Solving Mathematical Expressions with Symbol Changes

This problem requires us to first understand the given rules for symbol substitution in a mathematical expression and then calculate the value of the modified expression using the standard order of operations.

Understanding the Symbol Replacement Rules

The question provides specific rules on how to replace the standard mathematical operators:

• The minus sign (‘–’) is replaced by the division sign (‘÷’).
• The plus sign (‘+’) is replaced by the multiplication sign (‘×’).
• The division sign (‘÷’) is replaced by the minus sign (‘–’).
• The multiplication sign (‘×’) is replaced by the plus sign (‘+’).

Applying the Symbol Changes

The original expression is: $80 – 20 + 10 ÷ 8 × 10$

Applying the given rules, we substitute each symbol:

• ‘–’ becomes ‘÷’
• ‘+’ becomes ‘×’
• ‘÷’ becomes ‘–’
• ‘×’ becomes ‘+’

So, the new expression becomes: $80 \div 20 \times 10 – 8 + 10$

Evaluating the Modified Expression

Now we need to evaluate the expression $80 \div 20 \times 10 – 8 + 10$ using the BODMAS or PEMDAS rule, which defines the order of operations:

Brackets / Parentheses
Orders / Exponents
Division and Multiplication (from left to right)
Addition and Subtraction (from left to right)

Let's solve step-by-step:

1. First, perform the Division: $$80 \div 20 = 4$$ The expression is now: $4 \times 10 – 8 + 10$
2. Next, perform the Multiplication: $$4 \times 10 = 40$$ The expression is now: $40 – 8 + 10$
3. Finally, perform Addition and Subtraction from left to right: $$40 – 8 = 32$$ The expression is now: $32 + 10$$$32 + 10 = 42$$

The value of the expression after applying the symbol changes and evaluating is 42.

Final Answer Derivation

Following the steps above, the evaluation of $80 \div 20 \times 10 – 8 + 10$ results in 42.

Revision Table: Symbol Operations

Additional Information: Order of Operations

The order of operations is a crucial concept in mathematics to ensure consistent results when evaluating expressions with multiple operations. The acronyms BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) or PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) help remember the correct sequence.

• Operations within brackets or parentheses are always performed first.
• Powers or exponents are calculated next.
• Multiplication and division are performed next, working from left to right.
• Finally, addition and subtraction are performed, working from left to right.

Strictly following this order prevents ambiguity and ensures that everyone arrives at the same result for a given expression.