Simplify the following expressions:
`4/9 " of " 729/48`

Answer

To simplify the expression \( \frac{4}{9} \text{ of } \frac{729}{48} \), we will follow these steps:

### Step 1: Multiply the fractions
We start by multiplying the two fractions together:
\[ \frac{4}{9} \times \frac{729}{48} \]

### Step 2: Multiply the numerators and denominators
When multiplying fractions, we multiply the numerators together and the denominators together:
\[ \frac{4 \times 729}{9 \times 48} \]

### Step 3: Calculate the products
Calculating the products in the numerator and the denominator:
\[ \frac{2916}{432} \]

### Step 4: Simplify the fraction
Now we need to simplify \( \frac{2916}{432} \). We can find the greatest common divisor (GCD) of 2916 and 432 to simplify the fraction.

### Step 5: Find the GCD
To simplify the fraction, we can divide both the numerator and the denominator by their GCD. The GCD of 2916 and 432 is 108.

### Step 6: Divide both numerator and denominator by the GCD
Now we divide both the numerator and the denominator by 108:
\[ \frac{2916 \div 108}{432 \div 108} = \frac{27}{4} \]

### Step 7: Convert to a mixed number
To express \( \frac{27}{4} \) as a mixed number, we divide 27 by 4:
\[ 27 \div 4 = 6 \quad \text{(with a remainder of 3)} \]
So, \( \frac{27}{4} = 6 \frac{3}{4} \).

### Final Answer
Thus, the simplified expression is:
\[ 6 \frac{3}{4} \]

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