For most students, particularly in middle and high school, mathematics can be a bit confusing, especially when there are multiple ways to solve one problem. When it comes to operations or calculations with multiple operators, there are three popular acronyms that come into play: PEMDAS, BODMAS, and BIDMAS.
While PEMDAS, BODMAS, and BIDMAS may seem similar in their definition, they differ in the order of operations, making it important to understand them and use them correctly to get the correct answer.
Read on to find out the differences between PEMDAS, BODMAS, and BIDMAS more in-depth. Also, check out this article if you wonder how to use the Order of Operations (PEMDAS) correctly.
1- PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction)
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction, which is widely used in the United States to describe the order of operations.
The PEMDAS rule states that you should always start with the parentheses, then the exponents, followed by multiplication and division (from left to right), and finally, addition and subtraction (from left to right).
For example, to solve the equation (5+3)²/(2 x 4)– 2
- We will first solve the parentheses, which gives us 8
- Then the exponent, which gives us 64
- Then the division, which gives us 32
- Then multiplication, which gives us 128, and finally, subtraction which gives us 126.
If you wonder when to use PEMDAS and when not to, I wrote a whole article that I encourage you to check out or head over to Khan Academy.
| PEMDAS |
| – Parentheses – Exponents – Multiplication – Division – Addition – and Subtraction |
2- BODMAS (Brackets, Orders, Division, Multiplication, Addition, and Subtraction)
BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction, which is commonly used in the United Kingdom, India, and other Commonwealth countries.
BODMAS rule is similar to the PEMDAS rule, but the only difference is the order of multiplication and division. With BODMAS, you should always start with the brackets, then the orders (like square roots), followed by division and multiplication (from left to right), and finally, addition and subtraction (from left to right).
To solve the previous equation using BODMAS, the steps will be the same as using PEMDAS. I invite you to watch this video or the video below to learn more about PEMDAS.
| BODMAS |
| – Brackets – Orders – Division – Multiplication – Addition – and Subtraction) |
3- BIDMAS (Brackets, Indices, Division, Multiplication, Addition, and Subtraction)
BIDMAS (also known as BODMAS) stands for Brackets, Indices, Division, Multiplication, Addition, and Subtraction, which is commonly used in the UK, India, Bangladesh, Australia, Pakistan, New Zealand, and other English-speaking countries.
BIDMAS rule is similar to the BODMAS rule, except that indices are used instead of orders, meaning that the exponent rule from PEMDAS comes under indices.
To solve the equation using BIDMAS:
- Start with the brackets.
- Then the indices, followed by division and multiplication (from left to right)
- And finally, addition and subtraction (from left to right).
Note that even though PEMDAS, BODMAS, and BIDMAS have different orders, they all provide the same results when solving an equation as they follow the same mathematical principles.
| BIDMAS |
| – Brackets – Indices – Division – Multiplication – Addition – and Subtraction |
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Final thoughts
PEMDAS, BODMAS, and BIDMAS are all acronyms used to describe the order of solving mathematical equations. While they may seem similar, they have subtle differences that you need to know.
- PEMDAS puts them in the same level of precedence as multiplication and division and is commonly used in the United States.
- BIDMAS (AKA BODMAS ) gives indices a higher priority and is commonly used in the United Kingdom, India, Pakistan, and other Commonwealth countries.