Solve Scale Drawing Problems - 7th Grade Math
Card 1 of 25
Identify the missing value: scale $3\text{ in}:12\text{ ft}$, actual $20\text{ ft}$ corresponds to what drawing length?
Identify the missing value: scale $3\text{ in}:12\text{ ft}$, actual $20\text{ ft}$ corresponds to what drawing length?
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$5\text{ in}$. Set up proportion: $\frac{3}{12} = \frac{x}{20}$, solve for $x = 5$.
$5\text{ in}$. Set up proportion: $\frac{3}{12} = \frac{x}{20}$, solve for $x = 5$.
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What is the drawing length for $90\text{ ft}$ actual if the scale is $1\text{ in}:15\text{ ft}$?
What is the drawing length for $90\text{ ft}$ actual if the scale is $1\text{ in}:15\text{ ft}$?
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$6\text{ in}$. Divide: $90\text{ ft} \div 15\text{ ft/in} = 6\text{ in}$.
$6\text{ in}$. Divide: $90\text{ ft} \div 15\text{ ft/in} = 6\text{ in}$.
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What is the scale factor from drawing to actual for the scale $1:50$?
What is the scale factor from drawing to actual for the scale $1:50$?
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$50$. Scale factor equals the second number in the ratio.
$50$. Scale factor equals the second number in the ratio.
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What is the actual area if the drawing area is $12\text{ in}^2$ and the scale is $1\text{ in}:3\text{ ft}$?
What is the actual area if the drawing area is $12\text{ in}^2$ and the scale is $1\text{ in}:3\text{ ft}$?
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$108\text{ ft}^2$. Convert units: $3^2 = 9\text{ ft}^2/\text{in}^2$, so $12 \times 9 = 108$.
$108\text{ ft}^2$. Convert units: $3^2 = 9\text{ ft}^2/\text{in}^2$, so $12 \times 9 = 108$.
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What is the actual area if the drawing area is $8\text{ cm}^2$ and the scale is $1\text{ cm}:5\text{ cm}$?
What is the actual area if the drawing area is $8\text{ cm}^2$ and the scale is $1\text{ cm}:5\text{ cm}$?
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$200\text{ cm}^2$. Area scale factor is $5^2 = 25$, so $8 \times 25 = 200$.
$200\text{ cm}^2$. Area scale factor is $5^2 = 25$, so $8 \times 25 = 200$.
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What does the scale $1\text{ cm}:5\text{ m}$ mean about drawing length and actual length?
What does the scale $1\text{ cm}:5\text{ m}$ mean about drawing length and actual length?
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$1\text{ cm}$ on the drawing represents $5\text{ m}$ in real life. Scale shows ratio between drawing and real measurements.
$1\text{ cm}$ on the drawing represents $5\text{ m}$ in real life. Scale shows ratio between drawing and real measurements.
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What is the scale factor from actual to drawing for the scale $1:50$ (drawing:actual)?
What is the scale factor from actual to drawing for the scale $1:50$ (drawing:actual)?
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$\frac{1}{50}$. Reciprocal of scale factor converts from actual to drawing.
$\frac{1}{50}$. Reciprocal of scale factor converts from actual to drawing.
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What formula finds actual length from drawing length using scale factor $k$ (drawing to actual)?
What formula finds actual length from drawing length using scale factor $k$ (drawing to actual)?
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$\text{actual} = k\times \text{drawing}$. Multiply drawing length by scale factor to get actual.
$\text{actual} = k\times \text{drawing}$. Multiply drawing length by scale factor to get actual.
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What is the actual length for $7\text{ in}$ on a map with scale $1\text{ in}:12\text{ mi}$?
What is the actual length for $7\text{ in}$ on a map with scale $1\text{ in}:12\text{ mi}$?
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$84\text{ mi}$. Multiply: $7\text{ in} \times 12\text{ mi/in} = 84\text{ mi}$.
$84\text{ mi}$. Multiply: $7\text{ in} \times 12\text{ mi/in} = 84\text{ mi}$.
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What is the drawing length if the actual length is $18\text{ m}$ and the scale is $1\text{ cm}:3\text{ m}$?
What is the drawing length if the actual length is $18\text{ m}$ and the scale is $1\text{ cm}:3\text{ m}$?
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$6\text{ cm}$. Divide: $18\text{ m} \div 3\text{ m/cm} = 6\text{ cm}$.
$6\text{ cm}$. Divide: $18\text{ m} \div 3\text{ m/cm} = 6\text{ cm}$.
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What is the actual length if a segment is $6\text{ cm}$ on a drawing with scale $1\text{ cm}:4\text{ m}$?
What is the actual length if a segment is $6\text{ cm}$ on a drawing with scale $1\text{ cm}:4\text{ m}$?
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$24\text{ m}$. Multiply: $6\text{ cm} \times 4\text{ m/cm} = 24\text{ m}$.
$24\text{ m}$. Multiply: $6\text{ cm} \times 4\text{ m/cm} = 24\text{ m}$.
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Identify the correct area scale factor if the length scale factor is $k$ (drawing to actual).
Identify the correct area scale factor if the length scale factor is $k$ (drawing to actual).
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$k^2$. Area scales by the square of the length scale factor.
$k^2$. Area scales by the square of the length scale factor.
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What formula finds drawing length from actual length using scale factor $k$ (drawing to actual)?
What formula finds drawing length from actual length using scale factor $k$ (drawing to actual)?
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$\text{drawing} = \frac{\text{actual}}{k}$. Divide actual by scale factor to get drawing length.
$\text{drawing} = \frac{\text{actual}}{k}$. Divide actual by scale factor to get drawing length.
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What is the actual perimeter if a rectangle has drawing sides $4\text{ cm}$ and $7\text{ cm}$ with scale $1\text{ cm}:2\text{ m}$?
What is the actual perimeter if a rectangle has drawing sides $4\text{ cm}$ and $7\text{ cm}$ with scale $1\text{ cm}:2\text{ m}$?
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$44\text{ m}$. Drawing perimeter is $2(4+7) = 22\text{ cm}$, multiply by scale factor $2$.
$44\text{ m}$. Drawing perimeter is $2(4+7) = 22\text{ cm}$, multiply by scale factor $2$.
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Identify the missing value: scale $2\text{ cm}:5\text{ km}$, drawing $6\text{ cm}$ corresponds to what actual distance?
Identify the missing value: scale $2\text{ cm}:5\text{ km}$, drawing $6\text{ cm}$ corresponds to what actual distance?
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$15\text{ km}$. Set up proportion: $\frac{2}{5} = \frac{6}{x}$, solve for $x = 15$.
$15\text{ km}$. Set up proportion: $\frac{2}{5} = \frac{6}{x}$, solve for $x = 15$.
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Which proportion correctly matches drawing $d$ and actual $a$ for scale $1\text{ cm}:4\text{ m}$?
Which proportion correctly matches drawing $d$ and actual $a$ for scale $1\text{ cm}:4\text{ m}$?
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$\frac{d}{a}=\frac{1\text{ cm}}{4\text{ m}}$. Proportion sets up ratio of drawing to actual lengths.
$\frac{d}{a}=\frac{1\text{ cm}}{4\text{ m}}$. Proportion sets up ratio of drawing to actual lengths.
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What is the new area if a figure is reproduced with length scale factor $2$ and the original area is $9\text{ cm}^2$?
What is the new area if a figure is reproduced with length scale factor $2$ and the original area is $9\text{ cm}^2$?
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$36\text{ cm}^2$. Area scales by $2^2 = 4$, so $9 \times 4 = 36$.
$36\text{ cm}^2$. Area scales by $2^2 = 4$, so $9 \times 4 = 36$.
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What is the new drawing length if a $12\text{ cm}$ segment is reproduced at a scale factor of $\frac{1}{3}$?
What is the new drawing length if a $12\text{ cm}$ segment is reproduced at a scale factor of $\frac{1}{3}$?
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$4\text{ cm}$. Multiply original length by new scale factor: $12 \times \frac{1}{3} = 4$.
$4\text{ cm}$. Multiply original length by new scale factor: $12 \times \frac{1}{3} = 4$.
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What is the new drawing length if a $5\text{ cm}$ segment is reproduced at a scale factor of $\frac{3}{2}$?
What is the new drawing length if a $5\text{ cm}$ segment is reproduced at a scale factor of $\frac{3}{2}$?
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$7.5\text{ cm}$. Multiply original length by new scale factor: $5 \times \frac{3}{2} = 7.5$.
$7.5\text{ cm}$. Multiply original length by new scale factor: $5 \times \frac{3}{2} = 7.5$.
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What is the drawing area if the actual area is $400\text{ m}^2$ and the scale is $1:10$ (drawing:actual)?
What is the drawing area if the actual area is $400\text{ m}^2$ and the scale is $1:10$ (drawing:actual)?
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$4\text{ m}^2$. Area scale factor is $10^2 = 100$, so $400 \div 100 = 4$.
$4\text{ m}^2$. Area scale factor is $10^2 = 100$, so $400 \div 100 = 4$.
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Which ratio represents the same scale as $2\text{ cm}:6\text{ m}$, written as $1\text{ cm}:\text{? m}$?
Which ratio represents the same scale as $2\text{ cm}:6\text{ m}$, written as $1\text{ cm}:\text{? m}$?
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$1\text{ cm}:3\text{ m}$. Simplify ratio by dividing both parts by $2$.
$1\text{ cm}:3\text{ m}$. Simplify ratio by dividing both parts by $2$.
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A figure is enlarged by length factor $k=4$. If the original area is $7\text{ cm}^2$, what is the new area?
A figure is enlarged by length factor $k=4$. If the original area is $7\text{ cm}^2$, what is the new area?
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$112\text{ cm}^2$. Area scales by $k^2$: $7 \times 4^2 = 7 \times 16 = 112$.
$112\text{ cm}^2$. Area scales by $k^2$: $7 \times 4^2 = 7 \times 16 = 112$.
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A drawing is reduced by scale factor $k=\frac{1}{2}$. If a segment is $10\text{ cm}$, what is the new length?
A drawing is reduced by scale factor $k=\frac{1}{2}$. If a segment is $10\text{ cm}$, what is the new length?
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$5\text{ cm}$. Multiply original length by scale factor: $10 \times \frac{1}{2} = 5$.
$5\text{ cm}$. Multiply original length by scale factor: $10 \times \frac{1}{2} = 5$.
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What does the scale $1\text{ cm}:4\text{ m}$ mean about drawing length and actual length?
What does the scale $1\text{ cm}:4\text{ m}$ mean about drawing length and actual length?
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$1\text{ cm}$ on the drawing represents $4\text{ m}$ in real life. The scale shows the ratio between drawing and actual measurements.
$1\text{ cm}$ on the drawing represents $4\text{ m}$ in real life. The scale shows the ratio between drawing and actual measurements.
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State the scale factor $k$ from drawing to actual for the scale $1:50$.
State the scale factor $k$ from drawing to actual for the scale $1:50$.
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$k=50$. Scale factor equals the denominator when scale is $1:n$.
$k=50$. Scale factor equals the denominator when scale is $1:n$.
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