Not every mathematical expression contains parentheses. Evaluating expressions without grouping symbols is often the best starting point for mastering the order of operations, as it lets you focus directly on core operational hierarchy.
When parentheses are absent, you rely strictly on standard precedence levels outlined in PEMDAS and BODMAS.
The Basic Rule for Unbracketed Expressions
When an expression contains no grouping symbols, solve it using this simplified sequence:
- Exponents & Roots: Evaluate powers first when present.
- Multiplication & Division: Solve from left to right as they appear.
- Addition & Subtraction: Solve from left to right as they appear.
Example 1: Addition and Multiplication
Consider: 8 + 4 × 3
Multiplication holds higher priority than addition:
- Multiply first: 4 × 3 = 12
- Add next: 8 + 12 = 20
Answer: 20
Example 2: Division and Subtraction
Consider: 40 − 12 ÷ 3
Division holds higher priority than subtraction:
- Divide first: 12 ÷ 3 = 4
- Subtract next: 40 − 4 = 36
Answer: 36
Example 3: Combined Equal Priority Operations
Consider: 18 ÷ 3 × 5 + 2
Apply the left-to-right rule for division and multiplication before adding:
- Work left: 18 ÷ 3 = 6
- Multiply: 6 × 5 = 30 (Expression becomes:
30 + 2) - Add final term: 30 + 2 = 32
Answer: 32
Why Start Without Parentheses?
Working through unbracketed problems helps reinforce operational priority and left-to-right ties without the added layer of nested terms. Once these core principles become second nature, introducing parentheses and brackets feels logical and intuitive.
Build Your Skill Gradually
A proven progression for building calculation speed includes:
- Basic addition and subtraction expressions
- Two-step multiplication and division
- Mixed unbracketed operations
- Introducing basic parentheses
- Multi-step nested grouping problems
Check out our collection of step-by-step worked examples or common PEMDAS mistakes for more practical practice.