The most effective way to master the order of operations is to work through practical examples line by line. Applying standard precedence rules systematically helps build both accuracy and calculation speed.
As covered in our guide on common PEMDAS mistakes, writing down each step prevents simple arithmetic errors.
Example 1: Addition and Multiplication
Consider: 5 + 6 × 2
Multiplication takes priority over addition:
- Multiply first: 6 × 2 = 12
- Add next: 5 + 12 = 17
Answer: 17
Example 2: Division and Subtraction
Consider: 20 − 12 ÷ 4
Division takes priority over subtraction:
- Divide first: 12 ÷ 4 = 3
- Subtract next: 20 − 3 = 17
Answer: 17
Example 3: Multiplication and Division Together
Consider: 36 ÷ 6 × 4
According to the left-to-right rule, operations of equal priority are evaluated sequentially as they appear:
- Work from left: 36 ÷ 6 = 6
- Multiply next: 6 × 4 = 24
Answer: 24
Example 4: Using Parentheses
Consider: (7 + 5) × 3
As detailed in our tutorial on solving expressions with parentheses, grouping symbols override standard precedence:
- Parentheses first: 7 + 5 = 12
- Multiply next: 12 × 3 = 36
Answer: 36
Example 5: Multiple Operations Combined
Consider: 10 + 4 × (8 − 3)
Follow the complete PEMDAS hierarchy step by step:
- Evaluate parentheses first: 8 − 3 = 5 (Expression becomes:
10 + 4 × 5) - Perform multiplication: 4 × 5 = 20 (Expression becomes:
10 + 20) - Perform addition: 10 + 20 = 30
Answer: 30
Focus on the Calculation Process
When solving multi-step algebra problems, focus on identifying which operation comes next rather than rushing to the final answer. Developing structured solving habits makes tackling complex math problems simple and automatic.