To find the unit rate of area in square meters of the blackboard per square inch of area in the drawing, we need to follow a few steps:
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Calculate the area of the blackboard in square meters:
The dimensions of the blackboard are: \[ \text{Length} = \frac{9}{10} \text{ meters} \quad \text{and} \quad \text{Width} = \frac{7}{10} \text{ meters} \]
The area \( A \) is given by: \[ A = \text{Length} \times \text{Width} = \frac{9}{10} \times \frac{7}{10} = \frac{63}{100} \text{ square meters} \]
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Convert the area of the blackboard into square inches in the drawing:
According to the problem, \( \frac{1}{2} \) inch in the drawing represents \( 2 \) meters. Therefore: \[ 1 \text{ inch} = 2 \times 2 = 4 \text{ meters} \]
To find how many inches represent the dimensions of the blackboard:
- For the length \( \frac{9}{10} \) meters: \[ \frac{9/10 \text{ meters}}{4 \text{ meters/inch}} = \frac{9}{40} \text{ inches} \]
- For the width \( \frac{7}{10} \) meters: \[ \frac{7/10 \text{ meters}}{4 \text{ meters/inch}} = \frac{7}{40} \text{ inches} \]
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Calculate the area of the blackboard in square inches in the drawing:
The area in square inches is: \[ A_{\text{inches}} = \left( \frac{9}{40} \times \frac{7}{40} \right) \text{ square inches} = \frac{63}{1600} \text{ square inches} \]
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Compute the unit rate of area in square meters of the blackboard per square inch of area in the drawing:
We want to find: \[ \text{unit rate} = \frac{\text{area of blackboard in square meters}}{\text{area of drawing in square inches}} = \frac{\frac{63}{100} \text{ square meters}}{\frac{63}{1600} \text{ square inches}} \]
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Simplify the unit rate:
\[ \text{unit rate} = \frac{63}{100} \times \frac{1600}{63} = \frac{1600}{100} = 16 \text{ square meters per square inch} \]
Thus, the unit rate of area in square meters of the blackboard per square inch of area in the drawing is \(\boxed{16}\).