Solve Unit Rate Problems - 6th Grade Math

1. What is the unit price for $7 for $12$ bars?

   $\frac{7}{12}$ dollars per bar. Divide price by quantity: $\frac{7}{12}$ dollars per bar.

2. What is the time needed to travel $90$ miles at $45$ mph?

   $2$ hours. Divide distance by speed: $90 \div 45 = 2$ hours.

3. What is the unit rate in words per minute for $450$ words in $9$ minutes?

   $50$ words per minute. Divide total words by time: $450 ÷ 9 = 50$ wpm.

4. What is the cost per ounce for $6 for a $24$-ounce bottle?

   $0.25 per ounce. Divide price by ounces: $\$6 \div 24 = \$0.25$ per ounce.

5. What number of lawns can be mowed in $35$ hours at $\frac{4}{7}$ lawn per hour?

   $20$ lawns. Multiply rate by time: $\frac{4}{7} \times 35 = 20$ lawns.

6. What is the cost for $5$ pounds of apples at $2 per pound?

   $10. Multiply unit price by quantity: $\$2 \times 5 = \$10$.

7. What is the unit rate for $300$ words in $5$ minutes (words per minute)?

   $60$ words per minute. Divide words by minutes: $300 \div 5 = 60$ words per minute.

8. What is the unit rate in miles per hour for $150$ miles in $3$ hours?

   $50$ miles per hour. Divide total distance by total time: $150 ÷ 3 = 50$.

9. What is a unit rate, stated in words?

   A rate with a denominator of $1$ unit. Simplifies any rate to a per-one basis for easy comparison.

10. What is the unit rate in minutes per gallon for $12$ gallons in $4$ minutes?

    $\frac{1}{3}$ minute per gallon. Divide time by gallons: $4 \div 12 = \frac{1}{3}$ minute per gallon.

11. What is the distance at $\frac{3}{2}\ \text{mi/h}$ for $2$ hours?

    $3$ miles. Multiply speed by time: $\frac{3}{2} \times 2 = 3$ miles.

12. What rate in lawns per hour is $4$ lawns in $7$ hours?

    $\frac{4}{7}$ lawn per hour. Divide lawns by hours: $\frac{4}{7}$ lawns per hour.

13. What is the time in hours to travel $84$ miles at $28$ miles per hour?

    $3$ hours. Divide distance by speed: $84 ÷ 28 = 3$ hours.

14. What is the number of lawns mowed in $35$ hours at a rate of $\frac{4}{7}$ lawns per hour?

    $20$ lawns. Multiply rate by time: $\frac{4}{7} × 35 = 20$ lawns.

15. What is the speed in meters per second for $120$ m in $10$ s?

    $12$ m per s. Divide distance by time: $120 ÷ 10 = 12$ m/s.

16. What formula gives constant speed as a unit rate using distance $d$ and time $t$?

    $\text{speed}=\frac{d}{t}$. Speed equals distance divided by time.

17. What is the unit price if $3$ notebooks cost $7.50?

    $2.50 per notebook. Divide total cost by quantity: $\$7.50 \div 3 = \$2.50$.

18. What is the unit rate in minutes per item for $9$ minutes for $45$ items?

    $\frac{1}{5}$ minute per item. Divide time by items: $9 \div 45 = \frac{1}{5}$ minute per item.

19. What is the time formula using distance $d$ and constant speed $s$?

    $t=\frac{d}{s}$. Time equals distance divided by speed.

20. What is the constant speed for $150$ miles in $3$ hours?

    $50$ miles per hour. Divide distance by time: $150 \div 3 = 50$ mph.

21. What is the unit price if $12$ apples cost $6?

    $0.50 per apple. Divide total cost by number of items: $\$6 \div 12 = \$0.50$.

22. What is the unit price in dollars per pound for $9 for $3$ lb of apples?

    $3 per lb. Divide total cost by total weight: $\$9 ÷ 3 = \$3$.

23. What is the unit price in dollars per item for $18 for $6$ notebooks?

    $3 per notebook. Divide total cost by quantity: $\$18 ÷ 6 = \$3$.

24. What is the unit rate for $4$ lawns in $7$ hours (lawns per hour)?

    $\frac{4}{7}$ lawns per hour. Divide lawns by hours: $\frac{4}{7}$ lawns each hour.

25. What is the unit rate in gallons per minute for $12$ gallons in $4$ minutes?

    $3$ gallons per minute. Divide gallons by minutes: $12 \div 4 = 3$ gallons per minute.

26. What time is needed to travel $180$ miles at $60\ \text{mi/h}$?

    $3$ hours. Divide distance by speed: $180 \div 60 = 3$ hours.

27. What is the unit price in $\$/\text{lb}$ for $14 for $5$ lb?

    $2.80 per lb. Divide price by weight: $14 \div 5 = 2.80$ dollars per pound.

28. What is the unit rate for $18$ pages in $6$ minutes (minutes per page)?

    $\frac{1}{3}$ minute per page. Divide minutes by pages: $6 \div 18 = \frac{1}{3}$ minute per page.

29. What distance is traveled at $60\ \text{mi/h}$ for $2$ hours?

    $120$ miles. Multiply speed by time: $60 \times 2 = 120$ miles.

30. What is the constant speed if $\frac{3}{4}$ mile is walked in $\frac{1}{2}$ hour?

    $\frac{3}{2} \text{mi/h}$. Divide distance by time: $\frac{3/4}{1/2} = \frac{3}{2}$ miles per hour.

31. What is the better buy: $9 for $3$ items or $14 for $5$ items?

    $14 for $5$ items. Compare unit prices: $3 vs $2.80 per item; second is cheaper.

32. What is the constant speed in $\text{m/s}$ if you run $400$ m in $80$ s?

    $5\ \text{m/s}$. Divide distance by time: $400 \div 80 = 5$ meters per second.

33. What is the number of miles in $4$ hours at $55$ miles per hour?

    $220$ miles. Multiply speed by time: $55 \times 4 = 220$ miles.

34. What is the formula for unit rate if the rate is $\frac{a}{b}$?

    Unit rate is $\frac{a}{b}$ per $1$ of $b$ units. Shows how to express any rate as amount per one unit.

35. What is the unit rate in hours per lawn for $7$ hours to mow $4$ lawns?

    $\frac{7}{4}$ hours per lawn. Divide hours by lawns: $\frac{7}{4}$ hours per lawn.

36. What is the distance in miles at $12$ miles per hour for $5$ hours?

    $60$ miles. Multiply speed by time: $12 × 5 = 60$ miles.

37. What is the unit rate for $15 for $6$ pounds of rice (dollars per pound)?

    $2.50 per pound. Divide price by pounds: $\$15 \div 6 = \$2.50$ per pound.

38. What is the total cost for $8$ bottles if the unit price is $1.25 per bottle?

    $10. Multiply unit price by quantity: $\$1.25 × 8 = \$10$.

39. What is the unit price in dollars per ounce for $3 for $12$ oz?

    $0.25 per oz. Divide total cost by ounces: $\$3 ÷ 12 = \$0.25$.

40. What is the unit rate in pages per minute for $72$ pages in $6$ minutes?

    $12$ pages per minute. Divide total pages by time: $72 ÷ 6 = 12$ ppm.

41. What is the correct formula for unit rate from $\frac{a}{b}$ (with $b\ne 0$)?

    Unit rate $=\frac{a}{b}$ per $1$ unit of $b$. Shows how to express any ratio as a rate per one unit.

42. What is the better buy: $5 for $2$ lb or $9 for $4$ lb?

    $9 for $4$ lb. Compare unit prices: $2.50/lb vs $2.25/lb.

43. What is the unit rate in items per minute for $45$ items in $9$ minutes?

    $5$ items per minute. Divide total items by time: $45 \div 9 = 5$ items per minute.

44. What is a unit rate, in words?

    A rate with a denominator of $1$ unit. Simplifies comparison by showing the amount per single unit.

45. What is the unit rate for $18$ pages in $6$ minutes (pages per minute)?

    $3$ pages per minute. Divide pages by minutes: $18 \div 6 = 3$ pages per minute.

46. Identify the unit rate: $\frac{42 \text{miles}}{2 \text{hours}}$ simplified.

    $21$ miles per hour. Simplify the fraction: $\frac{42}{2} = 21$ miles per hour.

47. Identify the missing value: at $8$ items per minute, how many items in $6$ minutes?

    $48$ items. Multiply rate by time: $8 \times 6 = 48$ items.

48. What is the constant speed in miles per hour for $60$ miles in $2$ hours?

    $30$ miles per hour. Divide distance by time: $60 ÷ 2 = 30$ mph.

49. What is the number of lawns mowed in $35$ hours at $\frac{4}{7}$ lawns per hour?

    $20$ lawns. Multiply rate by time: $\frac{4}{7} \times 35 = 20$ lawns.

50. What is the better buy: $12 for $8$ lb or $14 for $10$ lb?

    $14 for $10$ lb. Compare unit prices: $1.50/lb vs $1.40/lb.

51. What is the unit price for $12 for $3$ notebooks?

    $4 per notebook. Divide total cost by number of items: $\$12 \div 3 = \$4$.

52. What is the unit rate for $4$ lawns in $7$ hours (hours per lawn)?

    $\frac{7}{4}$ hours per lawn. Divide hours by lawns: $\frac{7}{4}$ hours for each lawn.

53. What is the constant speed in $\text{mi/h}$ if you travel $150$ miles in $3$ hours?

    $50\ \text{mi/h}$. Divide distance by time: $150 \div 3 = 50$ miles per hour.

54. What is the unit rate in lawns per hour for $4$ lawns in $7$ hours?

    $\frac{4}{7}$ lawns per hour. Divide lawns by hours: $\frac{4}{7}$ lawns per hour.

55. What is the meaning of "unit rate" in a ratio such as $\frac{\$6}{3\text{ lb}}$?

    A rate per $1$ unit of the second quantity. The rate when the denominator equals 1.

56. What is the gallons used in $3$ hours at $2.5$ gallons per hour?

    $7.5$ gallons. Multiply rate by time: $2.5 \times 3 = 7.5$ gallons.

57. What is the distance formula using constant speed $s$ and time $t$?

    $d=s\cdot t$. Distance equals speed times time.

58. What is the distance traveled at $60$ mph for $2$ hours?

    $120$ miles. Multiply speed by time: $60 \times 2 = 120$ miles.

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