Parentheses – Definition With Examples

Parentheses or “round brackets” are the familiar ( ) symbols used in pairs to group things together or specify the order of operations in an equation.

Parentheses

In math, you will often have to use brackets while creating or solving equations. They help in grouping numbers and defining the order of operations. There are three types of brackets used in such cases:

  • Round Brackets or ( )
  • Square Brackets or Box Brackets or [ ]
  • Curly Brackets or Angle Brackets or { }

Brackets always come in pairs, and if there is an opening bracket, there has to be a closing bracket. The opening brackets are (, [  and {. Their corresponding closing brackets are ), ] and }.

Different Types of Brackets

 In this article, we will study the rules for using parentheses in math. 

How to Use Parentheses in Math?

In math, you can use parentheses in math to separate numbers. For instance, you can use them to mention negative numbers when writing an addition equation.

Here is an example to understand this better:

3 + (-5) = -2

The second use of parentheses in math is to multiply numbers. If there is no arithmetic operation present in an equation, the presence of parentheses means you have to apply multiplication.

Let us understand this with an example:

6 (4 + 2)

can be written as 6 x (4 + 2)

Therefore, the answer is 6 x 6 = 36.

The third and final use of parentheses in math is to group numbers and define the order of operations.

Order of Operations

Parentheses change the order of operations.

Here is the order you can follow when multiple symbols are present in an equation:

Order of Operations

If you come across parentheses in an equation, you will first look at the terms present within them. 

Let us understand this better with an example.

Take the problem: 9 – 10 ÷ 5 – 3 x 2 + 7

Let us solve this using the order of operations you have learned.

= 9 – 10 ÷ 5 – 3 x 2 + 7

= 9 – 2 – 3 x 2 + 7 (First, you divide)

= 9 – 2 – 6 + 7 (Then, you multiply)

= 7 – 6 + 7 (Then, you subtract)

= 1 + 7 (Then, you subtract)

= 8 (And finally, you add)

Now, let us look at the same problem with parentheses: 

9 – 10 ÷ (5 – 3) x 2 + 7

You need to calculate the numbers within the parentheses first.

= 9 – 10 ÷ 2 x 2 + 7 (Solve the expression inside the parentheses)

= 9 – 5 x 2 + 7 (Divide)

= 9 – 10 + 7 (Multiply)

= –1 + 7 (Add)

= 6

Did you notice? The answer to the same equation changed because parentheses were present in the equation!

Point to Remember: If there are parentheses inside other parentheses, you solve the inner expression first.

Let us understand this with an example:

Simplify the expression (2 + (3 x 4))

Here, we will solve the inner bracket first.

So, the expression will become (2 + 12) = 14

Solved Examples

Example 1: Simplify the expression: (2 + 4 x 6) 4 + (2 x 3)

Solution: Start by solving the expressions inside the parentheses.

= (2 + 24) – 4 + 6 (Multiply inside the parentheses)

= 26 – 4 + 6 (Solve the terms inside the parentheses)

= 22 + 6 (Add)

= 28

Example 2: Simplify the expression: ( 2 x (7 5)) ((6 ÷ 3) + 4)

Start by solving the innermost parentheses

= (2 x 2) – (2 + 4)

= 4 – 6

= –2

Example 3: Simplify the expression: 2 (3 + 5) + 8 (4 – 1)

First, solve the expressions within the parentheses.

Here, the parentheses also denote a multiplication sign.

= 2 x 8 + 8 x 3

= 16 + 24

= 40

Practice Problems

Parentheses - Definition With Examples

Attend this quiz & Test your knowledge.

1Simplify the expression: (3 + 2 x 8) – 4 + (5 x 7)

45
50
24
40
CorrectIncorrect
Correct answer is: 50
We know that the equation within the parentheses is solved first.
So, 19 - 4 + 35 = 50

2Simplify the expression: ( 4 x (6 – 2)) – ((8 ÷ 2) + 5 )

7
2
17
10
CorrectIncorrect
Correct answer is: 7
We know that the equation within the parentheses is solved first.
So, ( 4 x 4) – ( 4 + 5)
16 - 9 = 7

3Simplify the expression: 4 (3 + 2) + 4 (7 – 2)

10
50
20
40
CorrectIncorrect
Correct answer is: 40
We know that parentheses also denote multiplication.
So, 4 x 5 + 4 x 5
20 + 20 = 40

Frequently Asked Questions

Parentheses are used to group numbers or variables in math. They can change the solution to an expression and, therefore, the answer as well.

No. Parentheses denoted by ( ) are different from braces { }. They have distinct uses in math. They are used in nesting expressions. You will learn more about them later.

Yes. Sometimes, parentheses are also called round brackets.