`80 -: [48-{56-(60-36 -: 12xx4)}]` =

Options

A. 5
B. 8
C. 4
D. 2

Answer

To solve the expression \( 80 -: [48 - \{56 - (60 - 36 -: 12 \times 4)\}] \), we will follow the order of operations, often remembered by the acronym BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Identify the innermost bracket**: We start with the expression inside the parentheses:
\[ 60 - 36 -: 12 \times 4 \]

2. **Perform the multiplication**: Calculate \( 12 \times 4 \):
\[ 12 \times 4 = 48 \]
Now the expression becomes:
\[ 60 - 36 -: 48 \]

3. **Perform the division**: Now we need to handle the division:
\[ 36 -: 48 = \frac{36}{48} = \frac{3}{4} \]
So we can rewrite the expression as:
\[ 60 - \frac{3}{4} \]

4. **Convert 60 into a fraction**: To subtract, convert 60 into a fraction:
\[ 60 = \frac{240}{4} \]
Now we can perform the subtraction:
\[ \frac{240}{4} - \frac{3}{4} = \frac{240 - 3}{4} = \frac{237}{4} \]

5. **Substituting back into the curly brackets**: Now we substitute back into the curly brackets:
\[ 56 - \frac{237}{4} \]

6. **Convert 56 into a fraction**: Convert 56 into a fraction:
\[ 56 = \frac{224}{4} \]
Now perform the subtraction:
\[ \frac{224}{4} - \frac{237}{4} = \frac{224 - 237}{4} = \frac{-13}{4} \]

7. **Substituting back into the square brackets**: Now substitute back into the square brackets:
\[ 48 - \left(\frac{-13}{4}\right) = 48 + \frac{13}{4} \]

8. **Convert 48 into a fraction**: Convert 48 into a fraction:
\[ 48 = \frac{192}{4} \]
Now perform the addition:
\[ \frac{192}{4} + \frac{13}{4} = \frac{192 + 13}{4} = \frac{205}{4} \]

9. **Final division**: Now we have:
\[ 80 -: \left(\frac{205}{4}\right) = 80 \div \frac{205}{4} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ 80 \times \frac{4}{205} = \frac{320}{205} \]

10. **Simplifying the fraction**: Simplifying \( \frac{320}{205} \):
\[ \frac{320 \div 5}{205 \div 5} = \frac{64}{41} \]

Thus, the final answer is:
\[ \frac{64}{41} \]