Evaluating Expressions with Symbol Mapping

The problem asks us to evaluate a mathematical expression where standard arithmetic operations are represented by specific symbols. We are given the mapping of each symbol to its corresponding operation.

Understanding the Symbol Mapping

Let's first list the provided symbol-to-operation mapping:

Translating the Expression

The given expression is: 9 @ 114 $ 19 % 5 # 21

Now, we will replace each symbol with its corresponding arithmetic operation based on the mapping:

• Replace '@' with '+': The expression becomes 9 + 114 $ 19 % 5 # 21.
• Replace '$' with '/': The expression becomes 9 + 114 / 19 % 5 # 21.
• Replace '%' with '*': The expression becomes 9 + 114 / 19 * 5 # 21.
• Replace '#' with '-': The expression becomes 9 + 114 / 19 * 5 - 21.

So, the expression to evaluate is: $9 + 114 \div 19 \times 5 - 21$.

Evaluating the Expression Using Order of Operations (BODMAS/PEMDAS)

To find the value of the expression $9 + 114 \div 19 \times 5 - 21$, we need to follow the order of operations (BODMAS or PEMDAS):

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

Let's evaluate the expression step-by-step:

1. Division and Multiplication: We perform division and multiplication from left to right.
   • First, perform the division: $114 \div 19$.

     Calculating $114 \div 19$:

     $$ \frac{114}{19} = 6 $$

     The expression now becomes: $9 + 6 \times 5 - 21$.

   • Next, perform the multiplication: $6 \times 5$.

     Calculating $6 \times 5$:

     $$ 6 \times 5 = 30 $$

     The expression now becomes: $9 + 30 - 21$.

2. Addition and Subtraction: We perform addition and subtraction from left to right.
   • First, perform the addition: $9 + 30$.

     Calculating $9 + 30$:

     $$ 9 + 30 = 39 $$

     The expression now becomes: $39 - 21$.

   • Next, perform the subtraction: $39 - 21$.

     Calculating $39 - 21$:

     $$ 39 - 21 = 18 $$

     The final value of the expression is $18$.

Conclusion

By translating the symbols to operations and following the order of operations, we found the value of the expression 9 @ 114 $ 19 % 5 # 21 to be 18.

Revision Table: Evaluating Expressions

Additional Information: Order of Operations

The order of operations is a set of rules used to clarify which procedures should be performed first within a given mathematical expression. This ensures a unique result for every expression. The commonly used acronyms like BODMAS and PEMDAS help remember the order:

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

It's crucial to remember that Division and Multiplication have the same priority, and Addition and Subtraction have the same priority. When you have a sequence of these operations, you perform them from left to right in the expression.