Evaluating Mathematical Expressions with Order of Operations

To find the value of the expression $12 + 3(-2 \times 3) - (18 \div 6)$, we need to follow the order of operations. A common acronym to remember the order of operations is BODMAS or PEMDAS.

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

Let's evaluate the expression step-by-step according to the BODMAS/PEMDAS rule.

Step-by-Step Calculation of the Expression

The given expression is:

\(12 + 3(-2 \times 3) - (18 \div 6)\)

Step 1: Solve the operations inside the Brackets (Parentheses).

There are two sets of parentheses in the expression.

First parenthesis: \((-2 \times 3)\)

\(-2 \times 3 = -6\)

Second parenthesis: \((18 \div 6)\)

\(18 \div 6 = 3\)

Now substitute these values back into the main expression:

\(12 + 3(-6) - (3)\)

This simplifies to:

\(12 + 3 \times (-6) - 3\)

Step 2: Perform Multiplication and Division (from left to right).

In the current expression \(12 + 3 \times (-6) - 3\), we have a multiplication operation: \(3 \times (-6)\).

\(3 \times (-6) = -18\)

Substitute this value back into the expression:

\(12 + (-18) - 3\)

This is the same as:

\(12 - 18 - 3\)

Step 3: Perform Addition and Subtraction (from left to right).

Now we perform the addition and subtraction from left to right.

First, \(12 - 18\):

\(12 - 18 = -6\)

Now, substitute this result back into the expression:

\(-6 - 3\)

Finally, perform the last subtraction:

\(-6 - 3 = -9\)

Result of the Expression Evaluation

The value of the expression \(12 + 3(-2 \times 3) - (18 \div 6)\) is \(-9\).

Comparing the Result with Options

Let's compare our calculated result \(-9\) with the given options:

• Option 1: \(5\)
• Option 2: \(9\)
• Option 3: \(-9\)
• Option 4: \(-5\)

Our result, \(-9\), matches Option 3.

Revision Table: Mathematical Expression Evaluation

Additional Information: Understanding Order of Operations (BODMAS/PEMDAS)

The order of operations is a fundamental concept in mathematics. Without it, expressions could be interpreted in different ways, leading to different results. For example, \(2 + 3 \times 4\). If you add first (\(2+3=5\)) and then multiply (\(5 \times 4 = 20\)), you get 20. If you multiply first (\(3 \times 4 = 12\)) and then add (\(2 + 12 = 14\)), you get 14. The order of operations tells us multiplication comes before addition, so the correct answer is 14.

Remember that Division and Multiplication have the same priority, as do Addition and Subtraction. When operations of the same priority appear in an expression, you perform them from left to right.

Applying BODMAS or PEMDAS systematically helps avoid errors when evaluating complex expressions like the one in this question.