Solving the Operator Substitution Equation

This question requires us to apply a set of rules to change the mathematical operators in a given equation and then solve the new equation following the standard order of operations (BODMAS/PEMDAS).

Understanding the Operator Substitution Rules

The problem defines specific substitutions for the standard mathematical operators:

Applying the Substitution to the Equation

The given equation is:

\(7 \div 20 \ndash; 5 \times 20 + 2 = ?\)

Now, we replace each original operator with its corresponding new operator according to the rules:

• The ÷ between 7 and 20 becomes +.
• The – between 20 and 5 becomes ×.
• The × between 5 and 20 becomes ÷.
• The + between 20 and 2 becomes –.

So, the new equation after substitution is:

\(7 + 20 \times 5 \div 20 \ndash; 2 = ?\)

Solving the Equation using Order of Operations (BODMAS/PEMDAS)

We need to solve the new equation \(7 + 20 \times 5 \div 20 \ndash; 2\) by following the order of operations:

1. Brackets (None in this equation)
2. Orders or Exponents (None in this equation)
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

Let's perform the operations step by step:

First, perform the multiplication and division from left to right:

\(7 + \underline{20 \times 5} \div 20 \ndash; 2\)

\(7 + 100 \div 20 \ndash; 2\)

Next, perform the division:

\(7 + \underline{100 \div 20} \ndash; 2\)

\(7 + 5 \ndash; 2\)

Now, perform the addition and subtraction from left to right:

\(\underline{7 + 5} \ndash; 2\)

\(12 \ndash; 2\)

Finally, perform the subtraction:

\(12 \ndash; 2 = 10\)

So, the value that comes in place of ? is 10.

Revision Table: Key Concepts for Operator Substitution

Additional Information on Mathematical Reasoning

Operator substitution questions are common in mathematical reasoning and logical aptitude tests. They check your ability to follow instructions precisely and apply fundamental mathematical principles like the order of operations. Here are some related concepts:

• Symbol Substitution: Similar to operator substitution, but symbols (like #, @, $) represent numbers or operations.
• Coding-Decoding: Often involves substituting letters, numbers, or symbols based on a specific code or pattern, which can sometimes include mathematical operations.
• Equation Solving: The final step requires basic equation-solving skills once the operators are correctly substituted.

Always double-check the substitution rules and perform calculations step-by-step to avoid errors. These questions test analytical thinking and attention to detail.