Find: f. `1 (13)/(5) div 1 (5)/(7)`

Answer

To solve the problem \(1 \frac{13}{5} \div 1 \frac{5}{7}\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed fractions into improper fractions.

For \(1 \frac{13}{5}\):
- Multiply the whole number (1) by the denominator (5): \(1 \times 5 = 5\)
- Add the numerator (13): \(5 + 13 = 18\)
- So, \(1 \frac{13}{5} = \frac{18}{5}\)

For \(1 \frac{5}{7}\):
- Multiply the whole number (1) by the denominator (7): \(1 \times 7 = 7\)
- Add the numerator (5): \(7 + 5 = 12\)
- So, \(1 \frac{5}{7} = \frac{12}{7}\)

### Step 2: Set Up the Division of Fractions
Now we have:
\[ \frac{18}{5} \div \frac{12}{7} \]

### Step 3: Change Division to Multiplication
To divide by a fraction, we multiply by its reciprocal. Thus:
\[ \frac{18}{5} \div \frac{12}{7} = \frac{18}{5} \times \frac{7}{12} \]

### Step 4: Multiply the Fractions
Now we multiply the numerators and the denominators:
\[ \frac{18 \times 7}{5 \times 12} = \frac{126}{60} \]

### Step 5: Simplify the Fraction
Next, we simplify \(\frac{126}{60}\):
- Find the greatest common divisor (GCD) of 126 and 60, which is 6.
- Divide both the numerator and the denominator by 6:
\[ \frac{126 \div 6}{60 \div 6} = \frac{21}{10} \]

### Step 6: Convert to Mixed Number
Now we convert \(\frac{21}{10}\) to a mixed number:
- Divide 21 by 10. The quotient is 2 and the remainder is 1.
- Therefore, \(\frac{21}{10} = 2 \frac{1}{10}\).

### Final Answer
Thus, the final answer is:
\[ 2 \frac{1}{10} \]

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