# Parentheses – Definition, Symbol, Facts, Examples | What is Parenthesis in Math?

Parentheses are nothing but round brackets that are used to group objects together. There are generally used in mathematical expressions. In any math expression or equation, parenthesis has the highest order when compared with the arithmetic operations. Parenthesis are also called common brackets. This page will learn about the importance of parenthesis in mathematical expressions, its definition, and solved example questions.

## What are Parentheses?

Parentheses are the symbols in math. They are also called the round brackets. Parentheses are used to combine or group the numbers, variables, or operations in math. These are also part of the order of operations. The order of operations in maths is BODMAS (Bracket, Of or Order, Division, Multiplication, Addition, Subtraction).

The symbol of parenthesis is (). The change in the placement of round brackets in a math expression will change the result. So, everyone has to follow these rules to evaluate the expressions correctly. The following example shows how parentheses affect the result of the expression.

Example:
(5 x 4) – (7 + 4)
In the example, you need to evaluate the expressions provided in the brackets first.
5 x 4 = 20
7 + 4 = 11
(5 x 4) – (7 + 4) = 20 – 11 = 9
So, (5 x 4) – (7 + 4) = 9
Solve the expression 5 x 4 – 7 + 4
5 x 4 – 7 + 4 = 20 – 7 + 4
= 24 – 7 = 17
The result for the two expressions is not the same but both expressions are the same if we not consider parentheses symbols.

### Uses of Parentheses in Maths

The following are the places where majorly parentheses are used in mathematics.

• Round parentheses are used in mathematical expressions to give modification to the normal order of operations. The part of expression provided within the parenthesis will be evaluated first, then the remaining.
• It can be used to denote an open end of the interval.
• This symbol can be used to enclose the variables of a function i.e f(a).
• These are also used to express the greatest common divisor.
• Parentheses around a set of numbers (a, b, c d) represent n-tuple of numbers.
• Large parentheses around two numbers and numbers one below the other represent a binomial coefficient.
• Used to denote a congruence as a ≅ d(mod n)
• Large parentheses around an array indicate the matrix.

### Examples Using Parentheses

Example 1:
Evaluate the following mathematical expressions:
(i) 5 + 2 – 3
(ii) 5 + (2 – 3)
Solution:
(i) The given expression is
5 + 2 – 3 = 7 – 3
= 4
Therefore, 5 + 2 – 3 = 4
(ii) The given expression is
5 + (2 – 3) = 5 – 1 = 4
Therefore, 5 + (2 – 3) = 4

Example 2:
Solve the following math expressions:
(i) 5 × (2 + 6) + 6²
(ii) 25 – 8 × (2 + 5)
(iii) (3 + 5) x (6 − 4)
Solution:
(i) The given expression is
5 × (2 + 6) + 6² = 5 x 8 + 6²
= 5 x 8 + 36
= 40 + 36 = 76
Therefore, 5 × (2 + 6) + 6² = 76
(ii) The given expression is
25 – 8 × (2 + 5) = 25 – 8 x 7
= 25 – 56
= -31
Therefore, 25 – 8 × (2 + 5) = -31
(iii) The given expression is
(3 + 5) x (6 − 4) = 8 x 2
= 16
Therefore, (3 + 5) x (6 − 4) = 16

Example 3:
Solve 78 ÷ (3×13) + 15
Solution:
The given expression is 78 ÷ (3×13) + 15
78 ÷ (3×13) + 15 = 78 ÷ 39 + 15
= 2 + 15
= 17
Therefore, 78 ÷ (3×13) + 15 = 17.

### Frequently Asked Questions on Parentheses

1. What is the rule for parentheses in math?
Parentheses can be used to separate the numbers. If you need to add a negative number to the positive number, then we enclose the negative number in parentheses like a + (-b).

2. What is the Parentheses symbol?
Parentheses are also called the round bracket. Its symbol is ( ). Students have to include numbers or variables or operations inside those opening and closing around braces.

3. Do parentheses mean to multiply?
The parentheses not only mean order of operation it is also used for multiplication. For example 4(5) is nothing but 4 x 5 = 20.

4. What is Order of Operations?
The order of operations means giving priority to the operations. The mathematical expression is not evaluated from left to right. We need to follow the BODMAS rule to evaluate expressions. Not all arithmetic operations have the same priority. Based on the order of priority, operations are evaluated.

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