BODMAS And Simplification Of Brackets

An arithmetic expression that 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 the BODMAS rule and learn about the simplification of brackets.

Also check: What 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 used, which is the synonym of BODMAS.

It explains the order of operations to be performed while solving an expression. According to BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by ‘of’ (that means 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 expression means the expansion of brackets. We can remove brackets from an expression by expanding them by multiplication. We use the 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 terms. 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}

⇒1800÷10{18}

= 1800÷10×18
= 180×18
= 3,240

(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 the outside term with each term inside the bracket

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

99 Comments

  1. 4-4*4+4 What is the Answer and how to use bodmas?

    1. 4-4*4+4
      4-(4*4)+4
      4-16+4
      (4+4)-16
      8-16
      -8

  2. 10+(2+5+20+20+20)x2=?

    1. 10+(2+5+20+20+20)x2
      = 144

  3. if there are no brackets in an expression still this rules holds good? say 5+19*2 what is the answer?

    1. 5+19*2
      = 5+(19*2) [As per BODMAS rule]
      = 5+38
      = 43

      1. Question = 14 x 7 + 36 \ 4 + 14
        Answer = ???

      2. 14 x 7 + 36 / 4 + 14
        = (14 x 7) + (36 / 4) + 14
        = 121

  4. jyomendra prajapati

    8/2(2+2)

    1. 8/2(2+2)
      4 * 4
      16

  5. 8/2(2+2)
    Answer this

    1. 16 is the right answer.

      1. plz ans below
        5 5 5 = 6 in bodmas rule

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

    3. Shashi Bhush Singh

      What’s the answer of 6÷2(1+2)

      1. (6÷2)*(1+2)
        3*3
        9

    4. 8/2(2+2)
      8/2(4)
      8/8
      =1
      Ans:1

      1. The answer has to be 16 since according to BODMAS, multiplication and division would be solved from left to right like addition and subtraction. so it should be>>>
        8/2(2+2)
        8/2(4)
        (4)(4)
        =16
        Answer would be 16

    5. 8/2(2+2)
      = 4×4
      = 8

      1. 8/2(2+2)
        4(4)
        16

      2. Exactly but the 4 is still in parentheses which means eliminate it by multiplying it by 2. Then you go left to right 8 divided by 8 equals 1

  6. 2+5×9/3-8 can use bodmas ?

    1. 2+5×9/3-8
      2+(5×(9/3))-8
      2+(5×3)-8
      2+15-8
      17-8
      9

  7. Can anyone help:

    18/3(5-4+1)

    1. 12 is the right answer.

  8. If we have multiplication and division at the same time. then which one we will choose??

    1. As per BODMAS rule, first, do the division.

    2. Operation is from left to right. M & D have equal priority, so the one that comes first on the left must be solved first.

  9. 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

    1. Kanwaljit Singh Dhunna

      If the expression is 18/3(5-4+1), then solution will be
      = 18/3*(2)
      =18/3*2
      Here Division is first in sequence so,
      =6*2 = 12 should be the right answer.

    2. Second option is correct

    3. 12 is correct

    4. 18/3(5-4+1)
      18/3(0)
      Answer will be 0

    5. (5-4+1)
      5-5=0
      Please help

      1. 5-4+1
        =(5+1)-4
        =6-4
        =2

  10. 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

      1. 2+2(2+2*0)+2*0

      2. 2+2(2+2*0)+2*0
        2+2(2+(2*0))+(2*0)
        2+2(2+0)+0
        2+2(2)
        2+4
        6

  11. solve 48/2(9+3)

    1. (48/2)*(9+3)
      288

    1. 5-(5*5)+5
      5-25+5
      (5+5)-25
      10-25
      -15

  12. 10+67*2 please anyone help

    1. 10+67*2
      10+(67*2)
      10+134
      144

  13. solve 2y-8=5y

    1. 2y-8=5y
      2y-5y = 8
      -3y = 8
      y = -8/3

  14. Query:
    1. Solve: 5 – 2 – 1

    if the answer is 2 using BODMAS.

    2. Solve: 5 – 2 + 1

    What is the answer to this? Explain the steps as well how you are applying BODMAS here.

    1. 5-2-1
      5-(2+1)
      =5-3
      =2
      And
      5-2+1
      =(5+1)-2
      =6-2
      4

  15. 7+4×6=?

    1. 7+4×6
      =7+(4×6)
      =7+24
      =31

      1. What is the answer for
        10+5×3

      2. 10+5×3
        = 10+(5×3)
        = 10+15
        = 25

    2. 7+(4×6)
      7+24
      =31

    1. 9+(12-2 of 4)
      =9+(12-(2×4))
      =9+(12-8)
      =9+4
      =13

  16. {(-10)+2)×(-4)=?
    Please tell me the answer

    1. {(-10)+2)×(-4)}
      ={(-10+2)×(-4)}
      =(-8)×(-4)}
      =32

    2. ((-10)+2)x(-4))
      =((-10+2)x(-4))
      =(-8x-4)
      =32

  17. Can anyone help:

    12/2(6-7+4)*2= ?

    1. 12/2(6-7+4)×2
      =12/2(3)×2
      =12×3
      =36

      1. what if its 12/2(6-7/4)*2

      2. 12/2(6-7/4)*2
        = (12/2)(6-(7/4))*2
        = 51

  18. (3/2+5/3÷10/9)of5/12
    I need d working fast

    1. (3/2+5/3÷10/9)of5/12
      =(3/2+(5/3÷10/9))×5/12
      =(3/2+(5/2×9/10))×5/12
      =(3/2+3/2)×5/12
      =6/2×5/12
      =5/4

      1. Please how did you get 5/4, because according to my working i got =9.

  19. What is the correct answer please? 1+20×5=?

    1. 1+20×5
      Applying BODMAS rule for order of operations, we get;
      = 1+(20×5)
      = 1+100
      = 101 (Answer)

  20. What is bodmas

  21. (4+9)-2 of 4+6×24÷12
    Please solve this

    1. (4+9)-2 of 4+6×24÷12
      (4+9)-2 × 4+6×24÷12
      By applying the order of operations as per BODMAS rule, we can write the above expression as:
      (4+9)-2 × 4+6×(24÷12)
      13-2×4+6×2
      13-(2×4)+(6×2)
      13-8+12
      (13+12)-8
      25-8
      17 (Answer)

      1. IN QUESTION THERE IS “‘OF” AFTER -2
        SO WE HAVE TO SOLVE THIS AS
        ((4+9)-2)(4+6*24/12)
        (13-2)(4+6*2)
        11(4+12)
        11*16=171

  22. Does BODMAS only apply where brackets are included in the equation.
    Eg should the expression 30+5×2= be rewritten to apply multiplication before addition, as 2×5 +30, giving a totally different answer is BODMAS or sequential correct ?

    1. For 30+5×2 also, we will apply BODMAS rule.
      First multiplication and then addition.
      30+(5×2)
      = 30+10
      = 40

    1. Answer: -33

  23. 9+6÷(3×5)-10 = ?

    1. 9+6÷(3×5)-10
      = 9+6÷(15)-10
      = 9+2/5-10
      =2/5-1
      =-3/5

  24. I’m I to ask questions through this comment box?

  25. 476÷[26+56{42-56-(5×10)}]x2

  26. 9÷3(6×4÷8)

    1. 9÷3(6×4÷8)
      = 9÷3(6×(4÷8))
      = 9

    1. 5-5×5
      =5-(5×5)
      =5-25
      = -20

  27. What is the answer of 6×8+38÷34(13×7)+54-33÷4=?

    1. 6×8+38÷34(13×7)+54-33÷4
      6×8+{(38÷34)(13×7)}+54-(33÷4)
      195.46

  28. My question is from mathematics
    That is 45+3{34-18-14}÷3[17+3×4-(2×7)]

    1. 45+3{34-18-14}÷3[17+3×4-(2×7)]
      = 45 + 3(2)÷3(15)
      = 75

  29. how to do this question without any brackets 15 + 3 × 8 ÷ 4 – 2

    1. We have to use Bodmas rule if the brackets are not specified.
      15 + {3 × (8 ÷ 4)} – 2
      15+{3×2}-2
      15+6-2
      19

  30. (-20)+(-8)\(-2)-(3)

  31. 8/2(2+2)
    would the answer be 16 or 1? Do we expand the 2(2+2) and then divide or, divide 8/2 then multiply it by four?

  32. 8852+759 OF 20-1000/5

  33. How to solve this problem
    180 ÷ 9 + 145 ÷ 5- 6 of 9 + 63 ÷ 3

  34. Ma’am plz tell me bracket kaha lagate he jese agar 2*4+5*9+2 bracket kaha lagaege

    1. As per BODMAS rule,
      (2*4)+(5*9)+2
      = 8+45+2
      = 55

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