Scaling and Unit Rates - ISEE Upper Level: Quantitative Reasoning
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What is the new area if a rectangle with area $48$ is scaled by a linear factor of $\frac{1}{2}$?
What is the new area if a rectangle with area $48$ is scaled by a linear factor of $\frac{1}{2}$?
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$12$. Multiply the original area by the square of the linear scale factor to find the new area.
$12$. Multiply the original area by the square of the linear scale factor to find the new area.
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What is the unit rate in dollars per pound for $\$7.50$ for $3$ lb?
What is the unit rate in dollars per pound for $\$7.50$ for $3$ lb?
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$\$2.50$ per lb. Divide the total cost by the number of pounds to find the unit rate in dollars per pound.
$\$2.50$ per lb. Divide the total cost by the number of pounds to find the unit rate in dollars per pound.
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What is the unit rate in miles per hour for $150$ miles in $3$ hours?
What is the unit rate in miles per hour for $150$ miles in $3$ hours?
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$50$ mph. Divide the total miles by the total hours to determine the unit rate in miles per hour.
$50$ mph. Divide the total miles by the total hours to determine the unit rate in miles per hour.
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What is the unit rate in minutes per mile for $24$ minutes to run $3$ miles?
What is the unit rate in minutes per mile for $24$ minutes to run $3$ miles?
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$8$ min/mi. Divide the total minutes by the number of miles to find the unit rate in minutes per mile.
$8$ min/mi. Divide the total minutes by the number of miles to find the unit rate in minutes per mile.
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What is the unit rate in dollars per item for $\$18$ for $6$ notebooks?
What is the unit rate in dollars per item for $\$18$ for $6$ notebooks?
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$\$3$ per notebook. Divide the total cost by the number of notebooks to obtain the unit rate in dollars per notebook.
$\$3$ per notebook. Divide the total cost by the number of notebooks to obtain the unit rate in dollars per notebook.
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What is the scale factor from an original length of $12$ to a new length of $18$?
What is the scale factor from an original length of $12$ to a new length of $18$?
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$\frac{3}{2}$. Divide the new length by the original length to calculate the scale factor.
$\frac{3}{2}$. Divide the new length by the original length to calculate the scale factor.
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What is the new length if a $10$ cm segment is enlarged by a scale factor of $1.4$?
What is the new length if a $10$ cm segment is enlarged by a scale factor of $1.4$?
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$14$ cm. Multiply the original length by the scale factor to find the enlarged length.
$14$ cm. Multiply the original length by the scale factor to find the enlarged length.
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What is the new length if a $24$ m distance is reduced by a scale factor of $\frac{1}{3}$?
What is the new length if a $24$ m distance is reduced by a scale factor of $\frac{1}{3}$?
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$8$ m. Multiply the original distance by the scale factor to determine the reduced length.
$8$ m. Multiply the original distance by the scale factor to determine the reduced length.
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What is the scale factor if a model length is $9$ cm and the actual length is $36$ cm?
What is the scale factor if a model length is $9$ cm and the actual length is $36$ cm?
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$4$. Divide the actual length by the model length to find the scale factor from model to actual.
$4$. Divide the actual length by the model length to find the scale factor from model to actual.
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What is the perimeter scale factor when all side lengths are multiplied by $k$?
What is the perimeter scale factor when all side lengths are multiplied by $k$?
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$k$. The perimeter scales linearly with the side lengths, so the scale factor is $k$.
$k$. The perimeter scales linearly with the side lengths, so the scale factor is $k$.
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What is the area scale factor when all linear dimensions are multiplied by $k$?
What is the area scale factor when all linear dimensions are multiplied by $k$?
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$k^2$. Areas scale with the square of the linear dimensions, resulting in a factor of $k^2$.
$k^2$. Areas scale with the square of the linear dimensions, resulting in a factor of $k^2$.
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What is the volume scale factor when all linear dimensions are multiplied by $k$?
What is the volume scale factor when all linear dimensions are multiplied by $k$?
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$k^3$. Volumes scale with the cube of the linear dimensions, giving a factor of $k^3$.
$k^3$. Volumes scale with the cube of the linear dimensions, giving a factor of $k^3$.
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What is the new area if a figure with area $20$ is scaled by a factor of $3$?
What is the new area if a figure with area $20$ is scaled by a factor of $3$?
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$180$. Multiply the original area by the square of the scale factor to find the new area.
$180$. Multiply the original area by the square of the scale factor to find the new area.
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What is the new volume if a solid with volume $5$ is scaled by a factor of $2$?
What is the new volume if a solid with volume $5$ is scaled by a factor of $2$?
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$40$. Multiply the original volume by the cube of the scale factor to determine the new volume.
$40$. Multiply the original volume by the cube of the scale factor to determine the new volume.
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What is the scale factor if the area changes from $16$ to $64$ for similar figures?
What is the scale factor if the area changes from $16$ to $64$ for similar figures?
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$2$. The linear scale factor is the square root of the ratio of new area to original area.
$2$. The linear scale factor is the square root of the ratio of new area to original area.
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What is the scale factor if the volume changes from $27$ to $216$ for similar solids?
What is the scale factor if the volume changes from $27$ to $216$ for similar solids?
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$2$. The linear scale factor is the cube root of the ratio of new volume to original volume.
$2$. The linear scale factor is the cube root of the ratio of new volume to original volume.
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What is the new circumference if a circle with circumference $30$ is scaled by $\frac{2}{3}$?
What is the new circumference if a circle with circumference $30$ is scaled by $\frac{2}{3}$?
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$20$. Multiply the original circumference by the scale factor, as circumference is a linear dimension.
$20$. Multiply the original circumference by the scale factor, as circumference is a linear dimension.
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What is the unit rate in gallons per minute for $15$ gallons in $5$ minutes?
What is the unit rate in gallons per minute for $15$ gallons in $5$ minutes?
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$3$ gal/min. Divide the total gallons by the total minutes to find the unit rate in gallons per minute.
$3$ gal/min. Divide the total gallons by the total minutes to find the unit rate in gallons per minute.
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What is the unit rate in words per minute for $450$ words typed in $9$ minutes?
What is the unit rate in words per minute for $450$ words typed in $9$ minutes?
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$50$ wpm. Divide the total words by the total minutes to determine the unit rate in words per minute.
$50$ wpm. Divide the total words by the total minutes to determine the unit rate in words per minute.
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What is the unit rate in dollars per hour for $\$84$ earned in $7$ hours?
What is the unit rate in dollars per hour for $\$84$ earned in $7$ hours?
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$\$12$ per hour. Divide the total earnings by the total hours to calculate the unit rate in dollars per hour.
$\$12$ per hour. Divide the total earnings by the total hours to calculate the unit rate in dollars per hour.
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What is the time per item if $45$ items are produced in $9$ minutes?
What is the time per item if $45$ items are produced in $9$ minutes?
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$\frac{1}{5}$ min/item. Divide the total time by the number of items to find the unit rate in minutes per item.
$\frac{1}{5}$ min/item. Divide the total time by the number of items to find the unit rate in minutes per item.
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What is the cost for $8$ lb if the unit price is $\$2.75$ per lb?
What is the cost for $8$ lb if the unit price is $\$2.75$ per lb?
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$\$22$. Multiply the unit price by the number of pounds to compute the total cost.
$\$22$. Multiply the unit price by the number of pounds to compute the total cost.
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What is the distance traveled in $2.5$ hours at a unit rate of $48$ mph?
What is the distance traveled in $2.5$ hours at a unit rate of $48$ mph?
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$120$ miles. Multiply the speed by the time to calculate the distance traveled.
$120$ miles. Multiply the speed by the time to calculate the distance traveled.
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What is the actual distance if a map scale is $1$ in $=$ $20$ mi and the map shows $3.5$ in?
What is the actual distance if a map scale is $1$ in $=$ $20$ mi and the map shows $3.5$ in?
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$70$ mi. Multiply the map distance by the scale ratio to find the actual distance.
$70$ mi. Multiply the map distance by the scale ratio to find the actual distance.
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What is the map distance if the scale is $1$ cm $=$ $5$ km and the actual distance is $40$ km?
What is the map distance if the scale is $1$ cm $=$ $5$ km and the actual distance is $40$ km?
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$8$ cm. Divide the actual distance by the scale ratio to determine the map distance.
$8$ cm. Divide the actual distance by the scale ratio to determine the map distance.
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