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

11910
models
11 Start Fraction 9 over 10 End Fraction models

1485
of a model
Start Fraction 14 over 85 End Fraction of a model

6114
models
6 Start Fraction 1 over 14 End Fraction models

10119
of a model

Answer 1

To find out how many model airplanes Jeremy built during his time of 8 1/2 hours, we first need to convert the mixed numbers to improper fractions and then perform the division.

1. **Convert 8 1/2 hours to an improper fraction**:
\( 8 \frac{1}{2} = \frac{17}{2} \) (since \( 8 \times 2 + 1 = 17 \))

2. **Convert 1 2/5 hours to an improper fraction**:
\( 1 \frac{2}{5} = \frac{7}{5} \) (since \( 1 \times 5 + 2 = 7 \))

3. **Now, divide the total hours by the hours per airplane**:
\[
\text{Number of airplanes} = \frac{\text{Total hours}}{\text{Hours per airplane}} = \frac{\frac{17}{2}}{\frac{7}{5}}
\]

To divide fractions, multiply by the reciprocal of the second fraction:

\[
\frac{17}{2} \times \frac{5}{7} = \frac{17 \times 5}{2 \times 7} = \frac{85}{14}
\]

4. **Now simplify \(\frac{85}{14}\)**:
- When divided, \(85\) divided by \(14\) gives \(6\) with a remainder (since \(14 \times 6 = 84\)).
- Thus, \(85\) can be expressed as \(14 \times 6 + 1\), or:
\[
\frac{85}{14} = 6 \frac{1}{14}
\]

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