Evaluating Expressions with Operator Substitution

This question requires us to substitute the given letters with their corresponding mathematical operators and then evaluate the resulting expression according to the order of operations.

The mapping of letters to operators is as follows:

• 'A' means '+' (Addition)
• 'B' means '–' (Subtraction)
• 'C' means '×' (Multiplication)
• 'D' means '÷' (Division)

The given expression is:

\(44 \text{ A } 36 \text{ B } 60 \text{ D } 30 \text{ C } 5 = ?\)

Now, let's replace the letters with their respective operators:

\(44 + 36 - 60 \div 30 \times 5 = ?\)

To solve this expression, we must follow the order of operations, commonly known as BODMAS or PEMDAS. The order is: Brackets (or Parentheses), Orders (or Exponents), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).

Let's evaluate the expression step by step:

1. Division: Perform the division first.
   \(60 \div 30 = 2\)
   The expression becomes: \(44 + 36 - 2 \times 5\)
2. Multiplication: Next, perform the multiplication.
   \(2 \times 5 = 10\)
   The expression becomes: \(44 + 36 - 10\)
3. Addition and Subtraction: Now, perform addition and subtraction from left to right. First, the addition.
   \(44 + 36 = 80\)
   The expression becomes: \(80 - 10\)
4. Subtraction: Finally, perform the subtraction.
   \(80 - 10 = 70\)

So, the value of the expression is \(70\).

Let's verify the steps:

\(44 + 36 - 60 \div 30 \times 5\)

First, division:

\(44 + 36 - 2 \times 5\)

Next, multiplication:

\(44 + 36 - 10\)

Then, addition:

\(80 - 10\)

Finally, subtraction:

\(70\)

Revision Table: Operator Mapping

Additional Information: Order of Operations (BODMAS/PEMDAS)

The order of operations is a set of rules that dictates the sequence in which operations should be performed in a mathematical expression to ensure a unique result. The acronyms BODMAS and PEMDAS are commonly used to remember this order:

• BODMAS: Brackets, Orders (powers/roots), Division and Multiplication (left-to-right), Addition and Subtraction (left-to-right).
• PEMDAS: Parentheses, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right).

It is crucial to follow this order; otherwise, you will likely get an incorrect answer when evaluating expressions with multiple operations.