BODMAS Rule

As per the 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, the 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

Table of Contents:

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. Thus, the order of operations of BODMAS and PEMDAS is shown in the below figure.

BODMAS order of operations

BODMAS Rule Explanation

It explains the order of operations to be performed while solving an expression. According to the 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.

The BODMAS rule can be applied, if the expression involving more than one operator. In this case, first, we have to simplify the terms inside the bracket from the inner most bracket to the outermost bracket [{()}], and simplify the roots or exponents, if any. Then perform multiplication or division operation from left to right. Finally, perform addition or subtraction operation to get the accurate 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

This order must be followed to get accurate results.

Video Lesson on BODMAS Rule

BODMAS Rule has been explained in this video along with various examples. Watch this video to get completely acquainted with the BODMAS or PEDMAS rule and solve any maths equation effectively.

What is BODMAS Rule?
BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. The BODMAS is used to explain the order of operation of a mathematical expression. In some regions, the BODMAS is also known as PEDMAS which stands for Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction.

According to BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEDMAS rule is followed to solve it.

Example Question Using BODMAS Rule:
Take the following questions:
(3+5)-5+2

To solve this, the first bracket has to be solved which will give the following-
(8)-5+2
Now, an addition has to be solved:
(8)-7 = 1.

Also, learn:

Sometimes you may also come across 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

Tips to Remember BODMAS Rule:

The rules to simplify the expression using BODMAS rule are as follows:

  • First, simplify the brackets
  • Solve the exponent or root terms
  • Perform division or multiplication operation (from left to right)
  • Perform addition or subtraction operation (from left to right)

BODMAS Rule Solved Examples

Example 1:

\(\begin{array}{l}Solve\ \left ( \frac{1}{2} + \frac{1}{4}\right )\ of\ 16\end{array} \)

Solution- 

\(\begin{array}{l}Given:\ \left ( \frac{1}{2} + \frac{1}{4}\right )\ of\ 16\end{array} \)

Step 1: Solving the fraction inside the bracket first-

\(\begin{array}{l}\frac{1}{2} + \frac{1}{4} = \frac{3}{4}\end{array} \)

Step 2: Now the expression will be  (3/4) of 16

\(\begin{array}{l}=\frac{3}{4} \times 16\end{array} \)
\(\begin{array}{l}= 12\end{array} \)

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.

Example 4:

Simplify: 17 – 24 ÷ 6 × 4 + 8

Solution:

17 – 24 ÷ 6 × 4 + 8

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

17 – 4 × 4 + 8

Let’s perform the multiplication.

17 – 16 + 8

Finally, addition and subtraction.

25 – 16 = 9

Example 5:

Simplify the expression: 1/7 of 49 + 125 ÷ 25 – 12

Solution:

1/7 of 49 + 125 ÷ 25 – 12

= (1/7) × 49 + 125 ÷ 25 – 12

= 7 + 125 ÷ 25 – 12

= 7 + 5 – 12

= 12 – 12

= 0

Solved Problems On Bodmas

Question 1: Solve 8 + 9 ÷ 9 + 5 × 2 − 7.

Solution: 

The problem given is 8 + 9 ÷ 9 + 5 × 2 − 7.

The division operation is performed first.

9 ÷ 9 = 1

So, the expression reduces to 8 + 1 + 5 × 2 − 7

The multiplication operation is taken next,

5 × 2 = 10

So, the expression reduces to 8 + 1 + 10 − 7

The addition operation is

8 + 1 + 10 = 19

The final answer is 19 – 7 = 12.

Question 2: Simplify the expression [25 – 3 (6 + 1)] ÷ 4 + 9.

Solution: 

The problem given is [25 – 3 (6 + 1)] ÷ 4 + 9.

The round bracket is (6 + 1) = 7.

The next bracket is 3 (7) = 21

Take [25 – 21] ÷ 4 + 9

(25 – 21) = 4

Then division operation is performed,

4 ÷ 4 = 1

Then 1 + 9 = 10

The final answer is 10.

Question 3: Solve (1 / 4 + 1 / 8) of 64.

Solution: 

In the first step, consider (1 / 4 + 1 / 8) = (2 + 1) / 8 = 3 / 8

Take (3 / 8) of 64

Here the term “of” refers to the operation of multiplication.

(3 / 8) of 64 = (3 / 8) * 64

= 24

Question 4: Simplify the given expression: 180 ÷ 15 {(12 – 6) – (14 – 12)}.

Solution: 

Initially, the first ( ) brackets are simplified,

180 ÷ 15 {(12 – 6) – (14 – 12)}

= 180 ÷ 15 (6 − 2) (solve round bracket)

= 180 ÷ 15 (4) (solve curly bracket)

= 12 (4) (divide 180 by 15 = 12)

= 12 × 4 (if no operator is mentioned behind any given bracket, multiplication operation can be performed)

= 48

The final answer is 48.

Question 5: Simplify the following expression 3 + 24 × (15 ÷ 3) using the BODMAS rule.

Solution: 

The expression given is 3 + 24 × (15 ÷ 3).

The bracket is taken first.

(15 ÷ 3) = 5

Then 3 + 24 × 5

The calculation is done in order 24 = 2 × 2 × 2 × 2 = 16

16 × 5 = 80

The addition operation is performed next.

3 + 80 = 83

The final answer is 83.

Question 6:

\(\begin{array}{l} Solve\ 16[8-\{5-2(\overline{2-1}+1)\}] using\ BODMAS\ rule.\end{array} \)

Solution:

\(\begin{array}{l}Given:\ 16[8-\{5-2(\overline{2-1}+1)\}]\end{array} \)

First consider the vinculum or line bracket 16 [8 – {5 – 2 (1 + 1)}] = 16 [8 – {5 – 2 * 2}] ( solve the curved bracket)
= 16 [8 – {5 – 4}]( multiply the curly bracket )
= 16 [8 – 1] ( solve the curly bracket)
= 16 * 7 ( solve the inner part of the square bracket)
= 112
Hence, the final answer is 112.

Question 7: Solve the expression using BODMAS rule{50 – (2 + 3) + 15}.

Solution: 

Input Equation:

= {50 – (2 + 3) + 15}

= {50 – (5) + 15}

= {50 – 5 + 15}

= {45 + 15}

= {60}

= 60

Question 8: Simplify the expression using the BODMAS rule [18 – 2 (5 + 1)] ÷ 3 + 7.

Solution: 

Input Equation can be rewritten:

= [18 – 2 * (5 + 1)] / 3 + 7

= [18 – 2 * (6)] / 3 + 7

= [18 – 2 * 6] / 3 + 7

= [18 – 12] / 3 + 7

= [6] / 3 + 7

= (6 / 3) + 7

= 2 + 7

= 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

Q1

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.
Q2

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

Yes, we can use the BODMAS rule when there are no brackets also.
Q3

What does S represent in the BODMAS rule?

The letter S denotes the subtraction in the BODMAS rule of mathematics.
Q4

Which arithmetic operations are involved in the BODMAS rule?

The main arithmetic operations involved in the BODMAS rule are:
Addition
Subtraction
Multiplication
Division
Square roots or surds and indices
Q5

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 the right way so that the answer is correct.
Quiz on BODMAS Rule

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

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

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

  4. 8/2(2+2)

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

  6. 2+5×9/3-8 can use bodmas ?

  7. Can anyone help:

    18/3(5-4+1)

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

  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

  10. 626352/6243(72+2651)

  11. solve 48/2(9+3)

  12. 10+67*2 please anyone help

  13. solve 2y-8=5y

  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.

  15. 7+4×6=?

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

  17. Can anyone help:

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

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

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

  20. What is bodmas

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

    • (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)

      • 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 ?

  23. 9+6÷(3×5)-10 = ?

  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)

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

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

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

  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

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

  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.

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

  38. 5¾-2⅞+1½ what is the answer

    • 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

  40. 3+3 whats the answer?

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

  42. How we solve

    132÷4÷2+4

  43. Simplify 90 – [38 – {(-42) ÷ 3 – (53 − 89÷ 3) ÷ 3}

    • 90 – [38 – {(-42) ÷ 3 – (53 – 89 ÷ 3) ÷ 3} ]
      = 90 – [38 – {(-42) ÷ 3 – (53 – (89/3)) ÷ 3}]
      = 90 – [38 – {(-42/3) – (70/3) ÷ 3}]
      = 90 – [38 – {(-14) – (70/9)}]
      = 90 – [52 + (70/9)]
      = 90 – (538/9)
      = 272/9
      = 30.22

  44. 8÷2(3+1) = 1 or 16

    • 8 ÷ 2(3 + 1) = 8 ÷ [2(3 + 1)] or (8 ÷ 2)(3 + 1)
      If the given expression is taken as 8 ÷ [2(3 + 1)], then
      8 ÷ [2(3 + 1)] = 8 ÷ 8 = 1
      If the given expression is taken as (8 ÷ 2)(3 + 1), then
      (8 ÷ 2)(3 + 1) = (4)(4) = 16

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