Evaluating Mathematical Expressions by Substituting Operators

The problem requires us to evaluate a given expression by replacing specific letters with corresponding mathematical operators and then performing the calculation according to the order of operations.

The given mappings are:

• A denotes ‘+’ (Addition)
• B denotes ‘×’ (Multiplication)
• C denotes ‘-’ (Subtraction)
• D denotes ‘÷’ (Division)

The expression to evaluate is:

\( 34 \text{ A } 15 \text{ B } 3 \text{ C } 11 \text{ B } 2 \text{ A } (51 \text{ D } 17) = ? \)

Step-by-Step Evaluation Process

First, let's substitute the letters with their corresponding mathematical operators:

\( 34 + 15 \times 3 - 11 \times 2 + (51 \div 17) \)

Now, we follow the order of operations (often remembered by BODMAS or PEMDAS) to evaluate the expression:

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

Let's evaluate the expression step by step:

1. Evaluate the expression within the parentheses:

   \( (51 \div 17) = 3 \)

   The expression becomes: \( 34 + 15 \times 3 - 11 \times 2 + 3 \)

2. Perform Multiplication:

   Evaluate \( 15 \times 3 \):

   \( 15 \times 3 = 45 \)

   Evaluate \( 11 \times 2 \):

   \( 11 \times 2 = 22 \)

   The expression becomes: \( 34 + 45 - 22 + 3 \)

3. Perform Addition and Subtraction from left to right:

   First, \( 34 + 45 \):

   \( 34 + 45 = 79 \)

   The expression becomes: \( 79 - 22 + 3 \)

   Next, \( 79 - 22 \):

   \( 79 - 22 = 57 \)

   The expression becomes: \( 57 + 3 \)

   Finally, \( 57 + 3 \):

   \( 57 + 3 = 60 \)

So, the value of the expression is 60.

Conclusion on Expression Evaluation

By correctly substituting the letters with operators and following the order of operations, we found that the value of the given expression \( 34 \text{ A } 15 \text{ B } 3 \text{ C } 11 \text{ B } 2 \text{ A } (51 \text{ D } 17) \) is 60.

Revision Table: Operator Substitution

Additional Information: Understanding Order of Operations (BODMAS/PEMDAS)

The order of operations is a set of rules used to clarify which procedures should be performed first within a given mathematical expression. This ensures consistent results when evaluating expressions.

• BODMAS: Brackets, Orders (powers, square roots), Division and Multiplication, Addition and Subtraction.
• PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

Division and Multiplication have the same priority and should be performed from left to right. Similarly, Addition and Subtraction have the same priority and should be performed from left to right.