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 *blank 1* 1/5 = *blank 2*

Options for blank 1

A ÷
B ●
C -
D +

Options for blank 2

A 20/1
B 1/2
C 2
D 20

Answer 1

To solve this, we follow the steps provided:

Step 1: Write a ratio of scale factors.

- New scale factor: 1:10
- Old scale factor: 1:5

Using fractions,
the ratio of the new scale factor to the old scale factor is: \( \frac{1}{10} : \frac{1}{5} \)

Step 2: Simplify the ratio.

To simplify the ratio \( \frac{1}{10} : \frac{1}{5} \), we divide \( \frac{1}{10} \) by \( \frac{1}{5} \):

\[
\frac{1/10}{1/5} = \frac{1}{10} \times \frac{5}{1} = \frac{5}{10} = \frac{1}{2}
\]

So:

- The operation to perform is multiplication (which means we fill in blank 1 with "●").
- The simplified result is \( \frac{1}{2} \) (which means we fill in blank 2 with "B 1/2").

Final answers:

- Blank 1: B ●
- Blank 2: B 1/2