Solving Mathematical Expressions Using Order of Operations (BODMAS/PEMDAS)

To solve the given mathematical expression, we must follow the standard order of operations, commonly known as BODMAS or PEMDAS. This ensures that we arrive at the correct and consistent result.

Understanding the Order of Operations

The acronyms BODMAS and PEMDAS represent the sequence in which operations should be performed:

• B/P: Brackets or Parentheses first. Evaluate the expressions inside the brackets or parentheses.
• O/E: Orders or Exponents (powers, square roots, etc.) next.
• DM: Division and Multiplication come next. These are performed from left to right as they appear in the expression.
• AS: Addition and Subtraction come last. These are also performed from left to right as they appear.

Step-by-Step Solution of 60 ÷ [(16 - 8 ÷ 2) ÷ 3]

Let's solve the expression step by step:

\(60 \div [(16 - 8 \div 2) \div 3]\)

Step 1: Evaluate the innermost brackets

We first focus on the expression inside the parentheses: \( (16 - 8 \div 2) \). Inside these brackets, we have subtraction and division. According to the order of operations, division (\( \div \)) is performed before subtraction (\( - \)).

First, calculate the division:

\(8 \div 2 = 4\)

Now substitute this value back into the parentheses:

\(16 - 4\)

Next, perform the subtraction inside the parentheses:

\(16 - 4 = 12\)

So, the innermost part of the expression simplifies to 12. The original expression now becomes:

\(60 \div [(12) \div 3]\)

Step 2: Evaluate the square brackets

Now, we evaluate the expression inside the square brackets: \( [12 \div 3] \).

Perform the division:

\(12 \div 3 = 4\)

So, the expression inside the square brackets simplifies to 4. The overall expression is now:

\(60 \div 4\)

Step 3: Perform the final operation

We are left with a single division operation.

Calculate the final division:

\(60 \div 4 = 15\)

Therefore, the value of the expression \(60 \div [(16 - 8 \div 2) \div 3]\) is 15.

Verification of the Solution

Let's quickly review the steps:

• Start with the innermost brackets: \( (16 - 8 \div 2) \)
• Divide inside: \( 8 \div 2 = 4 \)
• Subtract inside: \( 16 - 4 = 12 \)
• Move to the square brackets: \( [12 \div 3] \)
• Divide inside: \( 12 \div 3 = 4 \)
• Perform the final division: \( 60 \div 4 = 15 \)

The step-by-step calculation confirms that the result is 15.

Revision Table: Key Points for Solving Expressions

Additional Information: Real-World Use of Order of Operations

Understanding the order of operations isn't just for math class; it's applied in many real-world situations and technologies. For instance, calculators and computer programs follow this order strictly to evaluate expressions correctly. In finance, calculating compound interest or loan payments involves formulas that require a specific order of operations. In physics, complex equations describing motion or energy also rely on these rules to ensure calculations are done accurately. Mastering BODMAS/PEMDAS is a fundamental skill for success in mathematics and related fields.