Proportional Scaling - ISEE Lower Level: Quantitative Reasoning
Card 1 of 24
What is the missing value $x$ in the proportion $\frac{x}{9}=\frac{14}{21}$?
What is the missing value $x$ in the proportion $\frac{x}{9}=\frac{14}{21}$?
Tap to reveal answer
$6$. Cross-multiply in the proportion and solve for the missing variable.
$6$. Cross-multiply in the proportion and solve for the missing variable.
← Didn't Know|Knew It →
What is the scale factor from a model height of $9$ cm to an actual height of $1.8$ m?
What is the scale factor from a model height of $9$ cm to an actual height of $1.8$ m?
Tap to reveal answer
Scale factor $=\frac{180}{9}=20$. Convert units and divide actual height by model height for the scale factor.
Scale factor $=\frac{180}{9}=20$. Convert units and divide actual height by model height for the scale factor.
← Didn't Know|Knew It →
What is the new circumference if a circle with circumference $14\pi$ is scaled by factor $\frac{3}{2}$?
What is the new circumference if a circle with circumference $14\pi$ is scaled by factor $\frac{3}{2}$?
Tap to reveal answer
$21\pi$. Circumferences scale linearly, so multiply original by the scale factor.
$21\pi$. Circumferences scale linearly, so multiply original by the scale factor.
← Didn't Know|Knew It →
What is the scale factor from $9$ inches to $6$ inches?
What is the scale factor from $9$ inches to $6$ inches?
Tap to reveal answer
Scale factor $=\frac{6}{9}=\frac{2}{3}$. The scale factor is the ratio of the new measurement to the original, simplified for a reduction.
Scale factor $=\frac{6}{9}=\frac{2}{3}$. The scale factor is the ratio of the new measurement to the original, simplified for a reduction.
← Didn't Know|Knew It →
What is the original length if the new length is $24$ and the scale factor is $3$?
What is the original length if the new length is $24$ and the scale factor is $3$?
Tap to reveal answer
$8$. Divide the new length by the scale factor to find the corresponding original length.
$8$. Divide the new length by the scale factor to find the corresponding original length.
← Didn't Know|Knew It →
What is the new length if a $12$ cm segment is scaled by a factor of $\frac{3}{2}$?
What is the new length if a $12$ cm segment is scaled by a factor of $\frac{3}{2}$?
Tap to reveal answer
$18$ cm. Multiply the original length by the given scale factor to determine the corresponding new length.
$18$ cm. Multiply the original length by the given scale factor to determine the corresponding new length.
← Didn't Know|Knew It →
What is the scale factor from an original length of $6$ to a new length of $15$?
What is the scale factor from an original length of $6$ to a new length of $15$?
Tap to reveal answer
Scale factor $=\frac{15}{6}=\frac{5}{2}$. The scale factor is calculated as the ratio of the new length to the original length, simplified to lowest terms.
Scale factor $=\frac{15}{6}=\frac{5}{2}$. The scale factor is calculated as the ratio of the new length to the original length, simplified to lowest terms.
← Didn't Know|Knew It →
What is the new area if a figure with area $16$ is scaled by linear factor $\frac{1}{2}$?
What is the new area if a figure with area $16$ is scaled by linear factor $\frac{1}{2}$?
Tap to reveal answer
$4$. Areas scale by the square of the linear factor, reducing the original area accordingly.
$4$. Areas scale by the square of the linear factor, reducing the original area accordingly.
← Didn't Know|Knew It →
What real distance corresponds to $3.5$ in on a map with scale $1$ in : $8$ mi?
What real distance corresponds to $3.5$ in on a map with scale $1$ in : $8$ mi?
Tap to reveal answer
$28$ miles. Multiply the map distance by the scale ratio to find the actual distance.
$28$ miles. Multiply the map distance by the scale ratio to find the actual distance.
← Didn't Know|Knew It →
What is the new area if a circle with area $36\pi$ is scaled by linear factor $\frac{1}{3}$?
What is the new area if a circle with area $36\pi$ is scaled by linear factor $\frac{1}{3}$?
Tap to reveal answer
$4\pi$. Circle areas scale by the square of the linear factor, reducing accordingly.
$4\pi$. Circle areas scale by the square of the linear factor, reducing accordingly.
← Didn't Know|Knew It →
What is the missing value $x$ in the proportion $\frac{4}{7}=\frac{x}{21}$?
What is the missing value $x$ in the proportion $\frac{4}{7}=\frac{x}{21}$?
Tap to reveal answer
$12$. Solve the proportion by cross-multiplying and dividing to find the missing value.
$12$. Solve the proportion by cross-multiplying and dividing to find the missing value.
← Didn't Know|Knew It →
What is the new perimeter if a figure with perimeter $30$ is scaled by factor $\frac{4}{3}$?
What is the new perimeter if a figure with perimeter $30$ is scaled by factor $\frac{4}{3}$?
Tap to reveal answer
$40$. Perimeters scale linearly, so multiply the original perimeter by the linear scale factor.
$40$. Perimeters scale linearly, so multiply the original perimeter by the linear scale factor.
← Didn't Know|Knew It →
What is the time needed to travel $150$ miles if you travel $100$ miles in $2$ hours?
What is the time needed to travel $150$ miles if you travel $100$ miles in $2$ hours?
Tap to reveal answer
$3$ hours. Use constant speed to find time by dividing new distance by speed.
$3$ hours. Use constant speed to find time by dividing new distance by speed.
← Didn't Know|Knew It →
What is the distance for $5$ hours if you travel $180$ miles in $3$ hours at constant speed?
What is the distance for $5$ hours if you travel $180$ miles in $3$ hours at constant speed?
Tap to reveal answer
$300$ miles. Determine constant speed and multiply by the new time to find the distance.
$300$ miles. Determine constant speed and multiply by the new time to find the distance.
← Didn't Know|Knew It →
What is the cost for $9$ pounds if $6$ pounds cost $\$15$ and cost is proportional to weight?
What is the cost for $9$ pounds if $6$ pounds cost $\$15$ and cost is proportional to weight?
Tap to reveal answer
$\$22.50$. Use the proportional relationship by multiplying the unit cost by the new weight.
$\$22.50$. Use the proportional relationship by multiplying the unit cost by the new weight.
← Didn't Know|Knew It →
What map distance corresponds to $30$ mi on a map with scale $1$ in : $6$ mi?
What map distance corresponds to $30$ mi on a map with scale $1$ in : $6$ mi?
Tap to reveal answer
$5$ in. Divide the actual distance by the scale ratio to find the map distance.
$5$ in. Divide the actual distance by the scale ratio to find the map distance.
← Didn't Know|Knew It →
What is the scale factor from a $1$ in map distance to a $5$ mi real distance?
What is the scale factor from a $1$ in map distance to a $5$ mi real distance?
Tap to reveal answer
Scale $=1$ in : $5$ mi. The scale expresses the ratio of map distance to actual distance.
Scale $=1$ in : $5$ mi. The scale expresses the ratio of map distance to actual distance.
← Didn't Know|Knew It →
What is the linear scale factor if volume changes from $8$ to $64$ for similar solids?
What is the linear scale factor if volume changes from $8$ to $64$ for similar solids?
Tap to reveal answer
Linear factor $=\sqrt[3]{\frac{64}{8}}=2$. The linear scale factor is the cube root of the ratio of new volume to original volume.
Linear factor $=\sqrt[3]{\frac{64}{8}}=2$. The linear scale factor is the cube root of the ratio of new volume to original volume.
← Didn't Know|Knew It →
What is the linear scale factor if area changes from $18$ to $72$ for similar figures?
What is the linear scale factor if area changes from $18$ to $72$ for similar figures?
Tap to reveal answer
Linear factor $=\sqrt{\frac{72}{18}}=2$. The linear scale factor is the square root of the ratio of new area to original area.
Linear factor $=\sqrt{\frac{72}{18}}=2$. The linear scale factor is the square root of the ratio of new area to original area.
← Didn't Know|Knew It →
What is the new volume if the original volume is $27$ and the linear scale factor is $\frac{1}{3}$?
What is the new volume if the original volume is $27$ and the linear scale factor is $\frac{1}{3}$?
Tap to reveal answer
$1$. Volumes scale by the cube of the linear factor, reducing the original volume accordingly.
$1$. Volumes scale by the cube of the linear factor, reducing the original volume accordingly.
← Didn't Know|Knew It →
What is the new area if the original area is $50$ and the linear scale factor is $3$?
What is the new area if the original area is $50$ and the linear scale factor is $3$?
Tap to reveal answer
$450$. Multiply the original area by the square of the linear scale factor to find the new area.
$450$. Multiply the original area by the square of the linear scale factor to find the new area.
← Didn't Know|Knew It →
What is the volume scale factor when the linear scale factor is $\frac{2}{3}$?
What is the volume scale factor when the linear scale factor is $\frac{2}{3}$?
Tap to reveal answer
Volume factor $=\left(\frac{2}{3}\right)^3=\frac{8}{27}$. The volume scale factor is the cube of the linear scale factor for similar solids.
Volume factor $=\left(\frac{2}{3}\right)^3=\frac{8}{27}$. The volume scale factor is the cube of the linear scale factor for similar solids.
← Didn't Know|Knew It →
What is the area scale factor when the linear scale factor is $5$?
What is the area scale factor when the linear scale factor is $5$?
Tap to reveal answer
Area factor $=5^2=25$. The area scale factor is the square of the linear scale factor for similar figures.
Area factor $=5^2=25$. The area scale factor is the square of the linear scale factor for similar figures.
← Didn't Know|Knew It →
What is the new width if a $10$ by $6$ rectangle is scaled so the length becomes $25$?
What is the new width if a $10$ by $6$ rectangle is scaled so the length becomes $25$?
Tap to reveal answer
New width $=15$. Determine the scale factor from lengths and apply it to the width for similarity.
New width $=15$. Determine the scale factor from lengths and apply it to the width for similarity.
← Didn't Know|Knew It →