37 - The Math Puzzle › One rule, five names
One rule, five names
PEMDAS in the United States. BODMAS or BIDMAS in the UK. BEDMAS in Canada. GEMDAS in some newer textbooks. Nothing in Japan. They all describe exactly the same rule, and most of them quietly mislead you about one part of it.
The rule
Brackets first. Then exponents. Then multiplication and division. Then addition and subtraction. That is the whole thing.
The names
- PEMDAS - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. United States.
- BODMAS - Brackets, Orders, Division/Multiplication, Addition/Subtraction. UK, India, Australia, much of Africa.
- BIDMAS - same thing, Indices instead of Orders.
- BEDMAS - Brackets, Exponents. Canada and New Zealand.
- GEMDAS or GEMS - Grouping instead of brackets, in some newer curricula.
- No acronym at all - Japan and many other countries teach the same rule without a mnemonic.
The bit they all get slightly wrong
Every one of these acronyms puts multiplication and division in a fixed order, and addition and subtraction in a fixed order. That is not how it works.
Multiplication and division rank equally, and you work them left to right. Addition and subtraction are the same. PEMDAS does not mean multiplication beats division, and BODMAS does not mean division beats multiplication. If it did, the two would disagree with each other, which would be a problem.
Try 12 ÷ 3 × 2. Left to right gives 8. Insisting on multiplication first gives 2. Only one of those is right.
Where you meet it
In the US Common Core sequence, parentheses arrive in 5th grade and whole-number exponents in 6th. Both standards are still current as of August 2026.
Practising it without a worksheet
37 - The Math Puzzle is built on this rule. Seven dice, and you have to land on exactly 37. Move a bracket and the answer moves with it, so you find out immediately whether you have the sequence right. No answer key, no waiting to be marked.