Evaluating Mathematical Expressions Using BODMAS

This question asks us to evaluate a mathematical expression by following the correct order of operations. The expression is given as:

20 - 2[25% of (15 × 8 ÷ 6 + 12)]

To solve this, we must use the BODMAS rule (or PEMDAS), which dictates the sequence for performing mathematical operations:

• Brackets (or Parentheses)
• Orders (powers, square roots, etc.) or Exponents
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Let's break down the expression step by step according to the BODMAS rule.

Step-by-Step Evaluation

We start with the innermost part of the expression, which is inside the parentheses:

(15 × 8 ÷ 6 + 12)

Step 1: Inside the Parentheses - Multiplication and Division

Within the parentheses, we have multiplication and division. We perform these operations from left to right.

• First, multiplication: \(15 \times 8 = 120\)
• Then, division: \(120 \div 6 = 20\)

The expression inside the parentheses now becomes:

\((20 + 12)\)

Step 2: Inside the Parentheses - Addition

Now, perform the addition inside the parentheses:

\(20 + 12 = 32\)

The original expression now simplifies to:

20 - 2[25% of 32]

Step 3: Calculate the Percentage

Next, we calculate "25% of 32". Remember that 25% can be written as \(\frac{25}{100}\) or \(\frac{1}{4}\).

\(25\% \text{ of } 32 = \frac{25}{100} \times 32 = \frac{1}{4} \times 32\)

Performing the multiplication:

\(\frac{1}{4} \times 32 = \frac{32}{4} = 8\)

The expression inside the square brackets [] is now 8. The main expression is now:

20 - 2[8]

Remember that 2[8] means \(2 \times 8\).

Step 4: Multiplication

Perform the multiplication:

\(2 \times 8 = 16\)

The expression is now:

20 - 16

Step 5: Subtraction

Finally, perform the subtraction:

\(20 - 16 = 4\)

The value of the expression is 4.

Summary of Steps

1. Solve inside parentheses: \(15 \times 8 \div 6 + 12 \implies 120 \div 6 + 12 \implies 20 + 12 = 32\)
2. Calculate percentage: \(25\% \text{ of } 32 = 8\)
3. Perform multiplication: \(2 \times 8 = 16\)
4. Perform subtraction: \(20 - 16 = 4\)

Thus, the result of the expression is 4.

Revision Table: BODMAS/PEMDAS Order

Additional Information: Percentage Calculation and Order of Operations

Understanding percentages and the strict order of operations is crucial for accurately solving mathematical expressions.

Understanding Percentage

A percentage represents a part of a whole expressed as a fraction of 100. For example, 25% means 25 out of 100, or \(\frac{25}{100}\). To find a percentage of a number, you convert the percentage to a decimal or fraction and multiply by the number.

Example: \(25\% \text{ of } 32 = \frac{25}{100} \times 32 = 0.25 \times 32 = 8\).

Importance of Order of Operations

The order of operations ensures that everyone gets the same answer when evaluating an expression. Without a standard order, different people might perform operations in a different sequence, leading to varying results. BODMAS/PEMDAS provides this standard.

For instance, in \(15 \times 8 \div 6\), doing division first (\(8 \div 6\)) and then multiplication would give a different result (and often involve fractions earlier) than doing multiplication first (\(15 \times 8\)) and then division, although in this specific case of sequential multiplication and division, the result is the same if done left-to-right as per the rule.

Always remember to work from left to right for operations at the same level (like division and multiplication, or addition and subtraction).