# Uses of Brackets | How to Use Brackets in Math? | Brackets Rule(DMAS Rule)

Uses of Brackets are given here. Find the various uses and types of brackets. Before knowing the complete details regarding the brackets, know the fundamental operations like addition, subtraction, multiplication, and division. Know the history, rules, and precedence order of brackets. Go through the below sections to know the complete details regarding the usage of brackets.

## History of Brackets

The word bracket is derived from the French word “Braguette” which the “piece around”. Anything that is written in brackets is defined as the piece of that bracket. Most brackets are used to enclose notes, references, explanations, etc. which are called crotchets as per the typographical brackets. Later, brackets were used as the group bracketed together for equal standing in some of the graded systems which are mostly used for sports brackets.

### Brackets Usage

Mathematical brackets are known as symbols and parentheses which are most often used to create groups or that which clarify the order in which operations are to be done in the given algebraic expression.

Brackets symbolÂ  Â  Â  Â  Â  Â  Â Name

Â  Â  Â  Â  Â  Â Â ( )Â Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Parentheses or common brackets

Â  Â  Â  Â  Â  Â Â { }Â Â Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Braces or Curly brackets

Â  Â  Â  Â  Â  Â Â [ ]Â Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Brackets or square brackets or box brackets

Â  Â  Â  Â  Â  Â Â  _Â Â  Â  Â  Â  Â  Â  Â Â  Â Â  Â  Â  Â  Â Vinculum

The Left Part of the Bracket indicates the start of the bracket and the right part indicates the end of the bracket.

While Writing mathematical expressions having more than one bracket, parenthesis is used in the innermost part followed by braces, and these two are covered by square brackets. You need to know about the Uses of brackets to perform aÂ  set of operations prior to the others.

### Types of Brackets, Braces, Paranthesis in Math

Mathematical brackets are used for grouping. These brackets can include:

• ( )
• [ ]
• { }

In the grouping of numbers, brackets come in pairs. There will be a pair of sets i.e., the opening bracket and a closing bracket. Brackets are generally used to give clarity in the order of operations.

Suppose that there is an expression: 3+5*7-2. You cannot understand which operation to perform at the beginning. Therefore, we include brackets to understand the precedence of operations. If the problem is given as (3+5)*(7-2) = 8*5 = 40.

In the above problem, the parentheses will tell you the usual order of operations and will give you visual clarity.

#### “( ) Brackets”

The symbols “(” “)” are known as parentheses. These are called Brackets or Round Brackets. They are called Round Brackets as they are not curly or square braces. The input of the function is enclosed in parentheses. Parenthesis means “to put beside” in Geek language. Things like additional information, asides, clarifications, citations are defined by Paranteseis. Any type of information written in parentheses can be as short as a word or number or a few sentences. If something is given in parenthesis, then that sentence must have the capability of standing on its own.

Example: The little puppy (Rocky) skipped across the garden to her mother.

#### “Square Brackets [ ]”

The square brackets are denoted inside the parentheses to define something to the sub-ordinate clause. Square brackets are defined by the symbol “[ ]”. The main purpose of using square brackets is writing in the conjunction or to insert a name or word for clarification.

Square brackets are needed to add clarifications.

Example: She [Rosy] hit the policeman

Example: Two teams in the FIFA football final match were from South America [ Argentina and Uruguay]

Missing words can also be added with the help of square brackets.

Example: It is [a] good answer.

Example: There are not present [my emphasis]

Square brackets are also used to modify the direct quotation.

Example: The direct quotation is “I love traveling” which can be modified as ” He love[s] traveling”.

These can also be used for nesting.

Example: (We use square brackets [in this way] inside the round brackets).

#### “Curly Brackets { }”

Mostly curly brackets are not used for general purposes. They are mostly used in programming or math concepts. They are mainly used to hold terms or terms and hold a list of items.

Example:

3{2+[5(3+1)+4]}

This is the example of lists

Example of programming languages:

$value=0; do{$value++;

if ($value >=20) { Print(“Value is equal to or greater than 10. Ending.”); exit; } } until ($value >=200);

Curly brackets can also be used in sets in mathematics.

Grouping of numbers resembles Sets.

Example: {1,2,4,6,9}

### Difference between ( ) and [ ] in math

Square brackets [ ] are used for commands whereas parenthesis or round brackets represent braces and to describe some special words.

### Multiple Level of Grouping

If you planning for an equation, then grouping within other grouping is a little bit confusing. To avoid that confusion, we use various brackets and group the numbers with order precedence. If we are using the brackets, then we can define the level of operations within the equation.

Example:

2 + {1+[2+3*(5+4)]}

In the above example, first, we go for the inner calculations.

Therefore, first, we have to go for the grouping of (5+4) = 9

Then, we go for the multiplication of 3 and 9 i.e., 18

For the next order, we go for the addition of 3 with 18, the result will be 21.

The next precedence will be the addition of 1 and 21, the result will be 22.

Then, we go for the last grouping of 2 and 22, Therefore, the result of the addition is 24.

With the above example, it is clear that finding a way of solving the equation will be easy.

### Questions on How to Use Brackets

Problem 1:

Simplify the expression : [(3*2) + (4*5)]/(7-3)

Solution:

Start solving the problem by simplifying the equation that is inside the parentheses i.e., 4 *5 = 20

Then, solve the equation of other parentheses, i.e., 3 * 2 = 6

Then simplify the equation within the square brackets i.e., [6 + 20]= 26

Now, solve the equation outside the parenthesis i.e., 7-3 = 4

Now finish the division of the two values = 26/4 = 6.5

Therefore, the final solution is 6.5

Problem 2:

Simplify the equation, [(3+2)*4 – (5*6)]/[1-(3+4)*2]

Solution:

Start solving the problem by simplifying the equation inside the parenthesis i.e., 5 *6 = 30

Then, solve the equation (3+2)*4 = %*4 = 20

Then, go for the next equation of 3+4 = 7, 7*4 = 28

Now, go for the other equation in the brackets i.e., 5*6=30

The second part of the equation is 3 + -7, then 7*2 = 14

Now, solve the equation of 1-14 = -13

Finally, divide the values -10/-13 = 0.769

Therefore, the final solution is -0.769

Thus, the three types of brackets are helpful for solving various equations. Check all the uses and importance of using the brackets and also know the preceding order.

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