Question
The table in the dining room of Heidi's dollhouse is 6 inches long. The table in Heidi's real dining room is 10 feet long.
What is the unit rate that compares the length of the table in the dining room to the length of the table in the dollhouse?
Enter your answer, as a mixed number in simplest form, by filling in the boxes.
$$
ft/in.
What is the unit rate that compares the length of the table in the dining room to the length of the table in the dollhouse?
Enter your answer, as a mixed number in simplest form, by filling in the boxes.
$$
ft/in.
Answers
GPT-4o mini
To find the unit rate comparing the lengths of the two tables, we first need both measurements in the same unit.
The length of the table in the dollhouse is 6 inches, while the length of the real dining room table is 10 feet.
1 foot equals 12 inches, so we can convert the 10 feet to inches:
\[
10 \text{ feet} \times 12 \text{ inches/foot} = 120 \text{ inches}
\]
Now we have:
- Real dining room table: 120 inches
- Dollhouse table: 6 inches
Next, we set up the comparison of the lengths:
\[
\text{Unit rate} = \frac{\text{length of real dining room table}}{\text{length of dollhouse table}} = \frac{120 \text{ inches}}{6 \text{ inches}}
\]
Now we perform the division:
\[
\frac{120}{6} = 20
\]
The unit rate is \( 20 \) inches per inch, but we need to express this rate in the form of feet per inch (ft/in). Since we have 120 inches in the real table, this can also be expressed as:
\[
\frac{120 \text{ inches}}{6 \text{ inches}} = \frac{120 \div 6}{6 \div 6} = \frac{20}{1}
\]
To write it in terms of feet per inch, we need to recognize that in this context, we can think of it as:
\[
\frac{20 \text{ inches}}{1 \text{ inch}} = \frac{20 \div 12}{1 \div 12} = \frac{20/12 \text{ ft}}{1 \text{ inch}} = \frac{5/3 \text{ ft}}{1 \text{ inch}}
\]
So, simplifying \( 20 \) gives us:
\[
\frac{5 \text{ ft}}{3 \text{ in}}.
\]
In mixed number form, this can also be expressed as:
\[
1 \frac{2}{3} \text{ ft/in}.
\]
Thus the final answer is \( \boxed{1} \) \( \frac{2}{3} \) \( \text{ft/in} \).
The length of the table in the dollhouse is 6 inches, while the length of the real dining room table is 10 feet.
1 foot equals 12 inches, so we can convert the 10 feet to inches:
\[
10 \text{ feet} \times 12 \text{ inches/foot} = 120 \text{ inches}
\]
Now we have:
- Real dining room table: 120 inches
- Dollhouse table: 6 inches
Next, we set up the comparison of the lengths:
\[
\text{Unit rate} = \frac{\text{length of real dining room table}}{\text{length of dollhouse table}} = \frac{120 \text{ inches}}{6 \text{ inches}}
\]
Now we perform the division:
\[
\frac{120}{6} = 20
\]
The unit rate is \( 20 \) inches per inch, but we need to express this rate in the form of feet per inch (ft/in). Since we have 120 inches in the real table, this can also be expressed as:
\[
\frac{120 \text{ inches}}{6 \text{ inches}} = \frac{120 \div 6}{6 \div 6} = \frac{20}{1}
\]
To write it in terms of feet per inch, we need to recognize that in this context, we can think of it as:
\[
\frac{20 \text{ inches}}{1 \text{ inch}} = \frac{20 \div 12}{1 \div 12} = \frac{20/12 \text{ ft}}{1 \text{ inch}} = \frac{5/3 \text{ ft}}{1 \text{ inch}}
\]
So, simplifying \( 20 \) gives us:
\[
\frac{5 \text{ ft}}{3 \text{ in}}.
\]
In mixed number form, this can also be expressed as:
\[
1 \frac{2}{3} \text{ ft/in}.
\]
Thus the final answer is \( \boxed{1} \) \( \frac{2}{3} \) \( \text{ft/in} \).