Simplify `2 + 3 xx (1)/(3) " of " 2 xx (6 xx (1)/(2))- [5- {(5)/(8) + 3 (3)/(8)-(1)/(8)}]`

Options

A. 6
B. `55//8`
C. 8
D. `77/6`

Answer

To simplify the expression \( 2 + 3 \times \frac{1}{3} \text{ of } 2 \times (6 \times \frac{1}{2}) - \left[ 5 - \left( \frac{5}{8} + 3 \frac{3}{8} - \frac{1}{8} \right) \right] \), we will follow these steps:

### Step 1: Simplify the expression inside the brackets
We start with the expression inside the brackets:
\[ 5 - \left( \frac{5}{8} + 3 \frac{3}{8} - \frac{1}{8} \right) \]

First, we need to simplify \( 3 \frac{3}{8} \):
\[ 3 \frac{3}{8} = \frac{3 \times 3 + 3}{8} = \frac{9 + 3}{8} = \frac{12}{8} = \frac{3}{2} \]

Now, we can rewrite the expression:
\[ 5 - \left( \frac{5}{8} + \frac{12}{8} - \frac{1}{8} \right) \]

Combine the fractions:
\[ \frac{5}{8} + \frac{12}{8} - \frac{1}{8} = \frac{5 + 12 - 1}{8} = \frac{16}{8} = 2 \]

So we have:
\[ 5 - 2 = 3 \]

### Step 2: Substitute back into the main expression
Now substitute back into the main expression:
\[ 2 + 3 \times \frac{1}{3} \text{ of } 2 \times (6 \times \frac{1}{2}) - 3 \]

### Step 3: Simplify the multiplication
Next, we simplify \( 3 \times \frac{1}{3} \):
\[ 3 \times \frac{1}{3} = 1 \]

Now, we simplify \( 6 \times \frac{1}{2} \):
\[ 6 \times \frac{1}{2} = 3 \]

So, we can rewrite the expression as:
\[ 2 + 1 \text{ of } 2 \times 3 - 3 \]

### Step 4: Calculate the "of" operation
The "of" operation means multiplication, so:
\[ 1 \text{ of } 2 \times 3 = 1 \times 2 \times 3 = 6 \]

### Step 5: Substitute and simplify
Now substitute this back into the expression:
\[ 2 + 6 - 3 \]

### Step 6: Final calculation
Now perform the addition and subtraction:
\[ 2 + 6 = 8 \]
\[ 8 - 3 = 5 \]

Thus, the simplified expression is:
\[ \boxed{5} \]