Understanding Operator Interchange in Equations

This problem requires us to solve a mathematical equation after interchanging certain operators. The rules given are:

• The addition sign (+) is interchanged with the subtraction sign (-).
• The multiplication sign (×) is interchanged with the division sign (÷).

We need to apply these rules to the given equation and then solve it following the standard order of operations, commonly known as BODMAS or PEMDAS.

Applying the Interchange Rules

The original equation is:

\(11 \div 42 \times 3 - 69 + 25 = ?\)

Applying the given interchange rules:

• ‘÷’ becomes ‘×’
• ‘×’ becomes ‘÷’
• ‘-’ becomes ‘+’
• ‘+’ becomes ‘-’

So, the new equation after interchanging the operators is:

\(11 \times 42 \div 3 + 69 - 25 = ?\)

Solving the Modified Equation using BODMAS/PEMDAS

Now, let's solve the modified equation \(11 \times 42 \div 3 + 69 - 25\) following the order of operations:

BODMAS/PEMDAS Order:

1. Brackets (Parentheses)
2. Orders (Exponents/Powers/Roots)
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

In our equation, we only have multiplication, division, addition, and subtraction. We perform multiplication and division first, from left to right.

Step 1: Perform the multiplication \(11 \times 42\)

\(11 \times 42 = 462\)

The equation becomes:

\(462 \div 3 + 69 - 25\)

Step 2: Perform the division \(462 \div 3\)

\(462 \div 3 = 154\)

The equation becomes:

\(154 + 69 - 25\)

Now, we perform addition and subtraction from left to right.

Step 3: Perform the addition \(154 + 69\)

\(154 + 69 = 223\)

The equation becomes:

\(223 - 25\)

Step 4: Perform the subtraction \(223 - 25\)

\(223 - 25 = 198\)

Final Answer for the Operator Interchange Problem

After applying the operator interchanges and solving the modified equation using the correct order of operations, we find that the value of the equation is 198.

Thus, the number that will come in the place of the question mark (?) is 198.

Revision Table: Operator Rules & Order

Additional Information: Understanding BODMAS/PEMDAS

The BODMAS or PEMDAS rule is crucial for solving mathematical expressions correctly, especially when multiple operations are involved. It provides a standard order to follow to ensure everyone arrives at the same correct answer for a given expression.

• B/P (Brackets/Parentheses): Solve any operations inside brackets first. If there are nested brackets, work from the innermost outwards.
• O/E (Orders/Exponents): Evaluate any powers, roots, or orders next.
• D/M (Division and Multiplication): Perform all division and multiplication operations from left to right in the expression. These operations have the same priority.
• A/S (Addition and Subtraction): Finally, perform all addition and subtraction operations from left to right. These operations also have the same priority.

Following this specific order prevents ambiguity and errors in calculations. In operator interchange problems, you first apply the interchange rules to get the new expression and then use BODMAS/PEMDAS to evaluate it.