Understanding Order of Operations (BODMAS)
Without a standard order of operations, the expression 2 + 3 × 4 could equal 20 or 14 depending on which operation you do first. BODMAS removes the ambiguity by giving every operation a priority level.
The BODMAS Rule
- B — Brackets: evaluate the contents of brackets first
- O — Orders: powers (indices) and roots come next
- DM — Division and Multiplication: equal priority, work left to right
- AS — Addition and Subtraction: equal priority, work left to right
Common Mistakes
The most common mistake is working left to right and ignoring priorities. For example, many students calculate 6 + 2 × 3 as (6 + 2) × 3 = 24, when the correct answer is 6 + (2 × 3) = 12.
Another common mistake is thinking that division always comes before multiplication. They have equal priority and are evaluated left to right.
Difficulty Levels
Easy (Year 5): Addition, subtraction, and multiplication. No brackets.
Medium (Years 6-7): All four operations plus brackets. Expressions with 3-4 operations.
Hard (Years 7-8): All operations including indices. Bracket insertion challenges.
Australian Curriculum Alignment
This tool supports the Australian Curriculum: Mathematics content descriptions for Number and Algebra across Years 5-8, covering order of operations with and without brackets and applying to multi-step problems.
Frequently Asked Questions
What is BODMAS?
BODMAS stands for Brackets, Orders (powers and roots), Division and Multiplication (left to right), Addition and Subtraction (left to right). It tells you the order in which to evaluate parts of a mathematical expression.
Why can't I just work left to right?
Mathematicians agreed on a standard order so that every expression has exactly one correct answer. Without BODMAS, 2 + 3 × 4 could be 20 or 14 depending on who reads it. The rule says multiplication comes first, so the answer is always 14.
What do brackets do?
Brackets override the normal order. Whatever is inside brackets gets evaluated first. For example, (2 + 3) × 4 = 5 × 4 = 20, because the brackets force the addition to happen before the multiplication.
Are multiplication and division equal priority?
Yes. When an expression has both multiplication and division, you work through them left to right, in the order they appear. The same rule applies to addition and subtraction — they share the same priority level.
What are orders or indices?
Orders means powers (indices) and roots. In BODMAS, they come after brackets but before multiplication and division. For example, in 2 + 3², you calculate 3² = 9 first, then add 2 to get 11.