ISEE Middle Level Mathematics Achievement Flashcards: Unit Rate Problems

What this deck covers

This deck focuses on Unit Rate Problems, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle Level Mathematics Achievement.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is a unit rate, in terms of a ratio $\frac{a}{b}$?

Answer: A rate with denominator $1$, written as $\frac{a}{1}$ per $1$ unit. A unit rate simplifies the ratio $\frac{a}{b}$ by dividing $a$ by $b$ to express the quantity per single unit of the denominator.

Flashcard 2: Find the missing value: at $4 per pound, what is the cost of $6$ pounds?

Answer: $24. Multiply the unit price per pound by the total pounds to calculate the overall cost.

Flashcard 3: What is the better buy: $12$ oz for $6$ dollars or $20$ oz for $9$ dollars?

Answer: $20$ oz for $9$ dollars. Compare unit prices: $\frac{6}{12} = 0.5$ $/oz vs $\frac{9}{20} = 0.45$ $/oz, so the lower cost per ounce indicates better value.

Flashcard 4: Find the time: at $30$ miles per hour, how long to travel $45$ miles (in hours)?

Answer: $1.5$ hours. Divide the total distance by the speed to find the time required in hours.

Flashcard 5: What is the unit rate for $18$ cookies for $24$ students (cookies per student)?

Answer: $0.75$ cookies per student. Divide the total cookies by the total students to find the distribution rate per student.

Flashcard 6: What is the unit rate for $9$ pages in $6$ minutes (pages per minute)?

Answer: $1.5$ pages per minute. Divide the total pages by the total minutes to calculate the reading or printing rate per minute.

Flashcard 7: What is the unit rate for $28$ dollars for $7$ notebooks (dollars per notebook)?

Answer: $4$ dollars per notebook. Divide the total cost by the total notebooks to find the price per individual notebook.

Flashcard 8: What is the unit rate for $360$ miles in $6$ hours (miles per hour)?

Answer: $60$ miles per hour. Divide the total distance by the total time to calculate the average speed per hour.

Flashcard 9: What is the unit rate for $\frac{3}{4}$ mile in $\frac{1}{2}$ hour (miles per hour)?

Answer: $1.5$ miles per hour. Divide the distance fraction by the time fraction to compute the speed per full hour.

Flashcard 10: What is the unit rate for $90$ seconds for $3$ laps (seconds per lap)?

Answer: $30$ seconds per lap. Divide the total time by the total laps to determine the time per individual lap.

Flashcard 11: What is the unit rate for $8$ dollars for $2$ pounds (dollars per pound)?

Answer: $4$ dollars per pound. Divide the total cost by the total weight to compute the price per single pound.

Flashcard 12: What is the cost per ounce if $12$ ounces cost $9$ dollars (dollars per ounce)?

Answer: $0.75$ dollars per ounce. Divide the total cost by the total ounces to find the price per single ounce.

Flashcard 13: What is the unit rate for $150$ words in $3$ minutes (words per minute)?

Answer: $50$ words per minute. Divide the total words by the total minutes to find the typing or reading rate per minute.

Flashcard 14: What is the unit rate for $2.5$ gallons in $5$ minutes (gallons per minute)?

Answer: $0.5$ gallons per minute. Divide the total volume by the total time to determine the flow rate per minute.

Flashcard 15: What is the unit rate for $1.2$ kilograms for $3$ boxes (kilograms per box)?

Answer: $0.4$ kilograms per box. Divide the total mass by the total boxes to find the weight per single box.

Flashcard 16: What is the unit rate for $3$ liters in $\frac{1}{2}$ hour (liters per hour)?

Answer: $6$ liters per hour. Divide the volume by the time fraction to scale the rate to a full hour.

Flashcard 17: What is the unit rate for $7$ notebooks for $28$ dollars (notebooks per dollar)?

Answer: $0.25$ notebooks per dollar. Divide the total notebooks by the total cost to compute the quantity obtained per dollar.

Flashcard 18: What is the unit rate for $6$ pencils for $\frac{3}{4}$ dollar (pencils per dollar)?

Answer: $8$ pencils per dollar. Divide the total pencils by the cost fraction to scale to the quantity per full dollar.

Flashcard 19: Identify the unit rate in $\frac{18\ \text{miles}}{2\ \text{hours}}$ as a simplified fraction.

Answer: $\frac{9}{1}$ miles per hour. Simplify the ratio by dividing numerator and denominator by 2 to express the rate per single hour as a fraction.

Flashcard 20: What is the unit rate for $45$ miles in $3$ hours (miles per hour)?

Answer: $15$ miles per hour. Divide the total distance by the total time to determine the constant speed per hour.

Flashcard 21: What is the unit rate for $5$ dollars for $2$ pounds (dollars per pound)?

Answer: $2.5$ dollars per pound. Divide the total cost by the total weight to determine the price per pound.

Flashcard 22: What is the unit rate for $12$ apples in $3$ bags (apples per bag)?

Answer: $4$ apples per bag. Divide the total number of apples by the total number of bags to find the constant rate per individual bag.

Flashcard 23: What is the better buy: $3$ lb for $7.50$ dollars or $5$ lb for $13$ dollars?

Answer: $3$ lb for $7.50$ dollars. Compare unit prices: $\frac{7.50}{3} = 2.5$ $/lb vs $\frac{13}{5} = 2.6$ $/lb, so the lower cost per pound indicates better value.

Flashcard 24: What is the unit rate for $3$ pounds for $12$ dollars (pounds per dollar)?

Answer: $0.25$ pounds per dollar. Divide the total weight by the total cost to find the amount of pounds obtained per dollar spent.

Flashcard 25: What is the unit rate for $2$ hours for $150$ miles (hours per mile)?

Answer: $\frac{1}{75}$ hour per mile. Divide the total time by the total distance to express the time required per mile as a fraction.