Asked by nobody
The dimensions of a blackboard are 9/10 of a meter by 7/10 of a meter. In a drawing of the blackboard shown, 1/2
of an inch represents 2 meters.What is the unit rate of area in square meters of the blackboard per square inch of area in the drawing?
of an inch represents 2 meters.What is the unit rate of area in square meters of the blackboard per square inch of area in the drawing?
Answers
Answered by
GPT-4o mini
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:
1. **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:
\[
A = \text{Length} \times \text{Width} = \frac{9}{10} \times \frac{7}{10} = \frac{63}{100} \text{ square meters}
\]
2. **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:
\[
\frac{7/10 \text{ meters}}{4 \text{ meters/inch}} = \frac{7}{40} \text{ inches}
\]
3. **Calculate the area of the blackboard in square inches in the drawing:**
The area in square inches is:
\[
A_{\text{inches}} = \left( \frac{9}{40} \times \frac{7}{40} \right) \text{ square inches} = \frac{63}{1600} \text{ square inches}
\]
4. **Compute the unit rate of area in square meters of the blackboard per square inch of area in the drawing:**
We want to find:
\[
\text{unit rate} = \frac{\text{area of blackboard in square meters}}{\text{area of drawing in square inches}} = \frac{\frac{63}{100} \text{ square meters}}{\frac{63}{1600} \text{ square inches}}
\]
5. **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 \(\boxed{16}\).
1. **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:
\[
A = \text{Length} \times \text{Width} = \frac{9}{10} \times \frac{7}{10} = \frac{63}{100} \text{ square meters}
\]
2. **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:
\[
\frac{7/10 \text{ meters}}{4 \text{ meters/inch}} = \frac{7}{40} \text{ inches}
\]
3. **Calculate the area of the blackboard in square inches in the drawing:**
The area in square inches is:
\[
A_{\text{inches}} = \left( \frac{9}{40} \times \frac{7}{40} \right) \text{ square inches} = \frac{63}{1600} \text{ square inches}
\]
4. **Compute the unit rate of area in square meters of the blackboard per square inch of area in the drawing:**
We want to find:
\[
\text{unit rate} = \frac{\text{area of blackboard in square meters}}{\text{area of drawing in square inches}} = \frac{\frac{63}{100} \text{ square meters}}{\frac{63}{1600} \text{ square inches}}
\]
5. **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 \(\boxed{16}\).