To find the value of the question mark ‘?’ in the given mathematical expression, we need to simplify the expression following the order of operations, commonly known as BODMAS or PEMDAS.

Understanding the Order of Operations (BODMAS/PEMDAS)

The BODMAS/PEMDAS rule helps us solve mathematical expressions with multiple operations in the correct order. It stands for:

• Brackets (or Parentheses)
• Orders (or Exponents/Powers and Roots)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

In the given expression, we have brackets, multiplication, division, subtraction, and addition. We also have "of", which indicates multiplication.

Step-by-Step Calculation of the Mathematical Expression

The given expression is:

\((44 \text{ of } 15) – [(450 \times 240 \div 60 – 40) \div 80 \times 25 + 50] – 10 = ?\)

Step 1: Evaluate the term outside the main brackets

Calculate ‘44 of 15’.

\(44 \text{ of } 15 = 44 \times 15\)

\(44 \times 15 = 660\)

Step 2: Evaluate the expression inside the square brackets [ ]

The expression inside the square brackets is \([(450 \times 240 \div 60 – 40) \div 80 \times 25 + 50]\).

First, evaluate the expression inside the parentheses ( ): \((450 \times 240 \div 60 – 40)\)

Within the parentheses, perform multiplication and division from left to right.

\(450 \times 240 = 108000\)

Now, the expression becomes \((108000 \div 60 – 40)\)

Perform the division:

\(108000 \div 60 = 1800\)

Now, the expression becomes \((1800 – 40)\)

Perform the subtraction:

\(1800 – 40 = 1760\)

So, the expression inside the square brackets now becomes \([1760 \div 80 \times 25 + 50]\)

Next, within the square brackets, perform division and multiplication from left to right.

\(1760 \div 80 = 22\)

Now, the expression becomes \([22 \times 25 + 50]\)

Perform the multiplication:

\(22 \times 25 = 550\)

Now, the expression becomes \([550 + 50]\)

Perform the addition:

\(550 + 50 = 600\)

So, the value of the expression inside the square brackets is 600.

Step 3: Substitute the calculated values back into the original expression

The original expression was \((44 \text{ of } 15) – [(450 \times 240 \div 60 – 40) \div 80 \times 25 + 50] – 10 = ?\)

Substituting the results from Step 1 and Step 2:

\(660 – 600 – 10 = ?\)

Step 4: Perform the final subtractions from left to right

\(660 – 600 = 60\)

Now, the expression becomes:

\(60 – 10 = ?\)

Perform the final subtraction:

\(60 – 10 = 50\)

Thus, the value of the question mark ‘?’ is 50.

Revision Table: Key Concepts for Mathematical Expressions

Additional Information: Common Pitfalls in Evaluating Expressions

• Ignoring BODMAS/PEMDAS: Not following the correct order is the most common mistake, leading to incorrect results. Always start with brackets, then orders, then division/multiplication (left to right), and finally addition/subtraction (left to right).
• Incorrect Handling of Division and Multiplication: Remember that division and multiplication have the same priority and should be performed from left to right as they appear in the expression. The same applies to addition and subtraction.
• Misinterpreting 'of': The term 'of' strictly means multiplication and should be treated as such, usually calculated before other operations outside brackets but after operations inside brackets.
• Calculation Errors: Simple arithmetic mistakes (addition, subtraction, multiplication, division) can occur. Double-checking calculations, especially with larger numbers, is crucial.

Practicing various problems involving different operations and brackets helps in mastering the order of operations and avoiding these pitfalls.