Evaluate each expression. See Example 5. 6 • 3 - 12 ÷ 4

Verified step by step guidance

1. Identify the order of operations to evaluate the expression correctly. Remember the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
2. Rewrite the expression clearly: \(6 \times 3 - 12 \div 4\).
3. Perform the multiplication and division first, moving from left to right. Calculate \(6 \times 3\) and \(12 \div 4\) separately.
4. Substitute the results of the multiplication and division back into the expression, so it becomes a simpler expression involving only addition or subtraction.
5. Finally, perform the subtraction to find the value of the expression.

Key Concepts

Order of Operations

The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed to ensure consistent results. The standard hierarchy is parentheses first, then exponents, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right).

Multiplication and Division

Multiplication and division are inverse operations and have the same precedence level. When both appear in an expression, they are evaluated from left to right. For example, in the expression 6 × 3 - 12 ÷ 4, multiplication and division must be handled before subtraction.

Subtraction

Subtraction is the operation of finding the difference between numbers and has lower precedence than multiplication and division. It is performed after all multiplication and division operations are completed, following the left-to-right rule for addition and subtraction.