BODMAS and PEMDAS: Order of Operations Made Simple
What the letters stand for, the trap most people fall into, and why mental maths tests working memory.
Is 6 + 4 × 2 equal to 20 or 14? Most people answer 20 at first. The agreed answer is 14, because of the order of operations. BODMAS and PEMDAS are two ways of remembering it.
How to play
Pick a section: addition and subtraction, multiplication, division, or the full order of operations with 50 questions. Work out each answer in your head and type it in. Questions start easy and get harder.
What the letters mean
BODMAS stands for Brackets, Orders (powers), Division and Multiplication, Addition and Subtraction. PEMDAS says the same thing with Parentheses and Exponents. Two details trip people up. Division and multiplication have the same rank, so you work left to right. The same goes for addition and subtraction.
Why it is a memory test too
Mental arithmetic makes you hold numbers in mind while you work on the next step. That is working memory. Longer expressions mean more to hold at once, which is why the later questions feel heavier.
What practice can change
Regular practice makes arithmetic faster and more automatic, which frees up attention. That is real improvement at maths. It is not evidence of better memory in general.
A worked example
Take 8 + 12 ÷ 4 × 2. Division and multiplication come before addition, and they are worked left to right: 12 ÷ 4 = 3, then 3 × 2 = 6. Finally 8 + 6 = 14. A common wrong answer is 8 + 12 = 20 first, then 20 ÷ 4 × 2 = 10.
Common mistakes
Doing everything left to right regardless of the operation is the most common error. The second is always doing multiplication before division, or addition before subtraction. They share the same rank, so you go left to right between them. Forgetting that a power applies only to the number right before it is another.
Questions people ask
Are BODMAS and PEMDAS different rules? No. They are two ways of remembering the same order.
Why do online puzzles cause arguments? They are often written in a confusing way on purpose. Brackets remove the doubt.
Does mental maths train my memory? It trains maths and the working memory it uses during the task.
Tips
Do the brackets first and write nothing down; say the intermediate result silently. Not medical advice.
Not medical advice. Stop if you feel dizzy, nauseous or strained.