We often experience situations where our answers and the calculator’s results are different in the solution of mathematical expressions that contain two or more numeric terms with the combination of different brackets. It happens due to a misunderstanding of the order and position to solve the operations.
For the correct answer, we have to know about the order that is known as BODMAS, in some countries is called PEMDAS. It helps to simplify complex arithmetic expressions or solve fundamental arithmetic problems. BODMAS provides the structure to solve the mathematical expression and find the correct result.
In this blog, we will discuss the rules of BODMAS, its role in calculations, and solving examples for better understanding. Let’s start our blog with the definition of BODMAS!
What is BODMAS?
BODMAS is a systematic rule that provides a sequence of operations to solve complex mathematical expressions and avoid errors. This helps to apply the operation first by using the rule and following the sequence.
BODMAS stands for Brackets, Orders, Division, multiplication, Addition, and subtraction. Each letter represents a specific mathematical operation.
The arithmetic expressions or mathematical expressions are made by the combination of two components:
- Numbers
- Operations and Operators
Numbers
Numbers are the fundamental building blocks of arithmetic expressions and represent quantities or values. Different types of numbers are given below that are used in the arithmetic expression:
- Natural Numbers: Positive integers (e.g., 1, 2, 3, …)
- Whole Numbers: Non-negative integers (e.g., 0, 1, 2, 3, …)
- Integers: Positive and negative whole numbers (e.g., -3, -2, -1, 0, 1, 2, 3, …)
- Rational Numbers: Numbers that can be expressed as a fraction (e.g., 1/2, 3/4, -2/5)
- Real Numbers: All rational and irrational numbers (e.g., √2, π)
These numbers form the basic arithmetic expression and help to solve problems.
Operations and Operators
These operations and operators are used to combine numbers for the construction of arithmetic expressions and help to find their value. Below we list some common arithmetic operations and their corresponding operators:
- Addition (+)
- Subtraction (-)
- Multiplication (×)
- Division (÷).
Recently, we read the definition and basics of BODMAS. Let’s move forward and learn about the rules of this method.
Rules of BODMAS
The BODMAS rule tells us the sequence, which operation is applied first to solving the mathematical expression. The basics of this rule are first come, then first applied:
| B | [{( )}] | Brackets |
| O | x² | Order of Powers or Roots (in some cases, ‘of’) |
| D | ÷ | Division |
| M | × | Multiplication |
| A | + | Addition |
| S | – | Subtraction |
Important Points related to BODAMS
- If any question has all types of brackets, we begin with the innermost brackets () and then move to curly and square brackets.
How to Apply BODMAS?
Follow the below steps to apply the BODMAS rule and find the solution to the arithmetic expression:
- Start with solving brackets. If any expression held.
- Next, calculate any powers or roots (like squares, square roots, cubes, etc.)
- Perform all operations (division, multiplication) from left to right. It doesn’t matter which comes first in the expression.
- Finally, perform all additions and subtractions from left to right.
If you still don’t understand how to apply, don’t worry. We’ll provide examples that help to understand the procedure to solve the expression and improve understanding of the BODMAS rule.
BODMAS Examples
Here, we solve the examples that improve understanding of the BODMAS and help calculate the expression value using the BODMAS rule.
Example: Solve the expression: 3 + 4 * (2 + 1) – 5.
Solution:
- Solve inside brackets first: 2 + 1 = 3
- Solve Multiplication: 4 * 3 = 12
- Do the Addition and subtraction: 3 + 12 – 5 = 10
Thus, 3 + 4 * (2 + 1) – 4 = 10
Example: Solve: 3² + 4 × (5 – 2) ÷ 6
Solution:
- Solve the operation within the brackets: 5 – 2 = 3
- Evaluate the exponent: 3² = 9
- Solve Division: 4 × 3 ÷ 6 = 12 ÷ 6 = 2
- Perform Addition: 9 + 2 = 11
Thus, 3² + 4 × (5 – 2) ÷ 6 = 11
To overcome the long manual calculation, students prefer to use the BODMAS calculator and get a quick answer with detailed steps.
Role of BODMAS in Mathematics
BODMAS plays an important role in solving expressions involving multiple operations in mathematics. Some reasons given below why it’s essential in mathematics:
- BODMAS provides a universal solution that ensures everyone can solve mathematical expressions without error in results.
- It simply complex problems by breaking down operations into a piecewise sequence. BODMAS tackles complex expressions easily and systematically.
- It creates a strong mathematical foundation for students, preparing them for advanced topics like algebra and calculus.
- BODMAS isn’t just about theory. It is also used in real-life situations, such as financial calculations, coding algorithms, and data analysis involving different terms or expressions.
Final Thoughts:
Understanding BODMAS is necessary for solving mathematical expressions involving multiple operations and operators. It provides a systematic way to solve arithmetic expressions and enhances problem-solving skills.
BODMAS also helps to tackle simple arithmetic or complex equations. It simplifies the calculation process, eliminates confusion, and ensures consistency. It forms a strong foundation for solving complex mathematical expressions.
