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}