2. Review Exercises

Answers to the odd-numbered problems are available at the end of the textbook.

For problems 1 to 4, express the decimal numbers in their word form.

1. a. 0.5   b. 0.007    c. 0.12   d. 0.029
2. a. 0.75   b. 0.3   c. 0.008   d. 0.04
3. a. 32.04   b. 200.2   c. 45,005.001   d. 1,005,071.25
4. a. 27.602   b. 470.5   c. 32,010.07   d. 3,500,007.45

For problems 5 and 6, perform the indicated arithmetic operations.

5. a. [latex]478.82 + 85.847[/latex]   b. [latex]65.09 − 24.987[/latex]   c. [latex]54.37 × 1.46d. 77.09 ÷ 8[/latex]
6. a. [latex]716.03 + 49.936[/latex]   b. [latex]15.71 − 3.509[/latex]   c. [latex]15.71 × 3.26d. 39.83 ÷ 9[/latex]

7. What is the difference between the least and the greatest numbers of the following? 0.012, 0.201, 0.02, 0.102
8. What is the sum of the least and the greatest numbers of the following? 0.041, 0.011, 0.014, 0.01
9. Which of the following is closest to 2? 2.011, 2.005, 1.996, 1.995
10. Which of the following is closest to 2? 2.011, 2.004, 1.997, 1.996

For problems 11 and 12, determine the missing values.

11. a. [latex]\displaystyle{\frac{6}{12} = \frac{?}{6} = \frac{24}{?}}[/latex]   b. [latex]\displaystyle{\frac{12}{45} = \frac{?}{15} = \frac{16}{?}}[/latex]
    c. [latex]\displaystyle{\frac{20}{25} = \frac{?}{5} = \frac{12}{?}}[/latex] d. [latex]\displaystyle{\frac{36}{48} = \frac{?}{36} = \frac{18}{?}}[/latex]
12. a. [latex]\displaystyle{\frac{9}{15} = \frac{?}{10} = \frac{15}{?}}[/latex]   b. [latex]\displaystyle{\frac{18}{27} = \frac{?}{18} = \frac{10}{?}}[/latex]
    c. [latex]\displaystyle{\frac{21}{35} = \frac{?}{25} = \frac{12}{?}}[/latex] d. [latex]\displaystyle{\frac{12}{28} = \frac{?}{70} = \frac{15}{?}}[/latex]

For problems 13 and 14, place the appropriate symbol (<, >, or =) between each of the fractions.

13. a. [latex]\displaystyle{\frac{24}{21}}[/latex] ▢ [latex]\displaystyle{\frac{11}{5}}[/latex]   b. [latex]\displaystyle{\frac{20}{44}}[/latex] ▢ [latex]\displaystyle{\frac{6}{15}}[/latex]   c. [latex]\displaystyle{\frac{18}{45}}[/latex] ▢ [latex]\displaystyle{\frac{16}{4}}[/latex]   d. [latex]\displaystyle{\frac{15}{25}}[/latex] ▢ [latex]\displaystyle{\frac{63}{100}}[/latex]
14. a. [latex]\displaystyle{\frac{15}{18}}[/latex] ▢ [latex]\displaystyle{\frac{30}{42}}[/latex]   b. [latex]\displaystyle{\frac{21}{24}}[/latex] ▢ [latex]\displaystyle{\frac{35}{40}}[/latex]   c. [latex]\displaystyle{\frac{40}{48}}[/latex] ▢ [latex]\displaystyle{\frac{35}{42}}[/latex]   d. [latex]\displaystyle{\frac{8}{38}}[/latex] ▢ [latex]\displaystyle{\frac{12}{57}}[/latex]

For problems 15 and 16, convert the improper fractions into mixed numbers in the simplest form.

15. a. [latex]\displaystyle{\frac{15}{10}}[/latex]   b. [latex]\displaystyle{\frac{39}{26}}[/latex]   c. [latex]\displaystyle{\frac{88}{12}}[/latex]d. [latex]\displaystyle{\frac{102}{9}}[/latex]
16. a. [latex]\displaystyle{\frac{18}{8}}[/latex]   b. [latex]\displaystyle{\frac{98}{12}}[/latex]   c. [latex]\displaystyle{\frac{88}{10}}[/latex]d. [latex]\displaystyle{\frac{48}{15}}[/latex]

For problems 17 and 18, reduce the fractions to their lowest terms.

17. a. [latex]\displaystyle{\frac{75}{345}}[/latex]   b. [latex]\displaystyle{\frac{124}{48}}[/latex]   c. [latex]\displaystyle{\frac{70}{14}}[/latex]d. [latex]\displaystyle{\frac{292}{365}}[/latex]
18. a. [latex]\displaystyle{\frac{36}{144}}[/latex]   b. [latex]\displaystyle{\frac{68}{10}}[/latex]   c. [latex]\displaystyle{\frac{80}{12}}[/latex]d. [latex]\displaystyle{\frac{61}{366}}[/latex]

For problems 19 and 20, convert the decimal numbers to proper fractions in lowest terms and the fractions to decimal numbers.

19. Question	Decimal Number	Proper Fraction
    a.	0.025	?
    b.	?	[latex]\displaystyle{\frac{5}{8}}[/latex]
    c.	0.08	?
    d.	?	[latex]\displaystyle{\frac{7}{25}}[/latex]
    e.	0.002	?
    f.	?	[latex]\displaystyle{\frac{39}{50}}[/latex]

20. Question	Decimal Number	Proper Fraction
    a.	0.06	?
    b.	?	[latex]\displaystyle{\frac{23}{50}}[/latex]
    c.	0.075	?
    d.	?	[latex]\displaystyle{\frac{27}{40}}[/latex]
    e.	0.004	?
    f.	?	[latex]\displaystyle{\frac{17}{25}}[/latex]

21. Find the total weight of three items that weigh [latex]\displaystyle{3\frac{2}{3}}[/latex] kg, [latex]\displaystyle{4\frac{1}{2}}[/latex] kg, and [latex]\displaystyle{5\frac{3}{8}}[/latex] kg.
22. Alex used [latex]\displaystyle{2\frac{1}{5}}[/latex] litres of paint for his bedroom, [latex]\displaystyle{1\frac{1}{4}}[/latex] litres for his study room, and [latex]\displaystyle{7\frac{1}{3}}[/latex] litres for his living room. How many litres of paint did he use for the three rooms?
23. Henry is [latex]\displaystyle{8\frac{1}{4}}[/latex] years old. Amanda is [latex]\displaystyle{2\frac{5}{12}}[/latex] years old. How many years younger is Amanda than Henry?
24. Harsha purchased [latex]\displaystyle{12\frac{1}{3}}[/latex] hectares of land and sold [latex]\displaystyle{4\frac{2}{5}}[/latex] hectares. How many hectares does she now own?
25. A car can travel [latex]\displaystyle{8\frac{1}{4}}[/latex] km with one litre of gas. How many kilometres can it travel using [latex]\displaystyle{45\frac{3}{5}}[/latex] litres of gas?
26. Samantha can walk [latex]\displaystyle{5\frac{3}{8}}[/latex] km in one hour. How far can she walk in [latex]\displaystyle{4\frac{1}{3}}[/latex] hours?
27. Alisha and Beyonce saved a total of $580. Two-fifths of Alisha’s savings equals $144. How much did each of them save?
28. Andy and Bob had $128. One-third of Bob’s amount is $25. How much did each of them have?
29. Lakshmi had $2,675.68 in her chequing account. She deposited 2 cheques in the amounts of $729.27 and $72.05 and withdrew $1,275.60. How much did she have in her account after the withdrawal?
30. George’s car had 12.47 litres of gas at the start of his trip to the United States. He added the following quantities of gas during his trip: 34.25 litres, 15.2 litres, and 20.05 litres. At the end of the trip, there were 7.9 litres of gas left in the car. How much gas was used during the trip?
31. Barbie’s hourly pay is $23.07. If Barbie worked 37.75 hours last week, calculate her gross pay for last week.
32. Carol’s overtime rate of pay is $57.45 per hour. If Carol worked 12.5 hours of overtime last week, calculate her gross overtime pay for last week.
33. Three-fourths of the number of boys at a school is equal to half of the number of girls. The school has 480 students in total. How many more girls are there than boys?
34. There are 3,400 spectators at a soccer match. Three-fifths of the number of men equals six-sevenths of the number of women. How many spectators are women?

For problems 35 to 46, evaluate the expressions.

35. [latex]\displaystyle{\left(5+ \frac{6}{10}\right)^3 + \sqrt{6^2 + 8^2}}[/latex]
36. [latex]\displaystyle{\left(\frac{5}{7}\right)^2 \div 5 + \sqrt{3^2 + 4^2}}[/latex]
37. [latex]\displaystyle{\sqrt{1.21} - (0.5)^2 + \sqrt{\frac{4}{25}}}[/latex]
38. [latex]\displaystyle{\sqrt{0.81} - (0.2)^2 + \sqrt{\frac{9}{36}}}[/latex]
39. [latex]\displaystyle{\left(\frac{1}{5}\right)^3 + \left(\frac{4}{25}\right)^2}[/latex]
40. [latex]\displaystyle{\left(\frac{2}{3}\right)^3 + \left(\frac{2}{9}\right)^2}[/latex]
41. [latex]\displaystyle{\left(\frac{5}{12}\right)^3\left(\frac{4}{5}\right)^2}[/latex]
42. [latex]\displaystyle{\left(\frac{4}{7}\right)^2\left(\frac{1}{4}\right)^3}[/latex]
43. [latex]\displaystyle{\left(2\frac{4}{5} - \frac{7}{10}\right) \div 2\frac{4}{52}}[/latex]
44. [latex]\displaystyle{\left(2\frac{5}{8} + 1\frac{5}{12}\right) \div 1\frac{1}{2}}[/latex]
45. [latex]\displaystyle{\left(3\frac{1}{5}\right) \div (1\frac{1}{5} + 1)}[/latex]
46. [latex]\displaystyle{\left(2\frac{2}{3}\right) \div (2\frac{2}{5} + 6)}[/latex]