Unit Rate Problems - ISEE Middle Level Mathematics Achievement

1. What is a unit rate, in terms of a ratio $\frac{a}{b}$?

   A rate with denominator $1$, written as $\frac{a}{1}$ per $1$ unit. A unit rate simplifies the ratio $\frac{a}{b}$ by dividing $a$ by $b$ to express the quantity per single unit of the denominator.

2. Find the missing value: at $4 per pound, what is the cost of $6$ pounds?

   $24. Multiply the unit price per pound by the total pounds to calculate the overall cost.

3. What is the better buy: $12$ oz for $6$ dollars or $20$ oz for $9$ dollars?

   $20$ oz for $9$ dollars. Compare unit prices: $\frac{6}{12} = 0.5$ $/oz vs $\frac{9}{20} = 0.45$ $/oz, so the lower cost per ounce indicates better value.

4. Find the time: at $30$ miles per hour, how long to travel $45$ miles (in hours)?

   $1.5$ hours. Divide the total distance by the speed to find the time required in hours.

5. What is the unit rate for $18$ cookies for $24$ students (cookies per student)?

   $0.75$ cookies per student. Divide the total cookies by the total students to find the distribution rate per student.

6. What is the unit rate for $9$ pages in $6$ minutes (pages per minute)?

   $1.5$ pages per minute. Divide the total pages by the total minutes to calculate the reading or printing rate per minute.

7. What is the unit rate for $28$ dollars for $7$ notebooks (dollars per notebook)?

   $4$ dollars per notebook. Divide the total cost by the total notebooks to find the price per individual notebook.

8. What is the unit rate for $360$ miles in $6$ hours (miles per hour)?

   $60$ miles per hour. Divide the total distance by the total time to calculate the average speed per hour.

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

   $1.5$ miles per hour. Divide the distance fraction by the time fraction to compute the speed per full hour.

10. What is the unit rate for $90$ seconds for $3$ laps (seconds per lap)?

    $30$ seconds per lap. Divide the total time by the total laps to determine the time per individual lap.

11. What is the unit rate for $8$ dollars for $2$ pounds (dollars per pound)?

    $4$ dollars per pound. Divide the total cost by the total weight to compute the price per single pound.

12. What is the cost per ounce if $12$ ounces cost $9$ dollars (dollars per ounce)?

    $0.75$ dollars per ounce. Divide the total cost by the total ounces to find the price per single ounce.

13. What is the unit rate for $150$ words in $3$ minutes (words per minute)?

    $50$ words per minute. Divide the total words by the total minutes to find the typing or reading rate per minute.

14. What is the unit rate for $2.5$ gallons in $5$ minutes (gallons per minute)?

    $0.5$ gallons per minute. Divide the total volume by the total time to determine the flow rate per minute.

15. What is the unit rate for $1.2$ kilograms for $3$ boxes (kilograms per box)?

    $0.4$ kilograms per box. Divide the total mass by the total boxes to find the weight per single box.

16. What is the unit rate for $3$ liters in $\frac{1}{2}$ hour (liters per hour)?

    $6$ liters per hour. Divide the volume by the time fraction to scale the rate to a full hour.

17. What is the unit rate for $7$ notebooks for $28$ dollars (notebooks per dollar)?

    $0.25$ notebooks per dollar. Divide the total notebooks by the total cost to compute the quantity obtained per dollar.

18. What is the unit rate for $6$ pencils for $\frac{3}{4}$ dollar (pencils per dollar)?

    $8$ pencils per dollar. Divide the total pencils by the cost fraction to scale to the quantity per full dollar.

19. Identify the unit rate in $\frac{18\ \text{miles}}{2\ \text{hours}}$ as a simplified fraction.

    $\frac{9}{1}$ miles per hour. Simplify the ratio by dividing numerator and denominator by 2 to express the rate per single hour as a fraction.

20. What is the unit rate for $45$ miles in $3$ hours (miles per hour)?

    $15$ miles per hour. Divide the total distance by the total time to determine the constant speed per hour.

21. What is the unit rate for $5$ dollars for $2$ pounds (dollars per pound)?

    $2.5$ dollars per pound. Divide the total cost by the total weight to determine the price per pound.

22. What is the unit rate for $12$ apples in $3$ bags (apples per bag)?

    $4$ apples per bag. Divide the total number of apples by the total number of bags to find the constant rate per individual bag.

23. What is the better buy: $3$ lb for $7.50$ dollars or $5$ lb for $13$ dollars?

    $3$ lb for $7.50$ dollars. Compare unit prices: $\frac{7.50}{3} = 2.5$ $/lb vs $\frac{13}{5} = 2.6$ $/lb, so the lower cost per pound indicates better value.

24. What is the unit rate for $3$ pounds for $12$ dollars (pounds per dollar)?

    $0.25$ pounds per dollar. Divide the total weight by the total cost to find the amount of pounds obtained per dollar spent.

25. What is the unit rate for $2$ hours for $150$ miles (hours per mile)?

    $\frac{1}{75}$ hour per mile. Divide the total time by the total distance to express the time required per mile as a fraction.

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