Solving Coding Language Expression with Operator Changes

This problem requires us to decode a mathematical expression based on given rules where standard operators are replaced by different ones. We need to apply these rules to the expression and then calculate the result using the correct order of operations.

Understanding the Coding Rules

The question provides specific rules for changing the operators:

• ‘+’ represents ‘×’
• ‘–‘ represents ‘+’
• ‘ב represents ‘÷’

Applying the Rules to the Expression

The given mathematical expression is:

\(2 \ndash 6 \times 3 + 4\)

Now, we substitute the operators according to the given coding rules:

• The ‘–‘ between 2 and 6 becomes ‘+’.
• The ‘ב between 6 and 3 becomes ‘÷’.
• The ‘+’ between 3 and 4 becomes ‘×’.

So, the expression transforms into:

\(2 + 6 \div 3 \times 4\)

Calculating the Transformed Expression

Now, we need to evaluate the new expression \(2 + 6 \div 3 \times 4\) following the order of operations (BODMAS/PEMDAS): Brackets, Orders (powers and square roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

Step 1: Perform Division and Multiplication from left to right.

• First, perform the division: \(6 \div 3 = 2\). The expression becomes \(2 + 2 \times 4\).
• Next, perform the multiplication: \(2 \times 4 = 8\). The expression becomes \(2 + 8\).

Step 2: Perform Addition.

• Finally, perform the addition: \(2 + 8 = 10\).

Thus, the value of the expression in the given code language is 10.

Summary of Calculation

Original expression: \(2 \ndash 6 \times 3 + 4\)

Coded expression: \(2 + 6 \div 3 \times 4\)

Calculation steps:

\(2 + (6 \div 3) \times 4\)

\(2 + 2 \times 4\)

\(2 + 8\)

\(10\)

The result of the expression \(2 \ndash 6 \times 3 + 4\) in the given code language is 10.

Revision Table: Operator Coding

Additional Information: Order of Operations

When solving mathematical expressions, especially those involving multiple operations, it is crucial to follow a specific order to ensure a correct result. This order is commonly known as BODMAS or PEMDAS.

• B/P: Brackets / Parentheses - Solve expressions inside brackets first.
• O/E: Orders / Exponents - Solve powers, square roots, etc., next.
• DM: Division and Multiplication - Perform these operations from left to right.
• AS: Addition and Subtraction - Perform these operations from left to right.

In our problem, after converting the operators, we had \(2 + 6 \div 3 \times 4\). We performed division (\(6 \div 3\)) first because it appears before multiplication when reading from left to right within the DM group. Then, we performed multiplication (\(2 \times 4\)). Finally, we performed the addition (\(2 + 8\)). Adhering to this order is key in solving such problems correctly.