Proportional Scaling - SSAT Middle Level: Quantitative
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What is the new volume if a volume of $12$ is scaled by a factor of $2$ in all dimensions?
What is the new volume if a volume of $12$ is scaled by a factor of $2$ in all dimensions?
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$96$. Multiply the original volume by the cube of the scale factor for similar solids.
$96$. Multiply the original volume by the cube of the scale factor for similar solids.
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What is the new area if a square with side $7$ is scaled by a factor of $\frac{2}{7}$?
What is the new area if a square with side $7$ is scaled by a factor of $\frac{2}{7}$?
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$4$. Square the scale factor and multiply by the original area of $49$ to get the scaled area.
$4$. Square the scale factor and multiply by the original area of $49$ to get the scaled area.
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What is the scale factor from an original length $L$ to a new length $L'$?
What is the scale factor from an original length $L$ to a new length $L'$?
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$k = \frac{L'}{L}$. The scale factor is defined as the ratio of the new length to the original length in proportional scaling.
$k = \frac{L'}{L}$. The scale factor is defined as the ratio of the new length to the original length in proportional scaling.
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What is the new length if an original length is $12$ and the scale factor is $\frac{3}{2}$?
What is the new length if an original length is $12$ and the scale factor is $\frac{3}{2}$?
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$18$. Multiply the original length by the scale factor to determine the scaled length.
$18$. Multiply the original length by the scale factor to determine the scaled length.
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What is the scale factor if a length changes from $8$ to $14$?
What is the scale factor if a length changes from $8$ to $14$?
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$\frac{7}{4}$. Divide the new length by the original length to compute the scale factor.
$\frac{7}{4}$. Divide the new length by the original length to compute the scale factor.
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What is the original length if the new length is $21$ and the scale factor is $\frac{3}{2}$?
What is the original length if the new length is $21$ and the scale factor is $\frac{3}{2}$?
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$14$. Divide the new length by the scale factor to recover the original length.
$14$. Divide the new length by the scale factor to recover the original length.
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What is the new perimeter if a figure with perimeter $30$ is scaled by a factor of $\frac{4}{3}$?
What is the new perimeter if a figure with perimeter $30$ is scaled by a factor of $\frac{4}{3}$?
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$40$. Perimeters of similar figures scale linearly by the scale factor.
$40$. Perimeters of similar figures scale linearly by the scale factor.
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What is the rule for how perimeter changes under a scale factor $k$?
What is the rule for how perimeter changes under a scale factor $k$?
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Perimeter multiplies by $k$. Since perimeters are sums of linear dimensions, they scale by the factor $k$.
Perimeter multiplies by $k$. Since perimeters are sums of linear dimensions, they scale by the factor $k$.
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What is the rule for how area changes under a scale factor $k$?
What is the rule for how area changes under a scale factor $k$?
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Area multiplies by $k^2$. Areas of similar figures scale by the square of the linear scale factor.
Area multiplies by $k^2$. Areas of similar figures scale by the square of the linear scale factor.
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What is the new area if an area of $50$ is scaled by a factor of $3$?
What is the new area if an area of $50$ is scaled by a factor of $3$?
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$450$. Multiply the original area by the square of the scale factor to find the new area.
$450$. Multiply the original area by the square of the scale factor to find the new area.
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What is the scale factor $k$ if area changes from $36$ to $81$ for similar figures?
What is the scale factor $k$ if area changes from $36$ to $81$ for similar figures?
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$\frac{3}{2}$. Take the square root of the ratio of new area to original area for similar figures.
$\frac{3}{2}$. Take the square root of the ratio of new area to original area for similar figures.
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What is the rule for how volume changes under a scale factor $k$ in all dimensions?
What is the rule for how volume changes under a scale factor $k$ in all dimensions?
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Volume multiplies by $k^3$. Volumes of similar solids scale by the cube of the linear scale factor.
Volume multiplies by $k^3$. Volumes of similar solids scale by the cube of the linear scale factor.
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What is the scale factor $k$ if volume changes from $8$ to $27$ for similar solids?
What is the scale factor $k$ if volume changes from $8$ to $27$ for similar solids?
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$\frac{3}{2}$. Take the cube root of the ratio of new volume to original volume for similar solids.
$\frac{3}{2}$. Take the cube root of the ratio of new volume to original volume for similar solids.
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What is the new width if a rectangle has width $9$ and is reduced by a scale factor of $\frac{2}{3}$?
What is the new width if a rectangle has width $9$ and is reduced by a scale factor of $\frac{2}{3}$?
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$6$. Apply the scale factor to the original width by multiplication to get the reduced width.
$6$. Apply the scale factor to the original width by multiplication to get the reduced width.
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What is the scale factor if a drawing uses $1$ inch to represent $4$ feet?
What is the scale factor if a drawing uses $1$ inch to represent $4$ feet?
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$1:48$. Convert feet to inches to express the ratio of drawing length to actual length as 1:48.
$1:48$. Convert feet to inches to express the ratio of drawing length to actual length as 1:48.
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What actual length (in feet) does $7$ inches represent if the scale is $1$ inch $=$ $3$ feet?
What actual length (in feet) does $7$ inches represent if the scale is $1$ inch $=$ $3$ feet?
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$21$ feet. Multiply the drawing length by the scale conversion factor to obtain the actual length.
$21$ feet. Multiply the drawing length by the scale conversion factor to obtain the actual length.
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What drawing length (in inches) represents $18$ feet if the scale is $1$ inch $=$ $6$ feet?
What drawing length (in inches) represents $18$ feet if the scale is $1$ inch $=$ $6$ feet?
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$3$ inches. Divide the actual length by the scale conversion factor to find the drawing length.
$3$ inches. Divide the actual length by the scale conversion factor to find the drawing length.
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What is the constant of proportionality $k$ if $y$ is proportional to $x$ and $y=15$ when $x=6$?
What is the constant of proportionality $k$ if $y$ is proportional to $x$ and $y=15$ when $x=6$?
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$k = \frac{5}{2}$. Divide the given $y$ by the corresponding $x$ to find the constant of proportionality.
$k = \frac{5}{2}$. Divide the given $y$ by the corresponding $x$ to find the constant of proportionality.
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What is $y$ if $y$ is proportional to $x$, $y=10$ when $x=4$, and $x=14$?
What is $y$ if $y$ is proportional to $x$, $y=10$ when $x=4$, and $x=14$?
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$35$. Determine $k$ from known values and multiply by the new $x$ to find the corresponding $y$.
$35$. Determine $k$ from known values and multiply by the new $x$ to find the corresponding $y$.
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What is the missing value $x$ in the proportion $\frac{3}{5}=\frac{x}{20}$?
What is the missing value $x$ in the proportion $\frac{3}{5}=\frac{x}{20}$?
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$12$. Cross-multiply the proportion and solve for the unknown value $x$.
$12$. Cross-multiply the proportion and solve for the unknown value $x$.
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What is the missing value $x$ in the proportion $\frac{7}{x}=\frac{21}{30}$?
What is the missing value $x$ in the proportion $\frac{7}{x}=\frac{21}{30}$?
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$10$. Cross-multiply the proportion to equate products and solve for $x$.
$10$. Cross-multiply the proportion to equate products and solve for $x$.
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What is the new length if $5$ cm on a map represents $40$ km, and the map length is $8$ cm?
What is the new length if $5$ cm on a map represents $40$ km, and the map length is $8$ cm?
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$64$ km. Use the unit rate from the given scale to multiply by the new map length for actual distance.
$64$ km. Use the unit rate from the given scale to multiply by the new map length for actual distance.
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What is the scale factor from $15$ to $10$, expressed as a simplified fraction?
What is the scale factor from $15$ to $10$, expressed as a simplified fraction?
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$\frac{2}{3}$. Divide the new value by the original to express the scale factor as a simplified fraction.
$\frac{2}{3}$. Divide the new value by the original to express the scale factor as a simplified fraction.
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What is the original volume if the new volume is $216$ and the linear scale factor is $3$?
What is the original volume if the new volume is $216$ and the linear scale factor is $3$?
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$8$. Divide the new volume by the cube of the scale factor to find the original volume.
$8$. Divide the new volume by the cube of the scale factor to find the original volume.
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What is the scale factor $k$ if a model is $\frac{1}{25}$ of the actual object in every length?
What is the scale factor $k$ if a model is $\frac{1}{25}$ of the actual object in every length?
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$k = \frac{1}{25}$. The scale factor is the ratio of model length to actual length when the model is smaller.
$k = \frac{1}{25}$. The scale factor is the ratio of model length to actual length when the model is smaller.
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