To determine how much of the science project Molly completes per hour, we need to find her rate of completion.
1. Identify the given values:
- Molly completes [tex]\(\frac{3}{10}\)[/tex] of her project.
- This completion occurs over a duration of [tex]\(\frac{4}{5}\)[/tex] hour.
2. Understand the rate concept:
- The rate of completion is the fraction of the project completed per unit of time (in this case, per hour).
3. Express the rate of completion:
- To find the completion rate, we divide the amount of the project completed by the time it takes to complete that amount.
4. Set up the division:
- The fraction of the project completed is [tex]\(\frac{3}{10}\)[/tex].
- The time taken to complete that fraction is [tex]\(\frac{4}{5}\)[/tex] hour.
5. Calculate the rate:
- We need to divide [tex]\(\frac{3}{10}\)[/tex] (completed project) by [tex]\(\frac{4}{5}\)[/tex] (hours).
- In fraction terms: [tex]\(\frac{3}{10} \div \frac{4}{5}\)[/tex].
- To perform this division, we multiply by the reciprocal of the divisor: [tex]\(\frac{3}{10} \times \frac{5}{4}\)[/tex].
6. Simplify the multiplication:
- Multiply the numerators: [tex]\(3 \times 5 = 15\)[/tex].
- Multiply the denominators: [tex]\(10 \times 4 = 40\)[/tex].
- So, [tex]\(\frac{3}{10} \times \frac{5}{4} = \frac{15}{40}\)[/tex].
7. Convert the fraction to simplest form:
- [tex]\(\frac{15}{40}\)[/tex] simplifies to [tex]\(\frac{3}{8}\)[/tex].
8. Convert to decimal (final step):
- The fraction [tex]\(\frac{3}{8}\)[/tex] is equal to 0.375.
Therefore, Molly completes [tex]\(0.375\)[/tex] of the science project per hour.
Thus, the answer is:
Molly completes [tex]\(0.375\)[/tex] of the science project per hour.
