Solving the Mathematical Expression: Percentage and BODMAS

The question asks us to evaluate a mathematical expression that involves percentages and several arithmetic operations within parentheses. To solve this, we need to follow the correct order of operations, often remembered by acronyms like BODMAS or PEMDAS.

BODMAS stands for:

• Brackets (or Parentheses)
• Order (or Exponents)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

The expression is: \(12 - 20\% \text{ of } (42 \times 5 \div 15 - 18 \times 10 \div 15 + 8)\)

We will break down the solution step-by-step.

Step 1: Evaluate the Expression Inside the Parentheses

First, we must solve the part of the expression inside the parentheses: \((42 \times 5 \div 15 - 18 \times 10 \div 15 + 8)\).

Inside the parentheses, we perform Multiplication and Division before Addition and Subtraction, working from left to right.

• Calculate the first multiplication and division: \(42 \times 5 \div 15\)
• \(42 \times 5 = 210\)
• \(210 \div 15 = 14\)

So the first part is 14.

• Calculate the second multiplication and division: \(18 \times 10 \div 15\)
• \(18 \times 10 = 180\)
• \(180 \div 15 = 12\)

So the second part is 12.

Now substitute these values back into the expression inside the parentheses:

\(14 - 12 + 8\)

Perform the subtraction and addition from left to right:

• \(14 - 12 = 2\)
• \(2 + 8 = 10\)

So, the value of the expression inside the parentheses is 10.

Step 2: Rewrite the Original Expression with the Parentheses Value

Now the original expression becomes:

\(12 - 20\% \text{ of } 10\)

Step 3: Calculate the Percentage

Next, we calculate \(20\% \text{ of } 10\).

\(20\%\) can be written as a decimal (\(0.20\)) or a fraction (\(\frac{20}{100}\)).

Using the decimal form:

\(0.20 \times 10 = 2\)

Using the fraction form:

\(\frac{20}{100} \times 10 = \frac{200}{100} = 2\)

So, \(20\% \text{ of } 10\) is 2.

Step 4: Perform the Final Subtraction

Substitute the percentage value back into the expression:

\(12 - 2\)

Perform the subtraction:

\(12 - 2 = 10\)

Conclusion

The value of the expression \(12 - 20\% \text{ of } (42 \times 5 \div 15 - 18 \times 10 \div 15 + 8)\) is 10.

Revision Table: Key Concepts

Additional Information: Understanding Percentages

A percentage is a way to express a number as a fraction of 100. The word "percent" comes from the Latin phrase "per centum," meaning "per hundred." The symbol for percentage is \(\%\).

• To convert a percentage to a decimal, divide by 100 (or move the decimal point two places to the left). Example: \(20\% = \frac{20}{100} = 0.20\).
• To calculate a percentage "of" a number, convert the percentage to a decimal or fraction and multiply by the number. Example: \(20\% \text{ of } 10 = 0.20 \times 10 = 2\).

Understanding percentages is crucial for various real-world applications, such as calculating discounts, interest rates, tax amounts, and statistics.