Evaluate the following :
`5""1/3 div 1""1/9`

Answer

To evaluate the expression \( 5 \frac{1}{3} \div 1 \frac{1}{9} \), we will follow these steps:

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

For \( 5 \frac{1}{3} \):
- Multiply the whole number (5) by the denominator (3): \( 5 \times 3 = 15 \)
- Add the numerator (1): \( 15 + 1 = 16 \)
- So, \( 5 \frac{1}{3} = \frac{16}{3} \)

For \( 1 \frac{1}{9} \):
- Multiply the whole number (1) by the denominator (9): \( 1 \times 9 = 9 \)
- Add the numerator (1): \( 9 + 1 = 10 \)
- So, \( 1 \frac{1}{9} = \frac{10}{9} \)

### Step 2: Rewrite the Division as Multiplication
Now, we rewrite the division of fractions as multiplication by the reciprocal of the second fraction.

\[ \frac{16}{3} \div \frac{10}{9} = \frac{16}{3} \times \frac{9}{10} \]

### Step 3: Multiply the Fractions
Now we can multiply the fractions:

\[ \frac{16 \times 9}{3 \times 10} \]

Calculating the numerator and denominator:

- Numerator: \( 16 \times 9 = 144 \)
- Denominator: \( 3 \times 10 = 30 \)

So we have:

\[ \frac{144}{30} \]

### Step 4: Simplify the Fraction
Now, we simplify \( \frac{144}{30} \).

To simplify, we can find the greatest common divisor (GCD) of 144 and 30. The GCD is 6.

Now, divide both the numerator and the denominator by 6:

\[ \frac{144 \div 6}{30 \div 6} = \frac{24}{5} \]

### Final Answer
Thus, the final answer is:

\[ \frac{24}{5} \]