Janie designed a miniature couch for a dollhouse based on her own couch. Janie's couch is 7 1/2feet long. The scale of the dollhouse is 1 inch : 2 feet. What is the length of the miniature couch for the dollhouse?

Answer 1

To find the length of the miniature couch for the dollhouse, we first need to convert Janie's couch length from feet to inches, and then apply the scale.

Janie's couch is 7 1/2 feet long. We'll convert this to inches:

7 1/2 feet = 7.5 feet

Now, converting feet to inches (since there are 12 inches in a foot):

\[ 7.5 \text{ feet} \times 12 \text{ inches/foot} = 90 \text{ inches} \]

Next, we apply the scale of 1 inch : 2 feet. This means that each 1 inch in the model represents 2 feet in real life. To find the length of the miniature couch, we can divide the total length in inches by the number of feet represented by each inch in the scale.

\[ \text{Length of miniature couch} = \frac{90 \text{ inches}}{2 \text{ feet/inch}} = 45 \text{ inches} \]

Therefore, the length of the miniature couch for the dollhouse is 45 inches.

Answer 2

as a fraction

Answer 3

To express the length of the miniature couch as a fraction, we start with the conversion we already performed. We found that Janie's couch is \(90\) inches long based on its length in feet.

Using the scale \(1\) inch : \(2\) feet, we determined the miniature couch length in inches is:

\[ \text{Length of miniature couch} = \frac{90 \text{ inches}}{2} = 45 \text{ inches} \]

To express \(45\) as a fraction:

\[ 45 = \frac{45}{1} \]

Thus, the length of the miniature couch can be expressed as the fraction:

\[ \frac{45}{1} \]

If you prefer a proper fraction, in a simplified form, there’s another method to represent it. The fraction \(45\) can also relate to the total in terms of inches to how it represents the hop between the real size and model size.

The length of the miniature couch as a fraction of its real size can be represented as follows:

Starting again from \(90\) inches:

\[ \frac{90 \text{ inches}}{2} = 45 \text{ inches} \]

This represents the scale directly, but for clarity on making it an original whole foot measurement we could say:

\[ \frac{90}{2} = \frac{90 \div 2}{1} = \frac{45}{1} = 45 \text{ inches} \]

The fraction remains simply \(45 \text{ inches} = \frac{45}{1}\).

Therefore, the length of the miniature couch expressed as a fraction is \(\frac{45}{1}\) or just 45 when expressed in simplest form.