Simplify the following (1 to 3) :
`1""5/13" of "2""3/7 div 68/91-(1""1/2-1""1/3)`

Answer

To simplify the expression \(1 \frac{5}{13} \text{ of } 2 \frac{3}{7} \div \frac{68}{91} - (1 \frac{1}{2} - 1 \frac{1}{3})\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
Convert the mixed numbers to improper fractions.
- \(1 \frac{5}{13} = \frac{1 \times 13 + 5}{13} = \frac{18}{13}\)
- \(2 \frac{3}{7} = \frac{2 \times 7 + 3}{7} = \frac{17}{7}\)
- \(1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}\)
- \(1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}\)

So, the expression becomes:
\[ \frac{18}{13} \text{ of } \frac{17}{7} \div \frac{68}{91} - \left(\frac{3}{2} - \frac{4}{3}\right) \]

### Step 2: Simplify the Subtraction in the Bracket
Calculate \(\frac{3}{2} - \frac{4}{3}\).
- Find a common denominator, which is 6.
- Convert \(\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}\)
- Convert \(\frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6}\)

Now, subtract:
\[ \frac{9}{6} - \frac{8}{6} = \frac{1}{6} \]

### Step 3: Calculate the Division and Multiplication
Now we have:
\[ \frac{18}{13} \text{ of } \frac{17}{7} \div \frac{68}{91} - \frac{1}{6} \]

First, calculate the division:
\[ \frac{18}{13} \text{ of } \frac{17}{7} = \frac{18}{13} \times \frac{17}{7} = \frac{306}{91} \]

Now, divide by \(\frac{68}{91}\):
\[ \frac{306}{91} \div \frac{68}{91} = \frac{306}{91} \times \frac{91}{68} = \frac{306}{68} \]

### Step 4: Simplify \(\frac{306}{68}\)
Now simplify \(\frac{306}{68}\):
- Divide both the numerator and denominator by 2:
\[ \frac{306 \div 2}{68 \div 2} = \frac{153}{34} \]

Now, simplify further:
- Divide both by 17:
\[ \frac{153 \div 17}{34 \div 17} = \frac{9}{2} \]

### Step 5: Final Calculation
Now we have:
\[ \frac{9}{2} - \frac{1}{6} \]
Find a common denominator, which is 6:
- Convert \(\frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6}\)

Now subtract:
\[ \frac{27}{6} - \frac{1}{6} = \frac{26}{6} \]

### Step 6: Simplify \(\frac{26}{6}\)
Finally, simplify:
\[ \frac{26 \div 2}{6 \div 2} = \frac{13}{3} \]

### Final Answer
The simplified expression is:
\[ \frac{13}{3} \]