Question

Maya created several possible ways to rearrange her hamster's cage to give the hamster more room to run around. Her drawings were made with a scale factor of 1:2, but she wants to change the scale factor to 1:6 so she can compare them more easily.

The diagram shows the lengths of the sides of her first scale drawing and the scale factors relating both drawings to the actual cage.

Identify the scale factor that relates the two scale drawings to each other. Then, find the length and width of the smaller scale drawing.

Scale Factor of 1:2 is
12 In top and bottom
6 left and right

Scale factor 1:6 unknown

The new scale factor is *blank 1* *blank 2* *blank 3* = *blank 4*

Options for blank 1 and 3

A 1/2
B 6/1
C 1/6
D 2/1

Options for blank 2

A ÷
B +
C-
D ●

Options for blank 4
A 3
B 3/1
C 1/3

Make sure no one can find this

Answer 1

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.

1. **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.

2. **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.

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**.

4. **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: \( 6 \text{ inches} \times \frac{1}{3} = 2 \text{ inches} \)

Thus, the dimensions of the smaller scale drawing would be **4 inches (length)** and **2 inches (width)**.