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. $7.53\bar{1}$

31. 91.575

33. $24.\bar{3}$

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. ${\displaystyle \frac{16}{7}}$
   2. ${\displaystyle \frac{25}{8}}$

9. 1. ${\displaystyle \frac{29}{5}}$
   2. ${\displaystyle \frac{27}{4}}$

11. 1. ${\displaystyle 2\frac{5}{7}}$
    2. ${\displaystyle 5\frac{5}{8}}$

13. 1. ${\displaystyle 7\frac{2}{3}}$
    2. ${\displaystyle 5\frac{1}{6}}$

15. Not equivalent

17. Not equivalent

19. Equivalent

21. Equivalent

23. Not equivalent

25. Equivalent

27. Equivalent

29. Equivalent

31. 1. (i) ${\displaystyle \frac{3}{2}}$
       (ii) ${\displaystyle \frac{2}{3}}$
    2. (i) ${\displaystyle \frac{4}{7}}$
       (ii) ${\displaystyle \frac{7}{4}}$

33. 1. (i) ${\displaystyle \frac{7}{6}}$
       (ii) ${\displaystyle \frac{6}{7}}$
    2. (i) $4$
       (ii) ${\displaystyle \frac{1}{4}}$

35. 1. (i) ${\displaystyle \frac{4}{7}}$
       (ii) ${\displaystyle \frac{7}{4}}$
    2. (i) ${\displaystyle \frac{5}{8}}$
       (ii) ${\displaystyle \frac{8}{5}}$

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. ${\displaystyle \frac{1}{3}}$

53. ${\displaystyle \frac{3}{4}}$

55. ${\displaystyle \frac{3}{4}}$

57. ${\displaystyle \frac{149}{240}}$

Exercise 2.4

1. ${\displaystyle \frac{2}{5}}$`

3. ${\displaystyle \frac{12}{15}}$

5. ${\displaystyle \frac{8}{7}}$

7. ${\displaystyle \frac{8}{9}}$

9. 1. ${\displaystyle 1\frac{1}{2}}$
   2. ${\displaystyle 1\frac{1}{3}}$

11. 1. ${\displaystyle 2\frac{1}{6}}$
    2. ${\displaystyle 18\frac{1}{12}}$

13. 1. ${\displaystyle 15\frac{11}{12}}$
    2. ${\displaystyle 14\frac{5}{12}}$

15. 1. ${\displaystyle \frac{309}{1000}}$
    2. ${\displaystyle 1\frac{9}{10}}$

17. 1. ${\displaystyle \frac{5}{9}}$
    2. ${\displaystyle \frac{3}{20}}$

19. 1. ${\displaystyle 1\frac{7}{24}}$
    2. ${\displaystyle 14\frac{5}{8}}$

21. 1. ${\displaystyle 3\frac{1}{2}}$
    2. ${\displaystyle 2\frac{1}{10}}$

23. 1. ${\displaystyle \frac{54}{125}}$
    2. ${\displaystyle \frac{11}{16}}$

25. 1. $4$
    2. ${\displaystyle 2\frac{1}{3}}$

27. 1. ${\displaystyle \frac{15}{88}}$
    2. ${\displaystyle 12\frac{1}{2}}$

29. 1. ${\displaystyle \frac{1}{14}}$
    2. ${\displaystyle 3\frac{1}{3}}$

31. 1. ${\displaystyle 1\frac{1}{2}}$
    2. ${\displaystyle \frac{3}{32}}$

33. 1. ${\displaystyle 1\frac{5}{9}}$
    2. ${\displaystyle 2\frac{2}{3}}$

35. 1. ${\displaystyle \frac{2}{5}}$
    2. ${\displaystyle 3\frac{3}{4}}$

37. 1. ${\displaystyle \frac{4}{9}}$
    2. ${\displaystyle 12\frac{2}{3}}$

39. 1. ${\displaystyle \frac{9}{25}}$
    2. ${\displaystyle \frac{36}{49}}$

41. 1. ${\displaystyle \frac{27}{64}}$
    2. ${\displaystyle \frac{625}{81}=7\frac{58}{81}}$

43. 1. ${\displaystyle \frac{16}{9}=1\frac{7}{9}}$
    2. ${\displaystyle \frac{625}{81}=7\frac{58}{81}}$

45. 1. ${\displaystyle \frac{1}{3}}$
    2. ${\displaystyle \frac{1}{7}}$

47. 1. ${\displaystyle \frac{2}{5}}$
    2. ${\displaystyle \frac{9}{4}=2\frac{1}{4}}$

49. 1. ${\displaystyle \frac{7}{4}=1\frac{3}{4}}$
    2. ${\displaystyle \frac{5}{2}=2\frac{1}{2}}$

51. ${\displaystyle \frac{2}{3}}$

53. ${\displaystyle 5\frac{7}{15}}$ hours

55. ${\displaystyle \frac{7}{8}}$ pounds

57. ${\displaystyle \frac{13}{28}}$ kg

59. ${\displaystyle \frac{1}{10}}$

61. 1,350 textbooks

63. ${\displaystyle 3\frac{1}{2}}$ km

65. 14 pieces

67. 200 doses

69. 304 bulbs

71. ${\displaystyle 2\frac{2}{5}}$

Exercise 2.5

1. 1. ${\displaystyle \frac{1}{5}}$
   2. $0.75$
   3. ${\displaystyle \frac{3}{50}}$

3. 1. $0.36$
   2. ${\displaystyle \frac{1}{250}}$
   3. $0.14$

5. 1. $0.5$
   2. ${\displaystyle \frac{2}{5}}$
   3. $0.06$

7. 1. ${\displaystyle \frac{1}{200}}$
   2. $0.36$
   3. ${\displaystyle \frac{1}{100}}$

9. 1. ${\displaystyle \frac{7}{2}}$
   2. $1.6$
   3. ${\displaystyle \frac{28}{5}}$

11. 1. $5.05$
    2. ${\displaystyle \frac{34}{5}}$
    3. $2.75$

13. 1. ${\displaystyle 2\frac{1}{4}}$
    2. $1.75$
    3. ${\displaystyle 4\frac{1}{50}}$

15. 1. $8.35$
    2. ${\displaystyle 16\frac{1}{200}}$
    3. $15.5$

17. 1. ${\displaystyle \frac{2}{3}}$
    2. $0.2\bar{5}$
    3. ${\displaystyle \frac{25}{99}}$

19. 1. $0.\overline{45}$
    2. ${\displaystyle \frac{2}{9}}$
    3. $0.\overline{285714}$

21. 1. ${\displaystyle \frac{8}{75}}$
    2. ${\displaystyle \frac{3}{256}}$

23. 1. ${\displaystyle \frac{27}{128}}$
    2. ${\displaystyle \frac{9}{4}=2\frac{1}{4}}$

25. 1. $1$
    2. ${\displaystyle \frac{5}{6}}$

27. 1. ${\displaystyle \frac{2}{3}}$
    2. ${\displaystyle \frac{85}{44}=1\frac{41}{44}}$

29. 1. ${\displaystyle \frac{369}{25}=14\frac{19}{25}}$
    2. ${\displaystyle \frac{707}{200}=3\frac{107}{200}}$

31. 1. ${\displaystyle \frac{55}{9}=6\frac{1}{9}}$
    2. ${\displaystyle \frac{1}{1024}}$

33. 1. ${\displaystyle \frac{169}{500}=0.338}$
    2. ${\displaystyle \frac{1}{100}=0.01}$

35. ${\displaystyle \frac{511}{192}=2\frac{127}{192}}$

37. ${\displaystyle \frac{12}{7}=1\frac{5}{7}}$

39. ${\displaystyle \frac{391}{100}=3\frac{91}{100}}$

41. ${\displaystyle \frac{2339}{70}=33\frac{29}{70}}$

43. ${\displaystyle \frac{1}{10}=0.1}$

45. ${\displaystyle \frac{3}{5}=0.6}$

47. $79$

49. ${\displaystyle \frac{73}{20}=3\frac{13}{20}=3.65}$

51. ${\displaystyle \frac{74}{25}=2\frac{24}{25}=2.96}$

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. ${\displaystyle \frac{24}{21}}$ < ${\displaystyle \frac{11}{5}}$
    2. ${\displaystyle \frac{20}{44}}$ > ${\displaystyle \frac{6}{15}}$
    3. ${\displaystyle \frac{18}{45}}$ < ${\displaystyle \frac{16}{4}}$
    4. ${\displaystyle \frac{15}{25}=\frac{63}{105}}$

15. 1. ${\displaystyle 1\frac{1}{2}}$
    2. ${\displaystyle 1\frac{1}{2}}$
    3. ${\displaystyle 7\frac{1}{3}}$
    4. ${\displaystyle 11\frac{1}{3}}$

17. 1. ${\displaystyle \frac{5}{23}}$
    2. ${\displaystyle \frac{31}{12}}$
    3. $5$
    4. ${\displaystyle \frac{4}{5}}$

19. 1. ${\displaystyle \frac{1}{40}}$
    2. $0.625$
    3. ${\displaystyle \frac{2}{25}}$
    4. $0.28$
    5. ${\displaystyle \frac{1}{500}}$
    6. $0.78$

21. ${\displaystyle 13\frac{13}{24}}$ kg

23. ${\displaystyle 5\frac{5}{6}}$ years

25. ${\displaystyle 376\frac{1}{5}}$ km

27. Alisha: $360, Beyonce: $220

29. $2,201.40

31. $870.89

33. 96 girls

35. ${\displaystyle 15\frac{27}{125}}$

37. ${\displaystyle 1\frac{1}{4}=1.25}$

39. ${\displaystyle \frac{21}{625}}$

41. ${\displaystyle \frac{5}{108}}$

43. ${\displaystyle \frac{3}{4}}$

45. ${\displaystyle 1\frac{5}{11}}$

Self-Test Exercises 2

1. 1. 20, 24
   2. 11, 30
   3. 18, 96
   4. 66, 24

2. 1. ${\displaystyle \frac{15}{2}=7\frac{1}{2}}$
   2. ${\displaystyle \frac{26}{3}=8\frac{2}{3}}$
   3. ${\displaystyle \frac{16}{9}=1\frac{7}{9}}$
   4. ${\displaystyle \frac{9}{55}}$

3. 1. ${\displaystyle \frac{55}{4}=13\frac{3}{4}}$
   2. ${\displaystyle \frac{28}{15}=1\frac{13}{15}}$
   3. ${\displaystyle \frac{1}{2}}$
   4. $6$

4. 1. $27.9028$
   2. $8.133$
   3. $2.13792$
   4. $2.297\bar{6}$

5. 1. Four thousandths
   2. Six and five hundredths
   3. Three hundred and two hundredths
   4. Seven and seventy-one thousandths

6. 1. ${\displaystyle \frac{5}{8}}$
   2. ${\displaystyle \frac{16}{5}=3\frac{1}{5}}$
   3. ${\displaystyle \frac{8}{11}}$
   4. $0.35$
   5. $1.8$
   6. $1.0\bar{6}$

7. 593.75km; 37.8 cm
8. $1,500

9. 1. ${\displaystyle 25\frac{13}{40}}$
   2. ${\displaystyle 8\frac{3}{4}}$
   3. ${\displaystyle 12\frac{17}{24}=12.708\bar{3}}$

10. 1. ${\displaystyle 8\frac{16}{19}}$
    2. ${\displaystyle 3\frac{91}{100}}$
    3. ${\displaystyle 4\frac{11}{270}}$

11. 13 deliveries
12. ${\displaystyle \frac{1}{3}}$; $80
13. $242.69
14. ${\displaystyle 9\frac{1}{8}}$ km