Divide Fractions by Fractions - 6th Grade Math

1. Compute $\frac{1}{2} \div 3$.

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

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

   $12$. $3 \times \frac{4}{1} = 12$ by the reciprocal rule.

3. Compute $\frac{2}{5} \div 4$.

   $\frac{1}{10}$. $\frac{2}{5} \times \frac{1}{4} = \frac{2}{20} = \frac{1}{10}$.

4. Identify the missing factor: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \underline{\ \ \ }$.

   $\frac{d}{c}$. The reciprocal of the divisor completes the multiplication.

5. What is the reciprocal of $\frac{c}{d}$ (with $c,d\ne 0$)?

   $\frac{d}{c}$. Flip the numerator and denominator.

6. What is $\frac{6}{7} \div \frac{3}{14}$?

   $4$. $\frac{6}{7} \times \frac{14}{3} = \frac{84}{21} = 4$.

7. Find the width: area $\frac{1}{2}$ sq mi and length $\frac{3}{4}$ mi.

   $\frac{2}{3}$ mi. $\text{Width} = \text{Area} \div \text{Length} = \frac{1}{2} \div \frac{3}{4}$

8. State the general rule for dividing fractions: $(\frac{a}{b}) \div (\frac{c}{d})$ equals what?

   $\frac{ad}{bc}$. Multiply by the reciprocal: $\frac{a}{b} \times \frac{d}{c}$

9. What is $\frac{5}{6} \div \frac{1}{3}$?

   $\frac{5}{2}$. $\frac{5}{6} \times \frac{3}{1} = \frac{15}{6} = \frac{5}{2}$.

10. Compute $\frac{3}{4} \div \frac{1}{2}$.

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

11. How many $\frac{3}{4}$-cup servings are in $\frac{2}{3}$ cup?

    $\frac{8}{9}$ serving. $\frac{2}{3} \div \frac{3}{4} = \frac{8}{9}$ of a serving.

12. Compute $\frac{1}{2} \div \frac{3}{4}$.

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

13. What is $ $\frac{1}{2} \div 3$?

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

14. Which expression matches "Each person's share of $\frac{1}{2}$ lb split among $3$ people"?

    $\frac{1}{2} \div 3$. Total amount divided by number of people.

15. What operation is equivalent to $ $\frac{a}{b} \div \frac{c}{d}$?

    $\frac{a}{b} \times \frac{d}{c}$. Division by a fraction equals multiplication by its reciprocal.

16. Compute $\frac{4}{9} \div \frac{2}{3}$.

    $\frac{2}{3}$. $\frac{4}{9} \times \frac{3}{2} = \frac{12}{18} = \frac{2}{3}$.

17. Compute $\frac{7}{8} \div \frac{7}{16}$.

    $2$. $\frac{7}{8} \times \frac{16}{7} = \frac{112}{56} = 2$.

18. What division expression represents "How many $ $\frac{3}{4}$-cup servings fit in $ $\frac{2}{3}$ cup"?

    $\frac{2}{3} \div \frac{3}{4}$. Total amount divided by size of each serving.

19. What is $1 \div \frac{3}{4}$?

    $\frac{4}{3}$. $\frac{1}{1} \times \frac{4}{3} = \frac{4}{3}$.

20. Identify the correct equation for rectangle width $w$: $A=\frac{1}{2}$, $L=\frac{3}{4}$.

    $w = \frac{1}{2} \div \frac{3}{4}$. Area = Length $\times$ Width, so Width = Area $\div$ Length.

21. What is $\frac{2}{5} \div 2$?

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

22. What is the missing number $x$ in $ $\frac{3}{4} \times x = \frac{2}{3}$?

    $\frac{8}{9}$. $x = \frac{2}{3} \div \frac{3}{4} = \frac{8}{9}$ by division.

23. What is $\frac{9}{10} \div \frac{3}{5}$?

    $\frac{3}{2}$. $\frac{9}{10} \times \frac{5}{3} = \frac{45}{30} = \frac{3}{2}$.

24. What is $ $\frac{5}{12} \div \frac{5}{6}$?

    $\frac{1}{2}$. $\frac{5}{12} \times \frac{6}{5} = \frac{30}{60} = \frac{1}{2}$ simplified.

25. Find and correct the error: $\frac{2}{3} \div \frac{3}{4} = \frac{2}{3} \times \frac{3}{4}$.

    Correct: $\frac{2}{3} \times \frac{4}{3}$. Should multiply by reciprocal $\frac{4}{3}$, not $\frac{3}{4}$.

26. Compute $\frac{5}{6} \div \frac{1}{2}$.

    $\frac{5}{3}$. $\frac{5}{6} \times \frac{2}{1} = \frac{10}{6} = \frac{5}{3}$.

27. What multiplication equation checks $\frac{2}{3} \div \frac{3}{4} = \frac{8}{9}$?

    $\frac{3}{4} \times \frac{8}{9} = \frac{2}{3}$. Check by multiplying quotient by divisor to get dividend.

28. Compute $4 \div \frac{2}{3}$.

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

29. What is $\frac{3}{4} \div 2$?

    $\frac{3}{8}$. $\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$.

30. What is $\frac{7}{8} \div \frac{7}{4}$?

    $\frac{1}{2}$. $\frac{7}{8} \times \frac{4}{7} = \frac{28}{56} = \frac{1}{2}$.

31. What does $\frac{2}{3} \div \frac{3}{4}$ mean in words?

    How many $\frac{3}{4}$ are in $\frac{2}{3}$. Division asks how many groups of the divisor fit in the dividend.

32. What is the reciprocal of $\frac{c}{d}$?

    $\frac{d}{c}$. Flip the numerator and denominator.

33. What does $\frac{2}{3} \div \frac{3}{4}$ represent in words?

    How many $\frac{3}{4}$ are in $\frac{2}{3}$. Division asks how many groups of the divisor fit in the dividend.

34. What operation is equivalent to dividing by a fraction $c/d$?

    Multiply by the reciprocal: $\times \frac{d}{c}$. Division by a fraction equals multiplication by its reciprocal.

35. How many $\frac{3}{4}$-cup servings are in $\frac{2}{3}$ cup of yogurt?

    $\frac{8}{9}$ serving. Divide total by serving size: $\frac{2}{3} \div \frac{3}{4}$.

36. What is the reciprocal of $3/4$?

    $\frac{4}{3}$. Flip the numerator and denominator to find the reciprocal.

37. Compute $\frac{5}{6} \div \frac{1}{3}$.

    $\frac{5}{2}$. $\frac{5}{6} \times \frac{3}{1} = \frac{15}{6} = \frac{5}{2}$.

38. Which expression matches "How many $\frac{3}{4}$-cup servings are in $\frac{2}{3}$ cup"?

    $\frac{2}{3} \div \frac{3}{4}$. Total amount divided by size of each serving.

39. What is the width if area is $ $\frac{1}{2}$ mi$^2$ and length is $ $\frac{3}{4}$ mi?

    $\frac{2}{3}$ mi. Width = Area ÷ Length = $\frac{1}{2} \div \frac{3}{4} = \frac{2}{3}$ mi.

40. What multiplication equation is equivalent to $x \div \frac{c}{d}$?

    $x \times \frac{d}{c}$. Division by a fraction equals multiplication by its reciprocal.

41. What is $\frac{3}{5} \div \frac{2}{5}$?

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

42. How much chocolate does each get if $3$ people share $\frac{1}{2}$ lb equally?

    $\frac{1}{6}$ lb each. Divide total amount by number of people: $\frac{1}{2} \div 3$.

43. What is $\frac{4}{9} \div \frac{2}{3}$?

    $\frac{2}{3}$. $\frac{4}{9} \times \frac{3}{2} = \frac{12}{18} = \frac{2}{3}$.

44. What is $\frac{2}{3} \div \frac{3}{4}$?

    $\frac{8}{9}$. $\frac{2}{3} \times \frac{4}{3} = \frac{8}{9}$ by the reciprocal rule.

45. Find the width if area is $\frac{1}{2}$ sq mi and length is $\frac{3}{4}$ mi: $w=\frac{1}{2} \div \frac{3}{4}$.

    $\frac{2}{3}$ mi. $\text{Area} \div \text{length} = \text{width}$: $\frac{1}{2} \times \frac{4}{3} = \frac{2}{3}$

46. What is $\frac{5}{6} \div \frac{1}{2}$

    $\frac{5}{3}$. $\frac{5}{6} \times \frac{2}{1} = \frac{10}{6} = \frac{5}{3}$ simplified.

47. Compute $\frac{3}{5} \div \frac{9}{10}$.

    $\frac{2}{3}$. $\frac{3}{5} \times \frac{10}{9} = \frac{30}{45} = \frac{2}{3}$.

48. Find the width: area $=\frac{1}{2}$ sq mi and length $=\frac{3}{4}$ mi.

    $\frac{2}{3}$ mi. Width = Area ÷ Length = $\frac{1}{2} \div \frac{3}{4} = \frac{2}{3}$.

49. State the rewrite rule for fraction division: $\frac{a}{b} \div \frac{c}{d}$.

    $\frac{a}{b} \times \frac{d}{c}$. Division becomes multiplication by the reciprocal.

50. What is each person's share if $3$ people split $\frac{1}{2}$ lb equally?

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

51. What is $ $\frac{7}{8} \div \frac{7}{4}$?

    $\frac{1}{2}$. $\frac{7}{8} \times \frac{4}{7} = \frac{28}{56} = \frac{1}{2}$ simplified.

52. State the general rule for dividing fractions: $a/b c/d$.

    $\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$. Multiply the first fraction by the reciprocal of the second.

53. What is each share if $3$ people split $\frac{1}{2}$ lb equally?

    $\frac{1}{6}$ lb. $\frac{1}{2} \div 3 = \frac{1}{6}$ lb per person.

54. What is the rule for dividing fractions: $\frac{a}{b} \div \frac{c}{d}$?

    $\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$. Multiply by the reciprocal: flip the second fraction and multiply.

55. What is $2 \div \frac{1}{5}$?

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

56. Which equation matches "How many $\frac{3}{4}$-cup servings are in $\frac{2}{3}$ cup"?

    $\frac{2}{3} \div \frac{3}{4}$. Total amount divided by serving size gives number of servings.

57. How much chocolate does each person get if $3$ people share $\frac{1}{2}$ lb equally?

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

58. Which equation matches "Each person's share of $\frac{1}{2}$ lb among $3$ people"?

    $\frac{1}{2} \div 3$. Total amount divided by number of people gives each share.

59. What is $\frac{4}{9} \div \frac{2}{3}$?

    $\frac{2}{3}$. $\frac{4}{9} \times \frac{3}{2} = \frac{12}{18} = \frac{2}{3}$ simplified.

60. What is the reciprocal of $\frac{c}{d}$ (with $c,d \ne 0$)?

    $\frac{d}{c}$. Flip the numerator and denominator.

61. Compute $\frac{2}{3} \div \frac{3}{4}$.

    $\frac{8}{9}$. $\frac{2}{3} \times \frac{4}{3} = \frac{8}{9}$ by the reciprocal rule.

62. What is $ $\frac{3}{5} \div \frac{2}{3}$?

    $\frac{9}{10}$. $\frac{3}{5} \times \frac{3}{2} = \frac{9}{10}$ by the reciprocal rule.

63. What is $ $\frac{2}{3} \div \frac{3}{4}$?

    $\frac{8}{9}$. $\frac{2}{3} \times \frac{4}{3} = \frac{8}{9}$ by the reciprocal rule.

64. Compute $\frac{2}{5} \div 3$.

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

65. Compute $3 \div \frac{1}{2}$.

    $6$. $3 \times \frac{2}{1} = 6$ by the reciprocal rule.

66. What is $1 \div $\frac{3}{7}$?

    $\frac{7}{3}$. $1 \times \frac{7}{3} = \frac{7}{3}$ by the reciprocal rule.

67. What is $ $\frac{9}{10} \div \frac{3}{5}$?

    $\frac{3}{2}$. $\frac{9}{10} \times \frac{5}{3} = \frac{45}{30} = \frac{3}{2}$ simplified.

68. Compute $3 \div \frac{2}{5}$.

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

69. State the general rule for dividing fractions: $\frac{a}{b} \div \frac{c}{d}$

    $\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$. Multiply by the reciprocal: flip the second fraction and multiply.

70. What is $\frac{3}{4} \div \frac{3}{8}$?

    $2$. $\frac{3}{4} \times \frac{8}{3} = \frac{24}{12} = 2$ simplified.

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