Rates and Unit Conversions - ISEE Lower Level Quantitative Reasoning

1. What is $2.5$ feet converted to inches using $12\ \frac{\text{in}}{\text{ft}}$?

   $30\ \text{in}$. Multiply the feet by the conversion factor to express the length in inches.

2. What is the unit rate (in $\text{dollars per pound}$) for $9 for $3$ lb of apples?

   $3\ \text{dollars per pound}$. Divide the total cost by the total pounds to find the dollars per pound.

3. Which conversion factor correctly converts yards to feet: $\text{yards}\times ?=\text{feet}$?

   Multiply by $3\ \frac{\text{ft}}{\text{yd}}$. Yards are converted to feet by multiplying by the factor of $3$ feet per yard.

4. Which option has a higher rate: $240$ words in $2$ min or $300$ words in $3$ min?

   $240\ \text{words in}\ 2\ \text{min}$. Compare typing rates by dividing words by minutes; the higher value has the greater rate.

5. What is the unit rate (in $\text{ounces per dollar}$) for $24$ oz costing $6?

   $4\ \text{oz per dollar}$. Divide the total ounces by the total cost to obtain the ounces per dollar.

6. What is $5$ minutes converted to seconds using $60\ \frac{\text{s}}{\text{min}}$?

   $300\ \text{s}$. Multiply the minutes by the conversion factor to express the time in seconds.

7. What is the unit rate (in $\text{words per minute}$) for $600$ words in $4$ minutes?

   $150\ \text{words per minute}$. Divide the total words by the total minutes to determine the words per minute.

8. What is the unit rate (in $\text{miles per hour}$) for $180$ miles in $3$ hours?

   $60\ \text{mph}$. Divide the total distance by the total time to find the speed in miles per hour.

9. Which conversion factor correctly converts minutes to seconds: $\text{minutes}\times ?=\text{seconds}$?

   Multiply by $60\ \frac{\text{s}}{\text{min}}$. Minutes are converted to seconds by multiplying by the factor of $60$ seconds per minute.

10. What is $90$ seconds converted to minutes using $60\ \frac{\text{s}}{\text{min}}$?

    $1.5\ \text{min}$. Divide the seconds by the conversion factor to express the time in minutes.

11. What is the unit rate (in $\text{gallons per minute}$) for $15$ gal in $5$ min?

    $3\ \text{gal/min}$. Divide the total gallons by the total minutes to obtain the gallons per minute.

12. What is $3$ hours converted to minutes using $60\ \frac{\text{min}}{\text{hr}}$?

    $180\ \text{min}$. Multiply the hours by the conversion factor to express the time in minutes.

13. What is $4$ yards converted to feet using $3\ \frac{\text{ft}}{\text{yd}}$?

    $12\ \text{ft}$. Multiply the yards by the conversion factor to express the length in feet.

14. Which conversion factor correctly converts feet to inches: $\text{feet}\times ?=\text{inches}$?

    Multiply by $12\ \frac{\text{in}}{\text{ft}}$. Feet are converted to inches by multiplying by the factor of $12$ inches per foot.

15. What is the unit rate (in $\text{dollars per item}$) for $12 for $4$ items?

    $3\ \text{dollars per item}$. Divide the total cost by the number of items to determine the cost per item.

16. What is the unit rate (in $\text{pages per minute}$) for $45$ pages in $15$ minutes?

    $3\ \text{pages per minute}$. Divide the total pages by the total minutes to calculate the pages per minute.

17. Which option is the better buy: $12$ oz for $3 or $20$ oz for $6?

    $12\ \text{oz for}\ \$3$. Compare unit rates by dividing ounces by dollars; the higher value indicates the better buy.

18. What is the unit rate (in $\text{feet per second}$) for $120$ ft in $6$ s?

    $20\ \text{ft/s}$. Divide the total feet by the total seconds to calculate the feet per second.

19. What is the total cost at a rate of $4 per ticket for $7$ tickets?

    $28. Multiply the rate per ticket by the number of tickets to find the total cost.

20. Which conversion factor correctly converts hours to minutes: $\text{hours}\times ?=\text{minutes}$?

    Multiply by $60\ \frac{\text{min}}{\text{hr}}$. Hours are converted to minutes by multiplying by the factor of $60$ minutes per hour.

21. Which option is faster: $150$ miles in $3$ hours or $180$ miles in $4$ hours?

    $150\ \text{miles in}\ 3\ \text{hours}$. Compare speeds by dividing distance by time; the higher rate is faster.

22. Which conversion factor correctly converts dollars per hour to dollars per minute?

    Multiply by $\frac{1\ \text{hr}}{60\ \text{min}}$. Dollars per hour are converted to dollars per minute by multiplying by the factor that accounts for $60$ minutes in an hour.

23. What is the unit rate (in $\text{minutes per mile}$) for $30$ minutes to run $5$ miles?

    $6\ \text{minutes per mile}$. Divide the total minutes by the total miles to determine the minutes per mile.

24. Which option is cheaper per pound: $5$ lb for $10 or $8$ lb for $20?

    $5\ \text{lb for}\ \$10$. Compare unit prices by dividing cost by pounds; the lower value is cheaper per pound.

25. What is the unit rate (in $\text{dollars per hour}$) for earning $84 in $7$ hours?

    $12\ \text{dollars per hour}$. Divide the total earnings by the total hours to find the dollars per hour.

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