Parenthesis, Braces and Brackets

Important Symbols in Math: Round, Square or Curly

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Parenthesis, Braces, and Brackets

You'll come across many symbols in mathematics and arithmetic. In fact, the language of math is written in symbols and of course a little bit of text for clarification. This article focuses on parenthesis, braces, and brackets to provide clarification on their uses.

The parenthesis look like a typical bracket, on a keyboard, they will be found above the nine and the zero and look like this: (  )  The parenthesis are used to group numbers or variables or both.

Examples of a parenthesis (  ):

When you see a question like this, you need to use the order of operations to solve it.
9 - 5 ÷ (8 - 3) x 2 + 6
The parenthesis must be done first which means they can be removed when the operation is performed, in this case (8-3) become 5:
= 9 - 5 ÷ 5 - 3 x 2 + 6
= 9 - 1   x  2 + 6
= 9 - 2 + 6

When you are asked to expand, it will mean doing everything within the parenthesis and then remove the parenthesis.

Parenthesis also mean multiplication.

In a question like this 3 (2 + 5), the parenthesis means to multiply, however, you won't multiply until you complete the operation which is 2 + 5, which will become 7 and then it would be multiplied by 3.

Examples of Brackets [  ]:
Typically the brackets are found beside the p on the keyboard, above the brackets are the braces.  Brackets are used after parenthesis and are used to group numbers and variables as well. Typically, it would be parenthesis first, then brackets then braces.

  Here is an example of brackets:

 4 – 3[4 –2(6 – 3)] ÷ 3
    = 4 – 3[4 – 2(3)] ÷ 3  (do the operation in the parenthesis first, leave the parenthesis)
    = 4 – 3[4 – 6] ÷ 3 (Do the operation in the bracket)
    = 4 – 3[–2] ÷ 3 (The bracket informs you to multiply the number within  which is -3 x -2)
    = 4 + 6 ÷ 3
    = 4 + 2
    = 6

Examples of Braces { }

Braces are also used to group numbers and variables. Here is an example using parenthesis, braces and brackets which is also referred to as 'nested parenthesis' :

 2 {1 + [4(2 + 1) + 3]}  Again, always working from the inside out.
= 2{1 + [4(3) + 3]}
= 2{1 + [12 + 3]}
= 2{1 + [15]}
= 2{16}
= 32

These brackets are also used in sets {2, 3, 6, 8, 10...}

These three types of brackets are sometimes referred to as, round, square and curly brackets. When working with nested parenthesis, the order from will always be: parenthesis, brackets, braces as shown:   {[( )]} 

You will encounter these parenthesis, brackets and braces more frequently in pre algebra and algebra.