BODMAS And Simplification Of Brackets

An arithmetic expression involving multiple operations is not as simple as operations involving two numbers. An operation on two numbers is easy but how to solve an expression with brackets and multiple operations and how to simplify a bracket? Let’s recollect BODMAS rule and learn about simplification of brackets.

BODMAS RULE

BODMAS is an acronym and it stands for Bracket, Of, Division, Multiplication, Addition and Subtraction. In certain regions, PEDMAS (Parentheses, Exponents, Division, Multiplication, Addition and Subtraction) is the synonym of BODMAS.

It explains the order of operations to solve an expression. According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right. Solving the problem in wrong order will result a wrong answer.

BODMAS RULE

 

Example- Solve \(\left ( \frac{1}{2} + \frac{1}{4} \right ) of 16\)

Solution-  \(\left ( \frac{1}{2} + \frac{1}{4} \right ) of 16\)

Step 1: Solving the fraction inside the bracket first-

\(\frac{1}{2} + \frac{1}{4} = \frac{3}{4}\)

 

Step 2: Now the expression will be \(\frac{3}{4} of 16\)

\(\frac{3}{4} \times 16\)

\(= 12\)

 

SIMPLIFICATION OF BRACKETS

Simplification of brackets in an expression means expansion of brackets. We can remove brackets from an expression by expanding them by multiplication. We use distributive law of multiplication over addition or subtraction. Generally, it can be written as:

BODMAS RULE

Notes: The order of brackets to be simplified is (), {}, [].

Example 2: Expand and simplify

BODMAS RULE

Solution:

  1. The terms inside the bracket are like terms. We can solve this by two methods.

Method 1:  Add the terms inside the bracket and multiply the number outside bracket with the sum.

BODMAS RULE

Method 2: Multiply the number outside the bracket with each term inside the bracket and add the products.

BODMAS RULE

  1. Here the terms are unlike. This can be simplified by multiplying the number outside the bracket with the terms inside the bracket and add the products.

BODMAS RULE

BODMAS RULE

Step 1: Simplify the terms inside {}.

Step 2: Simplify {} and operate with terms outside the bracket.

\(1800 \div 10{(12-6)+ (24-12)}\)

\(1800 \div 10 \left \{ 6 + 12 \right \}\)

\(\Rightarrow 180 \left \{ 18 \right \}\)

\(= 3240\)(ii) \(\frac{1}{2}\left [ \left \{ -2(1+2) \right \} 10\right ]\)<

Step 1: Simplify the terms inside () followed by {}, then [].

Step 2: Operate terms with the terms outside the bracket.

BODMAS RULE

Condition Rule
BODMAS RULE Open the bracket and add the terms.
BODMAS RULE Open the bracket and multiply the negative sign with each term inside the bracket.

(All positive terms will be negative and vice-versa)

BODMAS RULE Multiply term outside with each term inside the bracket

To solve more word problems on arithmetical operations, download BYJU’S – The Learning App and watch interactive videos.


Practise This Question

Ajit was asked to form the largest and the smallest five digit number by using digits 4, 9, 7, 2 and 1 without repeating the digits. What's the difference between the largest and the smallest number formed?