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August 18, 202239 Insightful Publications

**BODMAS Rule: **BODMAS Rule is an important method in Maths that is used to solve mathematical problems. It is a method of performing an arithmetic expression to solve mathematical equations. BODMAS is the acronym for B – Brackets, O – Order of powers or roots, D – Division, and M – Multiplication. A stands for addition, while S stands for subtraction.

This rule helps solve expressions with multiple operators in a simplified way. The solutions have to be simplified in this sequence only, from left to right. BODMAS is used when there are numerous expressions on a mathematical problem. The students must follow a set of rules while using the BODMAS approach. Read the following article to learn more about the BODMAS rule and BODMAS questions.

BODMAS rule, also known as the order of operations, is a series of operations in an arithmetic statement.

BODMAS is an acronym used for Brackets, Order, Division, Multiplication, Addition and Subtraction. In some regions, people/students use PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition and Subtraction) which is the synonym or equivalent of the BODMAS rule and can be used interchangeably.

It explains the mathematical operations to be performed while solving a mathematical expression. According to this rule, if multiple brackets \(\left( {{\rm{vinculum}}, +, \times, \div } \right)\) are there in the expression, start solving inside the vinculum or bar or line bracket first, round bracket then followed by curly bracket, then square bracket and then solve the order (means power and roots etc.), then division, multiplication, addition and then subtraction.

So, the BODMAS rule is used to evaluate mathematical expressions and to deal with complex calculations in a much easier way and correctly.

According to the rule, to solve any mathematical expression, first, solve the terms written inside the brackets, then simplify exponential terms and move ahead to division and multiplication operations, then, at last, addition and subtraction.

Here, multiplication and division can be considered level one operations as they must be solved first, addition and subtraction can be considered level two operations.

Simplification of terms inside the brackets can be done directly. This means we can perform the operations inside the bracket of division, multiplication, addition, and subtraction.

Sticking to this order of operations in the BODMAS rule always gives the correct answer. If there are multiple brackets in an expression, all the same brackets can be solved simultaneously.

Example, \((31+2)÷(13-2) = 33 ÷ 11 = 3\)

Look at the below diagram to understand the terms and operations denoted by the BODMAS acronym in the proper order.

BODMAS and PEMDAS are two acronyms used to remember the order of operation to be performed while solving a mathematical expression. BODMAS is the synonym of PEMDAS.

PEMDAS rule is almost similar to the BODMAS rule.

There is some difference in the abbreviation because certain terms are known by different names in different regions.

There are few conditions and rules for general simplification as given below:

Condition | Rule |

\(p + (q + r) \Rightarrow p + q + r\) | Open the bracket and add the terms. |

\(p – (q + r) \Rightarrow p – q – r\) | Open the bracket and multiply the negative sign with each term inside the bracket. (All positive terms will be negative and negative terms will be positive) |

\(p(q + r) \Rightarrow pq + pr\) | Multiply the outside term with each term inside the round bracket |

Let us solve some BODMAS questions or BODMAS examples following the above rules:

Example \(1:\,3 + \left( {6 + 7} \right) = 3 + 6 + 7 = 16\)

Example \({\rm{2: 15 – }}\left( {{\rm{3 + 2}}} \right){\rm{ = 15 – 3 – 2 = 15 – 5 = 10}}\)

Example \(2 \times \left( {3 \times 8} \right) = \left( {2 \times 3} \right) + \left( {2 \times 8} \right) = 6 + 16 = 22\)

First, simplify expression inside brackets.

Then, solve all the exponential terms.

Then, perform division or multiplication (go from left to right).

Then perform addition or subtraction (go from left to right).

The way of prioritising the mathematical operations to be performed first in order is called the BODMAS formula. Solve the expression inside the Brackets first, then perform Order or Of, then Division, then Multiplication, then Addition and then Subtraction.

In today’s storm, several mangoes have fallen from the tree in our garden. My brother has picked up in a basket. I counted that there are 50 mangoes in the basket. From there, I took 2 mangoes and my brother took 3 mangoes.

Sometime later, mother found 15 more mangoes in the garden. She divided all the mangoes equally among 12 girls and boys from the neighbourhood. How many mangoes did each get?

**First Task:** How many mangoes did me and my brother take?

\((2+3) [() placed in the first bracket ]

**Second Task: **After we took mangoes, how many were left in the basket?

\(\{ 50 – (2 + 3)\} [ \left\{ {} \right\}\) placed in the second bracket ]

If mother kept 15 more mangoes, the total number of mangoes will be \(\left\{ {50 – \left( {2 + 3} \right) + 15} \right\}\)

We have more work left. So, we need another bracket. We will call this bracket the square bracket.

**Third Task:** \(\left\{ {50 – \left( {2 + 3} \right) + 15} \right\}\) Divide equally among 12 people, each will get,

**Forth Task: **

\(\left[ {\left\{ {50 – \left( {2 + 3} \right)} \right\} + 15} \right] \div 12\)

\(= \left[ {\left\{ {50 – 5} \right\} + 15} \right] \div 12\) (Simplify inside round bracket)

\(= \left[ {45 + 15} \right] \div 12\) (Simplify inside curly bracket)

\(= 60 \div 12\) (Simplify inside square bracket)

\(= 5\) (Divide)

Therefore, each will get 5 mangoes.

Someone can make some common mistakes while applying the BODMAS rule to solve an expression and those mistakes are given below:

- The presence of multiple brackets may cause confusion and we may get the wrong answer.
- Errors occur due to the lack of proper understanding of the addition and subtraction of integers.

For example: \(2-5+6=-3+6=3\).

But if we simplify \(2-5+6=2-11=-9\), we will get a wrong answer. - By assuming that the division has higher precedence over multiplication and addition has higher precedence than the subtraction.

Multiplication and division are same level operations and must be performed from left to right sequence (whichever comes first in the expression) and the same with addition and subtraction which are same levels operations to be performed after multiplication and division.

If one solves division first before multiplication (which is on the left side of the division operation) as D comes before M in BODMAS, they may get the wrong answer.

Candidates looking for BODMAS questions for class 8 or BODMAS questions for class 7 or BODMAS questions for class 5 can check a few examples below:

**Q.1. Solve \(8+9÷9+5×2-7\).Ans:**

The given expression is \(8+9÷9+5×2-7\)

First, perform division operation i.e., \(9÷9=1\)

Thus, \(8+1+5×2-7\)

Then multiplication i.e., \(5×2=10\)

Now, \(8+1+10-7\)

Then perform addition i.e., \(8+1+10=19\)

Now, \(19-7=12\) (Subtracted)

Hence, the required answer is \(12\).

**Q.2. Simplify \(\left[ {25 – 3\left( {6 + 1} \right)} \right] \div 4 + 9.\)Ans:**

The given expression is \(\left[ {25 – 3\left( {6 + 1} \right)} \right] \div 4 + 9.\)

We will start solving inside the round bracket, i.e., \(\left( {6 + 1} \right) = 7\)

Next, multiply \(3\left( 7 \right)\;\) or \(3×7=21\)

Now, \(\left[ {25 – 21} \right] \div 4 + 9\)

There is one bracket left, i.e., \(\left[ {25 – 21} \right] = 4\)

After \(B\) and \(O,D\) comes.

Hence, \(4÷4=1\)

Lastly, \(1+9=10\)

Hence, the required answer is \(10\) after simplifying the expression.

**Q.3. Solve \(\left( {\frac{1}{4} + \frac{1}{8}} \right)\) of \(64\). Ans:**

First solve the expression inside the bracket i.e., \(\left( {\frac{1}{4} + \frac{1}{8}} \right) = \frac{{2 + 1}}{8} = \frac{3}{8}\)

Now the expression becomes, \(\frac{3}{8}\) of \(64\)

‘Of’ means multiply. So, \(\frac{3}{8} \times 64\)

Hence, the required answer is \(24\).

**Q.4. Simplify \(180 \div 15\{ (12 – 6) – (14 – 12)\} \).Ans:**

The given expression is \(180 \div 15\{ (12 – 6) – (14 – 12)\} \)

First simplify the terms inside \(()\) followed by \({}\).

Now,\(180 \div 15\{ (12 – 6) – (14 – 12)\} \)

\(=180÷156-2\) (Solved inside the round bracket)

\(=180÷154\) (Solved inside the curly bracket)

\(=124\) (Divided \(180\) by \(15\) i.e. \(12\))

\(=12×4\) (if there is no operator before bracket, consider as multiplication operator is there)

\(=48\) (Multiply \(12\) and \(4\))

Hence, the required answer is \(48\).

**Q.5. Simplify \(3 + {2^4} \times (15 \div 3)\) using BODMAS rule.Ans:**

The given expression is \(3 + {2^4} \times (15 \div 3)\)

Start calculating inside the bracket.

i.e., \({\rm{\;}}\left( {15 \div 3} \right) = 5\)

Now, \(3 + {2^4} \times 5\)

Then calculate the order i.e., \({2^4} = 2 \times 2 \times 2 \times 2 = 16\)

Then, \(16×5=80\)

Lastly, perform the addition, \(3+80=83\)

Hence, the required answer is \(83\).

**Q.6. Solve \(16[8 – \{ 5 – 2(\overline {2 – 1} + 1)\} ]\) using BODMAS rule.Ans:**

The given expression is \(16[8 – \{ 5 – 2(\overline {2 – 1} + 1)\} ].\)

First solve the vinculum or line bracket

Now, \(16\left[ {8 – \left\{ {5 – 2\left( {1 + 1} \right)} \right\}} \right]\)

\(= 16\left[ {8 – \left\{ {5 – 2 \times 2} \right\}} \right]\) (solved inside the curved bracket)

\(= 16\left[ {8 – \left\{ {5 – 4} \right\}} \right]\) (multiplied inside the curly bracket)

\(= 16\left[ {8 – 1} \right]\) (Solved inside the curly bracket)

\(=16×7\) (solved inside the square bracket)

\(=112\) (multiplied)

Hence, the required answer is \(112\)

In this article, we have learnt the BODMAS rule which has a very important role while solving a mathematical/arithmetic expression easily and correctly.

We covered the full form of the BODMAS rule, what is BODMAS rule is, its uses, how it is helpful to simplify big mathematical expressions correctly. It will help students a lot in mathematical calculations.

Below are the commonly asked BODMAS questions:

**Q.1: Do you use BODMAS when there are no brackets?Ans:** Yes, we use the BODMAS rule to get the correct answer even if there are no brackets. If there are no brackets, start solving from ‘order’ or ‘of’ followed by Division or multiplication (whatever comes first from left to right) then by addition or subtraction (whatever comes first from left to right).

**Q.2: Is the BODMAS rule correct?Ans:** Yes, the BODMAS (Bracket’s order or of Division Multiplication Addition Subtraction) rule is correct. But in some regions, people also use PEMDAS (Parentheses Exponent Multiplication Division Addition Subtraction) or BIDMAS (Brackets Indices Division Multiplication Addition Subtraction). By the way, all three acronyms are correct.

**Q.3: What is the BODMAS rule in maths?Ans:** BODMAS is an acronym used to remember the order of operations to be followed during solving mathematical expressions. According to this rule, first solve the expression inside the brackets (vinculum,(),{},[])(vinculum,(),{},[]) then solve order or of (power or roots), then division or multiplication (as division and multiplication is having the same precedence, perform whatever comes first from left to right), then solve the addition or subtraction (as addition and subtraction are having the same precedence, perform whatever comes first from left to right).

**Q.4: Do you multiply first if no brackets?Ans:** yes, we do multiply first if no bracket is there (provided multiplication comes first in the expression from left to right). Because, according to the BODMAS rule, inside the bracket should be solved first. If there is no bracket, then the next precedence will be division or multiplication (as both division and multiplication have the same order of preference) and if multiplication comes first in the mathematical expression from left to right.

**Q.5: What is the meaning of O in the BODMAS rule?Ans:** The meaning of

**Q.6: What is the BODMAS full form?Ans:** The full form of BODMAS is Brackets, Order or Of, Division, Multiplication, Addition, Subtraction.

**Q.7: Do you add first or multiply first?Ans:** We multiply first. As BODMAS rule tells what operation to be performed first while solving a mathematical operation. According to the BODMAS rule, we must multiply first and then add.

Now you have all the necessary information regarding the BODMAS rule, We hope this detailed article helps you.

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