What is the value of `(24 div4-2/3" of "21/8div 1/4)?`

Options

A. `-1`
B. `-96/15`
C. `91/16`
D. `-8`

Answer

To solve the expression \( (24 \div 4 - \frac{2}{3} \text{ of } \frac{21}{8} \div \frac{1}{4}) \), we will follow the order of operations, commonly known as the BODMAS/BIDMAS rule (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Identify the Expression**:
\[ 24 \div 4 - \frac{2}{3} \text{ of } \frac{21}{8} \div \frac{1}{4} \]

2. **Calculate the Division and Off Operation**:
- First, calculate \( 24 \div 4 \):
\[ 24 \div 4 = 6 \]
- Now, we need to calculate \( \frac{2}{3} \text{ of } \frac{21}{8} \div \frac{1}{4} \).

3. **Calculate \( \frac{21}{8} \div \frac{1}{4} \)**:
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{21}{8} \div \frac{1}{4} = \frac{21}{8} \times 4 = \frac{21 \times 4}{8} = \frac{84}{8} = \frac{21}{2} \]

4. **Calculate \( \frac{2}{3} \text{ of } \frac{21}{2} \)**:
- This means multiplying \( \frac{2}{3} \) by \( \frac{21}{2} \):
\[ \frac{2}{3} \times \frac{21}{2} = \frac{2 \times 21}{3 \times 2} = \frac{21}{3} = 7 \]

5. **Substitute Back into the Expression**:
- Now substitute back into the expression:
\[ 6 - 7 \]

6. **Final Calculation**:
- Now perform the subtraction:
\[ 6 - 7 = -1 \]

### Final Answer:
The value of the expression is \(-1\).