Evaluating the Given Mathematical Expression

The problem requires us to replace specific letters within an expression with mathematical operators and then evaluate the resulting expression. We are given the following replacement rules:

• ‘A’ is replaced by ‘+’ (Addition)
• ‘B’ is replaced by ‘-‘ (Subtraction)
• ‘C’ is replaced by ‘÷’ (Division)
• ‘D’ is replaced by ‘×’ (Multiplication)

The given expression is: 15A25B35C5D7

Applying the Replacements to the Expression

Let's substitute the letters in the expression with their corresponding operators:

15 A 25 B 35 C 5 D 7

Replacing the letters gives us:

15 + 25 - 35 ÷ 5 × 7

So the mathematical expression we need to evaluate is: $\text{15 + 25 - 35} \div \text{5} \times \text{7}$

Solving the Expression using Order of Operations (BODMAS/PEMDAS)

To correctly evaluate the expression, we must follow the standard order of operations, often remembered by acronyms like BODMAS or PEMDAS.

• B/P: Brackets/Parentheses first.
• O/E: Orders/Exponents (powers, square roots, etc.) next.
• DM: Division and Multiplication from left to right.
• AS: Addition and Subtraction from left to right.

Let's evaluate the expression $\text{15 + 25 - 35} \div \text{5} \times \text{7}$ step by step:

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

First, we encounter the division: $35 \div 5$.

$\text{35} \div \text{5} = \text{7}$

The expression becomes: $\text{15 + 25 - 7} \times \text{7}$

Next, we encounter the multiplication: $7 \times 7$.

$\text{7} \times \text{7} = \text{49}$

The expression now is: $\text{15 + 25 - 49}$

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

First, we perform the addition: $15 + 25$.

$\text{15 + 25} = \text{40}$

The expression becomes: $\text{40 - 49}$

Finally, perform the subtraction: $40 - 49$.

$\text{40 - 49} = \text{-9}$

Final Result of the Evaluation

After performing all the operations following the BODMAS/PEMDAS rule, the value of the expression 15A25B35C5D7 is -9.

Revision Table: Operators and Order

Additional Information: Understanding BODMAS/PEMDAS

The BODMAS (or PEMDAS) rule is crucial for solving mathematical expressions correctly. It provides a standard order to follow when multiple operations are present. If this order is not followed, the result may be incorrect. Remember that Division and Multiplication have the same priority and are performed from left to right as they appear in the expression. Similarly, Addition and Subtraction have the same priority and are performed from left to right after multiplication and division are completed.

For example, in the expression $35 \div 5 \times 7$, we perform division first because it appears to the left of multiplication: $(35 \div 5) \times 7 = 7 \times 7 = 49$. If we did multiplication first (which would be incorrect here), we might calculate $35 \div (5 \times 7) = 35 \div 35 = 1$, which is wrong.

Always work through the operations in the specified order to arrive at the correct single value for the expression.