Calculate the value of `(1 29/36 + 1 7/11 xx 4 1/8) div (5 1/9 - 63/8 div 9 9/20)`.

Answer

To solve the expression `(1 29/36 + 1 7/11 x 4 1/8) ÷ (5 1/9 - 63/8 ÷ 9 9/20)`, we will follow the order of operations (BODMAS/BIDMAS). Here’s the step-by-step solution:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert `1 29/36` to an improper fraction:
\[ 1 29/36 = \frac{1 \times 36 + 29}{36} = \frac{36 + 29}{36} = \frac{65}{36} \]

2. Convert `1 7/11` to an improper fraction:
\[ 1 7/11 = \frac{1 \times 11 + 7}{11} = \frac{11 + 7}{11} = \frac{18}{11} \]

3. Convert `4 1/8` to an improper fraction:
\[ 4 1/8 = \frac{4 \times 8 + 1}{8} = \frac{32 + 1}{8} = \frac{33}{8} \]

4. Convert `5 1/9` to an improper fraction:
\[ 5 1/9 = \frac{5 \times 9 + 1}{9} = \frac{45 + 1}{9} = \frac{46}{9} \]

5. Convert `9 9/20` to an improper fraction:
\[ 9 9/20 = \frac{9 \times 20 + 9}{20} = \frac{180 + 9}{20} = \frac{189}{20} \]

### Step 2: Substitute Back into the Expression
Now, substitute these values back into the original expression:
\[ \left(\frac{65}{36} + \frac{18}{11} \times \frac{33}{8}\right) \div \left(\frac{46}{9} - \frac{63}{8} \div \frac{189}{20}\right) \]

### Step 3: Solve the Numerator
1. Calculate `\(\frac{18}{11} \times \frac{33}{8}\)`:
\[ \frac{18 \times 33}{11 \times 8} = \frac{594}{88} \]
Simplifying `\(\frac{594}{88}\)` gives:
\[ \frac{297}{44} \]

2. Now add `\(\frac{65}{36} + \frac{297}{44}\)`. Find a common denominator (LCM of 36 and 44 is 792):
\[ \frac{65 \times 22}{792} + \frac{297 \times 18}{792} = \frac{1430 + 5346}{792} = \frac{6776}{792} \]

### Step 4: Solve the Denominator
1. Calculate `\(\frac{63}{8} \div \frac{189}{20}\)`:
\[ \frac{63}{8} \times \frac{20}{189} = \frac{1260}{1512} = \frac{105}{126} = \frac{5}{6} \]

2. Now subtract `\(\frac{46}{9} - \frac{5}{6}\)`. Find a common denominator (LCM of 9 and 6 is 18):
\[ \frac{46 \times 2}{18} - \frac{5 \times 3}{18} = \frac{92 - 15}{18} = \frac{77}{18} \]

### Step 5: Final Division
Now divide the results from the numerator and denominator:
\[ \frac{6776}{792} \div \frac{77}{18} = \frac{6776}{792} \times \frac{18}{77} = \frac{6776 \times 18}{792 \times 77} \]

### Step 6: Simplify the Final Result
Calculate the numerator and denominator:
1. Numerator: \(6776 \times 18 = 122008\)
2. Denominator: \(792 \times 77 = 61032\)

Now simplify:
\[ \frac{122008}{61032} = 2 \]

### Final Answer
The value of the expression is \(2\).