Evaluate each expression. See Example 5. 10 + 30 ÷ 2 • 3

Verified step by step guidance

1. Identify the order of operations to solve 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 to clearly see the operations: \(10 + 30 \div 2 \times 3\).
3. Perform the division and multiplication first, moving from left to right. Start with \(30 \div 2\).
4. Next, multiply the result of the division by 3: \((30 \div 2) \times 3\).
5. Finally, add 10 to the result of the multiplication to complete the expression: \(10 + \left((30 \div 2) \times 3\right)\).

Key Concepts

Order of Operations (PEMDAS/BODMAS)

The order of operations dictates the sequence in which mathematical operations are performed to ensure consistent results. Multiplication and division are performed before addition and subtraction, moving from left to right. This concept is essential to correctly evaluate expressions like 10 + 30 ÷ 2 • 3.

Division and Multiplication as Equal Priority Operations

Division and multiplication share the same priority level and are evaluated from left to right. In the expression 30 ÷ 2 • 3, you first divide 30 by 2, then multiply the result by 3. Understanding this prevents common mistakes in calculation.

Simplifying Arithmetic Expressions

Simplifying arithmetic expressions involves systematically applying operations step-by-step according to the order of operations. This ensures the expression is reduced to a single numerical value accurately, which is crucial for evaluating expressions like the one given.