Ratios and Rates in Context - ISEE Middle Level: Quantitative Reasoning
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What is the meaning of the rate $\$3$ per pound in a grocery context?
What is the meaning of the rate $\$3$ per pound in a grocery context?
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Each $1$ pound costs $\$3$. The rate $\frac{$3}{1}$ pound specifies the cost for each single pound of an item.
Each $1$ pound costs $\$3$. The rate $\frac{$3}{1}$ pound specifies the cost for each single pound of an item.
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Identify the equivalent ratio to $6:9$ in simplest form.
Identify the equivalent ratio to $6:9$ in simplest form.
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$2:3$. Simplify $6:9$ by dividing both terms by $3$ to obtain the equivalent ratio $2:3$.
$2:3$. Simplify $6:9$ by dividing both terms by $3$ to obtain the equivalent ratio $2:3$.
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What does the ratio $3:5$ mean when comparing apples to oranges?
What does the ratio $3:5$ mean when comparing apples to oranges?
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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.
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.
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What is the meaning of the ratio $
\frac{7}{2}$ in the context of miles per hour?
What is the meaning of the ratio $ \frac{7}{2}$ in the context of miles per hour?
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$7$ miles for every $2$ hours. The ratio $\frac{7}{2}$ represents a rate of $7$ miles traveled in $2$ hours.
$7$ miles for every $2$ hours. The ratio $\frac{7}{2}$ represents a rate of $7$ miles traveled in $2$ hours.
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What is the unit rate for $18$ pages in $3$ minutes?
What is the unit rate for $18$ pages in $3$ minutes?
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$6$ pages per minute. Divide total pages by minutes to compute the unit rate as $18 \div 3 = 6$.
$6$ pages per minute. Divide total pages by minutes to compute the unit rate as $18 \div 3 = 6$.
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What is the unit price if $5$ notebooks cost $\$12.50$?
What is the unit price if $5$ notebooks cost $\$12.50$?
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$\$2.50$ per notebook. Divide total cost by number of notebooks to find the price per unit as $\frac{$12.50}{5} = $2.50$.
$\$2.50$ per notebook. Divide total cost by number of notebooks to find the price per unit as $\frac{$12.50}{5} = $2.50$.
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Identify the rate described by "$240$ miles in $4$ hours" in miles per hour.
Identify the rate described by "$240$ miles in $4$ hours" in miles per hour.
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$60$ miles per hour. Divide distance by time to express the rate as $240 \div 4 = 60$ miles per hour.
$60$ miles per hour. Divide distance by time to express the rate as $240 \div 4 = 60$ miles per hour.
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Which ratio matches the statement: "$8$ girls and $12$ boys" as girls to boys?
Which ratio matches the statement: "$8$ girls and $12$ boys" as girls to boys?
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$8:12$ (equivalently $2:3$). The ratio of girls to boys is directly $8:12$, which simplifies by dividing by $4$ to $2:3$.
$8:12$ (equivalently $2:3$). The ratio of girls to boys is directly $8:12$, which simplifies by dividing by $4$ to $2:3$.
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Identify the better buy: $12$ ounces for $\$3$ or $20$ ounces for $$4$.
Identify the better buy: $12$ ounces for $\$3$ or $20$ ounces for $$4$.
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$20$ 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.
$20$ 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.
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Find the number of cups of water needed if the ratio water:rice is $2:1$ and there are $3$ cups of rice.
Find the number of cups of water needed if the ratio water:rice is $2:1$ and there are $3$ cups of rice.
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$6$ cups of water. Using the ratio $2:1$, scale by $3$ for rice to find water as $2 \times 3 = 6$ cups.
$6$ cups of water. Using the ratio $2:1$, scale by $3$ for rice to find water as $2 \times 3 = 6$ cups.
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What is the ratio of $30$ minutes to $2$ hours in simplest form?
What is the ratio of $30$ minutes to $2$ hours in simplest form?
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$30:120 = 1:4$. Convert $2$ hours to $120$ minutes, then simplify $30:120$ by dividing by $30$ to $1:4$.
$30:120 = 1:4$. Convert $2$ hours to $120$ minutes, then simplify $30:120$ by dividing by $30$ to $1:4$.
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What is the meaning of a constant rate when a situation is proportional?
What is the meaning of a constant rate when a situation is proportional?
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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.
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.
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Find the unit rate in miles per gallon if a car travels $180$ miles on $6$ gallons.
Find the unit rate in miles per gallon if a car travels $180$ miles on $6$ gallons.
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$30$ miles per gallon. Divide miles by gallons to find unit rate as $180 \div 6 = 30$ miles per gallon.
$30$ miles per gallon. Divide miles by gallons to find unit rate as $180 \div 6 = 30$ miles per gallon.
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What does the ratio $5:2$ mean when comparing cats to dogs in a shelter?
What does the ratio $5:2$ mean when comparing cats to dogs in a shelter?
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There are $5$ cats for every $2$ dogs. The ratio $5:2$ indicates the comparative number of cats to dogs present.
There are $5$ cats for every $2$ dogs. The ratio $5:2$ indicates the comparative number of cats to dogs present.
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What is the ratio of shaded to total if $9$ of $12$ squares are shaded, simplified?
What is the ratio of shaded to total if $9$ of $12$ squares are shaded, simplified?
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$9:12 = 3:4$. The ratio $9:12$ simplifies to $3:4$ by dividing both by $3$ for shaded to total squares.
$9:12 = 3:4$. The ratio $9:12$ simplifies to $3:4$ by dividing both by $3$ for shaded to total squares.
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Identify the unit rate for $15$ dollars for $6$ pounds of apples.
Identify the unit rate for $15$ dollars for $6$ pounds of apples.
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$\$2.50$ per pound. Divide total cost by pounds to compute unit rate as $15 \div 6 = 2.5$ dollars per pound.
$\$2.50$ per pound. Divide total cost by pounds to compute unit rate as $15 \div 6 = 2.5$ dollars per pound.
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Which statement correctly interprets the ratio $4:1$ as students to teachers?
Which statement correctly interprets the ratio $4:1$ as students to teachers?
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There are $4$ students for every $1$ teacher. The ratio $4:1$ compares students to teachers, meaning $4$ students per teacher.
There are $4$ students for every $1$ teacher. The ratio $4:1$ compares students to teachers, meaning $4$ students per teacher.
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What is the time needed at a rate of $12$ miles per hour to travel $36$ miles?
What is the time needed at a rate of $12$ miles per hour to travel $36$ miles?
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$3$ hours. Divide distance by rate as $36 \div 12 = 3$ to determine the time required.
$3$ hours. Divide distance by rate as $36 \div 12 = 3$ to determine the time required.
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Find the distance at a rate of $55$ miles per hour for $2$ hours.
Find the distance at a rate of $55$ miles per hour for $2$ hours.
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$110$ miles. Multiply rate by time as $55 \times 2 = 110$ to calculate total distance traveled.
$110$ miles. Multiply rate by time as $55 \times 2 = 110$ to calculate total distance traveled.
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Find the cost at a unit rate of $\$4$ per ticket for $7$ tickets.
Find the cost at a unit rate of $\$4$ per ticket for $7$ tickets.
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$\$28$. Multiply the unit rate by the number of tickets as $\ 4 \times 7 = $28$ to find total cost.
$\$28$. Multiply the unit rate by the number of tickets as $\ 4 \times 7 = $28$ to find total cost.
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What is the meaning of "per" in a rate such as $9$ dollars per hour?
What is the meaning of "per" in a rate such as $9$ dollars per hour?
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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.
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.
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What is the speed in feet per second for $300$ feet in $10$ seconds?
What is the speed in feet per second for $300$ feet in $10$ seconds?
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$30$ feet per second. Divide distance by time to find the rate as $300 \div 10 = 30$ feet per second.
$30$ feet per second. Divide distance by time to find the rate as $300 \div 10 = 30$ feet per second.
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What is the meaning of the ratio $\frac{2}{5}$ when comparing wins to total games?
What is the meaning of the ratio $\frac{2}{5}$ when comparing wins to total games?
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$2$ wins out of every $5$ games. The ratio $\frac{2}{5}$ expresses wins as a fraction of total games played.
$2$ wins out of every $5$ games. The ratio $\frac{2}{5}$ expresses wins as a fraction of total games played.
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What does a ratio of $1:4$ mean in a paint mixture of red to white?
What does a ratio of $1:4$ mean in a paint mixture of red to white?
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$1$ part red for every $4$ parts white. The ratio $1:4$ denotes the proportion of red paint to white paint in the mixture.
$1$ part red for every $4$ parts white. The ratio $1:4$ denotes the proportion of red paint to white paint in the mixture.
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What is the ratio of boys to total students if there are $12$ boys and $8$ girls?
What is the ratio of boys to total students if there are $12$ boys and $8$ girls?
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$12:20$ (equivalently $3:5$). Boys to total students is $12:(12+8)=12:20$, simplified by dividing by $4$ to $3:5$.
$12:20$ (equivalently $3:5$). Boys to total students is $12:(12+8)=12:20$, simplified by dividing by $4$ to $3:5$.
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