Grouping Symbols
Introduction
Grouping symbols are symbols used in math to group values together. The most common ones are parentheses ( ), which you place around a part of the sum to demonstrate that it needs to be done first, and is separate from the rest of the equation. As well as parenthesis, you can also use brackets [] or braces { }.
Terms
Lesson
When you see parenthesis within an equation, PEMDAS tells you that is what you have to solve first. For example, in the equation:
5 x (4 + 3) = ?
You need to solve the parenthesis first:
5 x (7) = ? 5 x 7 = 35
The parenthesis, therefore, works to group the 4 + 3 away from the rest of the equation, and show that it is a priority.
The other forms of grouping symbol work in the same way and are used when there are multiple parts to an equation. We would, therefore, use [] or {} to avoid having to use multiple sets of parentheses.
The order of operations for grouping symbols is:
1) Parenthesis ( ) 2) Brackets [ ] 3) Braces { }
So, if we see the following equation:
{2 + [(4 + 3) x 2 - 8] + 5} + 1 = ?
It can look a bit tricky, but we just need to work through the order of grouping symbols. First we solve the parenthesis:
{2 + [(7) x 2 - 8] + 5} + 1 = ?
Next, we solve everything in the brackets:
{2 + [7 x 2 - 8] + 5} + 1 = ?
Using order of operations (PEMDAS), we solve 7 x 2 and then + 8, which is 22
{2 + [22] + 5} + 1 = ?
Next, we solve everything in the braces:
{2 + 22 + 5} + 1 = ? {29} + 1 = ?
Then we solve the remaining parts of the problem:
29 + 1 = 30
As long as we remember to solve the parentheses first, then the brackets, then the braces, we can solve it in stages. Remember that a negative sign immediately before a grouping symbol means you need to reverse the sign of everything inside.
For example:
-(2 + 3 - 1) = -2 -3 + 1