Unit Rate Comparisons - SSAT Middle Level Quantitative

1. What is the unit rate for $12$ miles in $3$ hours (miles per hour)?

   $4$ miles per hour. Divide the total miles by the total hours to find the rate per single hour.

2. What is the unit rate for $3$ feet in $8$ seconds (feet per second)?

   $0.375$ feet per second. Divide the total feet by the total seconds to find the speed per single second.

3. Which is cheaper per item: $12$ dollars for $8$ pens or $15$ dollars for $10$ pens?

   They are equal at $1.50$ dollars per pen. Calculate cost per pen for each option by dividing total cost by number of pens; equal rates mean neither is cheaper.

4. What is the unit rate for $5$ miles in $12$ minutes (miles per minute)?

   $\frac{5}{12}$ miles per minute. Divide the miles by the minutes to express the speed per single minute as a fraction.

5. Which is greater: $3$ gallons in $12$ minutes or $5$ gallons in $25$ minutes?

   $3$ gallons in $12$ minutes (it is $0.25$ gallons per minute). Compare gallons per minute by dividing each total gallons by minutes; the higher rate is greater.

6. Identify the unit rate: $30$ dollars for $6$ hours of work (dollars per hour).

   $5$ dollars per hour. Divide the total earnings by the hours worked to determine the wage per single hour.

7. What is the unit price for $14$ dollars for $4$ pounds of rice (dollars per pound)?

   $3.50$ dollars per pound. Divide the total cost by the pounds to calculate the price per single pound.

8. Which is the better buy: $16$ ounces for $2.40$ dollars or $24$ ounces for $3.84$ dollars?

   $16$ ounces for $2.40$ dollars (it is $0.15$ dollars per ounce). Compare unit prices by dividing cost by ounces for each; the lower price per ounce is the better buy.

9. What is the unit rate for $500$ milliliters in $2$ liters (milliliters per liter)?

   $250$ milliliters per liter. Divide the milliliters by the liters to find the volume per single liter.

10. Which is faster: $120$ miles in $3$ hours or $150$ miles in $4$ hours?

    $120$ miles in $3$ hours (it is $40$ mph). Compare speeds in miles per hour by dividing miles by hours for each; the higher rate is faster.

11. What is the unit rate for $250$ miles on $10$ gallons (miles per gallon)?

    $25$ miles per gallon. Divide the total miles by the gallons used to calculate the efficiency per single gallon.

12. Which unit rate is larger: $18$ pages in $6$ minutes or $20$ pages in $8$ minutes?

    $18$ pages in $6$ minutes (it is $3$ pages per minute). Compare pages per minute by dividing each total pages by minutes; the higher rate indicates the larger unit rate.

13. What is the unit rate for $84$ miles in $2$ hours (miles per hour)?

    $42$ miles per hour. Divide the total miles by the total hours to find the speed per single hour.

14. What is the unit price for $6$ pounds of apples costing $9$ dollars (dollars per pound)?

    $1.50$ dollars per pound. Divide the total cost by the pounds to determine the price per single pound.

15. What is the unit rate for $7$ gallons in $2$ minutes (gallons per minute)?

    $3.5$ gallons per minute. Divide the total gallons by the total minutes to obtain the gallons per single minute.

16. What is the definition of a unit rate?

    A rate expressed per $1$ unit of the second quantity. A unit rate simplifies a ratio by dividing the first quantity by the second to express the amount of the first per single unit of the latter.

17. What is the unit rate for $90$ miles in $2$ gallons (miles per gallon)?

    $45$ miles per gallon. Divide the total miles by the gallons to compute the mileage per single gallon.

18. What is the unit rate for $9$ cookies in $3$ bags (cookies per bag)?

    $3$ cookies per bag. Divide the total cookies by the number of bags to find the average cookies per single bag.

19. What is the unit rate for $18$ dollars for $3$ movie tickets (dollars per ticket)?

    $6$ dollars per ticket. Divide the total cost by the number of tickets to calculate the price per single ticket.

20. What is the unit rate for $45$ words in $9$ seconds (words per second)?

    $5$ words per second. Divide the total words by the total seconds to determine the rate per single second.

21. What is the unit rate for $15$ dollars for $5$ notebooks (dollars per notebook)?

    $3$ dollars per notebook. Divide the total cost by the number of notebooks to determine the cost per single notebook.

22. What unit rate comparison decides the better buy: cost per item or items per cost?

    Use cost per $1$ item (unit price) to find the cheaper option. The unit price, or cost per single item, allows direct comparison to identify the lower cost option as the better buy.

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