Solving Coding Language Expression with Symbol Substitution

This question requires us to first understand the given code language where standard mathematical operators are replaced by other operators. After substituting the operators based on the provided rules, we need to evaluate the resulting expression using the standard order of operations (BODMAS/PEMDAS).

Understanding the Coding Language Rules

The rules for operator substitution are given as follows:

• ‘+’ represents ‘×’
• ‘÷’ represents ‘+’
• ‘-’ represents ‘÷’
• ‘×’ represents ‘-’

Evaluating the Expression

The given expression is: 12 \(\div\) 6 – 2 + 10 \(\times\) 5 = ?

Now, we substitute the operators in the expression according to the coding language rules:

• Replace ‘÷’ with ‘+’
• Replace ‘–’ with ‘÷’
• Replace ‘+’ with ‘×’
• Replace ‘×’ with ‘–’

Applying these substitutions to the expression 12 \(\div\) 6 – 2 + 10 \(\times\) 5, we get:

12 + 6 \(\div\) 2 \(\times\) 10 – 5

Step-by-Step Calculation using BODMAS/PEMDAS

Now we evaluate the new expression 12 + 6 \(\div\) 2 \(\times\) 10 – 5 using the order of operations (BODMAS/PEMDAS):

Brackets
Orders (powers, square roots, etc.)
Division and Multiplication (from left to right)
Addition and Subtraction (from left to right)

Step 1: Division

Perform the division operation first.

12 + 6 \(\div\) 2 \(\times\) 10 – 5

Calculate 6 \(\div\) 2:

\(6 \div 2 = 3\)

The expression becomes:

12 + 3 \(\times\) 10 – 5

Step 2: Multiplication

Next, perform the multiplication operation.

12 + 3 \(\times\) 10 – 5

Calculate 3 \(\times\) 10:

\(3 \times 10 = 30\)

The expression becomes:

12 + 30 – 5

Step 3: Addition and Subtraction

Finally, perform addition and subtraction from left to right.

12 + 30 – 5

First, perform the addition:

\(12 + 30 = 42\)

The expression becomes:

42 – 5

Now, perform the subtraction:

\(42 – 5 = 37\)

The final answer is 37.

Revision Table: Operator Substitution

Additional Information: Order of Operations (BODMAS/PEMDAS)

The order of operations is a set of rules used to clarify which operations come first in an expression with multiple operations. This ensures a unique result for any given expression.

The acronyms BODMAS and PEMDAS represent the same order:

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

It is important to remember that Division and Multiplication have equal priority and should be performed from left to right. Similarly, Addition and Subtraction have equal priority and should also be performed from left to right.