Solving the Mathematical Expression

To find the value of the given mathematical expression, we need to follow the order of operations, often remembered by the acronyms BODMAS or PEMDAS.

The expression is: \(30 - [40 - \{56 - (25 - 13 - 12)\}]\)

Let's break down the expression and solve it step by step, starting with the innermost grouping symbols (parentheses), then curly braces, and finally square brackets.

Step 1: Solve the innermost parentheses

The innermost part is \((25 - 13 - 12)\).

• First, calculate \(25 - 13\): \(25 - 13 = 12\).
• Then, subtract 12 from the result: \(12 - 12 = 0\).

So, \((25 - 13 - 12) = 0\).

The expression now becomes: \(30 - [40 - \{56 - 0\}]\)

Step 2: Solve the curly braces

Next, we solve the expression within the curly braces: \(\{56 - 0\}\).

• \(56 - 0 = 56\).

So, \(\{56 - 0\} = 56\).

The expression now becomes: \(30 - [40 - 56]\)

Step 3: Solve the square brackets

Now, we solve the expression within the square brackets: \([40 - 56]\).

• \(40 - 56\). Subtracting a larger number from a smaller number gives a negative result. \(56 - 40 = 16\), so \(40 - 56 = -16\).

So, \([40 - 56] = -16\).

The expression now becomes: \(30 - [-16]\)

Step 4: Perform the final subtraction

Finally, we perform the last operation: \(30 - [-16]\).

Subtracting a negative number is the same as adding the positive number.

• \(30 - [-16] = 30 + 16 = 46\).

The value of the expression is 46.

Summary of Calculation Steps

The final value of the expression \(30 - [40 - \{56 - (25 - 13 - 12)\}]\) is 46.

Revision Table: Order of Operations

Understanding the correct order of operations is crucial for solving mathematical expressions accurately. Here's a quick reminder of BODMAS/PEMDAS:

In this problem, we primarily used the Brackets/Parentheses and Subtraction operations, following the BODMAS/PEMDAS rule of solving grouping symbols from the innermost to the outermost.

Additional Information: Working with Nested Brackets

When you encounter expressions with multiple layers of brackets (like parentheses inside curly braces, inside square brackets), it's essential to tackle them from the inside out. This ensures that you evaluate the operations in the correct sequence before moving to the next level.

• Start with the innermost grouping symbols.
• Calculate the value within those symbols.
• Replace the inner symbols and their content with the calculated value.
• Move to the next layer of grouping symbols and repeat the process.
• Continue until all grouping symbols are removed.
• Finally, perform the remaining operations according to BODMAS/PEMDAS.

This systematic approach helps prevent errors and ensures you arrive at the correct value of the expression.