Order of Operations
Brackets, exponents, multiplication and division, then addition and subtraction.
About this topic
When an expression mixes several operations, a fixed order guarantees everyone gets the same answer. Work inside brackets first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right. Remember it as BODMAS or PEMDAS.
This is why 2 + 3 × 4 equals 14 and not 20: the multiplication is done before the addition. The rules are a shared convention, like punctuation in a sentence, and are essential for programming, spreadsheets and algebra. If you want a different order, brackets let you force it: (2 + 3) × 4 = 20.
Work through 8 − 2 × (1 + 2)². Brackets first gives 3, then the exponent gives 9, then 2 × 9 = 18, and finally 8 − 18 = −10. Writing each step on its own line stops mistakes. Fraction bars and roots act like brackets too, so everything in the numerator is calculated before dividing.
A classic error is thinking multiplication always comes before division, or addition before subtraction. They have equal rank, so you go left to right: 12 ÷ 3 × 2 is 8, not 2. Another is ignoring the sign: in 5 − 3 + 1 the answer is 3, not 1. Calculators and computer languages follow the same rules, so understanding them helps you type formulas correctly.
Key ideas
- Work inside brackets first
- Then exponents, then × and ÷ left to right
- Finally + and − left to right
Quick check
Use cases: where Order of Operations helps
- Homework: review the key idea behind Order of Operations before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Order of Operations without notes.
- Visual learning: play with the interactive lab to see how Order of Operations changes when you adjust its inputs.
- Teaching a friend: explain Order of Operations in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Order of Operations?
Brackets, exponents, multiplication and division, then addition and subtraction.
What will I learn in Order of Operations?
Work inside brackets first. Then exponents, then × and ÷ left to right. Finally + and − left to right.
Is Order of Operations part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Order of Operations lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Order of Operations?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.