How order of operations works
Order of operations is the agreed sequence for working out an expression, so everyone lands on the same answer. In the US it's taught as PEMDAS. In the UK and many other places it's BODMAS or BIDMAS. The letters differ, but the rules are the same.
- ParenthesesWork out anything inside brackets first. If brackets are nested, start with the innermost pair.
- ExponentsPowers come next. In 2 × 3², the exponent only touches the 3, so the answer is 18.
- Multiplication and divisionThese share one rank. Work through them from left to right, whichever comes first.
- Addition and subtractionThese also share one rank. Again, go from left to right.
The mistakes that catch most people
- Treating M as stronger than D, or A as stronger than S. They're equals. 12 ÷ 3 × 2 is 4 × 2 = 8, not 12 ÷ 6 = 2. 10 − 4 + 3 is 6 + 3 = 9, not 10 − 7 = 3.
- Reading strictly left to right. 3 + 2 × 4 is 3 + 8 = 11, because multiplication goes first. Reading left to right gives 20. Every puzzle here has a left-to-right trap answer, and you'll be told when you fall into it.
- Forgetting what an exponent applies to. By the usual convention, −3² means −(3²) = −9, while (−3)² = 9.
Why 8 ÷ 2(2 + 2) starts arguments
Written on one line, this expression is ambiguous. If you treat 2(2 + 2) as ordinary multiplication and work left to right, you get 8 ÷ 2 × 4 = 16. Some textbooks and many calculators treat multiplication with no × sign as binding tighter, which gives 8 ÷ 8 = 1. Neither camp is breaking the rules of arithmetic. The notation is just badly written. That's why every puzzle here uses explicit × and ÷ signs and parentheses, so there's one right answer. See the full breakdown of 8 ÷ 2(2 + 2).
Go further
- Order of operations solver: type any expression and see every step.
- Viral math problems, explained: 8 ÷ 2(2 + 2), 6 ÷ 2(1 + 2), −3² and more.
- Implicit multiplication explained: why some expressions have two answers.
Questions
When does the puzzle change?
At midnight in your local time. Everyone with the same date gets the same five problems.
Where is my streak saved?
In this browser on this device. Clearing your site data or switching browsers starts a fresh streak.
What counts toward my streak?
Finishing all five problems in a day, whatever your score. Miss a day and it resets.
How is the score worked out?
You get two tries per problem. A green square means right first time, yellow means right on the second try, and red means the answer was shown.