5/6 х 6/11 / 1 1/11

To solve the expression \( \frac{5}{6} \times \frac{6}{11} \div 1\frac{1}{11} \), we need to follow a couple of steps.

First, convert the mixed number \( 1\frac{1}{11} \) to an improper fraction:

\[ 1\frac{1}{11} = 1 + \frac{1}{11} = \frac{11}{11} + \frac{1}{11} = \frac{12}{11} \]

Now, we can rewrite the expression:

\[ \frac{5}{6} \times \frac{6}{11} \div \frac{12}{11} \]

When dividing by a fraction, you multiply by its reciprocal. So, we have:

\[ \frac{5}{6} \times \frac{6}{11} \times \frac{11}{12} \]

Next, we can simplify the multiplication step by step. Start by multiplying \( \frac{5}{6} \) and \( \frac{6}{11} \):

\[ \frac{5 \times 6}{6 \times 11} = \frac{30}{66} \]

Now simplify \( \frac{30}{66} \):

Both 30 and 66 can be divided by 6:

\[ \frac{30 \div 6}{66 \div 6} = \frac{5}{11} \]

Now we multiply \( \frac{5}{11} \) by \( \frac{11}{12} \):

\[ \frac{5 \times 11}{11 \times 12} = \frac{55}{132} \]

Now simplify \( \frac{55}{132} \):

Both 55 and 132 can be divided by 11:

\[ \frac{55 \div 11}{132 \div 11} = \frac{5}{12} \]

So, the final result is:

\[ \frac{5}{12} \]