Compute Unit Rates With Fractions - 7th Grade Math

1. What is $\frac{3}{4}$ cup in $\frac{1}{8}$ minute as cups per minute?

   $6$ cups per minute. Calculate $\frac{3/4}{1/8} = \frac{3}{4} \times \frac{8}{1} = 6$.

2. What is the unit rate for $\frac{5}{8}$ pound in $\frac{1}{4}$ minute (pounds per minute)?

   $\frac{5}{2}$ pounds per minute. Divide pounds by minutes: $\frac{5/8}{1/4} = \frac{5}{8} \times \frac{4}{1} = \frac{5}{2}$.

3. What is the unit rate for $\frac{1}{6}$ of a job in $\frac{1}{3}$ day (jobs per day)?

   $\frac{1}{2}$ job per day. Divide jobs by days: $\frac{ \frac{1}{6} }{ \frac{1}{3} } = \frac{1}{6} \times \frac{3}{1} = \frac{1}{2}$.

4. What is the unit rate for $frac{3}{7}$ pound in $frac{2}{7}$ minute (pounds per minute)?

   $\frac{3}{2}$ pounds per minute. Divide pounds by minutes: $\frac{3/7}{2/7} = \frac{3}{7} \times \frac{7}{2} = \frac{3}{2}$.

5. What is the unit rate for $\frac{7}{10}$ gallon in $\frac{1}{5}$ minute (gallons per minute)?

   $\frac{7}{2}$ gallons per minute. Calculate $\frac{7/10}{1/5} = \frac{7}{10} \times \frac{5}{1} = \frac{35}{10} = \frac{7}{2}$.

6. What is the unit rate for $\frac{8}{15}$ inch in $\frac{2}{5}$ second (inches per second)?

   $\frac{4}{3}$ inches per second. Compute $\frac{8/15}{2/5} = \frac{8}{15} \times \frac{5}{2} = \frac{40}{30} = \frac{4}{3}$.

7. What is the unit rate for $\frac{1}{6}$ mile in $\frac{1}{2}$ hour (miles per hour)?

   $\frac{1}{3}$ mile per hour. Find $\frac{1/6}{1/2} = \frac{1}{6} \times \frac{2}{1} = \frac{2}{6} = \frac{1}{3}$.

8. What is the unit rate for $\frac{3}{10}$ tank in $\frac{3}{5}$ hour (tanks per hour)?

   $\frac{1}{2}$ tank per hour. Compute $\frac{ \frac{3}{10} }{ \frac{3}{5} } = \frac{3}{10} \times \frac{5}{3} = \frac{15}{30} = \frac{1}{2}$.

9. What is $\frac{11}{12}$ mile in $\frac{1}{6}$ hour as miles per hour?

   $\frac{11}{2}$ miles per hour. Calculate $\frac{11/12}{1/6} = \frac{11}{12} \times \frac{6}{1} = \frac{66}{12} = \frac{11}{2}$.

10. What is the unit rate for $frac{2}{3}$ gallon in $frac{1}{6}$ hour (gallons per hour)?

    $4$ gallons per hour. Divide gallons by hours: $\frac{2/3}{1/6} = \frac{2}{3} \times \frac{6}{1} = 4$.

11. What is the unit rate for $\frac{7}{12}$ cup in $\frac{7}{18}$ minute (cups per minute)?

    $\frac{3}{2}$ cups per minute. Divide cups by minutes: $\frac{7/12}{7/18} = \frac{7}{12} \times \frac{18}{7} = \frac{3}{2}$.

12. What is $\frac{3}{5}$ liter in $\frac{9}{10}$ minute as liters per minute?

    $\frac{2}{3}$ liter per minute. Compute $\frac{3/5}{9/10} = \frac{3}{5} \times \frac{10}{9} = \frac{30}{45} = \frac{2}{3}$.

13. What is the unit rate for $\frac{1}{3}$ pound in $\frac{2}{9}$ hour (pounds per hour)?

    $\frac{3}{2}$ pounds per hour. Calculate $\frac{1/3}{2/9} = \frac{1}{3} \times \frac{9}{2} = \frac{9}{6} = \frac{3}{2}$.

14. What is the unit rate for $\frac{5}{6}$ kilometer in $\frac{2}{3}$ hour (kilometers per hour)?

    $\frac{5}{4}$ kilometers per hour. Divide kilometers by hours: $\frac{5/6}{2/3} = \frac{5}{6} \times \frac{3}{2} = \frac{5}{4}$.

15. What is the unit rate for $\frac{2}{5}$ inch in $\frac{3}{10}$ second (inches per second)?

    $\frac{4}{3}$ inches per second. Divide inches by seconds: $\frac{\frac{2}{5}}{\frac{3}{10}} = \frac{2}{5} \times \frac{10}{3} = \frac{4}{3}$.

16. What is the unit rate for $\frac{3}{7}$ mile in $\frac{9}{14}$ hour (miles per hour)?

    $\frac{2}{3}$ mile per hour. Compute $\frac{3/7}{9/14} = \frac{3}{7} \times \frac{14}{9} = \frac{42}{63} = \frac{2}{3}$.

17. What is the unit rate for $\frac{5}{8}$ square foot in $\frac{1}{4}$ minute (square feet per minute)?

    $\frac{5}{2}$ square feet per minute. Calculate $\frac{5/8}{1/4} = \frac{5}{8} \times \frac{4}{1} = \frac{20}{8} = \frac{5}{2}$

18. What is the unit rate for $\frac{3}{4}$ mile in $\frac{1}{2}$ hour (miles per hour)?

    $\frac{3}{2}$ miles per hour. Divide distance by time: $\frac{\frac{3}{4}}{\frac{1}{2}} = \frac{3}{4} \times \frac{2}{1} = \frac{3}{2}$.

19. What is the unit rate for $\frac{1}{2}$ mile in $\frac{1}{4}$ hour (miles per hour)?

    $2$ miles per hour. Divide distance by time: $\frac{1/2}{1/4} = \frac{1}{2} \times \frac{4}{1} = 2$.

20. What is the unit rate for $\frac{9}{16}$ cup in $\frac{3}{8}$ minute (cups per minute)?

    $\frac{3}{2}$ cups per minute. Divide cups by minutes: $\frac{\frac{9}{16}}{\frac{3}{8}} = \frac{9}{16} \times \frac{8}{3} = \frac{3}{2}$.

21. What is the unit rate for $\frac{7}{9}$ square yard in $\frac{1}{3}$ hour (square yards per hour)?

    $\frac{7}{3}$ square yards per hour. Divide square yards by hours: $\frac{7/9}{1/3} = \frac{7}{9} \times \frac{3}{1} = \frac{7}{3}$.

22. What is $\frac{7}{9}$ pound in $\frac{14}{27}$ hour as pounds per hour?

    $\frac{3}{2}$ pounds per hour. Calculate $\frac{7/9}{14/27} = \frac{7}{9} \times \frac{27}{14} = \frac{189}{126} = \frac{3}{2}$.

23. What is the unit rate for $\frac{3}{10}$ pound in $\frac{1}{20}$ minute (pounds per minute)?

    $6$ pounds per minute. Divide pounds by minutes: $\frac{ \frac{3}{10} }{ \frac{1}{20} } = \frac{3}{10} \times \frac{20}{1} = 6$.

24. What is the unit rate for $\frac{3}{8}$ mile in $\frac{5}{16}$ hour (miles per hour)?

    $\frac{6}{5}$ miles per hour. Divide miles by hours: $\frac{\frac{3}{8}}{\frac{5}{16}} = \frac{3}{8} \times \frac{16}{5} = \frac{6}{5}$

25. What is the unit rate for $\frac{2}{9}$ gallon in $\frac{4}{9}$ hour (gallons per hour)?

    $\frac{1}{2}$ gallon per hour. Divide gallons by hours: $\frac{ \frac{2}{9} }{ \frac{4}{9} } = \frac{2}{9} \times \frac{9}{4} = \frac{1}{2}$.

26. What is the unit rate for $\frac{7}{10}$ meter in $\frac{1}{5}$ second (meters per second)?

    $\frac{7}{2}$ meters per second. Divide meters by seconds: $\frac{7/10}{1/5} = \frac{7}{10} \times \frac{5}{1} = \frac{7}{2}$.

27. What is the unit rate for $\frac{11}{12}$ liter in $\frac{1}{6}$ minute (liters per minute)?

    $\frac{11}{2}$ liters per minute. Divide liters by minutes: $\frac{11/12}{1/6} = \frac{11}{12} \times \frac{6}{1} = \frac{11}{2}$.

28. What is the unit rate for $\frac{4}{5}$ page in $\frac{2}{3}$ minute (pages per minute)?

    $\frac{6}{5}$ pages per minute. Find $\frac{4/5}{2/3} = \frac{4}{5} \times \frac{3}{2} = \frac{12}{10} = \frac{6}{5}$

29. What is $\frac{9}{16}$ meter in $\frac{3}{8}$ second as meters per second?

    $\frac{3}{2}$ meters per second. Compute $\frac{9/16}{3/8} = \frac{9}{16} \times \frac{8}{3} = \frac{72}{48} = \frac{3}{2}$.

30. What is the unit rate for $\frac{2}{5}$ square meter in $\frac{3}{10}$ minute (square meters per minute)?

    $\frac{4}{3}$ square meters per minute. Find $\frac{\frac{2}{5}}{\frac{3}{10}} = \frac{2}{5} \times \frac{10}{3} = \frac{20}{15} = \frac{4}{3}$.

31. What is the unit rate for $\frac{1}{2}$ mile in $\frac{1}{4}$ hour (miles per hour)?

    $2$ miles per hour. Divide miles by hours: $\frac{\frac{1}{2}}{\frac{1}{4}} = \frac{1}{2} \times \frac{4}{1} = 2$

32. What is the unit rate for $\frac{4}{9}$ acre in $\frac{2}{3}$ hour (acres per hour)?

    $\frac{2}{3}$ acres per hour. Divide acres by hours: $\frac{4/9}{2/3} = \frac{4}{9} \times \frac{3}{2} = \frac{2}{3}$.

33. What is the unit rate for $\frac{4}{15}$ meter in $\frac{2}{5}$ second (meters per second)?

    $\frac{2}{3}$ meter per second. Divide meters by seconds: $\frac{4/15}{2/5} = \frac{4}{15} \times \frac{5}{2} = \frac{2}{3}$.

34. What operation finds a unit rate from $\frac{a}{b}$ units per $\frac{c}{d}$ units?

    Divide: $\frac{a}{b} \div \frac{c}{d}$. Division converts a rate to a unit rate (per 1 unit).

35. What is the unit rate for $\frac{2}{3}$ pound in $\frac{1}{6}$ hour (pounds per hour)?

    $4$ pounds per hour. Compute $\frac{2/3}{1/6} = \frac{2}{3} \times \frac{6}{1} = 4$.

36. What is $\frac{2}{9}$ acre in $\frac{1}{3}$ day as acres per day?

    $\frac{2}{3}$ acre per day. Find $\frac{2/9}{1/3} = \frac{2}{9} \times \frac{3}{1} = \frac{6}{9} = \frac{2}{3}$

37. What is the unit rate for $\frac{3}{5}$ of a tank in $\frac{3}{10}$ hour (tanks per hour)?

    $2$ tanks per hour. Divide tanks by hours: $\frac{\frac{3}{5}}{\frac{3}{10}} = \frac{3}{5} \times \frac{10}{3} = 2$.

38. What is $\frac{5}{6}$ kilometer in $\frac{1}{3}$ hour as kilometers per hour?

    $\frac{5}{2}$ kilometers per hour. Find $\frac{5/6}{1/3} = \frac{5}{6} \times \frac{3}{1} = \frac{15}{6} = \frac{5}{2}$.

39. What is the unit rate for $\frac{5}{12}$ mile in $\frac{1}{3}$ hour (miles per hour)?

    $\frac{5}{4}$ miles per hour. Divide miles by hours: $\frac{5/12}{1/3} = \frac{5}{12} \times \frac{3}{1} = \frac{5}{4}$.

40. What is $\frac{5}{18}$ job in $\frac{1}{6}$ hour as jobs per hour?

    $\frac{5}{3}$ jobs per hour. Find $\frac{\frac{5}{18}}{\frac{1}{6}} = \frac{5}{18} \times \frac{6}{1} = \frac{30}{18} = \frac{5}{3}$

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