Simplify the following expressions :
`5 1/3 div 4/15`

Answer

To simplify the expression \( 5 \frac{1}{3} \div \frac{4}{15} \), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction
First, we convert \( 5 \frac{1}{3} \) into an improper fraction.

To do this, we multiply the whole number (5) by the denominator (3) and then add the numerator (1):

\[ 5 \frac{1}{3} = \frac{(5 \times 3) + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \]

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

So, we have:

\[ \frac{16}{3} \div \frac{4}{15} = \frac{16}{3} \times \frac{15}{4} \]

### Step 3: Multiply the fractions
Now, we multiply the two fractions:

\[ \frac{16 \times 15}{3 \times 4} \]

Calculating the numerator and the denominator:

\[ 16 \times 15 = 240 \]
\[ 3 \times 4 = 12 \]

So, we have:

\[ \frac{240}{12} \]

### Step 4: Simplify the fraction
Now we simplify \( \frac{240}{12} \):

\[ \frac{240 \div 12}{12 \div 12} = \frac{20}{1} = 20 \]

### Final Answer
Thus, the simplified expression is:

\[ \boxed{20} \]

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