Solving Mathematical Expressions Using Order of Operations

To solve the given mathematical expression, we need to follow the order of operations, often remembered by the acronyms BODMAS or PEMDAS.

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

Step-by-Step Solution

Let's break down the expression: \(22 - (1/4)\{-5 - (-48) \div (-16)\}\).

Step 1: Solve the Innermost Brackets

First, we need to evaluate the expression inside the curly braces, specifically the division:

\((-48) \div (-16)\)

Dividing a negative number by a negative number results in a positive number.

\((-48) \div (-16) = 48 \div 16 = 3\)

Step 2: Continue Solving Inside the Braces

Now substitute the result back into the expression inside the curly braces:

\(\{-5 - 3\}\)

Subtracting 3 from -5 gives:

\(-5 - 3 = -8\)

Step 3: Perform Multiplication

Next, we perform the multiplication outside the curly braces:

\((1/4)\{-8\}\)

This is equal to \((1/4) \times (-8)\):

\((1/4) \times (-8) = -8/4 = -2\)

Step 4: Perform Subtraction

Finally, we perform the subtraction:

\(22 - (-2)\)

Subtracting a negative number is the same as adding the corresponding positive number:

\(22 - (-2) = 22 + 2 = 24\)

Summary of the Calculation

Let's write down the steps together:

\(22 - (1/4)\{-5 - (-48) \div (-16)\}\)

\(= 22 - (1/4)\{-5 - 3\}\) (Solved division inside braces)

\(= 22 - (1/4)\{-8\}\) (Solved subtraction inside braces)

\(= 22 - (-2)\) (Performed multiplication)

\(= 22 + 2\) (Changed subtraction of negative to addition)

\(= 24\) (Performed final addition)

Final Answer Verification

Let's review the options provided:

Our calculated result is 24, which matches Option 2.

Revision Table: Key Concepts

Additional Information: BODMAS vs PEMDAS

The acronyms BODMAS and PEMDAS are essentially the same and help remember the order of operations. The difference lies mainly in terminology:

• BODMAS: Brackets, Orders (powers, square roots, etc.), Division, Multiplication, Addition, Subtraction.
• PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Division and Multiplication are performed from left to right, whichever comes first. Similarly, Addition and Subtraction are performed from left to right, whichever comes first.

Understanding this order is crucial for correctly evaluating mathematical expressions and avoiding errors.