Rates and Unit Conversions - ISEE Middle Level: Quantitative Reasoning

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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