Types of Brackets, Their Uses, BODMAS Rule, Solved Problems, and FAQs

 Symbols used such as ( ), [ ], { }, and 〈 〉 used to enclose words or figures to separate them from the context are known as Brackets. They have multiple uses in various places. We have been using brackets in mathematics, accounting, science, coding, and even daily in writing anything. We have been using brackets for making emoticons too.

Now that you know just how much we use them. So, let’s get to know a bit more about brackets types.

Types And their Uses

1. Parentheses ( ):

Parentheses are the most popularly used type of brackets. Their job is to surround extra information in the sentence. 

Such information could be removed without really impacting the meaning of major information in the sentence. Most commonly, Parentheses are used to mention acronyms. Acronyms mean alphabets or symbols used to denote something.

For example,

• My father played in the National Basketball Association (NBA).
• He goes to Michigan State University (MSU).
• I need some paid time off (PTO).

Parentheses are also used to denote date range or life span.

For example,

• World War II (1939-1945) was very deadly.
• Jim Jones (1844-1900) was a very kind man.

Parentheses are also used to denote Page numbers.

For example,

• For homework, please read chapter 3 ( pg 43-57 )

Parentheses are also used to denote measurements.

For example,

• The model is 2 Feet (24 inches) high.

A few things that should be kept in mind while using Parentheses are:

• Stuff in parentheses should come after the main information.
• Do not use extra information as the main information.
• You should be able to make sense of the sentence even after removing stuff in Parentheses.

2. Square brackets [ ]:

Square brackets are also known as "crotchets", "closed brackets", or "hard brackets". Square brackets can be used in a quotation to add information that explains the text it follows. 

The square brackets show that the information has been added by someone other than the original author.

For example,

• Hedy Lamarr once said: "Most people save all their lives and leave it [their money] to somebody else."
• In the first ICC Cricket World Cup finals, the two teams were both from South America [Uruguay and Argentina].

Square brackets have application in law in the citation of law reports to identify parallel citations to non-official reporters.

For example,

• Gopal Prasad v Superior Court (1998) 5 Cal.2d 58, [9 Cal. Rptr. 19]

3. Curly brackets { }:

Curly brackets are also called Braces. Curly brackets are a major part of the C programming language. They are not used very frequently in writing. 

• In music, curly brackets are used to connect two or more lines.
• In programming languages, curly brackets are used to mark groups of statements and create a local scope.

4. Angle brackets ⟨ ⟩:

Angle brackets are also known as Chevrons or pointy brackets or triangular brackets, or diamond brackets. Chevrons are the first type of brackets to be used in written English.

• Angle brackets are used to write words that are thought instead of spoken. For example - ⟨ What an unusual insect! ⟩
• Angle brackets have various applications in mathematics, physics, mechanics, and programming languages.

Other Applications in mathematics

Brackets are mainly used to group numbers together. It is used to denote negative numbers too. Square brackets are sometimes used to denote the floor function. 

Respectively, some authors use outwards pointing square brackets to denote the ceiling function, as in ]π[ = 4. Parentheses show ordered pairs in set theory, whereas curly brackets show unordered sets.

BODMAS Rule:

In Bodmas,

• BO stands for Brackets of,
• D stands for division,
• M stands for multiplication, 
• A stands for addition, 
• S stands for subtraction. 

Bodmas means a thumb rule in which the sequence of an equation must be solved.

As per this rule in an equation, first of all, the brackets must be solved. After brackets are all solved, all divisions in the equation are to be solved. After Divisions are all solved, then comes multiplication. After that, all the additions and later all the subtractions. 

 This rule gives the optimum sequence to solve an equation.

• Example:

X = ( 25 + 55 ) / ( 55 * 26 )

X = 80 / 1430

X = 0.055944

• Example:

Y = ( 98 + 56 * 8 ) * 99 + 55 - 60

Y = ( 98 + 448 ) * 99 + 55 – 60

Y = ( 546 ) * 99 + 55 – 60

Y = 546 * 99 + 55 – 60

Y = 54054 + 55 – 60

Y = 54109 – 60

Y = 54049

• Example:

Z = 59 ( 69 ) ^ 2 -259 * 5000

Z = 59 + 4761 – 259 * 5000

Z = 59 + 4761 – 1295000

Z = 4820 – 1295000

Z = - 1290180 

Conclusion

We hope now you have a clear idea of how to use brackets in regards to the BODMAS rule. So practice adequately to grasp the concept. 

Frequently Asked Questions (FAQs)

1. What are the different types of Brackets?

There are four types of brackets. They are Parentheses ( ) , Square brackets [ ] , Curly brackets { } , and Angle brackets ⟨ ⟩.

2. What does Bodmas rule stand for?

BODMAS rule is an acronym for Brackets off, Division, Multiplication, Addition, and Subtraction.

3. What are the fields where brackets are used?

Brackets are used in several places such as mathematics, law, physics, coding languages, etc.