laskusääntöihin

Laskusäännöt, known in English as order of operations, are a set of conventions used in mathematics to clarify the order in which mathematical operations should be performed to ensure a consistent and unambiguous result. Without these rules, the same expression could be interpreted in multiple ways, leading to different answers.

The most common mnemonic used to remember the order of operations is PEMDAS or BODMAS. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). BODMAS stands for Brackets, Orders (powers and square roots, etc.), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right). Both mnemonics represent the same hierarchy of operations.

First, operations within parentheses or brackets are performed. Next, exponents or orders are calculated. Following this, multiplication and division are carried out, working from left to right across the expression. Finally, addition and subtraction are performed, also from left to right.

For example, in the expression 5 + 2 * 3, multiplication is performed before addition. Therefore, 2 * 3 = 6, and then 5 + 6 = 11. If addition were performed first, the result would be 5 + 2 = 7, and then 7 * 3 = 21, which is incorrect according to the laskusäännöt. Understanding and applying these rules is fundamental to solving mathematical problems correctly.