To find out how many pounds of nails the construction worker bought in the second week, we first need to calculate the amount he bought in the first week:
First week: \( 40 \frac{1}{10} \) pounds
To convert this mixed number into an improper fraction, we do the following:
- Convert \( 40 \frac{1}{10} \) to an improper fraction: \[ 40 \frac{1}{10} = \frac{40 \times 10 + 1}{10} = \frac{400 + 1}{10} = \frac{401}{10} \]
Next, we know that in the second week, he bought \( 2 \frac{1}{2} \) times as many nails as he did in the first week.
We can express \( 2 \frac{1}{2} \) as an improper fraction: \[ 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \]
Now, we can find the number of nails bought in the second week by multiplying the amount from the first week by \( \frac{5}{2} \):
Second week: \[ \text{Nails bought in second week} = \frac{401}{10} \times \frac{5}{2} \]
Now, we multiply the fractions: \[ = \frac{401 \times 5}{10 \times 2} = \frac{2005}{20} \]
Next, we simplify \( \frac{2005}{20} \): \[ = \frac{2005 \div 5}{20 \div 5} = \frac{401}{4} \]
Finally, to convert \( \frac{401}{4} \) back to a mixed number: \[ 401 \div 4 = 100 \quad \text{(which goes 100 times with a remainder)} \] Remainder: \[ 401 - (100 \times 4) = 401 - 400 = 1 \]
So, \( \frac{401}{4} = 100 \frac{1}{4} \).
Thus, the construction worker bought \( 100 \frac{1}{4} \) pounds of nails in the second week.