What is the value of `[88-44-:(22xx4)" of "((1)/(2)-(1)/(4)-:(1)/(8))]?`

Options

A. `(265)/(3)`
B. `(703)/(9)`
C. `(514)/(9)`
D. `(711)/(3)`

Answer

To solve the expression \[ 88 - 44 \div \left( 22 \times 4 \right) \text{ of } \left( \frac{1}{2} - \frac{1}{4} \div \frac{1}{8} \right) \], we will follow the order of operations, often abbreviated as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Identify the innermost brackets**:
We start with the circular bracket \(\left( \frac{1}{2} - \frac{1}{4} \div \frac{1}{8} \right)\).

**Hint**: Always start with the innermost brackets first.

2. **Solve the division inside the circular bracket**:
\[ \frac{1}{4} \div \frac{1}{8} = \frac{1}{4} \times \frac{8}{1} = \frac{8}{4} = 2 \]
Now the circular bracket becomes:
\[ \frac{1}{2} - 2 \]

**Hint**: Remember that dividing by a fraction is the same as multiplying by its reciprocal.

3. **Complete the circular bracket**:
\[ \frac{1}{2} - 2 = \frac{1}{2} - \frac{4}{2} = -\frac{3}{2} \]

**Hint**: Convert to a common denominator when subtracting fractions.

4. **Now substitute back into the expression**:
The expression now looks like:
\[ 88 - 44 \div \left( 22 \times 4 \right) \text{ of } -\frac{3}{2} \]

**Hint**: Substitute back carefully to avoid mistakes.

5. **Calculate \(22 \times 4\)**:
\[ 22 \times 4 = 88 \]

**Hint**: Simple multiplication can often be overlooked; double-check your calculations.

6. **Now substitute this back into the expression**:
\[ 88 - 44 \div 88 \text{ of } -\frac{3}{2} \]

**Hint**: Keep track of the operations as you substitute values.

7. **Calculate the division**:
\[ 44 \div 88 = \frac{44}{88} = \frac{1}{2} \]

**Hint**: Simplifying fractions can make calculations easier.

8. **Now substitute this back into the expression**:
\[ 88 - \frac{1}{2} \text{ of } -\frac{3}{2} \]

**Hint**: Ensure you understand the meaning of "of" in mathematical terms (it usually indicates multiplication).

9. **Calculate the multiplication**:
\[ \frac{1}{2} \times -\frac{3}{2} = -\frac{3}{4} \]

**Hint**: When multiplying fractions, multiply the numerators and denominators separately.

10. **Now substitute this back into the expression**:
\[ 88 - \left( -\frac{3}{4} \right) = 88 + \frac{3}{4} \]

**Hint**: Subtracting a negative is the same as adding a positive.

11. **Convert 88 to a fraction**:
\[ 88 = \frac{88 \times 4}{4} = \frac{352}{4} \]

**Hint**: Converting whole numbers to fractions can help with addition.

12. **Add the fractions**:
\[ \frac{352}{4} + \frac{3}{4} = \frac{352 + 3}{4} = \frac{355}{4} \]

**Hint**: Always ensure the denominators are the same before adding fractions.

### Final Answer:
The value of the expression is \(\frac{355}{4}\) or \(88.75\).