Question

Add 3/11 + 2/7*1 point5/1843/775/7743/18

Answer 1

To solve the expression \( \frac{3}{11} + \frac{2}{7} \cdot 1 \cdot \frac{5}{1843} \cdot \frac{775}{7743} \cdot \frac{1}{18} \), let's break this down step-by-step.

First, compute the multiplication part:

1. Start with \( \frac{2}{7} \cdot 1 = \frac{2}{7} \).
2. Next, multiply by \( \frac{5}{1843} \):
\[
\frac{2}{7} \cdot \frac{5}{1843} = \frac{10}{7 \cdot 1843}
\]
\( 7 \cdot 1843 = 12901 \), so:
\[
\frac{10}{12901}
\]

3. Then, multiply by \( \frac{775}{7743} \):
\[
\frac{10}{12901} \cdot \frac{775}{7743} = \frac{7750}{12901 \cdot 7743}
\]

To compute \( 12901 \cdot 7743 \), we just keep it as is for now:
\[
12901 \cdot 7743
\]

4. Finally, multiply by \( \frac{1}{18} \):
\[
\frac{7750}{12901 \cdot 7743} \cdot \frac{1}{18} = \frac{7750}{18 \cdot 12901 \cdot 7743}
\]

Now we need to add this result to \( \frac{3}{11} \).

To add \( \frac{3}{11} \) and \( \frac{7750}{18 \cdot 12901 \cdot 7743} \), we convert them to a common denominator. The common denominator will be \( 11 \cdot 18 \cdot 12901 \cdot 7743 \).

Calculate \( \frac{3}{11} \) in terms of the common denominator:
\[
\frac{3 \cdot 18 \cdot 12901 \cdot 7743}{11 \cdot 18 \cdot 12901 \cdot 7743}
\]

And for \( \frac{7750}{18 \cdot 12901 \cdot 7743} \):
\[
\frac{7750 \cdot 11}{11 \cdot 18 \cdot 12901 \cdot 7743}
\]

Now we can add these two fractions:
\[
\frac{3 \cdot 18 \cdot 12901 \cdot 7743 + 7750 \cdot 11}{11 \cdot 18 \cdot 12901 \cdot 7743}
\]

After performing the required calculations on the numerator, you can simplify if necessary.

However, the resulting expression can be quite large and cumbersome. If you need a numerical approximation or specific values, you'd typically want to use a calculator or computational tool at this point.

Let’s summarize:

1. Result of \( \frac{2}{7} \cdot \frac{5}{1843} \cdot \frac{775}{7743} \cdot \frac{1}{18} = \frac{7750}{18 \cdot 12901 \cdot 7743} \)
2. Add \( \frac{3}{11} \).

If you provide or require specific simplifications or a decimal approximation, let me know!