- BODMAS stands for Brackets, Orders, Division, Multiplication, Addition and Subtraction, and the O means Orders (powers and roots), not the word of
- Division and multiplication rank equally, as do addition and subtraction, and each pair is solved from left to right
- BODMAS, BIDMAS and PEMDAS all describe the same order of operations.
What Is the BODMAS Rule?
BODMAS is the rule that fixes the order of operations in mathematics. It tells you to solve Brackets first, then Orders such as powers and roots, then Division and Multiplication, and finally Addition and Subtraction. Following this order makes sure everyone evaluates an expression the same way and reaches the correct answer.
BODMAS explains the order in which the operations in a mathematical expression should be carried out. If an expression contains brackets, you solve them first, and then move through orders, division, multiplication, addition and subtraction. Working in any other order will usually give the wrong answer, which is exactly what the rule is designed to prevent.
What Does the Full Form of BODMAS Stand For?
In BODMAS, B stands for Brackets, O for Orders meaning powers and square roots, D for Division, M for Multiplication, A for Addition, and S for Subtraction. The letter O is often misread as the word of, but it actually means Orders, which covers indices and exponents in an expression.
- B - Brackets. Solve anything inside brackets first, because brackets have the highest priority.
- O - Orders. This covers powers, indices, exponents and square roots, sometimes called 'of'.
- D - Division. Carried out together with multiplication, working from left to right.
- M - Multiplication. Ranks equally with division, so the one on the left is done first.
- A - Addition. Performed after division and multiplication are complete.
- S - Subtraction. Ranks equally with addition and is solved left to right, last of all.
How Do You Solve a BODMAS Question Step by Step?
To solve a BODMAS question, first simplify everything inside the brackets, then evaluate orders such as powers and roots. Next, work through division and multiplication from left to right, because they rank equally. Finally, carry out addition and subtraction from left to right to reach the final answer.
Consider the expression 240 divided by 8, times 512, divided by 4, plus one half of {1800 divided by (11x24 divided by 8 x3 - 69) squared}. Following BODMAS, we clear the brackets first, then the order (the square), then the of, and finally the divisions and multiplications from left to right.
- Solve the innermost bracket: 11x24 divided by 8 x3 - 69 = 33x3 - 69 = 99 - 69 = 30.
- Apply the order (power): (30) squared = 900, so 1800 divided by 900 = 2.
- Treat 'of' as multiplication: one half of 2 = 1.
- Work division and multiplication left to right: 240 divided by 8 x512 divided by 4 = 30x512 divided by 4 = 15360 divided by 4 = 3840.
- Add the results: 3840 + 1 = 3841, which is the final answer.
A simpler example is 25 - 48 divided by 6 + 12 x2. Division and multiplication come first, so 48 divided by 6 = 8 and 12 x2 = 24. The expression becomes 25 - 8 + 24, and working addition and subtraction left to right gives 17 + 24 = 41.
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The BODMAS formula sets a fixed sequence: Brackets, Orders, Division, Multiplication, Addition, and Subtraction. Division and multiplication share the same rank, and so do addition and subtraction, so you handle each pair from left to right. This sequence removes ambiguity, so any correct calculation always produces the same result.
- Brackets - start with anything inside brackets, working from left to right.
- Orders - next solve powers, indices and square roots, again left to right.
- Division and Multiplication - these rank equally, so do them in the order they appear from left to right.
- Addition and Subtraction - the final step, also ranked equally and solved from left to right.
What Is the Difference Between BODMAS and PEMDAS?
BODMAS and PEMDAS describe the same order of operations using different words. BODMAS, common in the UK and India, means Brackets, Orders, Division, Multiplication, Addition, Subtraction. PEMDAS, used in the United States, means Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. BIDMAS is another version where Indices replaces Orders. All three give identical results.
Although the letters differ, the underlying rule is the same. Orders, indices and exponents all refer to the small superscript numbers that represent powers. Because division and multiplication share a rank, and addition and subtraction share a rank, you always resolve same-rank operations from left to right, whichever acronym you were taught.
Why Are Brackets Important in BODMAS?
Brackets are important because they let you group numbers and force certain operations to happen first, overriding the normal order. For example, writing the cost of items as (2x10) + (5x4) + (4x20) makes the expression clear and prevents mistakes. Without brackets, complex expressions become confusing and easy to miscalculate.
Imagine buying ten oranges where 2 cost Rs 10 each, 4 cost Rs 5 each and the remaining 4 cost Rs 20 each. Written plainly as 2x10 + 5x4 + 4x20 the expression is hard to read, but grouped as (2x10) + (5x4) + (4x20) it becomes a clear, organised calculation that equals 120.