Simplifying Mathematical Expressions using BODMAS/PEMDAS Rule

We are asked to simplify the mathematical expression: \(92 - 18 ( 9 + 36 \div 3 \times 12 - 27 \times 3) + 51\).

To simplify this expression, we need to follow the order of operations, commonly known as BODMAS or PEMDAS.

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

Step-by-Step Simplification

Step 1: Simplify the expression inside the parentheses

The expression inside the parentheses is \(9 + 36 \div 3 \times 12 - 27 \times 3\). According to BODMAS, we perform Division and Multiplication before Addition and Subtraction.

First, Division:

Next, Multiplication from left to right:

Now, substitute these values back into the parentheses:

Perform Addition and Subtraction from left to right:

So, the expression inside the parentheses simplifies to \(72\).

Step 2: Substitute the simplified value back into the original expression

The original expression becomes:

Note that the term \(18 (\dots)\) means \(18 \times (\dots)\).

Step 3: Perform Multiplication

According to BODMAS, Multiplication comes before Addition and Subtraction.

We can calculate this as:

So, \(18 \times 72 = 1296\).

Step 4: Substitute the multiplication result back

The expression now is:

Step 5: Perform Addition and Subtraction from left to right

First, Subtraction:

This is equivalent to \(92 + (-1296)\). When subtracting a larger number from a smaller number, the result is negative. The difference between 1296 and 92 is \(1296 - 92 = 1204\).

Next, Addition:

We are adding a positive number to a negative number. We find the difference between their absolute values and use the sign of the number with the larger absolute value. \(1204 - 51 = 1153\). The number with the larger absolute value is -1204, which is negative.

The final simplified value of the expression is \(-1153\).

Revision Table: Order of Operations

Additional Information: Understanding BODMAS/PEMDAS

The BODMAS or PEMDAS rule is crucial for ensuring a single correct answer when simplifying mathematical expressions involving multiple operations. Without a standard order, different people could get different results depending on which operation they perform first.

BODMAS stands for:

• Brackets
• Orders
• Division
• Multiplication
• Addition
• Subtraction

PEMDAS stands for:

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

These two acronyms represent the same order of operations. Division and Multiplication have equal priority and should be performed from left to right as they appear in the expression. Similarly, Addition and Subtraction have equal priority and are performed from left to right.