Understanding the Operator Substitution Problem

This problem requires us to evaluate a mathematical expression where standard arithmetic operators (+, -, *, /) are represented by letters (A, B, C, D). We first need to substitute the letters with their corresponding operators and then evaluate the resulting expression following the correct order of operations.

Mapping Operators to Letters

Based on the problem description, the mapping is as follows:

• ‘A’ denotes ‘addition’ ($+$)
• ‘B’ denotes ‘subtraction’ ($-$)
• ‘C’ denotes ‘multiplication’ ($\times$)
• ‘D’ denotes ‘division’ ($\div$)

Substituting Letters in the Expression

The given expression is: 6 C (57 B 8) D 7 B 32 A 9

Substituting the letters with their respective mathematical operators, we get:

Evaluating the Expression using Order of Operations (BODMAS/PEMDAS)

We evaluate the expression step-by-step following the BODMAS or PEMDAS rule (Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)).

Step 1: Evaluate the expression inside the Parentheses (Brackets).

The expression becomes:

Step 2: Perform Multiplication and Division from left to right.

First, perform the multiplication:

The expression becomes:

Next, perform the division:

The expression becomes:

Step 3: Perform Addition and Subtraction from left to right.

First, perform the subtraction:

The expression becomes:

Finally, perform the addition:

The value of the expression is 19.

Revision Table: Operator Mapping Summary

Understanding the correct mapping is crucial for solving such problems. Here is a quick summary:

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

When evaluating mathematical expressions, especially those involving multiple operations, we must follow a specific order to ensure a consistent and correct result. This order is commonly remembered using acronyms like BODMAS or PEMDAS.

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

Both acronyms represent the same hierarchy. Operations within brackets or parentheses are always performed first. Then comes orders or exponents. Division and multiplication have equal priority and are performed from left to right as they appear. Similarly, addition and subtraction have equal priority and are performed from left to right.

Applying BODMAS/PEMDAS systematically helps avoid errors in calculation.