Solve Fraction Multiplication Problems - 5th Grade Math

1. Which equation matches "$\frac{3}{5}$ of $30$ meters"?

   $\frac{3}{5} \times 30$. Write "of" as multiplication in the equation.

2. A board is $2\frac{1}{2}$ m long. You cut off $\frac{3}{5}$ of it. How long is the piece cut off?

   $1\frac{1}{2}\text{ m}$. $\frac{3}{5} \times \frac{5}{2} = \frac{15}{10} = \frac{3}{2} = 1\frac{1}{2}$ m.

3. What is $\frac{5}{6}$ of $18$?

   $15$. $\frac{5}{6} \times 18 = \frac{90}{6} = 15$.

4. What is $\frac{3}{4}$ of $2$ cups (how many cups)?

   $1\frac{1}{2}$ cups. $\frac{3}{4} \times 2 = \frac{6}{4} = 1\frac{1}{2}$.

5. What is $\frac{2}{3}$ of $12$?

   $8$. $\frac{2}{3} \times 12 = \frac{24}{3} = 8$.

6. What is the area of a rectangle with side lengths $\frac{3}{4}$ ft and $\frac{2}{3}$ ft?

   $\frac{1}{2} \, \text{ft}^2$. Area = length × width = $\frac{3}{4} \times \frac{2}{3} = \frac{1}{2}$

7. What is $\frac{2}{3}$ of $12$?

   $8$. $\frac{2}{3} \times 12 = \frac{24}{3} = 8$.

8. What is $\frac{4}{7}\times\frac{21}{8}$ in simplest form?

   $\frac{3}{2}$. Multiply and simplify: $\frac{84}{56} = \frac{3}{2}$.

9. Which expression represents "$\frac{3}{4}$ of $2\frac{2}{3}$" as a product?

   $\frac{3}{4}\times\frac{8}{3}$. Convert $2\frac{2}{3}$ to $\frac{8}{3}$ before multiplying.

10. What is $1\frac{1}{2}$ of $\frac{2}{3}$?

    $1$. $\frac{3}{2} \times \frac{2}{3} = \frac{6}{6} = 1$.

11. Identify the operation in the phrase "$\frac{4}{7}$ of $21$" when writing an equation.

    Multiplication: $\frac{4}{7}\times 21$. "Of" translates to multiplication in fraction word problems.

12. What is $\frac{2}{5}\times\frac{3}{4}$ in simplest form?

    $\frac{3}{10}$. Multiply numerators and denominators: $\frac{6}{20} = \frac{3}{10}$.

13. What is $\frac{3}{4}$ of $20$?

    $15$. $\frac{3}{4} \times 20 = \frac{60}{4} = 15$.

14. Identify the product: A recipe uses $\frac{3}{4}$ cup sugar per batch; for $2$ batches, how much sugar?

    $1\frac{1}{2}$ cups. $\frac{3}{4} \times 2 = \frac{6}{4} = 1\frac{1}{2}$.

15. What is the first step to multiply a mixed number by a fraction?

    Convert the mixed number to an improper fraction. Mixed numbers must be improper fractions before multiplying.

16. What is $\frac{5}{6}\times\frac{3}{10}$ in simplest form?

    $\frac{1}{4}$. Multiply and simplify: $\frac{15}{60} = \frac{1}{4}$.

17. What is $2\frac{1}{4}\times\frac{4}{9}$ in simplest form?

    1. $\frac{9}{4} \times \frac{4}{9} = \frac{36}{36} = 1$

18. What is $\frac{2}{3}\times 9$?

    $6$. $\frac{2}{3} \times 9 = \frac{18}{3} = 6$.

19. What is $\frac{7}{10}$ of $50$?

    $35$. $\frac{7}{10} \times 50 = \frac{350}{10} = 35$.

20. A recipe needs $\frac{3}{4}$ cup sugar. You make $\frac{2}{3}$ of the recipe. How much sugar?

    $\frac{1}{2}\text{ cup}$. $\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$ cup.

21. What is $1\frac{3}{5}\times\frac{5}{8}$ in simplest form?

    $1$. $1\frac{3}{5} = \frac{8}{5}$; then $\frac{8}{5} \times \frac{5}{8} = 1$.

22. What is $\frac{2}{5}$ of $25$?

    $10$. $\frac{2}{5} \times 25 = \frac{50}{5} = 10$.

23. What is $\frac{4}{5}$ of $25$?

    $20$. $\frac{4}{5} \times 25 = \frac{100}{5} = 20$.

24. What is $\frac{7}{9}\times\frac{3}{14}$ in simplest form?

    $\frac{1}{6}$. Multiply and simplify: $\frac{21}{126} = \frac{1}{6}$.

25. What operation does the word "of" usually indicate in fraction word problems?

    Multiplication. "Of" means "times" when working with fractions.

26. A ribbon is $12$ ft long. You use $\frac{5}{8}$ of it. How many feet do you use?

    $7\frac{1}{2}\text{ ft}$. $\frac{5}{8} \times 12 = \frac{60}{8} = 7\frac{1}{2}$ ft.

27. State the equation that represents "$\frac{a}{b}$ of $x$" using multiplication.

    $\frac{a}{b}\text{ of }x=\frac{a}{b}\times x$. "Of" in fraction problems means multiply.

28. What is $\frac{4}{7}$ of $21$?

    $12$. $\frac{4}{7} \times 21 = \frac{84}{7} = 12$.

29. State the first step to multiply a mixed number by a fraction.

    Convert the mixed number to an improper fraction. Mixed numbers must be improper fractions before multiplying.

30. What is $\frac{5}{4}\times\frac{8}{15}$ in simplest form?

    $\frac{2}{3}$. Cancel common factors: $\frac{5 \times 8}{4 \times 15} = \frac{40}{60} = \frac{2}{3}$.

31. A trail is $6$ miles. You hike $\frac{3}{4}$ of it. How many miles do you hike?

    $4\frac{1}{2}\text{ miles}$. $\frac{3}{4} \times 6 = \frac{18}{4} = 4\frac{1}{2}$ miles.

32. What is $\frac{3}{5}$ of $2\frac{1}{2}$?

    $1\frac{1}{2}$. $\frac{3}{5} \times \frac{5}{2} = \frac{15}{10} = 1\frac{1}{2}$.

33. What is $1\frac{1}{2}\times\frac{2}{3}$ in simplest form?

    1. $\frac{3}{2} \times \frac{2}{3} = \frac{6}{6} = 1$

34. What is the product $\frac{2}{3} \times \frac{9}{10}$ in simplest form?

    $\frac{3}{5}$. $\frac{2 \times 9}{3 \times 10} = \frac{18}{30} = \frac{3}{5}$.

35. What is $\frac{5}{6}$ of $18$?

    $15$. $\frac{5}{6} \times 18 = \frac{90}{6} = 15$.

36. What is $2\frac{1}{4} \times 4$?

    $9$. $\frac{9}{4} \times 4 = \frac{36}{4} = 9$.

37. What is $\frac{2}{3}$ of $1\frac{1}{2}$?

    $1$. $\frac{2}{3} \times \frac{3}{2} = \frac{6}{6} = 1$.

38. What is $1\frac{1}{2}\times\frac{2}{3}$ in simplest form?

    $1$. $1\frac{1}{2} = \frac{3}{2}$; then $\frac{3}{2} \times \frac{2}{3} = 1$.

39. What is $3\frac{1}{2}\times\frac{2}{7}$ in simplest form?

    1. $\frac{7}{2} \times \frac{2}{7} = \frac{14}{14} = 1$

40. What is $\frac{3}{4}$ of $20$?

    $15$. $\frac{3}{4} \times 20 = \frac{60}{4} = 15$.

41. What is $2\frac{1}{4}\times\frac{4}{9}$ in simplest form?

    $1$. $2\frac{1}{4} = \frac{9}{4}$; then $\frac{9}{4} \times \frac{4}{9} = 1$.

42. What is $\frac{3}{8}$ of $32$?

    $12$. $\frac{3}{8} \times 32 = \frac{96}{8} = 12$.

43. What is $\frac{1}{4}$ of $3\frac{1}{2}$?

    $\frac{7}{8}$. $\frac{1}{4} \times \frac{7}{2} = \frac{7}{8}$.

44. What is $\frac{5}{8} \times \frac{16}{25}$ in simplest form?

    $\frac{2}{5}$. $\frac{5 \times 16}{8 \times 25} = \frac{80}{200} = \frac{2}{5}$.

45. What is $\frac{3}{8}$ of $32$?

    $12$. $\frac{3}{8} \times 32 = \frac{96}{8} = 12$.

46. What is $\frac{3}{5}\times\frac{10}{9}$ in simplest form?

    $\frac{2}{3}$. Multiply numerators and denominators: $\frac{30}{45} = \frac{2}{3}$.

47. What is $1\frac{1}{2} \times 8$?

    $12$. $\frac{3}{2} \times 8 = \frac{24}{2} = 12$.

48. A tank holds $30$ gallons. It is filled to $\frac{3}{5}$ of its capacity. How many gallons is that?

    $18\text{ gallons}$. $\frac{3}{5} \times 30 = \frac{90}{5} = 18$ gallons.

49. What is $\frac{7}{8}\times\frac{4}{7}$ in simplest form?

    $\frac{1}{2}$. Cancel $7$s before multiplying: $\frac{1 \times 4}{8 \times 1} = \frac{4}{8} = \frac{1}{2}$.

50. What is $2\frac{1}{3} \times \frac{3}{7}$?

    $1$. $\frac{7}{3} \times \frac{3}{7} = \frac{21}{21} = 1$.

51. What is $\frac{2}{3}$ of $\frac{3}{5}$?

    $\frac{2}{5}$. $\frac{2}{3} \times \frac{3}{5} = \frac{6}{15} = \frac{2}{5}$ after simplifying.

52. A jug has $1\frac{1}{2}$ L of juice. You drink $\frac{2}{3}$ of it. How many liters do you drink?

    $1\text{ L}$. $\frac{2}{3} \times \frac{3}{2} = \frac{6}{6} = 1$ L.

53. What is $\frac{3}{4}$ of $12$?

    $9$. $\frac{3}{4} \times 12 = \frac{36}{4} = 9$.

54. What is $1\frac{3}{5} \times \frac{5}{8}$ in simplest form?

    1. $\frac{8}{5} \times \frac{5}{8} = \frac{40}{40} = 1$

55. What is the area of a rectangle with side lengths $1\frac{1}{2}$ m and $\frac{2}{5}$ m?

    $\frac{3}{5} \, \mathrm{m}^2$. Area = $\frac{3}{2} \times \frac{2}{5} = \frac{6}{10} = \frac{3}{5}$

56. What is $1\frac{1}{4} \times \frac{4}{5}$?

    $1$. $\frac{5}{4} \times \frac{4}{5} = \frac{20}{20} = 1$.

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