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}
]
