Question

Jeremy worked for 8+1/2
hours building model airplanes. If each airplane takes him 1+2/5
hours to make, how many models did he build? (1 point)
Responses

6+1/14
models
6 Start Fraction 1 over 14 End Fraction models

11+9/10
models
11 Start Fraction 9 over 10 End Fraction models

14/85
of a model
Start Fraction 14 over 85 End Fraction of a model

10/119
of a model

Answer 1

First, let's convert the mixed numbers to improper fractions to make the calculations easier.

1. **Convert the total hours worked:**
- \( 8 + \frac{1}{2} = \frac{16}{2} + \frac{1}{2} = \frac{17}{2} \) hours.

2. **Convert the time taken to build one airplane:**
- \( 1 + \frac{2}{5} = \frac{5}{5} + \frac{2}{5} = \frac{7}{5} \) hours.

3. **Now, we need to find out how many model airplanes Jeremy built. To do this, we'll divide the total hours worked by the hours taken to make one airplane:**
\[
\text{Number of models} = \frac{\text{Total hours worked}}{\text{Hours per model}} = \frac{\frac{17}{2}}{\frac{7}{5}}.
\]

4. **To divide fractions, multiply by the reciprocal:**
\[
\frac{17}{2} \times \frac{5}{7} = \frac{17 \times 5}{2 \times 7} = \frac{85}{14}.
\]

5. **Calculating \(\frac{85}{14}\) gives us:**
- Dividing \( 85 \) by \( 14 \) gives us \( 6 \) with a remainder:
- \( 85 \div 14 = 6\) with a remainder of \( 1 \):
- So, \( \frac{85}{14} = 6 + \frac{1}{14} \).

Therefore, Jeremy built \( 6 + \frac{1}{14} \) models.

The correct response is:

**6 + 1/14 models**