Evaluating Mathematical Expressions with Operator Replacements

This problem requires us to substitute letters with mathematical operators and then evaluate the resulting expression using the correct order of operations. We are given the following substitutions:

The given expression with letters is:

8 N 9 L 60 P 3 M 13

Substituting Letters with Operators

Now, let's replace each letter in the expression with the corresponding mathematical operator as defined:

• Replace 'N' with '×'
• Replace 'L' with '+'
• Replace 'P' with '÷'
• Replace 'M' with '-'

The expression becomes:

8 $\times$ 9 + 60 $\div$ 3 - 13

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

To solve this expression, we must follow the standard order of operations. The BODMAS or PEMDAS rule dictates the sequence:

• B/P: Brackets/Parentheses
• O/E: Orders/Exponents
• D/M: Division and Multiplication (from left to right)
• A/S: Addition and Subtraction (from left to right)

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

The expression is: 8 $\times$ 9 + 60 $\div$ 3 - 13

Step 1: Perform Division

According to the order of operations, Division comes before Multiplication, Addition, and Subtraction. We have 60 $\div$ 3.

60 $\div$ 3 = 20

The expression now is: 8 $\times$ 9 + 20 - 13

Step 2: Perform Multiplication

Next, we perform Multiplication. We have 8 $\times$ 9.

8 $\times$ 9 = 72

The expression now is: 72 + 20 - 13

Step 3: Perform Addition

Now, we perform Addition. We have 72 + 20.

72 + 20 = 92

The expression now is: 92 - 13

Step 4: Perform Subtraction

Finally, we perform Subtraction. We have 92 - 13.

92 - 13 = 79

The final value of the expression 8 N 9 L 60 P 3 M 13 is 79.

Revision Table: Operator Replacements and Evaluation

Additional Information: Understanding Order of Operations

The order of operations is crucial in mathematics to ensure that expressions are evaluated consistently. Without a defined order, different people could arrive at different answers for the same expression. BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) or PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) are mnemonics used worldwide to remember this order. Division and Multiplication have the same priority and should be 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.

In this problem, understanding the correct sequence – Division first, then Multiplication, followed by Addition, and finally Subtraction – was key to arriving at the correct numerical result after replacing the letter symbols with their corresponding operators.