Simplify the following expressions :
`1/2 " of " (16/7 + 5/3)`

Answer

To simplify the expression \( \frac{1}{2} \left( \frac{16}{7} + \frac{5}{3} \right) \), we can follow these steps:

### Step 1: Find a common denominator for the fractions inside the parentheses.
The denominators are 7 and 3. The least common multiple (LCM) of 7 and 3 is 21.

### Step 2: Rewrite each fraction with the common denominator.
- For \( \frac{16}{7} \):
\[ \frac{16}{7} = \frac{16 \times 3}{7 \times 3} = \frac{48}{21} \]
- For \( \frac{5}{3} \):
\[ \frac{5}{3} = \frac{5 \times 7}{3 \times 7} = \frac{35}{21} \]

### Step 3: Add the two fractions.
Now we can add the two fractions:
\[ \frac{48}{21} + \frac{35}{21} = \frac{48 + 35}{21} = \frac{83}{21} \]

### Step 4: Multiply the result by \( \frac{1}{2} \).
Now we need to take half of \( \frac{83}{21} \):
\[ \frac{1}{2} \left( \frac{83}{21} \right) = \frac{83}{42} \]

### Step 5: Simplify if possible.
The fraction \( \frac{83}{42} \) is already in its simplest form.

### Final Answer:
The simplified expression is:
\[ \frac{83}{42} \]