Understanding the Problem

The question asks us to find the value of a given mathematical expression after interchanging certain operators. We are told to swap '+' with '-' and '×' with '÷'. Then we need to evaluate the new expression to find the result.

Operator Interchange Rules

The rules for interchanging operators are:

• '+' becomes '-'
• '-' becomes '+'
• '×' becomes '÷'
• '÷' becomes '×'

Applying the Operator Changes

The original expression is: \(84 \times 7 - 21 \div 4 + 29\)

Applying the interchange rules:

• The '×' between 84 and 7 becomes '÷'.
• The '-' between 7 and 21 becomes '+'.
• The '÷' between 21 and 4 becomes '×'.
• The '+' between 4 and 29 becomes '-'.

So, the new expression becomes: \(84 \div 7 + 21 \times 4 - 29\)

Evaluating the Modified Expression

Now we need to evaluate the expression \(84 \div 7 + 21 \times 4 - 29\) using the order of operations (BODMAS/PEMDAS).

The order of operations is:

1. Brackets
2. Orders (powers, roots)
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

Let's evaluate step-by-step:

First, perform Division and Multiplication from left to right:

• Calculate \(84 \div 7\):
  \(84 \div 7 = 12\)
• Calculate \(21 \times 4\):
  \(21 \times 4 = 84\)

The expression now is: \(12 + 84 - 29\)

Next, perform Addition and Subtraction from left to right:

• Calculate \(12 + 84\):
  \(12 + 84 = 96\)
• Calculate \(96 - 29\):
  \(96 - 29 = 67\)

The final result is 67.

Final Answer

After interchanging the operators as specified and evaluating the new expression, the result is 67.

Revision Table: Operator Interchange & BODMAS

Review the key steps involved in solving this type of problem:

• Understand the operator interchange rules clearly.
• Rewrite the expression with the new operators.
• Apply the BODMAS/PEMDAS rule for correct evaluation sequence.
• Perform calculations step-by-step following the order of operations.

Additional Information: Order of Operations (BODMAS/PEMDAS)

The order of operations is a standard rule used to clarify which procedures should be performed first in a given mathematical expression. This ensures that everyone gets the same answer.

• BODMAS: Brackets, Orders, Division and Multiplication, Addition and Subtraction.
• PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

Both acronyms represent the same concept, just using slightly different terms. Division and Multiplication have the same priority and are performed from left to right. Similarly, Addition and Subtraction have the same priority and are also performed from left to right.