Question
Alaina was creating a 1:5 scale drawing of a rectangular-shaped room in her apartment. After she calculated that the dimensions of the scale drawing would be 10 inches long by 12 inches wide, she realized her drawing would be too big to fit on the paper she was using. Alaina decided to change the scale factor to 1:10
Complete each step to show how to use one scale drawing to create another scale drawing with a different scale factor.
Step 1: Write a ratio of scale factors.
Write a ratio of the new scale factor to the old scale factor.
The new scale factor is 1:10, and the old scale factor is 1:5.
Using fractions,
the ratio of the new scale factor to the old scale factor is: 1/10 : 1/5
Step 2: Simplify the ratio. 1/10/1/5 = 1/10 ● 1/5 = 1/2
The scale factor of the new drawing to the old scale drawing is 1:2
Step 3: multiply to find the new lengths.
Multiply the side lengths of the old scale drawing (that were 10 inches long by 12 inches) by the new scale factor to find the side lengths of the new scale drawing.
10 ● *blank 1* = *blank 2*
12 ● *blank 3* = *blank 4*
The new scale drawing of Alaina's room will be *blank 5* inches long by *blank 6* inches wide
Complete each step to show how to use one scale drawing to create another scale drawing with a different scale factor.
Step 1: Write a ratio of scale factors.
Write a ratio of the new scale factor to the old scale factor.
The new scale factor is 1:10, and the old scale factor is 1:5.
Using fractions,
the ratio of the new scale factor to the old scale factor is: 1/10 : 1/5
Step 2: Simplify the ratio. 1/10/1/5 = 1/10 ● 1/5 = 1/2
The scale factor of the new drawing to the old scale drawing is 1:2
Step 3: multiply to find the new lengths.
Multiply the side lengths of the old scale drawing (that were 10 inches long by 12 inches) by the new scale factor to find the side lengths of the new scale drawing.
10 ● *blank 1* = *blank 2*
12 ● *blank 3* = *blank 4*
The new scale drawing of Alaina's room will be *blank 5* inches long by *blank 6* inches wide
Answers
GPT-4o mini
Let's fill in the blanks step by step using the new scale factor of 1:10 and the old dimensions of the scale drawing (10 inches and 12 inches).
Step 3: multiply to find the new lengths.
1. For the length of the drawing:
\[
10 \text{ inches} \times \frac{1}{2} = \text{blank 2}
\]
Therefore:
\[
10 \times \frac{1}{2} = 5 \text{ inches} \quad \text{(blank 2)}
\]
2. For the width of the drawing:
\[
12 \text{ inches} \times \frac{1}{2} = \text{blank 4}
\]
Therefore:
\[
12 \times \frac{1}{2} = 6 \text{ inches} \quad \text{(blank 4)}
\]
So we complete the Step 3 calculation:
- For *blank 1*, we used \(\frac{1}{2}\) since that is the scale factor we calculated.
- For *blank 3*, we used \(\frac{1}{2}\) for the same reason (matching the scale factor).
- The new scale drawing of Alaina's room will thus be *blank 5* = 5 inches long and *blank 6* = 6 inches wide.
Final answers for the blanks:
- *blank 1* = \(\frac{1}{2}\)
- *blank 2* = 5
- *blank 3* = \(\frac{1}{2}\)
- *blank 4* = 6
- *blank 5* = 5
- *blank 6* = 6
So the new scale drawing of Alaina's room will be **5 inches long by 6 inches wide**.
Step 3: multiply to find the new lengths.
1. For the length of the drawing:
\[
10 \text{ inches} \times \frac{1}{2} = \text{blank 2}
\]
Therefore:
\[
10 \times \frac{1}{2} = 5 \text{ inches} \quad \text{(blank 2)}
\]
2. For the width of the drawing:
\[
12 \text{ inches} \times \frac{1}{2} = \text{blank 4}
\]
Therefore:
\[
12 \times \frac{1}{2} = 6 \text{ inches} \quad \text{(blank 4)}
\]
So we complete the Step 3 calculation:
- For *blank 1*, we used \(\frac{1}{2}\) since that is the scale factor we calculated.
- For *blank 3*, we used \(\frac{1}{2}\) for the same reason (matching the scale factor).
- The new scale drawing of Alaina's room will thus be *blank 5* = 5 inches long and *blank 6* = 6 inches wide.
Final answers for the blanks:
- *blank 1* = \(\frac{1}{2}\)
- *blank 2* = 5
- *blank 3* = \(\frac{1}{2}\)
- *blank 4* = 6
- *blank 5* = 5
- *blank 6* = 6
So the new scale drawing of Alaina's room will be **5 inches long by 6 inches wide**.