Solving Coding Language Mathematical Equations

This question asks us to solve a mathematical expression after changing the operators according to a specific code language. We are given the rules for how each standard mathematical operator (+, -, ×, ÷) is represented by another operator in this code.

Understanding the Coding Language Rules

The problem defines the following code rules for mathematical symbols:

• The symbol '+' represents '×' (multiplication).
• The symbol '-' represents '+' (addition).
• The symbol '×' represents '÷' (division).
• The symbol '÷' represents '-' (subtraction).

We can summarize these rules in a table for clarity:

Applying the Rules to the Equation

The given equation is: \(8 + 3 \times 4 - 2 = ?\)

Now, we will replace each original symbol in the equation with the symbol it represents in the given code language, based on the rules:

• The '+' between 8 and 3 becomes '×'.
• The '×' between 3 and 4 becomes '÷'.
• The '-' between 4 and 2 becomes '+'.

So, the transformed equation becomes:

\(8 \times 3 \div 4 + 2 = ?\)

Evaluating the Transformed Equation

To solve the transformed equation, \(8 \times 3 \div 4 + 2\), we need to follow the order of operations. The standard order of operations is often remembered using 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)

Our transformed equation is \(8 \times 3 \div 4 + 2\). It contains multiplication, division, and addition.

Following BODMAS/PEMDAS, we perform multiplication and division from left to right first.

1. First, perform the operations from left to right: \(8 \times 3 = 24\). The equation is now: \(24 \div 4 + 2\).
2. Next, perform the division: \(24 \div 4 = 6\). The equation is now: \(6 + 2\).
3. Finally, perform the addition: \(6 + 2 = 8\).

So, the result of the transformed equation is 8.

Final Answer

After transforming the equation \(8 + 3 \times 4 - 2\) according to the given code language rules (\(+\) means \(\times\), \(-\) means \(+\), \(\times\) means \(\div\), \(\div\) means \(-\)), we get the new expression \(8 \times 3 \div 4 + 2\). Evaluating this expression using the order of operations (BODMAS/PEMDAS) gives us the result 8.

Revision Table: Coding Language Operators

It's helpful to quickly reference the operator changes when solving such problems:

Additional Information: Types of Coding Language Problems

Coding language problems in reasoning tests often involve substituting symbols or letters based on a given key. Besides mathematical operations, they can include:

• Letter Coding: Letters are replaced by other letters or numbers following a pattern (e.g., shifting letters in the alphabet, replacing with position numbers).
• Number/Symbol Coding: Words are assigned numerical values or symbols based on specific rules (e.g., sum of letter positions, specific symbols for specific letters).
• Mixed Coding: A combination of letters, numbers, and symbols are used in the code.
• Sentence Coding: Entire sentences or phrases are coded, and you need to decode parts based on common words or patterns.

The key to solving these problems is carefully understanding the given rule or pattern and applying it consistently to the question asked, just like we did with the mathematical operators here.