What is the simplified value of
`(8.5 - 2 (1)/(2) )" of "16.5 - [ 27.4 -{ 10 (1)/(4)" of " 2.5 -(1 (1)/(2) - 1 (1)/(5) ) } ] ?`

Options

A. `97.075`
B. `99.925`
C. `96.925`
D. `101.075`

Answer

To simplify the expression given in the question, we will follow the order of operations step by step.

### Step 1: Rewrite the expression
The expression is:
\[ (8.5 - 2 \cdot (1/2)) \text{ of } (16.5 - [27.4 - \{10 \cdot (1/4) \text{ of } (2.5 - (1 \cdot (1/2) - 1 \cdot (1/5))\} ]) \]

### Step 2: Simplify the first part
Calculate \(2 \cdot (1/2)\):
\[ 2 \cdot (1/2) = 1 \]
So the first part becomes:
\[ 8.5 - 1 = 7.5 \]

### Step 3: Simplify the second part
Now we will simplify the second part:
\[ 16.5 - [27.4 - \{10 \cdot (1/4) \text{ of } (2.5 - (1 \cdot (1/2) - 1 \cdot (1/5))\}] \]

### Step 4: Calculate \(10 \cdot (1/4)\)
\[ 10 \cdot (1/4) = 2.5 \]

### Step 5: Simplify \(2.5 - (1 \cdot (1/2) - 1 \cdot (1/5))\)
Calculate \(1 \cdot (1/2)\) and \(1 \cdot (1/5)\):
\[ 1 \cdot (1/2) = 0.5 \]
\[ 1 \cdot (1/5) = 0.2 \]
Now, calculate:
\[ 0.5 - 0.2 = 0.3 \]
So,
\[ 2.5 - 0.3 = 2.2 \]

### Step 6: Calculate \(2.5 \text{ of } 2.2\)
Now calculate:
\[ 2.5 \cdot 2.2 = 5.5 \]

### Step 7: Substitute back into the expression
Now substitute back into the expression:
\[ 16.5 - [27.4 - 5.5] \]

### Step 8: Simplify inside the brackets
Calculate:
\[ 27.4 - 5.5 = 21.9 \]

### Step 9: Final calculation
Now calculate:
\[ 16.5 - 21.9 = -5.4 \]

### Step 10: Final expression
Now we have:
\[ 7.5 \text{ of } -5.4 \]

### Step 11: Calculate the final result
Calculate:
\[ 7.5 \cdot -5.4 = -40.5 \]

So the simplified value of the expression is:
\[ \boxed{-40.5} \]