Grouping Devices
This Grade 6 algebra skill from Yoshiwara Elementary Algebra explains grouping devices in mathematical expressions, including parentheses, brackets, and braces. Students learn the hierarchy of these grouping symbols and how to evaluate expressions with nested or multiple grouping devices systematically.
Key Concepts
Property Perform any operations inside parentheses first.
Like parentheses, a fraction bar is a grouping device . Expressions that appear above or below a fraction bar should be simplified first.
Examples Using parentheses, $3 \cdot (9 4)$ becomes $3 \cdot 5 = 15$.
Common Questions
What are grouping devices in math?
Grouping devices are symbols—parentheses (), brackets [], and braces {}—used to indicate which operations should be performed first in an expression.
What is the order for evaluating nested grouping devices?
Evaluate from the innermost grouping outward. Start inside the innermost parentheses or brackets first, then work outward through brackets and braces.
Why are different grouping symbols used?
Different symbols (parentheses, brackets, braces) are used for clarity when groupings are nested, making it easier to identify which symbols pair together.
How do you simplify an expression like 3 × [2 + (4 - 1)]?
First evaluate inside the innermost parentheses: 4 - 1 = 3. Then inside the brackets: 2 + 3 = 5. Then multiply: 3 × 5 = 15.
Where are grouping devices taught in Grade 6?
Grouping devices are introduced in the Yoshiwara Elementary Algebra textbook for Grade 6.