When expressions include multiple operations, a convention ensures everyone computes the same answer: multiplication and division before addition and subtraction, left to right. So 2 + 3 × 4 = 2 + 12 = 14, not 5 × 4 = 20.
Here is a problem that seems simple: what is 2 + 3 × 4? If you add first, you get 5 × 4 = 20. If you multiply first, you get 2 + 12 = 14. Both paths follow the symbols on the page — yet they produce different answers. Mathematics cannot have two correct answers to the same question, so mathematicians agreed on a convention: an agreed-upon rule that everyone follows, not because one way is mathematically superior, but because having a shared standard makes communication unambiguous. The convention says: multiply and divide before you add and subtract.
The reason multiplication is prioritized over addition is partly historical convention and partly practical: multiplication is a form of repeated addition, and treating it as a single operation before combining with other additions keeps expressions compact and useful. When you write 3 + 4 × 2, you mean "3, plus 4 groups of 2," which is 3 + 8 = 11. Writing (3 + 4) × 2 means something different — add first, then double the result — and parentheses are available precisely for those situations. Parentheses override the default order: whatever is inside parentheses is computed first, regardless of the operations involved.
When expressions contain only addition and subtraction, or only multiplication and division, you evaluate left to right — just as you read. So 12 ÷ 4 × 3 = 3 × 3 = 9 (not 12 ÷ 12 = 1). Left-to-right evaluation is the tiebreaker when operations have the same priority level. At this introductory stage, most problems involve multiplication combined with addition or subtraction, so the essential rule is: find all the multiplications first, compute them, then handle the additions and subtractions.
Understanding order of operations is not about memorizing a mnemonic — it is about understanding that mathematical expressions are a language with grammar. Just as a sentence's meaning depends on word order and punctuation, an expression's value depends on the order operations are applied. This grammar becomes essential when you write and interpret algebraic expressions in later grades, where the conventions you learn now will be taken for granted.