Order of Operations
The order of operations is the agreed sequence for evaluating an expression so everyone gets the same answer.
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The order of operations is the agreed sequence for evaluating an expression so everyone gets the same answer.
- Brackets first, then indices
- Division and multiplication next, left to right
- Addition and subtraction last, left to right
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Order of Operations?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Order of Operations. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Order of Operations in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Order of Operations gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Order of Operations in detail
The order of operations is the agreed sequence for evaluating a calculation so that everyone gets the same answer: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction, working left to right for operations of equal rank. It is often remembered as BIDMAS or BODMAS.
Without it, 2 + 3 × 4 could mean 20 or 14; the rules make it 14. Calculators and spreadsheets follow the same order, so knowing it helps you enter calculations correctly and write algebra unambiguously.
How the interactive helps you understand Order of Operations
Click a step, or use the Previous and Next buttons, to move through the sequence one stage at a time. Auto-play moves on for you.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Order of Operations.
Real-life uses and examples
- Spot Order of Operations in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Order of Operations by estimating first, then working it out step by step.
- Use Order of Operations when comparing prices, discounts or recipe quantities in everyday life.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Order of Operations.
- Memorising the steps for Order of Operations without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Order of Operations
What is Order of Operations?
The order of operations is the agreed sequence for evaluating an expression so everyone gets the same answer.
What are the most important points about Order of Operations?
The main points are: Brackets first, then indices; Division and multiplication next, left to right; Addition and subtraction last, left to right.
Why is Order of Operations useful?
Understanding Order of Operations gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Order of Operations?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Order of Operations?
Related topics in Mathematics include Equivalent Fractions, Mixed Numbers and Improper Fractions, Percentages.