![]() Although these terms (powerful, weak) are not used in mathematics, the sense is preserved in the language of “raising 5 to the 8th power.” Exponentiation is “powerful” and so it comes first! Addition/subtraction are “weak,” so they come last. Using a number as an exponent (e.g., 58 = 390625) has, in general, the “most powerful” effect using the same number as a multiplier (e.g., 5 ×8 = 40) has a weaker effect addition has, in general, the “weakest” effect (e.g., 5 + 8 = 13). The basic principle: “more powerful” operations have priority over “less powerful” ones. Conventions for reading and writing mathematical expressions See full rules for order of operations below. For example, in 2 + 3 × 10, the multiplication must be performed first, even though it appears to the right of the addition, and the expression means 2 + 30. ![]() In particular, multiplication is performed before addition regardless of which appears first when reading left to right. When the operations are not the same, as in 2 + 3 × 10, some may be given preference over others. One of these conventions states that when all of the operations are the same, we proceed left to right, so 10 − 5 − 3 = 2, so a writer who wanted the other interpretation would have to write the expression differently: 10 − (5 − 2). To avoid these and other possible ambiguities, mathematics has established conventions (agreements) for the way we interpret mathematical expressions. In mathematics, it is so important that readers understand expressions exactly the way the writer intended that mathematics establishes conventions, agreed-upon rules, for interpreting mathematical expressions.ĭoes 10 − 5 − 3 mean that we start with 10, subtract 5, and then subtract 3 more leaving 2? Or does it mean that we are subtracting 5 − 3 from 10?ĭoes 2 + 3 × 10 equal 50 because 2 + 3 is 5 and then we multiply by 10, or does the writer intend that we add 2 to the result of 3 × 10? ![]() In general, nobody wants to be misunderstood. ![]()
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