# Math - the meaning of braces { }

by Marie
(Alabama)

Grouping Symbols such as braces { } organize an algebra problem

Hello,

Can you please tell me what the brackets { } mean?

my e-mail is marie.xxxxx@us.army.mil

Thank you,

Marie xxxxxx

### Comments for Math - the meaning of braces { }

 Sep 16, 2013 Curly Brackets { } by: Staff Answer Part I { } are called curly brackets, or braces. These symbols are used in two ways: (1) to identify a set of elements. (2) to group portions within a mathematical expression { } is used to identify a set of elements Identifying a set using the { } symbols is used in the two of the most common set notation systems: a) ROSTER Notation, and b) SET BUILDER Notation. Three examples of ROSTER Notation are shown below. Consider a set of the following objects: knife fork spoon plate cup Using the ROSTER Notation { }, the set can be identified as: {knife, fork, spoon, plate, cup} Consider the set of all positive integers: 1 2 3 4 5 . . . Using the ROSTER Notation { }, this set can written as: {1, 2, 3, 4, 5, ...} Consider the set of integers beginning with -3, and ending with + 3: -3 -2 -1 0 1 2 3 Using the ROSTER Notation { }, this set can written as: {-3, -2, -1, 0, 1, 2, 3} -------------------------------------------------------

 Sep 16, 2013 Curly Brackets { } by: Staff ------------------------------------------------------- Part II -------------------------------------------------------

 Sep 16, 2013 Curly Brackets { } by: Staff ------------------------------------------------------- Part III { } is used to group parts of a mathematical expression Three of the most common symbols used to group portions of a mathematical expression are: ( ), parentheses - also called round brackets [ ], square brackets - also called box brackets { }, curly brackets - also called braces ( ), [ ], and{ } can be interchanged with one another. They all mean the same thing. The following expressions are equivalent to one another: 5(1 + 2) = 5[1 + 2] = 5{1 + 2} = 15 However, when a mathematical expression contains NESTED GROUPINGS, the ( ), [ ], and { } symbols are used to identify and separate those nested groupings. The parentheses ( ) is generally used for the most inner brackets, the square brackets [ ] is used for the middle brackets, and the curly brackets { } is used for the outer brackets. For example, the following expression contains nested groupings: {[5(1 + 5) + 6]/3} To evaluate this expression, the inner brackets ( ) will be evaluated first: (1 + 5) = 6 The middle brackets [ ] will be evaluated second: [5(1 + 5) + 6] = [5(6) + 6] = [30 + 6] = 36 The outer brackets { } will be evaluated last: {[5(1 + 5) + 6]/3} = {[5(6) + 6]/3} = {[30 + 6]/3} = {36/3} = 12 {[5(1 + 5) + 6]/3} = 12 -------------------------------------------------------

 Sep 16, 2013 Curly Brackets { } by: Staff ------------------------------------------------------- Part IV Thanks for writing. Staff www.solving-math-problems.com

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