Parentheses and grouping symbols play a critical role in algebra. When parentheses appear in an expression, the operations inside them override standard precedence rules and must be evaluated first. Mastering their use is fundamental to understanding the order of operations.
As outlined in our PEMDAS guide, the letter P (or B for Brackets in BODMAS) holds the highest priority level in any mathematical expression.
Simple Example
Consider the expression: (8 + 2) × 5
First, solve the operation inside the parentheses:
- Parentheses first: 8 + 2 = 10
- Multiply next: 10 × 5 = 50
Therefore, (8 + 2) × 5 = 50.
Without Parentheses
Compare that expression with the exact same numbers without parentheses: 8 + 2 × 5
According to standard rules, multiplication takes priority over addition:
- Multiply first: 2 × 5 = 10
- Add next: 8 + 10 = 18
The addition of parentheses completely changes the numerical result from 18 to 50.
Nested Parentheses
More complex expressions often contain grouping symbols nested inside other grouping symbols.
Consider the expression: 2 × (3 + (4 × 2))
When solving nested expressions, always work from the innermost set outwards:
- Innermost parentheses: 4 × 2 = 8 (Expression becomes:
2 × (3 + 8)) - Outer parentheses: 3 + 8 = 11 (Expression becomes:
2 × 11) - Final multiplication: 2 × 11 = 22
A Step-by-Step Strategy
When solving expressions containing parentheses, follow this sequence:
- Locate the innermost set of parentheses.
- Solve the mathematical operations inside them using standard precedence rules.
- Replace the parentheses with your calculated result.
- Repeat the process for remaining groupings before continuing with exponents, multiplication, division, addition, and subtraction.
Practice Makes Parentheses Easy
Grouping symbols are essential for advanced algebra and scientific notation. Practicing with basic grouping first builds a solid foundation for tackling multi-bracket operations.