Chapter 3 Review

In chapter 3 we reviewed fraction and mixed number conversions. We also reviewed how to add, subtract, multiply and divide fractions and mixed numbers. We learned that to multiply or divide fractions, we did not need a common denominator, but to add or subtract fractions, we did. We learned about equivalent fractions and how to find the simplest form. We also looked at several applications of fractions and mixed numbers.

Chapter 3 Review Problems

Convert the following mixed numbers into improper fractions:

1. $$5⁤\frac{4}{9}$$

   Check answer

   $$\frac{49}{9}$$

2. $$6⁤\frac{2}{7}$$

3. $$8⁤\frac{7}{11}$$

   Check answer

   $$\frac{95}{11}$$

4. $$5⁤\frac{15}{16}$$

Convert the following improper fractions into mixed numbers.

5. $$\frac{47}{6}$$

   Check answer

   $$7⁤\frac{5}{6}$$

6. $$\frac{85}{9}$$

7. $$\frac{93}{7}$$

   Check answer

   $$13⁤\frac{2}{7}$$

8. $$\frac{124}{11}$$

9. Convert $\frac{5}{12}$ into an equal fraction with a denominator of 96.

   Check answer

   $$\frac{40}{96}$$

10. Convert $\frac{5}{8}$ into an equal fraction with a denominator of 120.

11. Convert $\frac{13}{21}$ into an equal fraction with a denominator of 63.

    Check answer

    $$\frac{39}{63}$$

12. Convert $\frac{10}{27}$ into an equal fraction with a denominator of 162.

Convert the following fractions into simplest form.

13. $$\frac{75}{90}$$

    Check answer

    $$\frac{5}{6}$$

14. $$\frac{48}{108}$$

15. $$\frac{64}{112}$$

    Check answer

    $$\frac{4}{7}$$

16. $$\frac{28}{126}$$

Convert the following fractions and mixed numbers into a decimal. (Don’t forget to put a bar over any repeating parts.)

17. $$\frac{3}{16}$$

    Check answer

    0.1875

18. $$\frac{17}{33}$$

19. $$4⁤\frac{17}{25}$$

    Check answer

    4.68

20. $$9⁤\frac{7}{18}$$

Perform the following operations. Convert any improper fraction answers into mixed numbers and write all fraction answers in simplest form.

21. $$\frac{8}{11}\times \frac{33}{32}$$

    Check answer

    $$\frac{3}{4}$$

22. $$\frac{7}{15}\times \frac{20}{49}$$

23. $$\frac{6}{25}\times \frac{15}{18}$$

    Check answer

    $$\frac{1}{5}$$

24. $$\frac{8}{21}\times \frac{30}{44}$$

25. $$\frac{25}{18}÷\frac{5}{9}$$

    Check answer

    $$2⁤\frac{1}{2}$$

26. $$\frac{12}{25}÷\frac{27}{20}$$

27. $$\frac{45}{26}÷\frac{35}{14}$$

    Check answer

    $$\frac{9}{13}$$

28. $$\frac{50}{81}÷\frac{22}{63}$$

29. $$4⁤\frac{2}{3}\times 5⁤\frac{1}{7}$$

    Check answer

    24

30. $$1⁤\frac{7}{9}÷5⁤\frac{1}{3}$$

31. $$9⁤\frac{2}{6}\times 6⁤\frac{3}{8}$$

    Check answer

    $$59⁤\frac{1}{2}$$

32. $$10⁤\frac{1}{12}÷5⁤\frac{1}{2}$$

33. $$\frac{1}{2}+\frac{4}{5}$$

    Check answer

    $$1⁤\frac{3}{10}$$

34. $$\frac{13}{20}+\frac{4}{18}$$

35. $$\frac{3}{14}+\frac{4}{49}$$

    Check answer

    $$\frac{29}{98}$$

36. $$\frac{8}{55}+\frac{17}{22}$$

37. $$\frac{9}{10}-\frac{7}{15}$$

    Check answer

    $$\frac{13}{30}$$

38. $$\frac{11}{12}-\frac{3}{8}$$

39. $$\frac{11}{15}-\frac{1}{18}$$

    Check answer

    $$\frac{61}{90}$$

40. $$\frac{6}{25}-\frac{3}{20}$$

41. $$6⁤\frac{4}{7}+2⁤\frac{2}{3}$$

    Check answer

    $$9⁤\frac{5}{21}$$

42. $$9⁤\frac{1}{4}-6⁤\frac{2}{5}$$

43. $$4⁤\frac{7}{9}+8⁤\frac{3}{4}$$

    Check answer

    $$13⁤\frac{19}{36}$$

44. $$10⁤\frac{1}{6}-7⁤\frac{5}{8}$$

45. Convert 15.24 centimeters into inches. $(1\text{ in}=2.54\text{ cm})$

    Check answer

    6 in

46. Convert 7.5 kilograms into pounds. ( 1 kg ≈ 2.2 pounds ) Write your answer as a decimal.

47. Convert 49.6 miles per hour into kilometers per hour. ( 1 kph ≈ 0.62 mph )

    Check answer

    80 kph

48. Convert $14⁤\frac{1}{2}$ yards into inches. ( 1 yd = 36 inches )

49. Convert 564.5 mg into grams. ( 1 g = 1000 mg )

    Check answer

    0.5645 g

50. Larry ran 5/7 of a mile on Monday but only 2/5 of a mile on Tuesday. How much farther did he run on Monday than Tuesday?

51. A used car salesman told Jessica that her car payment will be reduced to $\frac{2}{3}$ of her current car payment. If her current car payment is $276, what will her new car payment be?

    Check answer

    $184

52. When visiting New York City, many travelers are amazed at how much walking they do to get around. Jesse’s family walked $4⁤\frac{2}{3}$ miles on their first day, $3⁤\frac{3}{4}$ miles on their second day and $5⁤\frac{1}{2}$ miles on their third day. What is the total amount they walked over their 3 day visit?

53. Ray is making a batch of brownies that calls for $2⁤\frac{1}{3}$ cups of flour. If he is making 6 batches of brownies, how much total flour will he need?

    Check answer

    14 cups flour

Adapted from Preparing for Algebra and Statistics, Third Edition, by Matt Teachout. License: CC BY 4.0. Copyright and sources.