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Message Subject Math: 6÷2(1+2) = ?
Poster Handle Anonymous Coward
Post Content
Multiplication and Division left to right at the same time!

The standard order of operations, or precedence, is expressed here:

terms inside parenthesis
exponents and roots
multiplication and division

This means that if a mathematical expression is preceded by one operator and followed by another, the operator higher on the list should be applied first. The commutative and associative laws of addition and multiplication allow terms to be added in any order and factors to be multiplied in any order, but mixed operations must obey the standard order of operations.

It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse). Thus 3/4 = 3 ÷ 4 = 3 • ¼; in other words the quotient of 3 and 4 equals the product of 3 and ¼. Also 3 &#8722; 4 = 3 + (&#8722;4); in other words the difference of 3 and 4 equals the sum of positive three and negative four. With this understanding, we can think of 1 - 2 + 3 as the sum of 1, negative 2, and 3, and add in any order: (1 - 2) + 3 = -1 + 3 = 2 and in reverse order (3 - 2) + 1 = 1 + 1 = 2. The important thing is to keep the negative sign with the 2.

The root symbol, &#8730;, requires a symbol of grouping around the radicand. The usual symbol of grouping is a bar (called vinculum) over the radicand.

Stacked exponents are applied from the top down.

Symbols of grouping can be used to override the usual order of operations. Grouped symbols can be treated as a single expression. Symbols of grouping can be removed using the associative and distributive laws.