Evaluating Mathematical Expressions Using BODMAS/PEDMAS

This question asks us to evaluate a mathematical expression following the standard order of operations. The universally accepted rule for the order of operations is often remembered using acronyms like BODMAS or PEDMAS.

• BODMAS stands for: Brackets, Order (powers/roots), Division and Multiplication (left-to-right), Addition and Subtraction (left-to-right).
• PEDMAS stands for: Parentheses, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right).

Both acronyms essentially describe the same order. We need to solve the expression step-by-step, starting with the operations inside the innermost brackets, then moving outwards, and finally performing division/multiplication and addition/subtraction in order from left to right.

Step-by-Step Evaluation of the Expression

The expression to evaluate is: \(5 - [96 \div 4 \text{ of } 3 - (16 - 55 \div 5)]\)

Step 1: Solve the innermost brackets

First, let's focus on the expression inside the parentheses \((16 - 55 \div 5)\).

Inside these parentheses, we have subtraction and division. According to BODMAS/PEDMAS, division comes before subtraction.

Calculate the division: \(55 \div 5 = 11\)

Now, substitute this value back into the parentheses:

\((16 - 11) = 5\)

The main expression now becomes:

\(5 - [96 \div 4 \text{ of } 3 - 5]\)

Step 2: Evaluate the "of" operation

Next, we handle the "of" operation inside the square brackets. "4 of 3" means \(4 \times 3\).

Calculate "4 of 3": \(4 \times 3 = 12\)

Substitute this value back into the expression:

\(5 - [96 \div 12 - 5]\)

Step 3: Solve the operations inside the square brackets

Now, evaluate the expression inside the square brackets \([96 \div 12 - 5]\). We have division and subtraction. Division comes before subtraction.

Calculate the division: \(96 \div 12 = 8\)

Substitute this value back into the brackets:

\([8 - 5] = 3\)

The main expression is now simplified to:

\(5 - 3\)

Step 4: Perform the final subtraction

Finally, perform the remaining subtraction:

\(5 - 3 = 2\)

Thus, the value of the expression \(5 - [96 \div 4 \text{ of } 3 - (16 - 55 \div 5)]\) is 2.

The final result of the evaluation is 2.

Revision Table: Order of Operations (BODMAS/PEDMAS)

Additional Information: Understanding BODMAS/PEDMAS

The BODMAS or PEDMAS rule is crucial for ensuring that everyone gets the same result when evaluating a mathematical expression. Without a standard order, expressions could be interpreted in multiple ways, leading to different answers.

• Grouping Symbols: Always start with the innermost grouping symbols (parentheses, brackets, braces). Work your way outwards.
• 'Of' vs. Multiplication: The term "of" typically indicates multiplication, especially in the context of fractions or percentages (e.g., "half of 10" means \(0.5 \times 10\)). In expressions like "4 of 3", it is treated as multiplication and evaluated at the "Order" or "Exponents" stage, before standard multiplication/division. Some interpretations place 'of' at the same priority as multiplication/division, but solving it before division/multiplication is safer as per traditional BODMAS.
• Left to Right Rule: For operations at the same level of priority (like multiplication and division, or addition and subtraction), you must perform them in the order they appear from left to right. For example, in \(10 \div 2 \times 5\), you do the division first (\(10 \div 2 = 5\)), then the multiplication (\(5 \times 5 = 25\)). Doing multiplication first (\(2 \times 5 = 10\), then \(10 \div 10 = 1\)) would be incorrect.