Question

Dan works on a construction team. He has completed 2/5 of his share of the day's work. If Dan's share of work is 3/7of his team's total work that day, what portion of the total amount of work has Dan completed?

Answer 1

To find out what portion of the total amount of work Dan has completed, we can follow these steps:

1. **Determine Dan's share of the total work**:
Dan's share of the work is given as \( \frac{3}{7} \) of the team's total work.

2. **Calculate the fraction of the total work Dan has completed**:
Dan has completed \( \frac{2}{5} \) of his share of work. Therefore, the portion of the total work he completed can be calculated by multiplying his share by the fraction he has completed:

\[
\text{Portion of total work completed by Dan} = \frac{2}{5} \times \frac{3}{7}
\]

3. **Perform the multiplication**:
To multiply these fractions, multiply the numerators and then the denominators:

\[
= \frac{2 \times 3}{5 \times 7} = \frac{6}{35}
\]

Thus, the portion of the total amount of work that Dan has completed is \( \frac{6}{35} \).

So, the final answer is:

\[
\boxed{\frac{6}{35}}
\]