Solving Mathematical Expressions with Letter Operators

The question asks us to find the value of a given expression where letters represent mathematical operators. We are provided with the following mapping:

• A denotes '+' (Addition)
• B denotes '×' (Multiplication)
• C denotes '-' (Subtraction)
• D denotes '÷' (Division)

The given expression is: 50 A 86 C 40 D 10 B 5

Substituting Letters with Operators

Let's replace the letters in the expression with their corresponding mathematical operators based on the provided mapping:

50 A 86 C 40 D 10 B 5 becomes:

50 + 86 - 40 ÷ 10 × 5

Applying the Order of Operations (BODMAS/PEMDAS)

To correctly evaluate this mathematical expression, we must follow the standard order of operations. This order is often remembered using acronyms like BODMAS or PEMDAS.

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

Our expression is 50 + 86 - 40 ÷ 10 × 5. There are no brackets or exponents, so we start with Division and Multiplication from left to right.

Step-by-Step Calculation

Let's evaluate the expression step by step:

Step 1: Perform Division.
In the expression 50 + 86 - 40 ÷ 10 × 5, the first operation according to BODMAS/PEMDAS (DM) is division: 40 ÷ 10.

\(40 \div 10 = 4\)

The expression now becomes: 50 + 86 - 4 × 5

Step 2: Perform Multiplication.
Next, we perform multiplication: 4 × 5.

\(4 \times 5 = 20\)

The expression now becomes: 50 + 86 - 20

Step 3: Perform Addition and Subtraction (from left to right).
Finally, we perform addition and subtraction from left to right. Addition comes first from the left: 50 + 86.

\(50 + 86 = 136\)

The expression now becomes: 136 - 20

Now, perform the final subtraction:

\(136 - 20 = 116\)

Final Value of the Expression

After following the order of operations, the value of the expression 50 A 86 C 40 D 10 B 5 is 116.

Revision Table: Operator Mapping

This table summarizes the mapping used in the problem:

Additional Information: Understanding BODMAS/PEMDAS

The BODMAS or PEMDAS rule is crucial for solving mathematical expressions correctly. It ensures that everyone gets the same answer for the same expression by following a universal sequence of operations.

• Brackets/Parentheses: Operations inside brackets are always performed first.
• Orders/Exponents: Powers and roots are evaluated next.
• Division and Multiplication: These have equal priority. You perform them from left to right as they appear in the expression.
• Addition and Subtraction: These also have equal priority. You perform them from left to right as they appear in the expression.

Failing to follow this order can lead to an incorrect result. In our problem, doing addition or subtraction before division or multiplication would give a different, wrong answer. Always remember DM (Division/Multiplication) before AS (Addition/Subtraction), performing from left to right within each pair.