Understanding the Symbol Substitution Problem

This problem requires us to substitute specific letters with mathematical operators based on the given rules and then evaluate the resulting expression to find the value of the question mark (?). The rules for substitution are clearly defined:

• 'A' stands for '÷'
• 'B' stands for '×'
• 'C' stands for '+'
• 'D' stands for '-'

The expression we need to evaluate is: 124 A 4 C 13 B 12 D 28 = ?

Substituting Symbols and Evaluating the Expression

First, let's replace the letters in the given expression with their corresponding mathematical operators:

Original expression: 124 A 4 C 13 B 12 D 28 = ?

After substitution: 124 ÷ 4 + 13 × 12 - 28 = ?

Now, we need to evaluate this arithmetic expression following the standard order of operations. A commonly used acronym for the order of operations is BODMAS or PEMDAS.

• B/P: Brackets or Parentheses first. (None in this expression)
• O/E: Orders or Exponents next. (None in this expression)
• DM: Division and Multiplication, from left to right.
• AS: Addition and Subtraction, from left to right.

Let's apply the BODMAS rules step-by-step:

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

First, perform the division:

\(124 \div 4 = 31\)

The expression becomes:

\(31 + 13 \times 12 - 28\)

Next, perform the multiplication:

\(13 \times 12 = 156\)

The expression now is:

\(31 + 156 - 28\)

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

Now, perform the addition:

\(31 + 156 = 187\)

The expression is simplified to:

\(187 - 28\)

Finally, perform the subtraction:

\(187 - 28 = 159\)

So, the value that comes in place of the question mark (?) is 159.

Revision Table: Key Concepts in Symbol Substitution

Additional Information: Order of Operations Explained

The order of operations is a set of rules used to clarify the sequence in which mathematical operations should be performed within an equation. This ensures consistency in calculations and guarantees a unique correct answer for any expression.

The BODMAS (or PEMDAS) rule dictates the hierarchy:

• Brackets / Parentheses
• Orders (powers, square roots, etc.) / Exponents
• Division and Multiplication (performed from left to right)
• Addition and Subtraction (performed from left to right)

When you have a mix of division and multiplication, or a mix of addition and subtraction, you work from left to right across the expression. In our problem, we performed division before multiplication because it appeared first from the left. Similarly, we performed addition before subtraction because it appeared first from the left in the remaining expression.