To determine the scale factor that relates the two scale drawings (1:2 and 1:6), we need to analyze how one scale can be converted into another.
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Scale factors:
- The first drawing has a scale of 1:2, meaning every 1 unit in the drawing represents 2 units in reality.
- The second drawing has a scale of 1:6, meaning every 1 unit in the drawing represents 6 units in reality.
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Finding the scale factor between the two drawings:
- We can set up a ratio to find the conversion between the two scale factors: \[ \frac{1/2}{1/6} = \frac{1/2} \times \frac{6/1} = \frac{6}{2} = 3 \]
This indicates that the scale ratio from the 1:2 drawing to the 1:6 drawing is a factor of 3.
- Filling in the blanks:
- Blank 1: Since we are scaling down from 1:2 to 1:6, we can represent this as 1/2 (the first scale).
- Blank 2: To calculate this effect (1/2 divided by 1/6), we use ÷.
- Blank 3: Means we use the second scale factor, which is 1/6.
- Blank 4: This indicates the result of the calculation from the two previous blanks, which is 3.
Thus, the complete statement is:
The new scale factor is 1/2 ÷ 1/6 = 3.
- Finding the length and width of the smaller scale drawing:
- For the original drawing with dimensions 12 inches (top and bottom) and 6 inches (left and right):
- For the smaller scale (1:6), we apply the conversion:
- Top and bottom: \( 12 \text{ inches} \times \frac{1}{3} = 4 \text{ inches} \)
- Left and right: \( 6 \text{ inches} \times \frac{1}{3} = 2 \text{ inches} \)
- For the original drawing with dimensions 12 inches (top and bottom) and 6 inches (left and right):
Thus, the dimensions of the smaller scale drawing would be 4 inches (length) and 2 inches (width).