Solving the Equation with Interchanged Operators

The problem asks us to find the value of the question mark (?) in a given equation after interchanging certain mathematical operators. The original equation is:

\(42 \times 7 \div 13 - 87 + 12 = ?\)

The rule for interchanging operators is:

• '+' is interchanged with '-'
• '×' is interchanged with '÷'

Let's apply these interchange rules to the original equation. The new equation becomes:

\(42 \div 7 \times 13 + 87 - 12 = ?\)

Solving the New Equation Step-by-Step

Now, we need to solve this new equation following the order of operations (BODMAS/PEMDAS: Brackets, Orders (powers, roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right)).

The equation is: \(42 \div 7 \times 13 + 87 - 12\)

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

First, perform the division: \(42 \div 7\)

\(42 \div 7 = 6\)

The equation is now: \(6 \times 13 + 87 - 12\)

Next, perform the multiplication: \(6 \times 13\)

\(6 \times 13 = 78\)

The equation is now: \(78 + 87 - 12\)

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

First, perform the addition: \(78 + 87\)

\(78 + 87 = 165\)

The equation is now: \(165 - 12\)

Finally, perform the subtraction: \(165 - 12\)

\(165 - 12 = 153\)

So, the value of the question mark (?) is 153.

Summary of the Calculation

Original Equation: \(42 \times 7 \div 13 - 87 + 12\)

Interchanged Operators:

• \(+\) becomes \(-\)
• \(-\) becomes \(+\)
• \(\times\) becomes \(\div\)
• \(\div\) becomes \(\times\)

New Equation: \(42 \div 7 \times 13 + 87 - 12\)

Calculation:

• \(42 \div 7 = 6\)
• \(6 \times 13 = 78\)
• \(78 + 87 = 165\)
• \(165 - 12 = 153\)

The result is 153.

Revision Table: Operator Interchange Rules

Additional Information: Order of Operations (BODMAS/PEMDAS)

When solving mathematical expressions, we follow a specific order to ensure everyone gets the same correct answer. This order is often remembered using acronyms like BODMAS or PEMDAS.

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

In the calculation \(42 \div 7 \times 13 + 87 - 12\), we first performed division (\(42 \div 7\)), then multiplication (\(6 \times 13\)), then addition (\(78 + 87\)), and finally subtraction (\(165 - 12\)). Division and multiplication are at the same level, as are addition and subtraction. Operations at the same level are performed from left to right.