[/latex]

39. 1. [latex]\displaystyle{\frac{9}{25}}[/latex]
    2. [latex]\displaystyle{\frac{36}{49}}[/latex]

41. 1. [latex]\displaystyle{\frac{27}{64}}[/latex]
    2. [latex]\displaystyle{\frac{625}{81} = 7\frac{58}{81}}[/latex]

43. 1. [latex]\displaystyle{\frac{16}{9} = 1\frac{7}{9}}[/latex]
    2. [latex]\displaystyle{\frac{625}{81} = 7\frac{58}{81}}[/latex]

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

47. 1. [latex]\displaystyle{\frac{2}{5}}[/latex]
    2. [latex]\displaystyle{\frac{9}{4} = 2\frac{1}{4}}[/latex]

49. 1. [latex]\displaystyle{\frac{7}{4} = 1\frac{3}{4}}[/latex]
    2. [latex]\displaystyle{\frac{5}{2} = 2\frac{1}{2}}[/latex]

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

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

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

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

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

61. 1,350 textbooks

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

65. 14 pieces

67. 200 doses

69. 304 bulbs

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

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. Five tenths
   2. Seven thousandths
   3. Twelve hundredths
   4. Twenty-nine thousandths

3. 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

5. 1. 564.667
   2. 40.103
   3. 79.3802
   4. 9.63625

7. 0.189

9. 1.996

11. 1. 3, 48
    2. 4, 60
    3. 4, 15
    4. 27, 24

13. 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]

15. 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]

17. 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]

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}{11}}[/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