Simplifying the Expression

This question requires simplifying a complex mathematical expression using the order of operations, commonly known as BODMAS or PEMDAS.

The expression to simplify is: $112 \div \left[16 \div 8 \times \{18 + 12 - (3 + 10 - (4 + 7))\}\right]$

BODMAS Rule Application

We follow the BODMAS rule for the order of operations:

• Brackets (Innermost first)
• Orders (Exponents)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Simplification Steps

1. Innermost Parentheses: Evaluate the expression inside the innermost parentheses $(4 + 7)$.

   Calculation: $4 + 7 = 11$

   The expression becomes: $112 \div \left[16 \div 8 \times \{18 + 12 - (3 + 10 - 11)\}\right]$

2. Next Parentheses: Evaluate the expression inside the next parentheses $(3 + 10 - 11)$.

   Calculation: $3 + 10 - 11 = 13 - 11 = 2$

   The expression simplifies to: $112 \div \left[16 \div 8 \times \{18 + 12 - 2\}\right]$

3. Braces: Evaluate the expression inside the braces $\{18 + 12 - 2\}$.

   Calculation: $18 + 12 - 2 = 30 - 2 = 28$

   The expression becomes: $112 \div \left[16 \div 8 \times 28\right]$

4. Brackets (Division): Inside the main brackets $\left[ \dots \right]$, perform the division $16 \div 8$ first, as it comes before multiplication from left to right.

   Calculation: $16 \div 8 = 2$

   The expression is now: $112 \div \left[2 \times 28\right]$

5. Brackets (Multiplication): Perform the multiplication inside the brackets: $2 \times 28$.

   Calculation: $2 \times 28 = 56$

   The expression simplifies to: $112 \div 56$

6. Final Division: Perform the final division: $112 \div 56$.

   Calculation: $112 \div 56 = 2$

The simplified value of the given expression is 2.