BODMAS And Simplification Of Brackets

As per BODMAS rule, we have to calculate the expressions given in the brackets first. The full form of BODMAS is Brackets, Orders, Division, Multiplication, Addition and Subtraction. Hence, second preference in BODMAS is given here to the orders or exponents (xn).  Later we perform the arithmetic operations (÷, ×, +, -). We will solve examples based on this rule in the below sections.

BODMAS RULE

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.

Learn more: Mathematics 

What is BODMAS RULE?

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

BODMAS Rule Explanation

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 ‘order’ (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 “O” 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 Full form

As we mentioned earlier, the full form of BODMAS is: Brackets, Orders, Division, Multiplication, Addition, Subtraction. While applying the BODMAS rule we should follow the order of these operations.

B Brackets ( ), { }, [ ] 
O Order of Square roots, indices, exponents and powers
D Division ÷, /
M Multiplication ×, *
A Addition +
S Subtraction

Also, learn:

Addition

Subtraction

Multiplication

Division

Sometimes we may also come across with percentages while simplifying the numerical expression using this BODMAS rule.

Conditions and Rules

A few conditions and rules for general simplification are given below:

Condition Rule
x + (y + z) ⇒ x + y + z Open the bracket and add the terms.
x – (y + z) ⇒ x – y – z Open the bracket and multiply the negative sign with each term inside the bracket.
(All positive terms will be negative and vice-versa)
x(y + z) ⇒ xy + xz Multiply the outside term with each term inside the bracket

BODMAS Rule Examples

Example 1: 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 terms inside the brackets can be done directly. That means we can perform the operations inside the bracket in the order of division, multiplication, addition and subtraction.

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

Example 2: Simplify: 14 + (8 – 2 × 3)

Solution: 14 + (8 – 2 × 3)

= 14 + (8 – 6)

= 14 + 2

= 16

Therefore, 14 + (8 – 2 × 3) = 16.

Example 3: Simplify the following.

(i) 1800 ÷ [10{(12−6)+(24−12)}]

(ii) 1/2[{−2(1+2)}10]

Solution:

(i) 1800 ÷ [10{(12−6)+(24−12)}]

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}]

Step 3: Simplify the terms inside [ ].

= 1800 ÷ 180
= 10

(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

BODMAS Rule without Brackets

The BODMAS rule can be applied to solve the mathematical expression without brackets too. Consider the following question to verify.

Question:- Simplify: 17 – 24 ÷ 6 × 4 + 8

Solution:

17 – 24 ÷ 6 × 4 + 8

As per BODMAS rule, we should perform the division first.

17 – 4 × 4 + 8

Let’s perform the multiplication.

17 – 16 + 8

Finally, addition and subtraction.

= 9

BODMAS Rule Problems

Try to solve the BODMAS Rule Questions given below to understand the application of the rule in simplifications.

  1. What is the value of 28 – [26 – {2 + 5 × (6 – 3)}]?
  2. Simplify: 2 + 5(4 + 2) + 32 – (1 + 6 × 3)
  3. Find the value of 7 + {8 – 3 of (√4 + 2)}.
More Related Links
Surds Exponent
Index Expanding brackets

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

Frequently Asked Questions on BODMAS Rule

What is the BODMAS Rule of Maths?

BODMAS is an acronym for the sequence of operations to be performed while simplifying the mathematical expressions. Thus, BODMAS stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction.

Can we use the BODMAS rule when there are no brackets?

Yes, we can use the BODMAS rule when there are no brackets also.

What does S represent in the BODMAS rule?

The letter S denotes the subtraction in BODMAS rule of mathematics.

Which arithmetic operations are involved in BODMAS rule?

The main arithmetic operations involved in BODMAS rule are:
Addition
Subtraction
Multiplication
Division
Square roots or surds and indices

What is the use of the BODMAS rule?

The BODMAS rule helps in simplifying the mathematical expression accurately. Using this rule, we can compute the given expression in a right way so that the answer is correct.

Quiz on BODMAS Rule

133 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

      1. 4-4*4+4
        4-16+4
        =4-20
        =-16

      2. 4-(4*4)+4
        =4-16+4
        =8-16
        =-8

    2. 4-4*4+4
      4-(4*4)+4 — Multiplication first since we have no brackets
      4-16+4 —- do all now since we have only + and –
      -8

      you can start with addition — 4(-16+4) flip what’s in the brackets, 4(4-16) getting -12 in brackets
      4(-12) removing the brackets now you’ll have 4-12 = -8

      or start with subtraction (4-16)+4, (-12)+4, -12+4 = -8

    3. 4-4*4+4
      4-16+4
      4-20
      16 answer

    4. 4-4*4+4
      =4-16+4
      =4-12
      =-8

    5. 4-4*4+4
      =4-16+4
      =8-16
      = -8

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

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

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

    2. 10+(2+5+20+20)*2
      =10+(47)*2
      =10+94
      =104

      1. poonam in your ans 20 is missing that’s why your ans is 104
        10(2+5+20+20+20)*2
        10+(67)*2
        10+134
        =144 (FINAL ANS)

  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

    2. 5+19×2
      = 5+38
      = 43

  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

      2. its 6/2(3)
        =6/6
        =1

    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. 16 is correct answer

  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.

      1. It’s 13

  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

      2. B- Bracket O – off D – divison M – multiplication A – addition S – subtraction

        so if bracket is there we do it from starting but if no bracket is there then we follow bodmas

        so ( 5-4 = 1+1 = 2 ) so 2 is answer are you satisfied

  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

      3. If it is 12/2(6-7+4)*2 -> 12/2 x 9 -> answer is 54

        If it is 12/2(6-7/4)*2 -> 12/2x (289/16) -> answer is 1734/16 or 867/8

  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

  35. Plz solve that, ATT = (16530404 – 0)+ {(0+0) – (10374804+0)}

    1. (16530404 – 0)+ {(0+0) – (10374804+0)}
      =(16530404)+ {–(10374804+0)}
      =6155600

  36. Hi! Can anyone please guide me how to solve this problem.
    26/3 – 16/3 ÷ 8/3 + 1/3
    The correct answer is 7 but my answer is 26/3.

    1. (26/3) – ((16/3) ÷ (8/3)) + (1/3)
      = (26/3) – 2 + (1/3)
      = (26-6+1)/3
      = 21/3
      = 7

  37. 9/3(6*4/8) what is the answer of this question

    1. 9/3(6*4/8)
      = (9/3)*(6/2)
      = (9/3)*(3)
      = 9

  38. 5¾-2⅞+1½ what is the answer

    1. 5¾-2⅞+1½
      Simplifying the mixed fractions, we get;
      (23/4)-(23/8)+(3/2)
      Taking the LCM of denominators (4, 8, 2) and rationalising them.
      (46-23+12)/8
      35/8

  39. 9-18+((15/3)*6)+12
    9-18+(5*6)+12
    9-18+30+12
    33

    1. 3+(3*3)-3+3
      3+9-3+3
      12

    1. (19/3)*(2 + 1)
      (19/3)*3
      19

  40. 3+3 whats the answer?

  41. What is the Answer
    75+75-25×0+2+2

    1. Given, 75+75-25×0+2+2
      As per BODMAS rule, here multiplication will be the first step
      75+75-(25×0)+2+2
      = 75+75+2+2
      = 154

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