**What is Parenthesis ?**

Parentheses or Bracket in Math is used to** pair number together**.

The symbol for Parentheses is **” ( ) “**

Any expression inside parenthesis tells that they are paired together.

**Why Parenthesis is used in math?**

There are multiple reasons of using brackets in Math expression.

**(01) Parenthesis used in Order of Operation**

We already know the PEMDAS rule for solving math expression.

PEMDAS rule states that algebraic expression is solved in following order.

P ⟹ Parenthesis

E ⟹ Exponents

MD ⟹ Multiplication or Division

AS ⟹ Addition or Subtraction

Now consider the below expression;

⟹ 2 x 9 – 7

Now according to PEMDAS rule, you will first solve multiplication and then subtraction.

⟹ 18 – 7

⟹ 11

But if pairing is done using parenthesis ( as shown below ) then you have to simplify the elements in bracket first.

⟹ 2 x (9 – 7)

Now the expression (9 – 7) is paired.

According to PEMDAS rule, we have to solve the parenthesis first.

⟹ 2 x (9 – 7)

⟹ 2 x 2

⟹ 4

**Note:**

Observe how the use of parenthesis changed the final result of above expression.**Conclusion**

The parenthesis tells that the elements are paired inside it and it should be simplified first in algebraic expression.

**(02) Two numbers separated by parenthesis signifies multiplication**

For Example

⟹ 2 ( 3 )

The numbers 2 & 3 are separated by parenthesis signifies multiplication between the two numbers.

2 (3) can be written as;

⟹ 2 x 3

⟹ 6

**Example 02**

3 ( 5 + 7 )

we can infer following from the above expression

⟹ ( 5 + 7 ) are present inside the bracket and are paired together.

⟹ Number 3 is just outside the bracket which signifies multiplication

Solving the above expression

3 ( 5 + 7 )

First simplify the pairs inside bracket as per PEMDAS rule

⟹ 3 ( 8 )

Number 3 & 8 are separated by bracket & can be written as;

⟹ 3 x 8

⟹ 24

Hence 24 is the solution of expression.

**(03) Using Parenthesis for Number Clarity.**

There are multiple ways brackets are used for showing numbers clearly in expression

**(i) Using Parenthesis to separate number from exponents**

\mathtt{(2)^{3}} ⟹ tells that number 2 is raised to the power of 3.

\mathtt{( 9+\ 5)^{5}} ⟹ tells that the pair ( 9 + 5 ) is raised to the power 5.

**(ii) Using Parenthesis to separate negative numbers**

⟹ 6 + ( -2 )

Parenthesis can be used to separate negative numbers in addition.

Using bracket helps in avoiding confusion in handling negative numbers in algebraic expression.

**Using Parenthesis in Math – Solved Problems**

**(01) Solve the below expressions involving brackets**

(a) 2 + ( 3 – 2 )

(b) 2 (3 + 6)

(c) (5 – 2) / 3

(d) (9 x 3) – 5**Solution**

(a) **2 + ( 3 – 2 )**

First solve the expression inside the bracket

⟹ 2 + ( 3 – 2 )

⟹ 2 + 1

⟹ 3

(b)** 2 (3 + 6)**

⟹ 2 (3 + 6)

⟹ 2 ( 9 )

We know that two numbers separated by parenthesis signifies multiplication.

⟹ 2 x 9

⟹ 18

(c) **(5 – 2) / 3**

First simplify the number inside the bracket

⟹ (5 – 2) / 3

⟹ 3 / 3

⟹ 1

(d) **(9 x 3) – 5**

⟹ 18 – 5

⟹ 13

**(02) Simplify the below expression with parenthesis**

\mathtt{( i) \ ( 2)^{2}}\\\ \\ \mathtt{( ii) \ ( 9-8)^{5}}\\\ \\ \mathtt{( iii) \ ( 2)^{3} \times \ 4\ +\ ( \ 3-2\ )}

**Solution**

\mathtt{( i) \ ( 2)^{2}}\\\ \\ \mathtt{\Longrightarrow \ 2\ \times \ 2}\\\ \\ \mathtt{\Longrightarrow \ 4}

\mathtt{( ii) \ ( 9-8)^{5}}\\\ \\ \mathtt{\Longrightarrow \ 1^{5}}\\\ \\ \mathtt{\Longrightarrow \ 1\ \times \ 1\times \ 1\times \ 1\times \ 1}\\\ \\ \mathtt{\Longrightarrow \ 1}

\mathtt{( iii) \ ( 2)^{3} \times \ 4\ +\ ( \ 3-2\ )}\\\ \\ \mathtt{\Longrightarrow \ 8\ \times \ 4\ +\ 1}

As per PEMDAS rule, solve multiplication first;

\mathtt{\Longrightarrow \ 32\ +\ 1}\\\ \\ \mathtt{\Longrightarrow \ 33}