Understand Unit Rate Concept - 6th Grade Math

1. What is the unit rate (first per second) for the ratio $3:4$?

   $\frac{3}{4}$ per $1$. Divide first quantity by second: $\frac{3}{4}$ gives amount of first per one second.

2. What is the unit rate for the ratio $3:4$ written as a fraction?

   $\frac{3}{4}$. Divide first quantity by second: $\frac{3}{4}$.

3. Identify the unit rate (miles per hour) for $150$ miles in $3$ hours.

   $50$ miles per hour. Divide total distance by time: $\frac{150}{3} = 50$.

4. Choose the correct unit rate for $8$ notebooks for $20: $\$\frac{5}{2}$ or $\$\frac{2}{5}$ per notebook?

   $\$\frac{5}{2}$ per notebook. Cost per item is $\frac{20}{8} = \frac{5}{2} = 2.50$ dollars each.

5. What is the unit rate (cost per pound) for $18 for $6$ lb of apples?

   $3 per lb. Divide cost by pounds: $\frac{18}{6} = 3$.

6. What does the unit rate $\frac{a}{b}$ mean in words for a ratio $a:b$?

   It means "$\frac{a}{b}$ units of the first quantity per $1$ unit of the second.". Unit rate shows the amount of first quantity for each single unit of second quantity.

7. What is the unit rate (cups of sugar per cup of flour) for a ratio $3:4$?

   $\frac{4}{3}$ cups sugar per $1$ cup flour. Second quantity per first: $\frac{4}{3}$ sugar per flour.

8. Identify the error: "For ratio $5:0$, the unit rate is $\frac{5}{0}$." What is the correct statement?

   No unit rate exists because $b=0$ and division by $0$ is undefined. Cannot divide by zero; unit rate requires $b \ne 0$.

9. What is the unit rate (dollars per item) for $12$ items costing $3 total?

   $\$ \frac{1}{4}$ per item. Divide total cost by number of items: $\frac{3}{12} = \frac{1}{4}$.

10. Identify the unit rate (words per minute) for $240$ words in $6$ minutes.

    $40$ words per minute. Divide total words by time: $\frac{240}{6} = 40$.

11. Find the unit rate (minutes per mile) for $30$ minutes to run $5$ miles.

    $6$ minutes per mile. Divide minutes by miles: $\frac{30}{5} = 6$.

12. Find the unit rate in $\text{notebooks per dollar}$ for $8$ notebooks that cost $20.

    $\frac{2}{5}$ notebook per dollar. Divide quantity by cost: $\frac{8}{20} = \frac{2}{5}$ notebooks per dollar.

13. What is the unit rate (items per dollar) for $12$ items costing $3 total?

    $4$ items per dollar. Divide number of items by cost: $\frac{12}{3} = 4$.

14. Which quantity must be $1$ in a unit rate: the numerator or the denominator?

    The denominator must be $1$ (the "per $1$" amount). Unit rates always express "per one" of something.

15. Find the unit rate in $\text{minutes per page}$ for $45$ pages in $9$ minutes.

    $\frac{1}{5}$ minute per page. Divide time by pages: $\frac{9}{45} = \frac{1}{5}$ minute to read one page.

16. Identify the unit rate (cost per ounce) for $6 for $8$ ounces.

    $\$\frac{3}{4}$ per ounce. Divide total cost by ounces: $\frac{6}{8} = \frac{3}{4}$.

17. Find the unit rate in $\text{pages per minute}$ for $45$ pages in $9$ minutes.

    $5$ pages per minute. Divide total pages by time: $\frac{45}{9} = 5$ pages read in one minute.

18. Identify the unit rate for the ratio $2.5:0.5$ (first per second).

    $5$ per $1$. Divide first by second: $\frac{2.5}{0.5} = 5$ units of first per one second.

19. Which quantity must be $1$ in a unit rate written as $\frac{a}{b}$?

    The second quantity (the denominator) is $1$ unit. Unit rates always have a denominator of 1.

20. What is the unit rate in hamburgers per dollar if $15$ hamburgers cost $75?

    $\frac{1}{5}$ hamburger per dollar. Divide hamburgers by dollars: $\frac{15}{75} = \frac{1}{5}$.

21. Identify the unit rate (dollars per pound) for $18 for $6$ lb of apples.

    $3 per pound. Divide price by weight: $\frac{18}{6} = 3$.

22. Find and correct the unit rate error: "Ratio $10:2$ gives unit rate $\frac{2}{10}$ per $1$."

    Correct unit rate is $\frac{10}{2}=5$ per $1$. Unit rate divides first by second, not second by first.

23. What is the unit rate (kilometers per liter) for $150$ km on $10$ L of gas?

    $15$ km per liter. Divide distance by fuel: $\frac{150}{10} = 15$.

24. What is the unit rate (second per first) for the ratio $3:4$?

    $\frac{4}{3}$ per $1$. Flip the ratio to get second per first: $\frac{4}{3}$ units of second per one first.

25. What is the unit rate (pounds per dollar) if $6$ lb of apples cost $18?

    $\frac{1}{3}$ lb per dollar. Divide pounds by dollars: $\frac{6}{18} = \frac{1}{3}$.

26. Identify the unit rate for the ratio $\frac{3}{4}:\frac{1}{2}$ (first per second).

    $\frac{3}{2}$ per $1$. Divide fractions: $\frac{3/4}{1/2} = \frac{3}{4} \times \frac{2}{1} = \frac{3}{2}$.

27. What is the unit rate (items per dollar) for $15$ hamburgers for $75?

    $\frac{1}{5}$ hamburger per dollar. Divide items by dollars: $\frac{15}{75} = \frac{1}{5}$.

28. What unit rate corresponds to the ratio $3:4$ (first quantity per $1$ of second)?

    $\frac{3}{4}$ per $1$. Divide the first quantity by the second: $\frac{3}{4}$.

29. What is the unit rate (dollars per item) for $75 for $15$ hamburgers?

    $5 per hamburger. Divide total cost by number of items: $\frac{75}{15} = 5$.

30. Which option is the unit rate for $8$ notebooks for $12: $\frac{12}{8}$ or $\frac{8}{12}$ dollars per notebook?

    $\frac{12}{8}=\frac{3}{2}$ dollars per notebook. Price per item means dollars divided by notebooks.

31. What is the unit rate (dollars per ticket) for $54 for $6$ tickets?

    $9 per ticket. Divide cost by tickets: $\frac{54}{6} = 9$.

32. Identify the error: A student says the unit rate for $8:2$ is $\frac{2}{8}$. What is correct?

    Correct unit rate is $\frac{8}{2} = 4$. For $8:2$, divide first by second: $\frac{8}{2} = 4$.

33. What is the unit rate (pages per minute) for $45$ pages in $9$ minutes?

    $5$ pages per minute. Divide pages by minutes: $\frac{45}{9} = 5$.

34. What is the definition of a unit rate for a ratio $a:b$ with $b\ne 0$?

    The unit rate is $\frac{a}{b}$, meaning "$a$ per $1$ of $b$.". Expresses how many units of $a$ for each single unit of $b$.

35. Find and correct the unit rate statement: "Ratio $6:2$ means $\frac{2}{6}$ per $1$."

    Correct unit rate is $\frac{6}{2}=3$ per $1$. The error shows reciprocal; correct is $\frac{6}{2} = 3$ per $1$.

36. Find the unit rate (teachers per student) for a ratio of $24$ students to $3$ teachers.

    $\frac{1}{8}$ teacher per student. Divide teachers by students: $\frac{3}{24} = \frac{1}{8}$.

37. Choose the correct rate language for the unit rate of the ratio $9:12$.

    $\frac{3}{4}$ of the first quantity for each $1$ of the second. Simplify $\frac{9}{12} = \frac{3}{4}$ for the unit rate.

38. Find the unit rate (days per page) for reading $45$ pages in $9$ days.

    $\frac{1}{5}$ day per page. Divide days by pages: $\frac{9}{45} = \frac{1}{5}$.

39. Find the unit rate (miles per minute) for $5$ miles in $30$ minutes.

    $\frac{1}{6}$ mile per minute. Divide miles by minutes: $\frac{5}{30} = \frac{1}{6}$.

40. What is the unit rate (liters per kilometer) for $150$ km on $10$ L of gas?

    $\frac{1}{15}$ L per km. Divide fuel by distance: $\frac{10}{150} = \frac{1}{15}$.

41. What is the unit rate (cups flour per cup sugar) for the ratio $3$ cups flour to $4$ cups sugar?

    $\frac{3}{4}$ cup flour per $1$ cup sugar. Divide flour by sugar: $\frac{3}{4}$ per $1$ cup sugar.

42. Choose the correct unit rate for $8$ gallons in $4$ hours: $2$, $12$, or $\frac{1}{2}$ gal/hr?

    $2$ gallons per hour. Divide total gallons by hours: $\frac{8}{4} = 2$.

43. Identify the unit rate (dollars per hamburger) for $75 for $15$ hamburgers.

    $5 per hamburger. Divide total cost by number of items: $\frac{75}{15} = 5$.

44. What is the unit rate (cups sugar per cup flour) for the ratio $3$ cups flour to $4$ cups sugar?

    $\frac{4}{3}$ cup sugar per $1$ cup flour. Divide sugar by flour: $\frac{4}{3}$ per 1 cup flour.

45. What is the unit rate in $\text{hamburgers per dollar}$ for $15$ hamburgers for $75?

    $\frac{1}{5}$ hamburger per dollar. Divide items by cost: $\frac{15}{75} = \frac{1}{5}$ hamburger per dollar spent.

46. Find the unit rate in $\text{cost per notebook}$ for $8$ notebooks that cost $20.

    $\$\frac{5}{2}$ per notebook. Divide total cost by quantity: $\frac{20}{8} = \frac{5}{2}$ dollars per notebook.

47. What is the unit rate (minutes per page) for $45$ pages in $9$ minutes?

    $\frac{1}{5}$ minute per page. Divide minutes by pages: $\frac{9}{45} = \frac{1}{5}$.

48. Find the unit rate in $\text{miles per hour}$ for $120$ miles in $3$ hours.

    $40$ miles per hour. Divide distance by time: $\frac{120}{3} = 40$ miles in one hour.

49. What is the unit rate (miles per minute) for $30$ minutes to run $5$ miles?

    $\frac{1}{6}$ mile per minute. Divide distance by time: $\frac{5}{30} = \frac{1}{6}$.

50. What condition must be true to define the unit rate $\frac{a}{b}$ for a ratio $a:b$?

    $b \ne 0$. Can't divide by zero; ensures unit rate is defined.

51. What is the unit rate (cups of sugar per cup of flour) for flour:sugar = $3:4$?

    $\frac{4}{3}$ cups sugar per $1$ cup flour. Divide cups of sugar by cups of flour: $\frac{4}{3}$.

52. What is the unit rate in $\text{dollars per hamburger}$ for $75 for $15$ hamburgers?

    $5 per hamburger. Divide total cost by number of items: $\frac{75}{15} = 5$.

53. Which value must be nonzero in a ratio $a:b$ to form the unit rate $\frac{a}{b}$?

    $b \ne 0$. Division by zero is undefined, so the denominator cannot be zero.

54. What is the unit rate (miles per hour) for $120$ miles in $3$ hours?

    $40$ miles per hour. Divide total miles by hours: $\frac{120}{3} = 40$.

55. Find the unit rate (pages per day) for reading $45$ pages in $9$ days.

    $5$ pages per day. Divide total pages by days: $\frac{45}{9} = 5$.

56. Identify the unit rate (miles per hour) for $120$ miles in $3$ hours.

    $40$ miles per hour. Divide miles by hours: $\frac{120}{3} = 40$.

57. Identify the unit rate (pages per minute) for $45$ pages in $9$ minutes.

    $5$ pages per minute. Divide pages by minutes: $\frac{45}{9} = 5$.

58. What does the unit rate $\frac{a}{b}$ mean in words for the ratio $a:b$?

    $\frac{a}{b}$ units of the first quantity for each $1$ unit of the second. This expresses the ratio with the second quantity normalized to 1.

59. Find the unit rate in $\text{hours per mile}$ for $120$ miles in $3$ hours.

    $\frac{1}{40}$ hour per mile. Divide time by distance: $\frac{3}{120} = \frac{1}{40}$ hour to travel one mile.

60. What is the unit rate in dollars per hamburger if $75 buys $15$ hamburgers?

    $5 per hamburger. Divide total cost by number: $\frac{75}{15} = 5$.

61. What is the unit rate (cups of flour per cup of sugar) for a ratio $3:4$?

    $\frac{3}{4}$ cup flour per $1$ cup sugar. First quantity per second: $\frac{3}{4}$ flour per sugar.

62. What is the unit rate (minutes per mile) for $30$ minutes to run $5$ miles?

    $6$ minutes per mile. Divide total time by distance: $\frac{30}{5} = 6$.

63. Which unit rate matches the ratio $7$ notebooks for $21$ dollars: dollars per notebook?

    $3$ dollars per notebook. Divide dollars by notebooks: $\frac{21}{7} = 3$.

64. What is the unit rate in $\text{cups of sugar per cup of flour}$ for a ratio $3:4$?

    $\frac{4}{3}$ cups of sugar per cup of flour. For every $1$ cup of flour, there are $\frac{4}{3}$ cups of sugar.

65. Identify the restriction on $b$ in the ratio $a:b$ when forming $\frac{a}{b}$.

    $b\ne 0$. Division by zero is undefined, so denominator cannot be zero.

66. What unit rate corresponds to the ratio $5:2$ (first quantity per $1$ of second)?

    $\frac{5}{2}$ per $1$. Divide the first quantity by the second: $\frac{5}{2}$.

67. What is the unit rate in $\text{cups of flour per cup of sugar}$ for a ratio $3:4$?

    $\frac{3}{4}$ cup of flour per cup of sugar. For every $1$ cup of sugar, there are $\frac{3}{4}$ cups of flour.

68. What is the definition of a unit rate for a ratio $a:b$ with $b \ne 0$?

    Unit rate is $\frac{a}{b}$, meaning "$a$ per $1$ of $b$.". Expresses how much of the first quantity corresponds to one unit of the second.

69. What is the unit rate (cups of flour per cup of sugar) for flour:sugar $= 3:4$?

    $\frac{3}{4}$ cup flour per $1$ cup sugar. Divide cups of flour by cups of sugar: $\frac{3}{4}$.

70. Identify the unit rate (ounces per dollar) for $6 for $8$ ounces.

    $\frac{4}{3}$ ounces per dollar. Divide ounces by cost: $\frac{8}{6} = \frac{4}{3}$.

71. Which unit rate matches the ratio $7$ notebooks for $21$ dollars: notebooks per dollar?

    $\frac{1}{3}$ notebook per dollar. Divide notebooks by dollars: $\frac{7}{21} = \frac{1}{3}$.

72. Which quantity must be $1$ when you express a ratio as a unit rate?

    The second quantity (the denominator) must be $1$. Unit rates compare to exactly one unit, making the denominator $1$.

73. What is the unit rate (pounds per dollar) for $6$ lb for $18?

    $\frac{1}{3}$ pound per dollar. Divide weight by price: $\frac{6}{18} = \frac{1}{3}$.

74. Find the unit rate (students per teacher) for a ratio of $24$ students to $3$ teachers.

    $8$ students per teacher. Divide students by teachers: $\frac{24}{3} = 8$.

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