Understanding Parentheses In Mathematics
Parentheses As Grouping Symbols
Parentheses are grouping symbols that help organize mathematical expressions and clarify the order in which operations should be performed. For example, in the expression (7 + 4) + (9 – 3), the parentheses group the numbers being added and subtracted, ensuring these calculations are completed first.
Parentheses follow the order of operations, meaning any calculations inside parentheses are done before moving to other parts of the expression. This rule applies to both arithmetic and algebraic expressions. For example:
3 + (4×2) tells us to first evaluate 4 × 2, giving us 3 + 8 = 11.
Parentheses can also be used to represent multiplication, as you often see when applying the distributive property. For example:
5 × (6 + 7) is the same as writing 5 (6 + 7) or (5 × 6) + (5 × 7)
Similarly, 6 (2 × 10) is the same as writing (6 × 2) + (6 × 10)
Why Are Parentheses Important?
Clear Communication With Parentheses
Parentheses help keep things clear and easy to understand. Parentheses make sure that everyone evaluates expressions in the same order by explicitly showing which operations to perform first. Without parentheses, the same expression could be interpreted in multiple ways, leading to different results.
Parentheses also help students see how operations work together. For example, the distributive property shows how multiplication interacts with addition. Here’s an example of what that looks like:
9 (2 x 10) is the same as saying (9 x 2) + (9 x 10)
This ability to group and simplify in this way is a stepping stone to solving more complex math problems later on.
Parentheses And Other Grouping Symbols
Parentheses are part of a broader category of grouping symbols, including square brackets [ ] and curly braces { }. While these symbols are used in specific contexts, parentheses are likely to be the most commonly encountered in elementary school mathematics.
