Rates and Unit Conversions - ISEE Middle Level Quantitative Reasoning

1. Find the unit rate: $18 for $6\ \text{tickets}$.

   $\$3\ \text{per ticket}$. Divide total cost by number of tickets to find the rate per unit.

2. Convert $3.5\ \text{ft}$ to inches.

   $42\ \text{in}$. Multiply by $12$ since $1$ foot equals $12$ inches.

3. State the formula for time in terms of distance and rate.

   $t=\frac{d}{r}$. Time is found by dividing distance by rate to solve for duration.

4. State the formula that relates distance, rate, and time.

   $d=rt$. The distance equals rate multiplied by time, forming the fundamental relationship in rate problems.

5. Convert $2500\ \text{mL}$ to liters.

   $2.5\ \text{L}$. Divide by $1000$ because $1$ liter equals $1000$ milliliters.

6. Convert $2\ \text{hr}$ to minutes.

   $120\ \text{min}$. Multiply by $60$ because $1$ hour equals $60$ minutes.

7. A recipe uses $\frac{3}{4}\ \text{cup}$ sugar per batch. How much sugar for $4$ batches?

   $3\ \text{cups}$. Multiply the amount per batch by the number of batches to find the total required.

8. A car travels $150\ \text{mi}$ in $3\ \text{hr}$. What is its rate?

   $50\ \text{mi/hr}$. Divide distance by time using $r=\frac{d}{t}$ to find the constant rate.

9. Convert $1500\ \text{g}$ to kilograms.

   $1.5\ \text{kg}$. Divide by $1000$ since $1$ kilogram equals $1000$ grams.

10. What unit must distance have if rate is in $\text{mi/hr}$ and time is in hours?

    $\text{miles}$. Units must be consistent in the distance formula, so distance uses miles when rate is miles per hour and time is hours.

11. Convert $4\ \text{kg}$ to grams.

    $4000\ \text{g}$. Multiply by $1000$ because $1$ kilogram equals $1000$ grams.

12. At $12\ \text{mi/hr}$, how far do you travel in $30\ \text{min}$?

    $6\ \text{mi}$. Convert minutes to hours and multiply rate by time using $d=rt$.

13. Convert $0.5\ \text{hr}$ to seconds.

    $1800\ \text{s}$. Convert hours to minutes by multiplying by $60$, then minutes to seconds by multiplying by $60$.

14. State the formula for rate in terms of distance and time.

    $r=\frac{d}{t}$. Rate is calculated by dividing distance by time to determine speed or pace.

15. Convert $2\ \text{yd}$ to feet.

    $6\ \text{ft}$. Multiply by $3$ as $1$ yard equals $3$ feet.

16. What is $2\ \text{mi/min}$ in $\text{mi/hr}$?

    $120\ \text{mi/hr}$. Multiply by $60$ to convert from per minute to per hour, since an hour has $60$ minutes.

17. Convert $180\ \text{s}$ to minutes.

    $3\ \text{min}$. Divide by $60$ since $1$ minute equals $60$ seconds.

18. Convert $3\ \text{L}$ to milliliters.

    $3000\ \text{mL}$. Multiply by $1000$ as $1$ liter equals $1000$ milliliters.

19. At $8\ \text{ft/s}$, how long does it take to go $200\ \text{ft}$?

    $25\ \text{s}$. Divide distance by rate using $t=\frac{d}{r}$ to solve for time.

20. What is the cost per ounce if $12\ \text{oz}$ costs $3?

    $\$0.25\ \text{per oz}$. Divide total cost by total ounces to determine the unit price.

21. Convert $1.5\ \text{yd}$ to inches.

    $54\ \text{in}$. Convert yards to feet by multiplying by $3$, then feet to inches by multiplying by $12$.

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