# Mastering BODMAS Rule: Examples and Comprehensive Guide

Comprehensive Definition, Description, Examples & Rules

## Introduction to BODMAS Rule

BODMAS means Brackets, Order or Exponents, Division, Multiplication, Addition, and Subtraction. It is a short form for an order of mathematical operations to be followed when performing calculations. This particular order helps to carry out mathematical operations without any discrepancies or mistakes and ensures that a consistent and stable answer is achieved in all mathematical problems. The history of BODMAS goes as far back as the ancient Greek and Babylonian civilizations. In the 16th century especially, BODMAS gained popularity and significance through the works of mathematicians like Johannes Wildmann.

## What Is BODMAS?

The BODMAS rule states the following order of calculation: Brackets, Order or Exponents, Division, Multiplication, Addition, and Subtraction are abbreviated as BODMAS. It is an abbreviation for the sequence of mathematical operations to be used when completing calculations. Any mathematical problem with a variety of mathematical operations is to be first solved by calculating the number given in brackets, then simplifying the exponents, and then carrying out the mathematical operations in the given order of division, then multiplication, then addition, and finally subtraction. This particular order aids in the execution of mathematical operations without errors or uncertainties, resulting in a consistent and steady response in all mathematical problems.

## BODMAS Rule Examples

Here are some BODMAS rule examples to help you understand the acronym and its applications better:

(9/3) + 6

- First, solve the problem in brackets, i.e. divide 9 by 3 which will give you 3.
- Now add this number, i.e. 3 to 6.
- The final answer is hence, 9.

10*2+9-4

- According to the order of calculations, begin solving the problem by multiplying 10 by 2 which gives you 20.
- Now add this answer, i.e. 20, to 9 which gives you 29.
- Finally, subtract 4 from 29, which gives you the final answer 25.

## BODMAS Rule in Mathematics

BODMAS is applied to an array of mathematical expressions to ease calculations. Mathematical expressions that have more than one mathematical operation employ BODMAS to follow a given set of steps to compute the final answers for the expressions. BODMAS is also applied in various real-life applications like engineering, finance, computer programming, and physics. In engineering, BODMAS can be used to design various structures or design flawless electrical currents; in physics, it is used to calculate various formulas to derive different physical quantities; in finance, it is used to carry out problems related to compound and simple interest; an in computer programming, it is employed to develop algorithms and create codes for various functions.

## BODMAS Rule and Parentheses

Brackets have a crucial role to play in BODMAS. The very beginning of the acronym is with the abbreviation for brackets, which means that if any mathematical expression has brackets involved, those brackets need to be computed and solved on priority and then one has to move on to the next operations. BODMAS helps solve mathematical expressions that have nested brackets or various sets of brackets, one within the another. Whenever there is more than one pair of brackets in an expression, the rule is to compute the operation and entities given in the innermost bracket first and then move on to the outer brackets. This general rule of parentheses or brackets is crucial to ensure that any error or fallacy is avoided when dealing with more than one bracket in a mathematical expression.

## Orders in BODMAS

Exponents or power refers to the number of times a number is multiplied by itself. A number raised to the power of another number ‘x’ represents that the initial number which is raised to a certain power is multiplied by itself the ‘x’ number of times. So, for example, 7^5 would mean 7*7*7*7*7. Exponents or power are solved after solving the entities in the brackets and before delving into the next mathematical operations like division, multiplication, addition, and finally subtraction.

## Division and Multiplication in BODMAS

After brackets and order or exponents, come division and multiplication. After you have computed the entities in the brackets and simplified the exponents, you move on to the next mathematical operation, i.e. division and then multiplication. Here are some BODMAS examples to help you understand the rule better:

**25/5*7**

- Begin the calculation by dividing 25 by 5 which will give you 5 as the answer.
- Now multiply the answer by 7 to attain the final answer, i.e. 35.

**7*8/8**

- Begin the calculation by dividing 8 by 8 which will give you 1 as the answer.
- Now multiply the answer by 7 to attain the final answer, i.e. 7.

## Addition and Subtraction in BODMAS

Here are the important steps to follow when solving mathematical expressions that have both addition and subtraction, to avoid confusion between the applications of the two:

- Begin by solving the numbers given in the brackets.
- Then move on to solving any numbers that involve division.
- Further, solve numbers having multiplication as a mathematical operation.
- Only after completing the above steps, move on to solving numbers that have the addition operation ascribed to them and then subtraction.
- Be careful when dealing with negative numbers as a single sign can change the whole solution.

## Common Mistakes in Applying BODMAS

Here is a list of some common mistakes and errors people commit while applying BODMAS to mathematical expressions, and useful tips on how to avoid them:

- One of the most common mistakes is to not solve numbers given in the brackets as the first step. Always make sure that you clear and simplify the entities given in the brackets before jumping on to other mathematical operations.
- Do not ignore the negative signs in front of certain numbers to avoid any miscalculations.
- Remember the BODMAS by heart before solving any mathematical expression with multiple operations.

## Challenges and Complex BODMAS Sums

Go through the following tips and strategies to handle complex BODMAS sums easily:

- Break down complex mathematical expressions into simpler mathematical expressions by breaking up the brackets as a first step.
- After you have completed the calculations within the brackets present, simplify the exponents to make the expression easier.
- Strictly follow the BODMAS rule and remember the order of operations to avoid any miscalculations or discrepancies.

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## Key Takeaways

- BODMAS means Brackets, Order or Exponents, Division, Multiplication, Addition, and Subtraction. It is a short form for an order of mathematical operations to be followed when performing calculations.
- This particular order helps to carry out mathematical operations without any discrepancies or gaffs and ensures that a consistent and stable answer is achieved in all mathematical problems.
- BODMAS is applied to an array of mathematical expressions to ease calculations. Mathematical expressions that have more than one mathematical operation employ BODMAS to follow a given set of steps to compute the final answers for the expressions.
- BODMAS is also applied in various real-life applications like engineering, finance, computer programming, and physics.

## Quiz

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## Frequently Asked Questions

It is crucial to abide by the order of operations because this particular order helps to carry out mathematical operations without any discrepancies or mistakes and ensures that a consistent and stable answer is achieved in all mathematical problems.

Some exceptions to the BODMAS rule in maths are the advanced mathematical functions like logarithms and trigonometry have their own rule of priority to be followed while solving problems and do not go by the prescribed order of operations in BODMAS.

You can improve your BODMAS skills by regularly practicing solving mathematical expressions that involve more than one mathematical operation. Indulge in regular tests and practice worksheets like the Edulyte worksheet below that help you pinpoint your strengths and weaknesses and work on them accordingly.