BODMAS And Simplification Of Brackets


An arithmetic expression which involves multiple operations such as addition, subtraction, multiplication and division are not easy to solve as compared to 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.

Also checkWhat Is Bodmas

BODMAS RULE

BODMAS is an acronym and it stands for Bracket, Of, Division, Multiplication, Addition and Subtraction. In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, 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 the wrong order will result in a wrong answer.

Note: The “of” in the BODMAS full form is also called “Order”, which refers to the numbers which involve powers, square roots, etc. Check the examples below to have a better understanding of using the BODMAS rule.

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 Examples

Solution:

(i) 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 Example 1

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

BODMAS RULE Solution

(ii) 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 Example 2

BODMAS RULE Example 3

Step 1: Simplify the terms inside {}.

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

1800÷10(12−6)+(24−12)

1800÷10{6+12}

⇒180{18}

=3240

(ii) 1/2[{−2(1+2)}10]

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

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

1/2[{−2(1+2)}10]

= 1/2 [{-2(3)} 10]

= 1/2 [{-6} 10]

= 1/2 [-60]

= -30

Conditions and Rules

Condition Rule
BODMAS RULE 1 Open the bracket and add the terms.
BODMAS RULE 2 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 3 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.

8 Comments

  1. 8/2(2+2)
    Answer this

    1. 16 is the right answer.

    2. 8/2(2+2)
      8/2(4)
      4*4=16 Ans.

  2. Can anyone help:

    18/3(5-4+1)

    1. 12 is the right answer.

  3. for question 2:
    18/3(5-4+1)
    If the expression is 18/3(5-4+1), then solution will be
    = 18/3*(2)
    =18/6 =3

    If the expression is (18/3). (5-4+1), the solution will be
    = (6)* (2) =12

  4. 626352/6243(72+2651)

    1. For this question – 626352/6243(72+2651), explanation below
      = (626352/6243) * 2723
      = (208784/2081) * 2723
      Since, a * b/c = (a * b)/c
      = (208784/2081) * 2723 = 568518832 / 2081
      = 273195.01778

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