Solving Complex Mathematical Expressions

To solve the given mathematical expression, we need to follow the order of operations. A common acronym used to remember the order is BODMAS or PEMDAS.

• B/P: Brackets/Parentheses (solve the innermost ones first)
• O/E: Orders/Exponents
• D/M: Division and Multiplication (from left to right)
• A/S: Addition and Subtraction (from left to right)

The given expression is:

$$22 - [9 -\{6 - (10 - 4 + 3)\}] \div 2 \times 3$$

Step-by-Step Calculation

Let's solve the expression step-by-step following the BODMAS rule:

Step 1: Solve the innermost Parentheses ()

First, calculate the value inside the parentheses:

$$(10 - 4 + 3)$$

Perform subtraction and addition from left to right:

$$10 - 4 = 6$$

$$6 + 3 = 9$$

So, the expression becomes:

$$22 - [9 -\{6 - 9\}] \div 2 \times 3$$

Step 2: Solve the Braces {}

Next, calculate the value inside the braces:

$$\{6 - 9\}$$

$$6 - 9 = -3$$

So, the expression becomes:

$$22 - [9 - \{-3\}] \div 2 \times 3$$

Step 3: Solve the Brackets []

Now, calculate the value inside the brackets:

$$[9 - \{-3\}]$$

Subtracting a negative number is the same as adding its positive counterpart:

$$9 - (-3) = 9 + 3 = 12$$

So, the expression becomes:

$$22 - 12 \div 2 \times 3$$

Step 4: Perform Division and Multiplication (from left to right)

We have division and multiplication next. We solve from left to right.

First, perform the division:

$$12 \div 2 = 6$$

The expression is now:

$$22 - 6 \times 3$$

Next, perform the multiplication:

$$6 \times 3 = 18$$

The expression is now:

$$22 - 18$$

Step 5: Perform Subtraction

Finally, perform the subtraction:

$$22 - 18 = 4$$

The final value of the expression is 4.

Final Answer Summary

The calculated value of the expression is 4.

Revision Table: Order of Operations (BODMAS/PEMDAS)

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

Additional Information: Nested Grouping Symbols

When dealing with nested grouping symbols like parentheses inside braces inside brackets, you always start with the innermost set of symbols and work your way outwards. This ensures that the operations are performed in the correct sequence as defined by BODMAS/PEMDAS.

• Innermost first: Solve calculations within ()
• Next: Solve calculations within {} using the result from ()
• Next: Solve calculations within [] using the result from {}
• Then proceed with the rest of the expression according to the order of operations.

This systematic approach prevents errors in evaluating complex expressions.