Solving Symbol Substitution Expression

The question asks us to evaluate a given expression where standard mathematical operators (+, ×, -, ÷) are represented by letters (A, B, C, D). We need to first substitute the letters with their corresponding operators and then calculate the value of the expression following the order of operations.

Symbol Substitution Rules

The question provides the following rules for substituting symbols:

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

Original and Substituted Expression

The given expression is:

\(56 \text{ A } 102 \text{ C } 30 \text{ D } 6 \text{ B } 7\)

Substituting the letters with their corresponding operators, the expression becomes:

\(56 + 102 - 30 \div 6 \times 7\)

Applying the Order of Operations (BODMAS/PEMDAS)

To correctly evaluate the substituted expression, we must follow the standard order of mathematical operations, commonly remembered by acronyms like BODMAS or PEMDAS.

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

Let's evaluate the expression \(56 + 102 - 30 \div 6 \times 7\) step-by-step according to the BODMAS/PEMDAS rule.

Step 1: Perform Division and Multiplication (from left to right)

First, we encounter division:

\(30 \div 6 = 5\)

The expression now is:

\(56 + 102 - 5 \times 7\)

Next, perform multiplication:

\(5 \times 7 = 35\)

The expression now is:

\(56 + 102 - 35\)

Step 2: Perform Addition and Subtraction (from left to right)

First, perform addition:

\(56 + 102 = 158\)

The expression now is:

\(158 - 35\)

Finally, perform subtraction:

\(158 - 35 = 123\)

Final Result

The value of the expression \(56 \text{ A } 102 \text{ C } 30 \text{ D } 6 \text{ B } 7\) after substituting the symbols and applying the order of operations is 123.

Revision Table: Symbol to Operator Mapping

Additional Information: Understanding BODMAS/PEMDAS

The BODMAS or PEMDAS rule is fundamental in mathematics for ensuring that expressions are evaluated consistently, leading to a single correct answer. Without a defined order, different people might perform operations in a different sequence, resulting in different outcomes.

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

Both acronyms represent the same hierarchy. Division and Multiplication have the same priority and are performed from left to right as they appear in the expression. Similarly, Addition and Subtraction have the same priority and are performed from left to right.

In our calculation, we first handled division (\(30 \div 6\)) and then multiplication (\(5 \times 7\)) before proceeding to addition (\(56 + 102\)) and finally subtraction (\(158 - 35\)).