ISEE Middle Level Quantitative Reasoning Flashcards: Ratios And Rates In Context

What this deck covers

This deck focuses on Ratios And Rates In Context, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle Level Quantitative Reasoning.

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: Which ratio matches the statement: "$8$ girls and $12$ boys" as girls to boys?

Answer: $8:12$ (equivalently $2:3$). The ratio of girls to boys is directly $8:12$, which simplifies by dividing by $4$ to $2:3$.

Flashcard 2: Identify the unit rate for $15$ dollars for $6$ pounds of apples.

Answer: $2.50 per pound. Divide total cost by pounds to compute unit rate as $15 \div 6 = 2.5$ dollars per pound.

Flashcard 3: What is the ratio of $30$ minutes to $2$ hours in simplest form?

Answer: $30:120 = 1:4$. Convert $2$ hours to $120$ minutes, then simplify $30:120$ by dividing by $30$ to $1:4$.

Flashcard 4: What is the speed in feet per second for $300$ feet in $10$ seconds?

Answer: $30$ feet per second. Divide distance by time to find the rate as $300 \div 10 = 30$ feet per second.

Flashcard 5: Find the cost at a unit rate of $4 per ticket for $7$ tickets.

Answer: $28. Multiply the unit rate by the number of tickets as \ 4 \times 7 = \28$ to find total cost.

Flashcard 6: Find the unit rate in miles per gallon if a car travels $180$ miles on $6$ gallons.

Answer: $30$ miles per gallon. Divide miles by gallons to find unit rate as $180 \div 6 = 30$ miles per gallon.

Flashcard 7: Find the number of cups of water needed if the ratio water:rice is $2:1$ and there are $3$ cups of rice.

Answer: $6$ cups of water. Using the ratio $2:1$, scale by $3$ for rice to find water as $2 \times 3 = 6$ cups.

Flashcard 8: What does the ratio $5:2$ mean when comparing cats to dogs in a shelter?

Answer: There are $5$ cats for every $2$ dogs. The ratio $5:2$ indicates the comparative number of cats to dogs present.

Flashcard 9: What is the meaning of the ratio $\frac{2}{5}$ when comparing wins to total games?

Answer: $2$ wins out of every $5$ games. The ratio $\frac{2}{5}$ expresses wins as a fraction of total games played.

Flashcard 10: What is the unit price if $5$ notebooks cost $12.50?

Answer: $2.50 per notebook. Divide total cost by number of notebooks to find the price per unit as \frac{\12.50}{5} = $2.50$.

Flashcard 11: What is the time needed at a rate of $12$ miles per hour to travel $36$ miles?

Answer: $3$ hours. Divide distance by rate as $36 \div 12 = 3$ to determine the time required.

Flashcard 12: What is the meaning of the ratio $\frac{7}{2}$ in the context of miles per hour?

Answer: $7$ miles for every $2$ hours. The ratio $\frac{7}{2}$ represents a rate of $7$ miles traveled in $2$ hours.

Flashcard 13: What is the unit rate for $18$ pages in $3$ minutes?

Answer: $6$ pages per minute. Divide total pages by minutes to compute the unit rate as $18 \div 3 = 6$.

Flashcard 14: What is the meaning of "per" in a rate such as $9$ dollars per hour?

Answer: For each $1$ hour, the amount is $9. The word 'per' in a rate indicates the quantity associated with each single unit of the denominator.

Flashcard 15: What is the ratio of boys to total students if there are $12$ boys and $8$ girls?

Answer: $12:20$ (equivalently $3:5$). Boys to total students is $12:(12+8)=12:20$, simplified by dividing by $4$ to $3:5$.

Flashcard 16: What is the ratio of shaded to total if $9$ of $12$ squares are shaded, simplified?

Answer: $9:12 = 3:4$. The ratio $9:12$ simplifies to $3:4$ by dividing both by $3$ for shaded to total squares.

Flashcard 17: What does the ratio $3:5$ mean when comparing apples to oranges?

Answer: There are $3$ apples for every $5$ oranges. The ratio $3:5$ compares the number of apples to oranges, indicating $3$ apples per $5$ oranges.

Flashcard 18: Identify the better buy: $12$ ounces for $3 or $20$ ounces for $4.

Answer: $20$ ounces for $4 (lower \/$ounce). Compare unit prices:$\frac{$3}{12} = $0.25$vs.$\frac{$4}{20} = $0.20$, so the lower rate is better.

Flashcard 19: Identify the equivalent ratio to $6:9$ in simplest form.

Answer: $2:3$. Simplify $6:9$ by dividing both terms by $3$ to obtain the equivalent ratio $2:3$.

Flashcard 20: What does a ratio of $1:4$ mean in a paint mixture of red to white?

Answer: $1$ part red for every $4$ parts white. The ratio $1:4$ denotes the proportion of red paint to white paint in the mixture.

Flashcard 21: What is the meaning of the rate $3 per pound in a grocery context?

Answer: Each $1$ pound costs $3. The rate \frac{\3}{1}$ pound specifies the cost for each single pound of an item.

Flashcard 22: Find the distance at a rate of $55$ miles per hour for $2$ hours.

Answer: $110$ miles. Multiply rate by time as $55 \times 2 = 110$ to calculate total distance traveled.

Flashcard 23: What is the meaning of a constant rate when a situation is proportional?

Answer: The ratio $\frac{y}{x}$ stays the same for all pairs. In proportional situations, a constant rate means the ratio of output to input remains unchanged.

Flashcard 24: Which statement correctly interprets the ratio $4:1$ as students to teachers?

Answer: There are $4$ students for every $1$ teacher. The ratio $4:1$ compares students to teachers, meaning $4$ students per teacher.

Flashcard 25: Identify the rate described by "$240$ miles in $4$ hours" in miles per hour.

Answer: $60$ miles per hour. Divide distance by time to express the rate as $240 \div 4 = 60$ miles per hour.