A carpenter worked 10 weeks on a particular job, 5 1/2 days per week and 7 3/4 hours per day. How many hours did the carpenter work on the job?

To find the total number of hours the carpenter worked on the job, we can break down the problem into steps.

### Step 1: Calculate the number of hours worked per week.
The carpenter worked \(5 \frac{1}{2}\) days per week and \(7 \frac{3}{4}\) hours per day.

First, convert the mixed numbers to improper fractions or decimals for easier multiplication:
- \(5 \frac{1}{2} = 5.5\) days per week
- \(7 \frac{3}{4} = 7.75\) hours per day

Now, multiply the number of days per week by the number of hours per day to get the total hours worked per week:
\[
5.5 \times 7.75 = 42.625 \text{ hours per week}
\]

### Step 2: Calculate the total number of hours worked over 10 weeks.
Multiply the number of hours worked per week by the total number of weeks:
\[
42.625 \times 10 = 426.25 \text{ hours}
\]

So, the carpenter worked **426.25 hours** on the job.

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Would you like any further details on this problem?

Here are some related questions:
1. How do you convert mixed numbers to improper fractions or decimals?
2. How would the total hours change if the carpenter worked an additional half day each week?
3. Can you explain the importance of consistent units when performing such calculations?
4. What are some strategies for quickly estimating work hours in practical scenarios?
5. How would overtime calculations affect the total hours worked in a different scenario?

**Tip:** When dealing with mixed numbers in calculations, converting them to decimals can make multiplication and division more straightforward.

Learn how to calculate the total hours worked by a carpenter over 10 weeks, with detailed steps and solutions. This problem involves multiplying fractions and decimals to determine work hours. Suitable for students in Grades 6-8.

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