The value of ` 21 xx [ (9 - 4) div { (8 div 8 " of " 4) + (4 div 4 " of " 2 ) } ] ` is

Options

A. 140
B. 80
C. 100
D. 20

Answer

To solve the expression \( 21 \times \left[ (9 - 4) \div \{ (8 \div 8 \text{ of } 4) + (4 \div 4 \text{ of } 2) \} \right] \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Calculate the expression inside the first parentheses:**
\[ 9 - 4 = 5 \]
So, we can rewrite the expression as:
\[ 21 \times \left[ 5 \div \{ (8 \div 8 \text{ of } 4) + (4 \div 4 \text{ of } 2) \} \right] \]

**Hint:** Start by simplifying expressions inside parentheses.

2. **Calculate the expressions involving "of" (which means multiplication):**
- For \( 8 \div 8 \text{ of } 4 \):
\[ 8 \div 8 = 1 \quad \text{and then} \quad 1 \text{ of } 4 = 1 \times 4 = 4 \]
- For \( 4 \div 4 \text{ of } 2 \):
\[ 4 \div 4 = 1 \quad \text{and then} \quad 1 \text{ of } 2 = 1 \times 2 = 2 \]

Now substitute these values back into the expression:
\[ 21 \times \left[ 5 \div \{ 4 + 2 \} \right] \]

**Hint:** Remember to perform operations in the correct order, especially multiplication and division.

3. **Calculate the sum inside the curly braces:**
\[ 4 + 2 = 6 \]
So now we have:
\[ 21 \times \left[ 5 \div 6 \right] \]

**Hint:** Always simplify expressions step by step.

4. **Now perform the division:**
\[ 5 \div 6 = \frac{5}{6} \]
Substitute this back into the expression:
\[ 21 \times \frac{5}{6} \]

**Hint:** When dividing, you can express the division as a fraction.

5. **Multiply \( 21 \) by \( \frac{5}{6} \):**
\[ 21 \times \frac{5}{6} = \frac{21 \times 5}{6} = \frac{105}{6} \]

**Hint:** Simplify fractions where possible.

6. **Simplify \( \frac{105}{6} \):**
\[ \frac{105}{6} = 17.5 \]
However, we can also express this as:
\[ 17 \frac{1}{2} \text{ or } 17.5 \]

**Hint:** If the answer is not in whole numbers, check if it can be expressed as a mixed number.

### Final Answer:
The value of the expression is \( 17.5 \) or \( 17 \frac{1}{2} \).