Measurement With Unit Rates - ISEE Lower Level Mathematics Achievement

1. What is the unit rate in pages per minute for $45$ pages in $15$ minutes?

   $3$ pages per minute. Divide total pages by total minutes to determine reading speed per minute.

2. What is the better buy: $9 for $6$ bottles or $14 for $10$ bottles?

   $14 for $10$ bottles (unit price $1.40). Calculate unit prices and select the lower one for better value per bottle.

3. What is the total pay for $7$ hours at a unit rate of $12 per hour?

   $84. Multiply hourly rate by hours worked to determine total compensation.

4. What is the total cost at $2.50 per lb for $6$ lb of grapes?

   $15. Multiply unit price by quantity to compute total expenditure for the grapes.

5. What is the unit rate for $12$ miles in $3$ hours?

   $4$ miles per hour. Divide total miles by total hours to determine the constant speed as a unit rate.

6. What is a unit rate in a ratio such as $12$ miles in $3$ hours?

   A rate per $1$ unit of the second quantity (here, miles per $1$ hour). A unit rate simplifies the ratio by dividing to express the first quantity per single unit of the second, facilitating comparisons.

7. What is the unit rate in inches per minute for $36$ inches in $4$ minutes?

   $9$ inches per minute. Divide total inches by total minutes to obtain growth or movement rate per minute.

8. What is the unit rate in dollars per square foot for $180 to cover $60$ ft$^2$?

   $3 per ft$^2$. Divide total cost by area covered to compute cost per square foot.

9. What is the unit rate for $450$ words typed in $9$ minutes?

   $50$ words per minute. Divide total words by total minutes to find the typing speed as words per minute.

10. What is the unit price if $5$ notebooks cost $15?

    $3 per notebook. Divide total cost by the number of items to find the price per single notebook.

11. What is the time at $60$ miles per hour to travel $180$ miles?

    $3$ hours. Divide distance by speed to find the time required for the trip.

12. What is the unit rate in cents per ounce if $12$ oz costs $3?

    $25$ cents per ounce. Divide total cost in cents by ounces to find the price per ounce unit rate.

13. What operation finds the unit rate for $a$ units per $b$ units?

    Compute $\frac{a}{b}$ to get the amount per $1$ unit. Division of the numerator by the denominator yields the rate per one unit, standard for unit rate calculations.

14. What is the speed in feet per minute for $20$ ft per second?

    $1200$ ft per minute. Convert seconds to minutes by multiplying the per-second rate by $60$ to get feet per minute.

15. What is the best buy: $12 for $8$ bars or $15 for $10$ bars?

    Neither; both are $1.50 per bar. Compare unit prices by dividing cost by quantity for each option, revealing equivalent rates.

16. What is the total cost at $3 per ft$^2$ to cover $75$ ft$^2$?

    $225. Multiply unit cost per square foot by total area to find overall expense.

17. What is the pace in minutes per mile for $24$ minutes to run $3$ miles?

    $8$ minutes per mile. Divide total time by distance to express pace as time per single mile.

18. What is the cost per pound if $8$ lb of apples cost $20?

    $2.50 per lb. Divide total cost by total pounds to compute the price per pound unit rate.

19. What is the speed in miles per hour for $150$ miles in $3$ hours?

    $50$ miles per hour. Divide distance by time to calculate average speed in miles per hour.

20. What is the unit rate in feet per second for $120$ ft in $6$ s?

    $20$ ft per second. Divide distance by time to find speed in feet per second.

21. What is the unit rate in dollars per hour if $96 is earned in $8$ hours?

    $12 per hour. Divide total earnings by hours worked to compute hourly wage rate.

22. What is the correct unit rate in miles per minute for $120$ miles in $2$ hours?

    $1$ mile per minute. Convert hours to minutes and divide total miles by total minutes to get miles per minute.

23. What is the distance at $55$ miles per hour for $2$ hours of driving?

    $110$ miles. Multiply speed by time to calculate total distance traveled at constant rate.

24. What is the unit rate in gallons per minute for $15$ gallons in $5$ minutes?

    $3$ gallons per minute. Divide total gallons by total minutes to find the flow rate per minute.

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