Simplify the given expression:
`{32 + (45% "of" 400 - 20 × 6)} ÷ {25% "of" 72 + (11 × 3 - 4 × 7)}`

Options

A. 6
B. 2
C. 4
D. 8

Answer

To simplify the expression `{32 + (45% "of" 400 - 20 × 6)} ÷ {25% "of" 72 + (11 × 3 - 4 × 7)}`, we will follow the order of operations (BODMAS/BIDMAS rules). Let's break it down step by step.

### Step 1: Calculate 45% of 400
\[ 45\% \text{ of } 400 = \frac{45}{100} \times 400 = 180 \]

**Hint:** To find a percentage of a number, multiply the percentage (as a fraction) by the number.

### Step 2: Calculate 20 × 6
\[ 20 \times 6 = 120 \]

**Hint:** Multiplication is straightforward; just multiply the two numbers.

### Step 3: Substitute the values into the expression
Now we substitute these values back into the expression:
\[ 32 + (180 - 120) \]

**Hint:** Always substitute calculated values back into the expression to simplify further.

### Step 4: Simplify the expression inside the first bracket
\[ 180 - 120 = 60 \]

**Hint:** Subtract the smaller number from the larger number.

### Step 5: Calculate 25% of 72
\[ 25\% \text{ of } 72 = \frac{25}{100} \times 72 = 18 \]

**Hint:** Again, use the percentage as a fraction to find the value.

### Step 6: Calculate 11 × 3 and 4 × 7
\[ 11 \times 3 = 33 \]
\[ 4 \times 7 = 28 \]

**Hint:** Perform multiplication as needed for each term.

### Step 7: Substitute the values into the second bracket
Now we substitute these values:
\[ 18 + (33 - 28) \]

**Hint:** Substitute calculated values back into the expression for further simplification.

### Step 8: Simplify the expression inside the second bracket
\[ 33 - 28 = 5 \]
So, we have:
\[ 18 + 5 = 23 \]

**Hint:** Again, subtract the smaller number from the larger number and then add.

### Step 9: Substitute back into the main expression
Now we have:
\[ \frac{32 + 60}{23} \]

**Hint:** Substitute the simplified brackets back into the main expression.

### Step 10: Calculate the numerator
\[ 32 + 60 = 92 \]

**Hint:** Add the two numbers together.

### Step 11: Final division
Now we perform the division:
\[ \frac{92}{23} = 4 \]

**Hint:** Divide the numerator by the denominator to get the final answer.

### Final Answer
The simplified expression is:
\[ \boxed{4} \]